I ‘ . v . . . Q ‘ _ # ‘ . . r\ 7"“?!3!‘Y'Y'W737w"":7"‘“.3.';”'7"""VW'W""7'“ I 9" ~‘....vfoa:rovnor"vpy'nvqofiMn-‘wq’i m; "rv' , vr‘.:.'.‘.' v.7vv- r v_..7—v ' ‘ .,.T-,,_ ~ ~ - - _ . . _ , -_,.,.,_,,_;V‘T , . . A . o . ' ' ‘ . . ' .; . ' ~ ‘ ‘ - 1 ‘ ’ I Q .E.‘ ‘ a o . ' ”.1 . . . I o . 9 v v ‘ .5": ’ I . .¥~ ; . ‘ , . ' ' . V t A . n , .‘ .. . . . ’ n. ‘ . , A,..._.L,‘....,.1.l" AN INVESTIGATION OF THE EFFECTIVENESS OF SHEET METAL DRAWING LUBRICANTS by Donald F. 1311'}! A THESIS Submitted to the College of Engineering“ 4 Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 1956 wrists n 9 3 .4; Abstract Many sheet-metal parts are produced by the operation called draw- ing. A major difficulty encountered is the selection of a suitable drawing lubricant. Previous attempts to solve this problem have not met with SUCCESS. This experiment was conducted to determine the most effective drawing lubricant for use in a cupping die. The experiment was restricted to cold rolled mild steel which was .040 inches in thickness. Twelve lubri- cants were tested. These lubricants represent those presently used by sheet-metal working plants. Lubricant effectiveness was assumed to be proportional to the reduc- tion in friction between the sheet metal and the die members. The reduction in friction was measured in three ways: 1. Reduced drawing force 2. Increased cup wall thinning 3. Increased die temperature In addition to the maximum drawing force, the characteristic curve for drawing force was also found. The data was analyzed using statistical methods of analysis. Tests for homogeneity of standard deviations and significance in difference of means were applied. The lubricants were then rated with the best lubricant having the lowest mean and lowest standard deviation. The lubricant found to be most effective in reducing friction was chlorinated wax. The second most effective lubricants were dry wax and medium pigment. Recommendations are suggested for future research on other technical and economical factors which must be known before efficient selection of drawing lubricants will be possible. II. III. IV. Table of Contents Introduction . .................. Theory of Drawing ................ The Experiment Plan ............... Selection of Lubricants Selection of Sheet Metal Design of Cupping Die and Force Measuring Equipment Temperature Measuring Equipment Thickness Measuring Equipment Blank Preparation Setup of Die and Press (Trail Run) Sequence of Testing Lubricant and Sample Size The Experiment Procedure The Experiment .................. Results and Analysis of Data ........... Discrimination of Data Means and Standard Deviations Rating of Lubricants by Deflection Rating of Lubricants by Wall Thickness Correlation Analysis Conclusions and Recommendations ........ Conclusions Recommendations 14 15 17 28 31 33 33 _ 35 38 39 43 57 57 59 B4 68 72 75 75 76 Figure Number toms: 10 11 12 l3 14 15 16 17 18 19 20 21 Table of Illustrations Cut-Away View of a Draw Die Examples of Cupping Drawing Wrinkles Thickening and Extrusion Forces During Cupping Cup Breaks Wall Thicknesses --- Flanged Cup Wall Thicknesses --- Straight Cup Blank Hardness Histogram Tensile Force Histogram Elongation Histogram Blank Surface Finish Histogram Blank Surface Finish Graph Blank Thickness Histogram Cupping Die Design General Electric Hand Pyrometer Cup Wall Thickness Measurements Trial Run Force Curves Excessive Wall Thickening at Position "A" Press Controls and Cupping Die Left-Front View Press, Cupping Die and Sanborn Multi-Channel Analyzer Right-Front View ii Page 10 11 12 13 18 20 21 24 25 27 29 32 34 37 47 52 54 Table of Illustrations Continued sags. 22 Work Bench Arrangement Opposite Press 55 23 Cupping Characteristic Curves 55 24 Wall Thickness Position "C" Lubricant "C" Histogram 61 25 Standard Deviation Values for Lubricants 62 26 . Mean Values for Lubricants 63 27 Correlation of Standard Deviations . Scatter Diagram 73 28 Correlation of Means Scatter Diagram 74 iii __ l Present day st)". teal parts a signifies real operations use ale variety of lubric equal success or lail‘ Mothers and some Wis. The engineer proper lubricant for brand names as w ell Actually the pregam is too often throu {l1 both Costly and tim This thesis t Also to make l sheet-metal used steel, this Protec exclusively. Otl \tss steel and b' and A draw (if SWD‘QXQ give me dullhtate the l clt - ,. “mg mpg s‘ “ Was 1 “View surt r I Q Intro duction Present day styling makes the drawing of more complex sheet- metal parts a significant manufacturing problem. Many of the sheet- metal operations use lubricants as an aid to working the metal. A wide variety of lubricants are presently being used with apparently equal success or failure. Some of the lubricants are more costly than others and some are more difficult to clean off of the sheet-metal parts. The engineer is presented with the problem of selecting the proper lubricant for a particular draw die. He has a vast list of brand names as well as chemical names from which to choose. Actually the present method of obtaining the proper drawing lubricant is too often through a process of trial and error. This process is both costly and time consuming. This thesis tested lubricants in order to find their effectiveness and also to make comparisons in drawing forces. Since most of the sheet-metal us ed on operations of this type is low carbon cold rolled steel. this project was designed to test lubricants for this metal exclusively. Other important sheet metals such as aluminum, stain- less steel and brass could also be tested in the same manner. A draw die was built because testing in an actual draw die should give more valid results than special test fixtures which do not duplicate the true drawing situation. The draw die built was for pro- ducing cups since cupping is the only true drawing operation. It was assumed that the lubricant is used to reduce friction between surfaces having a relative motion. Since the force caused by friction in a draw die would add to the stress placed upon the sheet—metal, this friction force may be great enough to cause breakage when an improper lubricant is used. Therefore the lubricant which most effectively lowers friction should be desirable: If all forces in a draw die. except blankholding force. are exerted by the punch. by measuring a reduction in force exerted by the punch, the reduction in friction forces by each lubricant may be measured. To do this, Strain gages were mounted in the punch. l ‘1‘ ll .4» I The above condition holds true only when other variables are held constant or nearly constant. Control of unwanted variables was an important consideration in setting up the experiment plan. Close specifications were placed on surface finish and age hardening of the sheet-metal. blankholding force drawing speed. blank size and the amount of lubricant used. Other methods used to measure the lubricant effectiveness in reducing friction were: To measure the wall thickness To measure the die temperature The first of these measures is based on the assumption that greater stress caus es: 1. Thinning or necking of the sheetometal. 2. Breaking or fracturing of the sheet-metal. The second is based upon the fact that heat would be generated by friction. It was assumed that the temperature of the die would be an indicator of the amount of friction present. Since a large number of lubricants are used in draw dies, a careful selection of a few for the test was necessary. The lubricants selected represented the basic types found to be the most successful in actual plant use. These were standard lubricants as purchased from the supplier and have not been altered. Secondary objectives could also be gained from this experiment. The strain gage curves provided the maximum force required to draw a specific size and shape of cup from a known metal. Also the char- acteristic curve for the drawing operation was found. These will be great aids in understanding and teaching the fundamental theory of drawing. I. Theory of Drawing An understanding of the theory of drawing sheet-metal is necessary before the reasoning behind this experiment may be fully appreciated. The theory presented here has been supported by experiment and is in agreement with most authors.1' 2- 3 Because the cupping operation most truely represents sheet- metal drawing it will be used to present the theory of drawing. First an analysis should be made of what happens as the punch and die first start to draw the blank. Refer to Figure 1. The edge of the blank is being pulled or "drawn" in towards the center. The blank edge is forced down to a smaller circumference. This reduc- tion in edge circumference is also evident in Figure 2. Such a re- duction means that a compressive force is being applied to the metal. The compressive force produced will cause wrinkles to occur at the edge of the blank. These wrinkles are practically impossible to remove after they have started. The wrinkles are undesirable from an appearance and strength standpoint as shown in Figure 3. To prevent the wrinkles from occurring, the blankholder is added to the die. This blankholder is a ring which fits around the punch. The outer ram of a press is used to obtain pressure for the blankholder. 1 Crane, E. V. , Plastic Workifl in Presses, John Wiley & Sons, New York, 1948. Sachs, G, , Principles and Methods of Sheet-Metal Fabricating, Reinhold, New York, l955, 3 Hinman, C. W., Pressworking of Metals, McGraw-liill, New York, 1941, Punch m / Movement of Blank Edge .' . ‘ at Beginning C;;gé?:AkEdge of Drawing \ ,pa ’ 4// / , ,\ ///’ \\\ /// /// \\\ f x l l ~~:: W Cup after \\\\ partial drawing Die Figure 1. Cut-Away View of Drew Die Figure 2. Examples of Cupping —-_ “L. — _._—.- __._.——__——.——-‘_«——.————~. Figure 3. Draw Wrinkles The pressure exerted by the blankholder prevents wrinkles from starting in the sheet-metal blank. The metal is being compressed but cannot wrinkle. Therefore the metal thickens and extrudes. This con- dition is shown in Figure 4. The thickening of the metal may be found by measuring the wall thickness of a cup when the original blank thickness is known. The extruding effect may also be shown. On the blank shown in Figure 2. a line drawn across the blank and through the center measures four and five-eighths inches long. The same line when measured on the cup measures about five and three-quarters inches long. . If drawing were a pure stretching operation, this much radial elongation would have caused failure of the metal. Actually, this increased length is then due only partially to stretching of the metal. The remaining increase in length is a result of extrusion caused by the compressive force which is present due to the excess of metal. Therefore these terms --- compression, wrinkling, thickening, extrusion and excess 0f metal all refer to the condition at the outer extremity of the blank during a cupping operation. (,Blankbolder / //5/ Die 'Radial Extrusion Increment from g Edge of Blank /' i // Circumfer- ential Compression / / Blank Thickening Perpendicular to Plane of Blank Figure 4. :Thickening and Extrusion When the sheetemetal thickness is large relative to the blank diameter then the metal is rigid enough to thicken without wrinkling. In this case. the blankholder may be eliminated. Besides the compressive forces described, certain bending forces are also present during cupping. The bending forces occur at the radii where the flange and side wall and where the side wall and bottom meet. These forces consist of tension on the outside of the bend and compression on the inside of the bend. The third set of forces are those which are caused by friction. Friction occurs between the sheet-metal blank and the blankholder, punch and die. This friction is present due to the fact that the sheet- metal flows past these surfaces as the cupping operation progresses. Figure 5 illustrates the forces occurring during cupping. The function of the punch is now defined. It must exert a force of a magnitude great enough to overcome friction, bend the metal at the corners and compress and extrude the metal in the flange area or top of the cup. The force exerted by the punch to accomplish this work is shown in Figure 5. Notice that the punch actually exerts its force by pushing on the bottom of the cup. This action causes a tensile stress at the point where the bottom radius and the side wall of the cup meet. This point is where the maximum tension will occur in the cup. If the cup breaks. it will normally break at this point as illustrated in Figure 6. Breaks that occur at other points in the cup are usually due to defective material. The maximum tension point may be found by locating the smallest cup wall thickness. The wall thickness at this point will be somewhat less than the original blank thickness. Figure 7 shows a typical flanged cup and wall thicknesses at various Points. Figure 8 illustrates these conditions for a straight cup. The thickness variations shown occur only when no ironing occurs in the draw die. The maximum tensile force caused by the punch pressing on the cup bottom must not exceed the ultimate strength of the metal. Other- wise failure will occur. This tensile force is actually composed of three forces. First. a tensile force is necessary to overcome friction. Secondly. a tensile force is necessary to bend. Thirdly. a tensile force is necessary to compress and extrude the metal in the top of the cup. Therefore the sum of these three tensile forces must not exceed the ultimate tensile strength of the metal. Circumferential Comoression Friction Tension in Side Wall Bending Force Exerted by Punch Figure 5. Forces During Cupping 10 Figure 6. Cup Breaks 11 ORIGINAL BLANK THICKNESS --— .040" Maximum Compressive Stress —.O46” .045” i \\ \ / ¥ . 043 " —""‘ “‘— // / j/“J/ / // // //fl>l Zero Stress ' POil’ii \ / .04o"—"" i'“ E \ . \ \ l l .O35"‘__’J Eff" . 7 JCI Maximum \ \ \ \ jkéiiiiée .040”j t'.040” Low Stress in Cup Bottom Figure 7. Wall Thicknesses - Flanged Cup \- . 12 . Maximum Compressive Stress ORlGlNAL BLANK THICKNESS ~-- .040” .047" i ~-<-—— / i // i .044" i f 0042” —_" Zero Stress Point \ // / .04o"‘—’i +— \ Maximum Tensile Stress .o.’>4"--—W W L Q/ /O./ / /. // //>\.\ i \ \\ % .040” .040” Low Stress in Cup Bot tom Figure 8. ‘NalI Thicknesses - Straight Cup II. The Experiment Plan The operation of a cupping die involves many variables. To obtain valid results, most of these variables must be held constant or nearly constant so that the desired variables may be measured. When the variables cannot be held constant to the degree desired, then a statis- tical approach is necessary to determine the relative effect and inter- action of these variables. The variables occurring in a cupping die are listed below. Those variables which were held "constant" are indicated as such. The vari- ables to be measured are indicated as "variables. " Variables in the sheet metal: 14 Hardness Constant Thickness Constant Surface Finish Constant Ultimate Tensile Strength Constant Direction of Rolling Constant Variables in the die: Hardness Constant Surface Finish Constant Punch Radius Constant Die Radius Constant Die Clearance Constant Blankholding Force Constant Temperature (Die) Variable Drawing Speed Constant Drawing Lubricant Variable Variables in the cup produced: Wall Thickness Variable Surface Markings (Galling, Variable scratching, scoring or orange peel) Wrinkling or Breaking Variable Variables in forces required: Force exerted by punch Variable Force due to friction Variable Force due to bending Constant Force due to circumferential Constant compression The discussion of the experimental procedure which was developed is divided into the following subjects: 1. 2. 3. 8. 9. Selection of Lubricants Selection of Sheet Metal Design of Cupping Die and Force Measuring Equipment . Temperature Measuring Equipment . Thickness Measuring Equipment . Blank Preparation . Setup of Die and Press (Trial Run) Sequence of Testing Lubricants and Sample Size The E xperiment Procedure Selection of Lubricants The desired characteristics of a drawing lubricant are as follows: To reduce friction. To stop galling and scoring. To cool the die and part. To reduce die wear. To not stain the sheet metal. To not cause subsequent corrosion. To be applicable . To be cleanable. To be economical. To not affect the operator - - non-toxic. 15 Eleven lubricants were selected for testing. The twelfth lubricant tested was the protective oil placed on the sheet metal at the steel mill. This is referred to as "mill oil. " The lubricants selected are commonly used in sheet-metal working plants today. Some lubricants are used to a greater extent than others. These lubricants are used as a result of testing different compounds by trial and error. The poorer lubricants were eliminated. In other words, the experiences of many men have contributed to the selected list of lubricants. The lubricants selected for testing are listed below: Lubricant Code Letter Mill Oil Wet Soap Dry Wax Plastic Reclaimed Oil Molybdenum Disulfide Wet Wax Lard Oil Pigmented - Medium Chlorinated Wax Heavy Oil Graphite grxsmonmoochp A code letter was assigned to each lubricant. These code letters were used for identification in the remainder of the project. Thus, a tendency for bias towards particular lubricants was lessened. The lubricants were applied to the blanks with a brush. This was the most suitable means of application for this experiment. The brush could be easily cleaned between lubricants and the brush produced a uniform coating of lubricant. Both sides of the blank were fully covered with lubricant. No lubricant was placed directly on the die surfaces. Lubricant did, however, accumulate there and the die was cleaned each time the lubricant was changed. 16 Handling the blanks with tongs prevented removal of the lubricant when placing the blanks in the die. Selection of Sheet Metal Since one of the more common sheet metals used in the automo- tive industry is cold rolled mild carbon steel, it was selected for this experiment. The hardness of the sheet metal must be held nearly constant because this variable would otherwise interfere with measurement of other variables. Therefore an aluminum killed steel was selected because aluminum killed steels age harden very slowly. If a rim steel had been used, age hardening might have caused too much variation in hardness. To further control the hardness, all of the sheet metal that was used in the experiment was cut from a single coil. This also assured relatively uniform chemical and physical properties. The specifications of the sheet metal were as follows: SAE 1010 Cold Rolled Steel Fully Annealed Deep Drawing Aluminum Killed . 041 inches thick 10 inches wide x 80 inches long To be coated with rust preventative oil The above thickness was selected because it was a common thick- ness available in this metal. The stock width and length were deter- mined by the blank diameter to be used for the cupping operation. After 2400 pieces had been blanked, 240 blanks were randomly . selected and tested for hardness in order to represent the hardness variation within the total lot. The hardness of the pieces in this sample is shown in Figure 9. l7 Frequency U 'r' \ ,4 “1"- Lot Size 2400 Sample Size 240 e 4% Average Rockwell 30-T 41 .43 20 a, g . j l 27 27 ., , 27 : ii "-' g ‘4 1:9 i :13. as? .6 i3.“- = :4. 3.2- :3 i» l {1 5,}. .g ”i %? 31 V 4 . , - r t l"! iii i} e: 3‘; ' 13 rts 4“. 4 ' I“ ‘ _ {51 ‘i l L' :4: , 8 e9 'Q a F” f " .i El : [1.“- f. t; ‘ 11‘ -: - 5' .‘T ' - - 4. J b: 's i ' I 0‘ {fl 4' t a: . 7.x . - 4 a“; '5 1 :‘i. .14 ‘ El 39 41 42 43 44 45 Rockwell Hardness Superficial 30-T Figure 9. Blank Hardness Histogram 18 46 47 The bell-shaped curve indicated that a random distribution actually existed. Tensile tests were then run in a Baldwin Test Machine to find the ultimate tensile strength, the per cent elongation and their vari- ation. Speciments were cut out both with the direction of rolling and across the direction of rolling. Since rolling might have caused a severe fibre condition in the sheet metal, it was desired to know if significant differences in tensile strength and elongation were caused by the direction of rolling. Histograms were plotted for the force and elongation data. These results are shown in Figures 10 and 11. The sample means and the deviations were computed in order to determine whether or not there was a significant difference of means} A five per cent confidence interval was selected for this analysis. 4 Grant. E. L., Statistical Qualitl Control, McGraw-Hill, New York, 1952, pp 96- 97 19 mmofi OmOH mvofi §.HG.E.41IA .. 0V0 H Across Grain With Grain .m H N C003 m .. danflai Ins... ‘ _ _ E: as \IoO H H 500$ . IIII ILIII II I ,. «rugs-l E32 gins—n their); 0 no H : on.© u m c_0L mmoLU( V. m lllflfi'illflnh mNOH ONOH 239:? MHOH 0. no 7. Au :4 d. K. 7. 1. 0 >ocmzowuu Pounds In 20 Force Tensile Force HistOQrams Figure 10. _I ID v H Across Grain Key: With Grain L Hm. om. Fl MVF " LDUS‘ meao. u m c_cio c.;; N F. u L005 mnno. u m c_wuo mmouu< on. m0. 1 0, RV 7, ,0 .D 4 14 9a 41 nu >ocoacoua Inches Elongation in Elongation Histograms Figure 11. 21 Tests of Significance were now applied as follows:5 Test B4 Test for difference in variability in two samples. (Test for homogeneity) Tensile Force: :610 33:2 2. 06 6 Elongation: 03352 = 5. 29 76175 DF1 and D172 3 14 Tensile Force --- Using Table E, the probability is above 0. 05 that this difference may occur by chance. Therefore the samples are homogeneous. Elongation --- Using Table E, the probability is less than 0. 01 that this difference may occur by chance. Therefore the samples are not homogeneous. Test B2 Test for difference between two sample means. Tensile Force: t = 1035.3 - 1030.7 (9. 05)2 + (6. 30)2 15 - 1 t = 1.57 DF = 28 Tensile Force --- Probability from Table = .134. Using 0.05 probability for this experiment, a signifi- cant difference does not exist. The probability is . 134 that the difference occurs by chance. Since a significant difference in tensile strength due to direction of rolling does not exist, the direction of rolling does not have to be considered when locating the blanks in the cupping die. 5 Juran. 1. M. , Quality Control llandbofl McGraw—Hill, New York, 1951, pp 380 and 382 22 The variances of the elongation samples were not homogeneous. Therefore the test for significant difference of means was not made. This lack of homogeneity may account for the earing effect on the top edge of the cups produced in the experiment. Due to the large sample size, this variable was factored out of the experiment results. The surface finish of the sheet metal was held nearly constant by the specification that it be cut from a single coil. Some variation still existed due to the surface finish of the rollers, the speed of roll- wi ing, the temperature of rolling and the reduction made at the various passes. Surface finish measurements were made with a Model BL-102 Brush Surface Analyzer Pickup. Root Mean Square Meter readings in microinches were found for eighty randomly selected blanks. These values are shown in Figure 12. A short strip of oscillograph tape was run to illustrate the sur- face finish graphically. A typical tape is shown full size in Figure 13. The thickness of the sheet metal should be. nearly constant because the sheets were cut from the same coil. 23 Frequency Total Lot 2400 Sample Size 80 25 “'24 Average Surface Finish '3" 76 o 9 ifi 1;! l 1‘ .3, 2o H - \O 1‘ 2.§’I§(H U W ‘ v \ . . . -. ‘. (£311 ‘IN‘ “ H Ul 4Q". 14 a won. fiat.- .. s '! ..i ,"\“ '<. «.‘E-unsg'gl I . l. J c ". is" T. ‘ i w ‘1’: 10 -’ v Y1_ ‘w‘ t “” 9 9 '. 4 . , . f :4 D, ”a .1t_ '1- T L . '3‘ a "i I 3E ' f; .i V; 1""- :3 ~ ~ l .- _ .I ,. t L ‘ O i" E 3 i; f. O h I ‘0 \O 85'9QL“V$ 81-85 ¢.v. 76-80. 61—55 56-60 3 ... 51-55E ... Surface Finish in Microinches Figure 12. Blank Sunface Finish Histogram 24 Microinches 200 i One Small Division 150 g :f:’ 100f'" 50_; 50.3 100:; 1 50 200 _; ’ Surface Covered in 10 Microinches Inches ——>- Figure 13. Blank Surface Finish Graph 25 The thicknesses of 240 blanks were selected at random and measured with. hand micrometers. These thicknesses are shown in Figure 14. Note that in this case a bell-shaped curve didnot result. Due to the wide range of thicknesses, it was suspected that a size- able drawing force error might result. Therefore the drawing force was calculated for the minimum and maximum thicknesses encountered. These calculations are shown on pages 92 and 93 of the appendix. An error of plus or minus 6. 9% from the mean drawing force could exist. Since this error would cause incorrect measurement of the reduction of the force due to friction, a means of factoring the thickness variable out of the experiment was devised. The blanks were sorted by thickness into the following catagories: . 040 - . 0409 inches . O41 - .0419 .042 - .0429 . 043 - .0439 .044 - .0449 .045 - .0459 .046 - .0469 .047 - .0479 . 048 - . 0489 .049 - .0499 Frequency 80 60 A O 20 Lot Size 2400 Average Thickness .0442 Sample Size 240 .048 EN Blank Thickness Figure 14. 27 in Pi e; v v C) .043 Inches Blank Thickness Histogram The blanks were then divided equally among the twelve lubricants to be tested. Each sample of 200 blanks for each lubricant had an identical number of blanks of each thickness. Therefore no lubricant had any advantage due to variations in blank thickness. Design of Cupping Die and Force Measurinjg Equipment To enable measurement of the punch force, die temperature and side wall thinning so as to check lubricant effectiveness in reducing fric- tion force, a suitable die was required. A draw die of desired accuracy was already available. This die was constructed so that the punch and die steels could be easily interchanged. One of the available die steels was selected for use in this experiment. It was decided, however, that a new punch steel would have to be designed and built. Only solid punches were available. A hollow punch was desired for this experiment. There are two main reasons for using a hollow punch. First, the cross-sectional area in compression was reduced. Thus the strain would be greater and more readily measured. Secondly, the hollow punch permitted mounting the strain gages close to the end of the punch. Since the punch force was to be measured, this was the proper position for strain gages. The punch exerts its force where the bottom radius and side blend together at the tangent point. Hollowing out the punch end has no effect on the contour of cup produced. The cup bottom is an area of low stress or strain. 28 / \\ / /t Figure 15. Cupping Die Design (Full Scale) 29 Due to clearances in the die, placement of the strain gages in other parts of the die would have been difficult. Refer to Figure 15 for a cross-sectional view of the die. Two strain gages were mounted in the punch steel. One gage was cemented vertically to measure the punch force exerted. This will be the major gage for the experiment. A second gage was cemented horizontally in the punch steel. A gage was placed in this position to measure the circum- ferential force on the punch steel. Measurements from this gage were not used to support the experiment conclusions. Both strain gages measured compressive strains or forces. It may be difficult to actually calculate or calibrate the circumferential force due to the non-uniform area on which it acts. The characteristic curve may be obtained however. In Figure 15, notice the groove cut in the punch riser and die shoe to carry the four strain gage leads out of the die. A slanted hole in the punch steel carries the leads through to the groove. This method was necessary to prevent the blankholder from cutting or mashing the leads. The strain gage specifications were as follows: Baldwin SR -4 Strain Gages Type A-18 3/16 inches minimum width Resistance 120. 5 t . 3 ohms Gage Factor 1. 70 1|: 2% Lot 232-11 C-55 Melted beeswax was poured into the hollow punch steel to protect the strain gages and leads from moisture and from the lubricants. Since the punch steel is mounted on the lower or die shoe, the lubricants tended to run down into the punch. Room was left in the center of the beeswax for the punch-steel retaining screw. The draw-die specifications are included on page 94 of the appendix. Critical die dimensions are given. The clearance has been made so that no burnishing or ironing of the cup side wall would occur because ironing would have caused an increased thinning of the side wall and an increased 30 punch force. Ironing would have made it extremely difficult to measure the true drawing punch force because it would have been impractical to calculate and factor out the increase in punch force due to ironing. Temperature Measurigg E quipment Die temperature rise should be a good indicator of the heat generated by friction. A greater temperature rise would indicate par- tial failure of the lubricant. The three main components of a cupping die would normally have the following relationship as far as friction and temperature: Punch Steel Lowest temperature due to the least amount of motion or sliding in relation to the sheet metal. Blankholder Medium temperature due to the maximum amount of motion or sliding in relation to the sheet metal. The larger mass pre- vents the blankholder from attaining the highest temperature. Die Steel - Highest temperature due to the maximum amount of sliding in relation to the sheet metal. The die steel temperature was measured with a General Electric Type FH-l Hand Pyrometer. This pyrometer gave an almost instan- taneous reading. The specifications of the pyrometer are given on page 95 of the appendix. Figure 16 illustrates the pyrometer and its attachments. The flexible extension cable facilitated getting the probe into the die. Temperature measurements were taken only after every fifth cup. 31 __._:‘..__-‘ ‘2 _———j——- fi— __, ._ .—.———-— v7 . i 7 ,_ Figure 16. General Electric Hand Pyrometer (Courtesy General Electric Company) 32 Thickness Measuring Equipment A deep-throat micrometer was selected for measuring the wall thickness of each cup. Fast accurate readings were possible. Another decision was to make three wall thickness measurements on each cup drawn. Thus the maximum thinning as well as the maximum thicken- ing of the side wall was found. Figure 17 shows the positions at which the wall thicknesses were measured. Each position was designated by a letter and they were recorded separately on the test data forms. Blank Preparation The blanks as cut had a small burr on the edge. If left in this condition, the burr might have scratched the die surface. Also the burr might have broken off during drawing. Pieces of metal in the die would certainly have altered the accuracy of the measurements. De- fects would have been produced in the cup such as galling, scoring or imbedded metal particles. To eliminate this condition, the burrs were completely removed by using a flexible -belt sanding machine. Thus the contour of the blank was not altered. Then care was taken to wipe off all burr fragments and sand particles which stuck in the mill oil on the blanks. After the thickness measurements had been taken and the sorting was completed, the blanks were wrapped in aluminum foil to prevent any contamination or rusting. 33 [7 /7 [Z Z/ v. >fiv—¢ A 17 [f Z/ Z77 Figure 17. Near Top of Cup "Position A” Near Center of Side Wall of Cup ”Position 8" Hear Bottom Radius of Side Wall of Cup "Position C” DRAWN CUP THICKNESS MEASUREMENTS Cup Wall Thickness Measurements 34 Setup of Die and Press (Trial Run) Before certain adjustments could be determined and the experiment procedure written, the die had to be setup and a trial run made. After setting up the die and calibrating the Sanborn Recorder, the press was started. The press clutch air pressure was adjusted to fifty pounds per square inch. This pressfire was recommended by the press manufacturer. The press counterbalance air pressure was adjusted to twenty pounds per square inch. Such a pressure was needed to counterbalance the weights of the ram, the punch shoe and the die steel. The press strokes per minute was set at forty. This was recom- mended as the minimumSPM for continual operation of the press. The cushion air pressure was set at fifteen pounds per square inch. A blank was inserted in the die and a cup drawn. The cup broke indicating too much blankholding force. The pressure was readjusted to ten pounds per square inch. The resulting cup was without breaks or wrinkles. The pressure was again readjusted to five pounds per square inch. The re- sulting cup had small wrinkles. Therefore, ten pounds per square inch was selected as the cushion setting. With the cushion set at ten pounds per square inch, the blankholding force would be as follows: Cushion Rating --- 13 tons at 100 psi 13 = x THU 10 x a l. 3 tons or 2, 600 pounds Blankholding Force = 2, 600 pounds For the trial run, an oil similar to mill oil was placed on both sides of each blank. After drawing, the cups were too hot to handle, indicating a generation of heat caused by friction. Part of the heat is generated from working the sheet metal. ' 35 Another decision made during the trial run was that the Sanborn Recorder attenuator could be set on (1) thus obtaining greater sensitivity. The deflection readings would not go off of the scale at this setting. Figure 18 shows the deflection readings as taken during the trial run. Both the vertical and circumferential deflections are shown. Fifteen cups were run with an average deflection of 23. 7 millimeters. All of the cups produced during the trial run had the defect of "ears. ' This would indicate that some directionality or direction of rolling does exist in the sheet metal. The ears were not severe, how- ever, and would be cut off during the trimming operation. This defect will not mar the final product. Ears were present on all cups drawn in the experiment. This defect was not recorded as such because it was common to all lubricants tested. 36 10 mm/sec Tape Speed Run Force Curves 37 Trial a t 09 9C rr | GO 8 (TC.- C m .lhe Uh TCC CC rnr rn max. 0% L L _ L a L L L . 1 L _ - . .. . . L .. . m u . _ L w L . L Till-..L h s i. L 414;! FiiLYimlfi -1 . 4 . 9.4-..714i4. 4-: 1 L L L _ L L L L h L L L L L ‘ FLL. _-L -L ._-_L m... L L L . L n L L L- TL. L .d L _. L . _ . _ . _ L I - h L .5 L _.a. :M B Y.” . L? L L L L . L L L L L o . . ii 1. .Liu L L L n. T... L r -1 L . L It! .hl s. I. + __ .v ,.*- In” 1%. all: Ii v IW . L . L L .ili-¢a.+ttwy.4l L l. “11% U--LT ILL L . Llllir- .. L. + -LTL +3.? fills- L 1.. L L L L Lllilit.-... 5+. . m i. _ :ttu ...L rtJ. «I . _ A . . . . L -w -L L .1 1414-6 1 . . ._ L L-.L--L- .L... ----L ELL _. _ P L L L L L L L L L . L L a d d u u q q d - 0000000000 czocx aoz mLoom O 5 O 5 0 5 O 5 O 5 2 O 7 5 7 O 7 5 ’ ’ I I I I ’ I ’ 21087 6.53 2 111 moaned c_ mouou Figure 18. An I'orange peel" effect was also produced on all of the cups. This was a good indication that the lubricant used was not functioning properly. No burnishing or ironing was present indicating that the die clear- ance was sufficient as estimated. With the press speed set at forty strokes per minute, the contact velocity of the drawing punch would be as follows:6 Velocity = 0.5233 x SPM x dy-y2 y = Cup Depth = l. 781 inches d = Press Stroke = 6. 000 inches SPM = Strokes per Minute = 40 V = 55 feet per minute This contact velocity is quite high for drawing. Because of‘this velocity, the cupping operation used for the experiment would be con- sidered a severe working of the sheet metal. Sequence of Testing Lubricants and Sample Size Actually, it was impractical to determinean exact sample size since the expected variation in readings was not known. The sample size was set at 200 cups per lubricant as a starting point. A total of 2, 400 blanks were required for the twelve lubricants. When continual breakage or scoring of cups occurred in one sample for a particular lubricant, the experiment was halted for that sample. Thus all 200 blanks were not run for each lubricant. Cup damage would indi- cate failure of the lubricant without measuring the reduction in punch force or thinning of the side wall. Further use of the lubricant would be unnecessary. To reduce the effects of sequence of testing lubricants, the sample of 200 was divided into four sub-samples of fifty cups each. By doing this, randomness was introduced into the sequence. Each lubricant could follow any other of the twelve lubricants. To introduce randomness, a table of random numbers was used. 7 e _ Crane. p 195, Op. Cit. Wilson. E. B. Jr. , An lntroducdon to Scientific Research, McGraw- Hill, New York, 1952, p 287 38 When converted to code letters, the sequence of testing lubricants was as follows: J K L F K E A L L M E K K B B H C F J M D L F F A G J D G M B C C C E G B E H H J M A H G D A D The Experiment Procedure The experiment procedure was divided into the following three catagories: 1. Press Adjustments 2. Sanborn Recorder Calibration 3. Running the Experiment Since the entire experiment cannot be run at one time, the Sanborn Recorder and the Minster Press were completely adjusted for each separate running of samples. Each day the experiment was run, all three procedures were followed for the initial setup. After that, only procedure three was followed. These detailed procedures are included on pages 90 through 96 of the appendix. It was assumed that one strain gage mounted in the punch was sufficient to measure the variation in punch force due to changes in the friction force. Four strain gages would have been used if it was desired to find the average punch force. Verification of the above assumption was deemed necessary. Therefore after the major portion of the experi- ment was completed, three additional strain gages were mounted in the punch and several cups made. The results were recorded on tape by the Sanborn Recorder. Samples of the test data forms used to record data are shown on the following pages. 39 LUBRICANT: TEST DATA SA MPLE NUMBE R Cup No. Vertical Deflection Circum- ferential Deflection Wall Thickness A B Temp. cocoqaacnwswmw .— O —_—1>. t-I H p... M p..- (A) H #3 H 01 H a p .4 h.- an pa CO N O N H N N M 02 ,LZAL LL25 Temperature in Degrees Fahrenheit Wall Thickness in Inches Deflection in Millimeters 4O LUBRICANT: TEST DATA (CONTINUED) SA MPLE NUMBE R Cup No. Vertical Deflection Circum- ferential Deflection Wall Thickness A B C Temp. 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 $2 43 44 45 46 47 48 49 50 Temperature in Degrees Fahrenheit Wall Thickness in Inches Deflection in Millimeters 41 DR AWING DEFECTS RECORD Defect Description Lubricant Code Letter Sample No. Cup No. 42 III. The Expe rim ent The experiment was completed without serious difficulty or interferences. Minor disturbances which occurred during the experi- ment are recorded in this section. The room temperature varied somewhat during the course of the experiment. The range in room temperature was from 70 to 76 degrees Fahrenheit. Therefore any temperature averages had to be adjusted to a. common room temperature of 70 degrees. The same experiment procedure was followed for each sample. It was expected that the duration times for each sample would then be uniform. If such a condition existed the die temperature rise could then be used with validity to show presence of friction. A factor existed however, which prevented uniformity of duration times. This factor was the viscosity of the lubricant. Lubricants with high viscosity were easily applied and the duration time for running these lubricants was low. Other lubricants with low viscosity were very difficult to apply uniformly on the blank surfaces. The duration time for these lubricants was higher. Because of the variation in duration times, die temperature could not be us ed as a factor in determining which lubricant was most effective in reducing friction in a cupping die. The following pages list the duration times for each of the forty- eight samples as recorded during the experiment. Lubricant Code Letter EXPE RIMENT DURATION TIMES A Cups Made 55 154 200 200 63 47 93 85 Duration Tim e- Hrs. 44 .08 .41 .20 .ll .00 .00 .95 .95 .10 .80 .67 .67 .08 .00 .87 .77 .33 .27 .21 .30 .13 .33 .17 .25 .50 .33 .33 .33 .25 .30 .33 .38 Sample Number nth-DONH ubWNt—e $00th ACOMH rhOONt-t uhCADNt—e waH wthv-e Lubricant Code Letter J M Cups Made 200 200 200 148 Duration Time-Hrs. Sample Number 45 HHHI—l .33 .33 .27 .17 .17 .91 .83 .83 .08 .00 .91 .20 .30 .25 .00 .88 ukwND-e «thH unwan- Awash- The cupping die used incorporated a solid-knockout arrangement for ejecting the cup from inside of the die steel opening. Another dif- ficulty was encountered here. When a lubricant with low viscosity was being tested, the cups stuck to the knockout-pad ejector with such adhesiveness that several hard blows were necessary to release the cup. This slowed the experiment considerably and increased the dura- tion time for those lubricants. Before each temperature reading was taken with the hand pyro- meter, the die surface was wiped clean with a towel. This was neces- sary to prevent lubricant from filling the ceramic cup which housed the thermocouple. Again, with the lubricants having low viscosity, cleaning of the die steel was hampered. This allowed the die to cool before the reading could be taken. Thus, another factor entered the experiment which invalidated the use of die temperature as an indica- of friction. Measurement of the cup wall thickness at position "A" was found to be difficult. Due to the rapid thickening of the wall near the top edge, a very slight shift in the micrometer caused considerable change in the reading taken. A more gradual change in wall thickness was found at positions "B" and "C. " This condition accounts for the wider range of thickness readings at position "A. A cross-section of a typical cup is shown in Figure 19. 46 Micrometer Ball Anvil ‘N b \ \ \ \ N N 3 ' [:I \ N N N \ \ \ \ \L\\\\a\\\3) Position ”A” Slight Vertical Shift of micrometer Causes Large Change in Reading Position "8” and Position ”C" Less Chance for Error due to Gradual Wall Thickening and Thinning CROSS—SECTION THROUGH CENTER OF CUP Figure 19. Excessive Wall Thickening at Position ”A” 47' When lubricants with high viscosity were being tested, as the die closed lubricant would spray all over the work area. Shields had to be placed around the press to help control or limit the spraying to a more confined area. The cleaning job after using such a lubricant was a factor which lengthened the time required to run the overall experiment. The following pages show the filled test data forms for one of the lubricants. Also shown is one of the drawing defects records taken of the experiment. These examples show how the data varied from cup to cup. The remaining test data forms are not included here. Histograms of the data are included and these show the frequency and range of read- ings for each lubricant. Most of the histograms are in the appendix of this thesis. Photographs were taken of the experiment setup. Figure 20 is a photograph showing the press controls and the cupping die. Also seen in the photograph are the dial gages for setting clutch air pressure, counterbalance air pressure, cushion air pressure and strokes per minutes of the ram. The palm buttons may also be seen at the front of the press. The cupping die is visible with the punch steel and blank- holder on the lower shoe. The press ram is in the extreme. up position at this time. 48 TEST DATA LUBRICANT: J SAMPLE NUMBER ’1 Cup Vertical Circum- Wall Thickness Temp. No. Deflection ferential Deflection A B C 1 14.0 8.0 .040 .035 .032 70 2 20.5 12.0 .043 .034 .032 3 20.5 13.0 .042 .033 .037 4 21.0 15.5 .041 .032 .035 5 22.5 15.5 .039 .032 .034 6 19.0 7.5 .042 .032 .033 71 7 18.0 7.0 .040 .031 .035 8 19.0 4.0 .045 .032 .031 9 20.0 14.0 .041 .031 .031 10 18.0 5.5 .039 .030 .032 11 18.5 10.0 .045 .031 .034 72 12 19.5 10.0 .043 .030 .031 13 19.0 3.5 .039 .032 .030 14 17.0 9.5 .038 .030 .029 15 18.0 9.0 .040 .031 .030 16 18.5 7.0 .038 .031 .030 75 17 19.0 13.5 .042 .031 .032 18 20.0 9.5 .044 .032 .032 19 19.0 3.0 .040 .031 .031 20 18.5 8.0 .041 .031 .033 21 21.5 7.5 .042 .034 .032 73 22 21.0 18.5 .043 .034 .034 23 20.5 17.5 .044 .033 .032 24 20.0 11.0 .038 .031 .030 L_25 19.5 9.5 .038 .030 .030 Temperature in Degrees Fahrenheit Wall Thickness in Inches Deflection in Millimeters 49 TEST DATA (CONTINUED) LUBRICANT: J SAMPLE NUMBER 1 Cup Vertical Circum- Wall Thickness Temp. No. Deflection ferential ‘Deflecflon .A B C 26 20.5 17.0 .042 .034 .033 75 27 16.0 7.0 .045 .031 .032 28 16.0 6.5 .039 .030 .029 29 21.5 17.0 .042 .033 .031 30 22.0 15.5 .040 .030 .029 31 18.5 9.5 .037 .029 .028 75 32 24.0 8.5 .043 .031 .035 33 18.0 10.5 .039 .030 .028 34 18.0 7.0 .037 .028 .030 35 18.0 6.5 .037 .028 .028 36 19.0 13.0 .037 .029 .029 75 37 18.0 6.5 .038 .030 .030 38 20.5 10.5 .038 .031 .031 39 18.0 6.5 .040 .030 .031 40 17.5 10.0 .041 .030 .030 41 17.5 7.5 .045 .030 .032 75 42 18.0 10.0 .041 .030 .029 43 19.5 11.5 .045 .030 .030 44 18.5 7.5 .043 .029 .021 45 18.0 9.0 .040 .029 .030 46 18.5 5.5 .037 .029 .029 75 47 20.0 5.5 .044 .032 .031 48 17.0 11.0 .037 .028 .028 49 23.0 11.5 .040 .029 .029 L__§0 23.0 13.0 .041 .032 .029 75 Temperature in Degrees Fahrenheit Wall Thickness in Inches Deflection in Millimeters 50 DRAWING DEFECTS RECORD Lub-r‘i‘chza‘h‘tm" . Code Sample Cup Defect Description Letter No. No. Cup Broke B 2 21 I! H H H 23 H H _ H H 35 Small Wrinkles C 1 8 H H H H 10 H H H H 14 Cup Broke H 1 1 1 H H H II All Cup Broke F 2 All Severe Wrinkles D 1 4 Cup Broke M 2 2 If H H H 25 H H H H 26 Cup Broke F 3 2 H H II I! All Cup Broke A 2 3 H H H H 6 H H H H 7 Wrinkles D 1 Cup Broke G l H H II » H 2 H H H H 3 51 F0 Igure 20. Press Controls and Cupping Die Left-Front View 52 The Sanborn Multi-Channel Analyzer may be seen in Figure 21. Also shown here is a right-front view of the press and cupping die. The strain-gage leads from the die to the analyzer are visible. The air cushion which operates the blankholder is visible between the legs of the press. The general work area in front of the press is shown in Figure 22. From left to right are shown the following articles: Cup Disposal Truck Deep- Throat Micrometer in Vise Broken Cups ' Test Data Form in Clipboard Lubricant Pail with'Mixing Stick Aluminum Tongs and Blank Hand Pyrometer Stack of Blanks and Paint Brush The cupping characteristic curves are shown in Figure 23. These curves were cut out of the tape from the Sanborn Analyzer. The same general curve was present for all lubricants. The only change was in the average height of the curve. The curves show a high instantaneous force when the cupping operation starts. A more gradual reduction of force follows. This indicates, as predicted, that the initial part of a cupping operation is the most severe. 53 o . ~. . Figure 21. Press, Cupping Die and Sanborn Multi-Channel Analyzer Right-Front View 54 Figure 22. Work Bench Arrangement Opposite Press 55 .. t o Vi ill it H . .L _ ‘ . . L '4‘ Ill!!! i ii, ii . .H L l .. 4 A ,. . .. .v. Jillirltllft “01 lilivl 'il: L L . . . . 5. . . ... .F ..L ... L In - 4—4- .- 4F".~ ; . . .t L..- liilll l - ii v .. . . . . . o "E" o-vfilv-c— o~1r~ ——. ._.-- r—Jb‘ T—a t l l l .$.L. l l l V l l Tape Movement <1; letting up Tapered Trailing Edge of Force) (Gradual — a C .I e t 9 r.d e t V 05 V.n r.G 66 e e N.L (High Force instantly) Mal u Cup Heig ZJZBO Curves istic Cupping Character Figure 25. 56 IV. Results and Analysis of Data In order to conveniently compute the means and the standard deviations of the test results, the deflection values were partitioned into cells of one millimeter and the wall thicknesses into cells of . 001 inches. Partitioning the raw data also permitted the construc- tion of histograms which graphically portray the experimental results. For the force histograms, it was found more convenient to work with the deflection readings rather than the force in pounds. The de- flection readings are used from here on in place of force. Conversion of deflection to pounds of force was then not necessary. With the above cell sizes, the histograms have from ten to twenty cells, as recommended by most statisticians. 8'9A total of twenty-eight histograms were plotted. For each lubricant, a histogram was made for the deflection data. Then histograms were made for each of the wall thickness measurement positions. A typical histogram is shown in Figure 24. All of the other histograms contain the same informa- tion and are included in the appendix. A statistical analysis will not be applied to the lubricants which caused high cup breakage. The per cent of breakage is in itself. suffi- cient to use as a method of rating these lubricants. Discrimination of Data The following groups of data were then ready for analysis: Deflection Wall Thickness Position "A” Wall Thickness Position "B" Wall Thickness Position "C” Temperature 8 Grant, p, 46, Op. Cit. 9 Juran, p, 360, Op. Cit. 57 Due to difficulties encountered when running the experiment, the following groups of data were not considered to be reliable for making an analysis: Wall Thickness Position "A" Wall Thickness Position "B" Temperature Several reasons for not relying on the temperature data were -‘_ nu discussed previously. Difficulty in applying the lubricant to the blank caused a variation in duration times for each sample of fifty blanks. In some instances, the die was allowed a longer time for cooling between operations. Difficulty in cleaning the die steel prior to measuring temperature also permitted cooling of the die steel. It was necessary to remove all lubricant from the die steel for each temperature reading. Otherwise the sensitive thermocouple probe would have become covered with lubricant. This lubricant would have insulated the thermocouple slightly and caused an error in the readings. With certain lubricants, it was difficult to remove the cup from the die. The lubricants were very tacky and acted as an ad- hesive. This also permitted cooling of the die steel causing an addi- tional variation in temperature measurements. Refer to Figure 19. Due to the rapid change in wall thickness at position "A, " a slight shift of the micrometer caused a large varia- tion in the reading obtained. This possibility of error thus partially invalidated the data recorded. The same condition existed, to a lesser degree, at position "B" and therefore the data was also somewhat in- validated. Rather than take the risk of uncontrollable variables affecting the analysis, these data were not used for the analysis of the lubricants. The deflection data and the wall—thickness position "C" data were utilized for analysis. The data for each lubricant was analyzed by 58 comparing averages and variabilities. The following are then the measurements to be used in the analysis of lubricants: Deflection: Average Variability Wall Thickness Position "C": Average Variability Standard Deviations and Means The standard deviation and mean were calculated for each histo— gram by the short method. 10 An example of this method and sample calculations are included on pages 102 and 103 of the appendix. A sum- mary of the results is shown on the following page. The lubricants for which these calculations were not made and their per cents of cup breakage are as follows: Lubricant Per cent Code Letter Breakage H 70. 6 G 75. 3 E 77. 8 A 92. 7 F 95. 7 The means and standard deviations are illustrated graphically in Figures 25 and 26 to show the degree of correlation existing between deflection and wall thickness results. If correlation does exist, when analyzed by later tests, then wall thickness measurements of drawn parts may be used to find the drawing force required. Use of strain gages and other intricate equipment would not be necessary. 10 Grant, p. 58, Op. Cit. 59 Lubricant Deflection Wall Thickness Sample Code L __ Size Letter X s X s A HIGH BREAKAGE B 27.75 2.82 28.47 1.53 154 C 25.95 3.52 29.81 1.60 200 D 27.11 3.92 29.37 1.69 200 E HIGH BREAKAGE F HIGH BREAKAGE G HIGH BREAKAGE H HIGH BREAKAGE J 24.74 4.52 30.27 1.61 200 K 26.65 2.90 31.13 1.58 200 L 27. 15 4. 35 30. 57 l. 58 200 M 25.66 3.68 29.95 1.35 148 Note: Deflection is directly proportional to frictional force. Wall Thickness is indirectly proportional to frictional force. Wall-Thickness Position "C" data was used. Deflection in millimeters. Wall Thickness in thousandths of an inch. 60 55 5O 45 40 Frequency m ix i» U! C) u: M O H U 10 Mean = 29.81 Yq—q Standard Deviation = 1.60 IDOFCD N K\“V|fi o r\ v with Ktrfi Kt NNNNNN wall Thickness in Thousandths of an Inch Figure 24. Wall Thickness Position ”C” Lubricant ”C” Histogram 61 Inch in Thousandths of an Thickness Wall Key: Wall Thickness Def lect ion _ 2.0 4.6 1.9 4.4 1.8 4.2 in 1.7 4.0 L Q) . 1 .5 * 3 .s .5 ~ ’ f 4 ._ ll 2 c '. ,4 .. i o 1 a 4 ‘1 fi— " 3 .4 : i: L. V U 'i e. -. , a; If! : ' a, L 1.3 i “i g “ 3.2 ‘3; t "g ‘ Q 5* .* . 1'2 l 3 .0 l i g 3 BREAKAGE\ ’ i 1 ~ 4 i . t i . / 2 8 . i , i A E Figure 25. N\ D L J F Lubricant Code Letter Standard Deviation Values for Lubricants 62 Thickness in Thousandths of an Inch Wall ....l Key: Wall Thickness Deflection I "i- 28.5 29.0 29.5 30.0 30.5 31.0 31.5 52.0 .T ‘7 ‘ “ .I ‘1 Jv‘--“ .f' T, Figure 20. {0 D L B A BREAKAGE K4 /’ / ,l\\\ \ [ill / Lubricant Code Letter F G I Nean Values for Lubricants 65 28.0 27.5 27.0 26.5 26.0 25.5 25.0 24.5 24.0 in Millimeters Deflection Rating of Lubricants by Deflection Differences did occur between the means and the standard devia- tions of the seven lubricants analyzed. These differences were used to rate the lubricant's effectiveness. First, tests were made to elimin- ate discrimination between lubricants where a significant difference did not exist. Ratings of lubricants based on deflection measurements were de- veloped first. A suitable test for significant difference of standard devi- 11 A description of this test is included ations or homogeneity was found. on pages 104 and 105 of the appendix. Sample calculations are on page 106 of the appendix. The results of the tests are shown on the following page. Where the test results indicate homogeneity, a significant differ- ence of standard deviations does not exist. The lubricants were then rated by standard deviations. The lu- bricant having the lowest standard deviation was given a number one rating as this lubricant. would cause less variation of force required for cupping and better control of the operation could be maintained. The rating is as follows: Lubricant Temporary Revised Code Letter Rating Rating B l 1 K 2 1 C 3 2 M 4 2 D 5 2 L 6 3 J 7 3 h.— ll I uran, p. 382, Op. Cit. 64 HOMOGENEITY OF STANDARD' t-i m m H- vesseaaaomwwwww grahgrxuograsoo mesa. arts ran ssr DEVIATIONS FOR DEFLECTION F - F' Homo- }: DF] DFZ 3 Difference geneous 1. 56 200 154 1. 29 Greater NO 1. 93 200 154 1. 29 Greater NO 2 . 56 200 154 1 . 29 Greater NO 1 . 06 200 154 1. 29 Less YES ‘1 2. 37 200 154 1. 29 Greater NO 77 l. 70 148 154 1. 31 Greater NO , 1.24 200 200 1. 26 Less YES i 1. 65 200 200 1. 26 Greater NO l l . 47 200 200 1. 26 Greater NO 1. 53 200 200 1. 26 Greater NO 1.10 148 200 1. 29 Less YES 1. 33 200 200 1. 26 Greater NO 1. 82 200 200 l. 26 Greater NO 1. 23 200 200 l. 26 Less YES 1. 14 200 148 1. 29 Less YES 2. 43 200 200 1. 26 Greater NO 1. 08 200 200 1. 26 Less YES 1. 51 200 148 1. 29 Greater NO 2. 25 200 200 1. 26 Greater NO 1 . 6 1 148 200 1 . 29 Greater NO 1. 40 200 148 1. 29 Greater NO F Calculated value of F. F' Value of F from Table E. A confidence interval of 0. 05 was chosen for this experiment. If F is less than the value of F', then the probability is greater than 0. 05 that the difference may occur by chance. The difference is not significant. Therefore the samples and their deviations are homogeneous. If F is greater than the value of F', then the probability is less than 0.05 that the difference may occur by chance. The difference is significant. Therefore the samples and their deviations are not homogeneous. 65 A test for determining significance in difference of means was found. 12 A description of this test and sample calculations are included on pages 107 and 108 of the appendix. This test may be applied only to those means having standard deviations which are homogeneous. Applying this test to non—homogeneous samples would not yield meaningful results. A test for determining significance in difference of means when the samples are not homogeneous was found. 13 A description of this test and sample calculations are included on pages 109 and 110 of the A”: n appendix . The lubricants were given a temporary rating according to their deflection means. The lubricant having the lowest mean was given a number one rating. Low deflection indicated a low punch force which in turn indicated a low friction force. A low friction force indicates that the lubricant is funtioning properly. Presence of less friction causes less strain and wall thinning is not as severe. Better cups result. Where a significant difference of means did not exist, the rating was revised to account for this fact. Where a significant difference did exist, the temporary rating was left intact. The revised rating shown is then the rating of the lubricants based on difference of means for deflection data. 12 Jman, p, 380, Op. Cit. 13 Ireson, W, G. and Grant, E. L. . Handbook of Industrial Engineering and Managemeng Prentice-Hall, New York, p. 852-853. 66 r-i rams wo*§ SIGNIFICANT DIFFERENCE OF DEFLECTION MEANS (Homogeneous Samples) __ __ t - t' Sign. X - X' t DF _t_'_ Differ- We £115.12... 1.16 3. 10 398 l. 96 Greater YES .04 . 10 398 1.96 Less NO . 29 . 74 346 1. 96 Less NO 1.10 3. 54 352 1. 96 Greater YES ‘3? and-32(—T Deflection Means of the two samples in question. t Calculated value of t. t' Value of t from Table C. The confidence interval for this experiment was set at 0. 05. When t is greater than the value of t', then the probability is less than 0. 05 that the difference occurs due to chance. A significant difference between means does exist. When t is less than the value of t', then the probability is greater than 0. 05 that the difference occurs due to chance. A significant difference between means does not exist. SIGNIFICANT DIFFERENCE OF DEFLECTION MEANS (Non-homogeneous Samples) "if _ “'3 t v t' t - t' Sign. ‘ --— -~-- ~------ Difference Diff erenge . 92 2. 09 343 1. 96 Greater YES . 70 2. 17 398 1. 96 Greater YES .46 1. 33 398 1.96 Less NO .60 1. 57 343 1.96 Less NO The interpretation of the values here is the same as that shown above. 67 The rating of lubricants by deflection means was as follows: Lubricant Temporary Revised Code Letter Rating Rating J 1 1 M 2 2 C 3 2 K 4 3 D 5 3 L 6 3 B 7 4 When the degrees of freedom (v) was computed for the non- homogeneous samples, the result was 343. The degrees of freedom (DF) when computed for the homogeneous samples of the same size was 346. Therefore with the large samples used in the experiment, the degrees of freedom remain relatively the same regardless of whether the samples are homogeneous or not. The test for signifi- cance of difference between means of homogeneous samples was applicable to all samples. Therefore only one test was applied from this point on. Rating of Lubricants by Wall Thickness The test for significance of difference between standard devi- ations was then applied to the wall thickness data measured at posi- tion ”C. " The results are shown on the following page. Notice the large percentage of homogeneity which existed. When the standard deviations are homogeneous, a significant difference does not exist. The lubricants were then rated with the lubricant having the lowest standard deviation receiving a number one rating. Where a significant difference did not exist, the next lowest lubricant received the same rating as the previous lubricant. Where a significant differ- ence did exist, the rating number was changed to a higher figure. 68 The rating was as follows: Lubricant Temporary Revised Code Letter Rating Rating M 1 1 B 2 1 K 3 2 L 4 2 C 5 2 J 6 2 D '7 2 The test for significance in difference of means was made for the wall thickness data. The lubricants were given a temporary rating by means. The lubricant with the highest mean was given a number one rating. A high wall thickness mean indicated less thin- ning of the cup side wall. Less wall thinning was assumed to indi- cate a lower friction force which in turn should indicate a better lubricant . Where a significant difference existed, the rating was left in- tact. Where a significant difference did not exist, the rating was revised to agree with this fact. The results of this test are shown on the following page. The revised rating is then the rating based on the wall thickness means as follows: Lubricant Temporary Revised Code Letter Rating Rating K 1 1 L 2 2 J 3 2 M 4 3 C 5 3 D 6 4 B 7 5 69 ___-____ _ _ _-_‘—_'_L-I ___ _— l HOM CGENEITY OF STANDARD DEVIATIONS FOR WALL THICKNESS POSITION C '-] (b m q-o- grssgraéoéésseo Hooooooonommmmmw w: Et‘N rsw gar F - F' Homo- F DFl DFZ __F_'_ Difference geneous 1. 10 200 154 1. 29 Less YES 1. 22 200 154 1. 29 Less YES 1. 11 200 154 1. 29 Less YES 1. 07 200 154 1. 29 Less YES 1. O7 200 154 1. 29 Less YES ‘.‘ l. 28 154 148 1. 31 Less YES 1 1. 12 200 200 1. 26 Less YES i 1. 01 200 ' 200 1. 26 Less YES i 1. 03 200 200 1. 26 Less YES 1. 03 200 200 1. 26 Less YES , 1 . 41 200 148 l. 29 Greater NO 1. 10 200 200 1.26 Less YES 1. 14 200 200 1. 26 Less YES 1. 14 200 200 1. 26 Less YES 1. 57 200 148 1. 29 Greater NO 1. 04 200 200 1. 26 Less YES 1. 04 200 200 1. 26 Less YES 1. 42 200 148 1. 29 Greater NO 1. 00 200 200 1. 26 Less YES 1. 37 200 148 1. 29 Greater NO 1. 37 200 148 1. 29 Greater NO F Calculated value of F. F’ Value of F from Table E. A confidence interval of 0. 05 was chosen for this experi- ment. If F is less than the value of F', then the probability is greater than 0. 05 that the difference may occur by chance. The difference is not significant. and their deviations are homogeneous. Therefore the samples If F is greater than the value of F', then the probability is less than 0. 05 that the difference may occur by chance. The difference is significant. and their deviations are not homogeneous. 70 Therefore the samples i-I m m a. goers st" anti-JO 9? é: SIGNIFICANT DIFFERENCE OF WALL THICKNESS MEANS __ __ t .- t' Sign. X - X' t 2}: _t_'_ Difference Difference . 56 3. 53 398 1. 96 Greater YES . 30 1. 88 398 1. 96 Less NO . 46 2. 86 398 1. 96 Greater YES . 44 2. 67 398 1. 96 Greater YES .90 5. 15 352 1.96 Greater YES . 32 2. 01 346 l . 96 Greater YES .14 .88 346 1.96 Less NO 3? and 35 Wall Thickness Means of the two samples in question. t Calculated value of t. t' Value of t from Table C. The confidence interval for this experiment was set at 0. 05. When t is greater than the value of t', then the proba- bility is less than 0. 05 that the difference occurs due to chance. A significant difference between means does exist. When t is less than the value of t', then the probability is greater than 0.05 that the difference occurs due to chance. A significant difference between means does not exist. 71 Correlation Analysis Correlation tests were made to determine if a relationship does exist between the deflection and wall thickness data. If such a correlation exists, wall thickness measurements of drawn parts could be used to determine the drawing force required and in turn the effectiveness of the lubricant in reducing friction and the expen- sive and time-consuming application of strain gages would not be necessary. The results could be used to aid in the selection of lu- bricants as well as predicting overload of presses. 1 The Original Data Method of correlation analysis was selected for this test. 14 This method was more lengthly but provided greater accuracy in the results. It was found that a computer was necessary I to make the correlation tests. Errors in the fifth or sixth significant figure caused large errors in the final results. Sometimes the re- sults would be entirely impractical. A description of the correlation test and sample calculations are included on pages 111 and 112 of the appendix. This test was used to find the correlation coefficient between the means of the deflection and wall thickness data. The test was also used to find the correlation coefficient between the standard deviations of the deflection and wall thickness data. Scatter dia- grams were made to further illustrate the correlation of the data. Figure 27 shows the scatter diagram for standard deviations. Fig- ure 28 shows the scatter diagram for means. All of the test results are noted on each diagram. u. 1 4 1mm. p. 472, Op. cm, 72 in Thousandths of an Inch Thickness Wall 2.1 2.0 1.9 1.8 1.6 1.5 1.3 1.2 ‘Correlation Coefficient r = Coefficient of Determination .1655 r2: .0274 Standard Devi ation =.0954 0‘...“ __— -‘ 4 —'—+— ——I- ”—- ——— .- 0 O ___. all—__- «nu-Jp— u—I-I— "‘—'— -———. lv\ 0 \~ Regression Lise a) <3 o: v o (n (3 cu e- 0 (V n «x xx «i Ni V v v v Deflection in Millimeters Slope b = .035 Intercept a = 1.4343 ' (When x = 0) Figure 27. Correlation of Standard Deviations Scatter Diagram 73 in Thousandths of an Inch Thickness Wall Correlation Coefficient r = .3948 2 r Coefficient of Determination = .1559 52.0 , , SWandard DeVIatl n = .7294 a l .\V i 51.0 \ o \N KL \ 30.5 \x \49‘ y. \‘ 30.0\ c \ \. U \4\ \ 1// 29.5 , 7‘.V . \~ 0 \ . ‘\\‘ 29.0 / ‘ e\ \ f x. 28 5 R gression Line 7“ ' 5 28.0 0 in C) K\ 0 an 7% MN TO 23. 8’. ti} ii} 2‘3 2‘3 R R 98 Deflection in Millimeters Slope b = -.3279 Intercept a = 38.6050 (When x = 0) Figure 28. Correlation of Means Scatter Diagram 74 , V. Conclusions and Recommendations Conclusions The four statistical ratings and the percents of cup breakage were combined to obtain a final rating. No weighing factors were used in this combination of ratings. The final rating is as follows: Wall Lubricant % Deflec. . Thick. Final and Code Break. X s X 8 Total Rating K Chlorinated Wax 00. 0 3 1 1 2 7 1 l J Pigmented - Med. 00. 0 1 3 2 2 8 2 M Graphite 00. 0 2 2 3 1 8 2 C Dry Wax 00. 0 2 2 3 2 9 3 L Heavy Oil 00. 0 3 3 2 2 10 4 D Plastic 00. 0 3 2 4 2 ll 5 B Soap 23. 0 4 1 5 1 11 5 H Lard Oil 70. 6 6 G Wet Wax 75.3 7 E Reclaimed Oil 77. 8 8 A Mill Oil 92. 7 9 F Molybdenum Disulf. 95.7 10 Correlation. Correlation does not exist between the means or between the standard deviations of the force and wall thickness data. Therefore wall thickness measurements cannot be used to determine the drawing force or the effectiveness of the lubricant in reducing friction. Characteristic Force Curve. The characteristic force curve for drawing has an almost vertical leading edge with a gradually reducing t1“fling edge. Thus the maximum drawing force occurs at the first instances when the punch contacts the sheet-metal blank. 75 The maximum drawing force is relative to the ratio between the punch diameter and the blank diameter. Leaving a flange on the cup has no effect on the maximum drawing force required. Recommendations From experience gained in this eperiment, the need for future research in several areas became evident. The conclusions reached here pertain only to one technical aspect of lubricant selection. Other factors should be analyzed and evaluated before efficient lubricant selections can be made. Technical Factors. It is recommended that the following technical factors be determined by experiment to aid in the selection of lubricants: 1. The effectiveness of other drawing lubricants not tested in this experiment. 2. The effectiveness of drawing lubricants for other sheet metals such as stainless steel, brass, magnesium and aluminum. 3. The effects of different drawing speeds. on the lubricant used. 4. The effects of varying the die or blank tempera- ture on the lubricant required. 5. The effects of different die or punch radii on the lubricant required. Economical Factors. It is recommended that the following economical factors be determined by experiment to aid in the selection of lubricants: 1. Cost of lubricants. 2. Ease of application. 3; Ease of cleaning. 4. Method of application. 76 5. Miscellaneous effects such as skin disease, corrosion and staining. 6. Effects on subsequent manufacturing operations such as welding, brazing, soldering, plating and painting. Only when all of these factors have been analyzed can efficiency of lubricant selection be determined. From the results of this experiment, it is recommended that chlorinated wax be used under the stated conditions until future experi- ments prove otherwise. Theory of Drawing. It is recommended that the characteristic curve for drawing force as well as the other conclusions be utilized for teaching the theory of drawing. Factual support will increase the significance of the theory. Drawing Force. It is recommended that future experiments be made to determine actual drawing forces for various shapes of parts and types of sheet metal. Afterwards, a suitable drawing force formu- la could be developed. 77 Appendix Bibliography Butler, W. G. , Draw Die Development Through Tryout, Fisher Body Engineering, Detroit, Michigan, 1954. Crane, E. V., Plastic Working in Presses, John Wiley 8; Sons, New Your, 1948. Deane, M. A., The Effects of Lubricants on Sheet Metal Operations, Chevrolet MotorDivisIon, Flint, Michigan, 1949. Fink, E. D., Sheet Metal Mathematics, Delmar Publishers, Inc., ,..._,‘ Albany, New York, 1947. 1‘. Grant, E. L., Statistical Quality Control, McGraw-Hill, New York, j 1952. [ Hinman, C. W., Pressworking of Metals, McGraw-Hill, New York, 1941. Hinman, C. W. , Die Engineering Layouts and Formulas, McGraw- Hill, New York, 1943. ~ Ireson, W. G. and Grant, E. L. , Handbook of Industrial Engineering and Management, Prentice-Hall, New York, 1955. Jevons, J. D. , The Metullurgy of Deep Drawing and Pressing, John Wiley & Sons, New York, 1940. Juran, J. M., Quality-Control Handbook, McGraw-Hill, New York, 1951. Lucas, C. W., Press Work Pressures, McGraw-Hill, New York, 1935. Marshall, E. C. , Practical Die Design and Die Making, McGraw- Hill, New York, 1937. Nadai, A., Plasticity, McGraw-Hill, New York, 1931. Sachs, G., Principles and Methods of Sheet-Metal Fabricating, Reinhold PuinsHing Corp. , NewTorkj955. Stanley, F. A., Punches and Dies, McGraw-I—Iill, New York, 1943. BIBLIOGRAPHY OF RELATED TEXTS AND ABSTRACTS Sheetmetal Work Pamphlets American Iron and Steel Institute Steel Products Manual 1. Alloy steel plates 2. Carbon steel plates and rolled floor plates ,. . 3. Carbon steel plates i 4. Cold rolled carbon steel strip 5. Flat rolled electrical steel I | 6. Hot rolled alloy steels 7. Hot rolled carbon steel strip 8. Tin mill products 9. Tolerances for alloy steel sheets and strip Die Design Handbood'r: 1955 A. S. T. E. Detroit, Michigan Determining the Correlation of Metallurgical Tests With the Deep- Drawing Performance of Sheet Steel 1951 D. B. Ballantyne Buick Motor Division Flint, Michigan The problem investigated in this report is that of determining before blanking whether or not designated coils of sheet metal are of a drawing quality suitable for fabricating Buick hoods, right front fenders and right rear fender panels. Samples from 100 coils for each part were inspected for drawing performance; specimens pre- pared from samples were tested to determine relationships of their mechanical chemical and microstructural deep-drawing properties to their drawing performance. Included are scatter diagrams for the correlation of variables. 80 The Econonical Use of Kirksite in Draw Dies 1950 Donald A. Bergdahl G. M. C. Truck Pontiac, Michigan Bliss Power Press Handbook 1950 E. W. Bliss Company Toledo, Ohio Die Designing and Estimating 1942 Charles Bohmer American Industrial Publishers George Dannes Cleveland, Ohio Thr Friction and Lubrication of Solids 1954 F. P. Bowden Oxford at the Claredon Press D. Tabor Oxford, England Area of contact between solids. Surface temperature of rubbing solids. Effect of frictional heating on surface flow. Friction and surface damage of sliding metals. Mechanism of metallic friction. Boundary friction of lubricated rmtals. Action of extreme pressure lubricants. Breakdown of lubricant films. Nature of contact between colliding solids. Adhesion between solid surfaces - the influence of liquid films. Chemical reaction produced by friction and impact. A Mathematics for the Sheet Metal Worker 1943 C. E. Buell Pitman Publishing Corp. New York Design Data for Punch Press Tools 1951 E. H. Burnham Rochester Products Rochester, New York Sheet Metal Theory and Practice 1944 John C. Butler John Wiley and Sons, Inc. New York Draw Die Development Through Tryout 1954 W. G. Butler Fisher-Die Engineering Detroit, Michigan 81 Standards Book 1955 Chevrolet Motor Division General Motors Corporation Flint, Michigan Applications of Cemented Carbides to Tools and Dies 1947 W. S. Clayton Ternstedt Division Trenton, New Jersey Plastics as a Die Material in Automotive Stamping Dies 1954 J. R. Clements Fisher-Die Engineering Detroit, Michigan Tool Design 1943 Charles Bradford Cole American Technical Society Chicago, Illinois Die Design Manuals Iand II 1948 C. R. Cory Fisher Body Division Detroit, Michigan Plastic Working of Metals and Non- Metallic Materials in Presses E. V. Crane 1948 John Wiley & Sons, Inc. New York Information relative to drawing. Chapter II. Essential Metallurgy Mechanics of metals, sturcture of metals, atoms, crystal structure, alloys, compressive and tensile movements, plastic range physical properties, grouping of operations according to stresses. Chapter VII. Cold-Working of Plastic Metals Plasticity. Experiments in strain-hardening. Upper and lower limits of the plastic range. Tentative rates of strain- hardening. The plastic cycle. Structural changes. Ductility differences. Temperature and plasticity. Hot and cold working. Rate and uniformity of plastic working. 82 Chapter VIII. The Drawing Group of Press Operations Metal movement and stresses in drawing. Drawing formu- lae. Blankholding theory. Blank and shell relations, redrawing limits and methods. Wall thickening and thinning. Ironing. Drawing rectangular and irregular shapes. Types of dies. Chapter 1X. Plastic States, Metallic and Non- Metallic Crystoplastic, thermoplastic, soluplastic, thermosetting, solusetting. Temperature and plasticity. Elasticity. Internal structure. Pressure welding in powders. Creep. Speed of flow. Polymers. States of internal bonding. Mixtures. Plasti- cizers. Sheet Metal Worker's Manual 1942 J. S. Daugherty Frederick J. Drake and Company L. Broemel Chicago, Illinois The Testing and Inspection of Engineering Materials 1955 Harmer E. Davis McGraw-Hill Book Co., Inc. George Earl Troscell New York Clement T. Wiskocil General features of mechanical testing. Measurement of laod, length and deformation with common testing apparatus. Static. Tension and compression tests. Static shear and bending tests. Hardness tests. Impact tests. Fatigue and creep tests of metals. Nondestructive tests. The Effects of Lubricants on Sheet Metal Operations 1949 Martin A. Deane Chevrolet Motor Division Flint, Michigan Principles and theories of lubrication. Factors including die design, die construction, die alignment, surface finish of die and stock. Principal requirements of a good lubricant. Princi- pal oils, fats and pigments. Lubricants tested. Improvements due to proper lubricants. Recommendations of lubricants for deep drawing. Reclamation. Lubricant applicator equipment. 83 Punches, Dies and Gauges Dowd & Curtis Forming Press Dies Dreis and Krump McGraw-Hill Book Co., Inc. New York 1945 Dreis and Krump Mfg. Company Chicago, Illinois Economic Material Utilization in Pressed Metal Operations 1953 F. S. Edwards Chevrolet Division Cleveland, Ohio Carbides and Their Application to Sheet Metal Dies 1950 Bernard M. Fair Sheet Metal Mathematics Eugene D. Fink Die. Design Standards Die Enrin eerin g Theory of Lubrication Mayo Dyer Horsey Pressworking of Metals C. W. Hinman 84 Chevrolet Motor Division Flint, Michigan 1947 Delmar Publishers, Inc. Albany, New York 1.953 Fisher Body Division General Motors Corporation Detroit, Michigan 1953 General Moto rs Corporation Detroit, Michigan 1936 John Wiley 8: Sons, Inc. New York 1941 McGraw-Hill Book Co. , Inc. New York Chapter III. Stamping and Forming Mild Steels S. A. E. Steel specifications. Nomenclature of mild steels. Cold-rolled steel strip for deep drawing. Steel temper difficulties in drawing operations. Lubricants for drawing steel. Ductility tests for drawing and forming. Chapter IV. Stamping and Forming Non- Ferrous Metals Specifications for non-ferrous metals. Typical mechanical properties of wrought aluminum alloys. Lubricants for drawing aluminum. Crain size is the measure of softness in brass. Chapter V. Specifications for Ordering Sheet Materials Testing for hardness and ductility. Lubricants for drawing steel. Lubricants for drawing brass and copper. Lubricants for drawing zinc. Lubricants for drawing aluminum. Applying lubri- cants both sides of strip. Chapter XX. Drawing Dies Plastic flow in drawing metals. Analyzing redrawing opera- tions. Time for metal flow. Die Engineering Layouts and Formulas 1943 C. W. Hinman McGraw-Hill Book Co. , Inc. New York The Industrial Arts Index Indexes The Engineering lndes Readers' Guide to Periodical Literature Technical Book Review Index The Metallurgy of Deep Drawing and Pressing 1940 J. D'udley Jevons John Wiley 8: Sons, Inc. New York Chapter III. Defects and Difficulties (General) Defects and difficulties attributable to the metal used. Unsuitable crystal structure. Directionality. Special defects and unsuitable physical properties. Troubles attributable to too high a speed of drawing. Unsatisfactory lubrication. Insufficient supply of lubricant. Lubricant unsuited to the metal. Inadequate film strength. Troubles due to non-removal of lubricant. Stain- ing. corrosion and adhering lubricant. Chapter VI. Defects and Difficulties (Steel) The theory of lubrication. Fluid friction. Solid Friction. Theory applied to lubrication in actual drawing operations. Sur- faces bearing an absorbed film. Properties desired of a drawing lubricant. Oiliness. Measurement of slipperiness. Film strength Resistance of temperature. Cost. Ease of removal. Spreading power. Adhesiveness. Corrosiveness. Stability. Typical Lub- ricants . Chapter XII. The Testing of Sheet Metal Chemical analysis. Microscopical examination. Hardness tests. Bend tests. Slotted-strip test. Tear-length test. Cupping tests. Actual drawing tests. Special tensile testing. Wedge- drawing tests. Chapter XIII. Properties Which Determine the Behavior of Metal During Deep-Drawing Chemical composition. Crystal size. Average grain size. Ductility and tenacity. Work—hardening. Reaction to speed of deformation. Hardness. Directionality. Reaction to annealing. Surface condition. Die Design and Diemaking Practice 1930 Franklin D. Jones The Industrial Press New York 86 Chapter XII. Classes of Drawing Dies and General Designing Information Formation of wrinkles in drawing. Depth of the first draw- ing operation. Diameter obtained in one drawing operation. Troubles encountered in drawing light gage metal. Effects pro- duced by trapped oil, air and water. Press-room lubricants. Lubricants for drawing brass. Lubricants for drawing steel. Lubricants for aluminum and zinc. Lubricants for non-metallic materials. Grain growth and its cause. Annealing temperature at which grain growth occurs. Grain growth in hot-rolled stock. Restriction of grain growth. The Use of Plastics as an Aid in Die Construction 1955 T. L. Kubani Fisher- Die & Machine Plant Detroit, Michigan Press Work Pressures 1935 C. W. Lucas McGraw-Hill Book Co., Inc. New York Analysis of Drawing Stresses as an Aid to Automotive Draw Die Design 1953 C. A. Luthe Fisher Body Division Cleveland, Ohio A study of sheet steel properties, drawing stresses and strains, and how they are considered in draw die design. Findings and deductions from past research preferences and actual industrial data. Stresses automotive die problems. including the determina- ting factors of draw beads, irregular binder surfaces, drawing radii die friction and corner relief notches. Includes tables and graphs of data on sheet steel properties and test results. Bibliography includes an extensive reference to past work on deep drawing. Mechanical Engineers' Handbook 1941 Lionel S. Marks McGraw—Hill Book Co. , Inc. ’ New York 87 Lubricants 772-780 (I) Cleansing 2179 (b) Coefficients of friction 241 (c) Effect of temperature 2175 (d) Extreme Pressure 777 (e) Film strength 2175 (f) For press work 1768 (g) Oiliness 777 (11) Tests 776 (i) Viscosity 245 Lubrication 2175-2181 (a) Factors 2175 (b) Fluid 1016 (c) Semifluid 1016 (d) Viscous 232 Practical Die Design and Die Making E. C. Marshall An Approach to Die Design W. H. McGlothlin 1937 McGraw-Hill Book Co. , Inc. New York 1949 General Motors Institute Flint, Michigan Improvements to Press and Die Operations 1954 A. W. Miller Harrison Radiator Lockport. New York A Progressive Die Manual for Pressed Metal 1949 Paul W. Morrow Plasticity A. Nadai Sheet Metal Work William Neubecker 88 Chevrolet Motor Div. Flint, Michigan 1931 McGraw-Hill Book Co. , Inc. New York 1946 American Technical Society Chicago, Illinois Modern Industrial Die Design 1947 Edmund A. Nowolinski Author Detroit, Michigan An Engineering Approach to Die Tryout ' 1954 J. A. Patterson Fisher Body Division Pontiac. Michigan Sheet Metal Industries Periodicals Industrial Newspapers. Ltd. London, England Modern Industrial Press Andresen, Inc. Pittsburgh, Pennsylvania Inspection of Metals 1941 Harry B. Pulsifer The American Society of Metals Cleveland, Ohio Chapter II. Tests for Composition Sampling. Bend Test. Magnetic tests. Solution rates. Spectroscope lines. Microscopic patterns. Analysis of S. A. E. Steel. Chapter IV. Hardness Testing File texting. Brinell. Rockwell. Schleroscope. I‘-,‘Ionotron. Vickers. Hardness conversion tables. Chapter V. Tensile Testing Including Shear Lever machines. Hydraulic machines. Calibration. Diagrams. Test specimens. Precautions. Calculations. Chapter VI. Soundness Testing Bend and fracture tests. Resonance test. X- Ray negatives. Magnetic and Magnaflux tests. Crack intensification. Chapter IX. Grain Size Testing Structural grain size. Fracture grain size. McQuaid—Ehn grain size. Normality. Austenitic grain size. Measuring grain size. Grain size chart. 89 Chapter XI. Impact, Fatigue and Creep Testing Izod. Charpy. Test specimens. Ranges. Fatigue machines. Corrosion fatigue. Creep ranges. Resistant compositions. Principles and Methods of Sheet-Metal Fabricating 1955 George Sachs Reinhold Publishing Corp. New York Information relative to drawing. Part I: Sheet Metal and Sheet Metal Parts Chapter II. Formability Tests General principles of formability tests for flanged. straight, curved and recessed parts. Chapter III. Sheet Metals Development of ferrous, non-ferrous and composite sheet materials. Chapter IV. General Properties of Sheet Metals Specifications and grain size requirements for sheet metals. Stretcher strains, directionality and stress cracking. Part II: Principles of Forming Various Part Types Chapter IV. Forming of Deep Recessed Parts Classification of deep-recessed parts. Strains and failures in cupping. Buckling and hold-down problems. Forming of very deep parts. Material problems in forming deep-recessed parts. Part III: Principles Of Deep Drawing Chapter I. Drawing and Thin Walled Cylindrical Cups Factors governing the draw force and cup strength. Strains and failures encountered in cupping. Forming limits for cupping thin blanks. Hold-down problems. Chapter II. Redrawing of Tubular Parts Classification of redrawing processes. Factors governing the draw forces and strength of a drawpiece. Reductions between anneals. Further problems of progressive redrawing. Reducing Operations. 90 Chapter IV. Drawing a Thick Walled Cylindrical Cups General problems of cupping thick blanks. Stress and strain relationships. Condition of the cup edges. Forming limits . Chapter V. Drawing of Box Shaped Parts General problems, strains and failures and blank develop- ment for box-shaped parts. Forming limits. Redrawing. Part IV: Press-die Formingr of Sheet-Metal Parts :1 Chapter I. Equipment, Tools and Lubrication for Press-Die .- Forming of Sheet Metal Parts ‘ Classification of lubricants. [ 3 Chapter III. Press Die Forming of Recessed Parts Die forming of closed, open, deep-recessed, semi-tubular, disk-shaped double—curvature and smoothly contoured parts. Economical Utilization of Sheet Metal in Presswork 1954 H. R. Schaal Chevrolet Motor Division Flint. Michigan Punches and Dies 1943 Frank A. Stanley McGraw-Hill Book Co. , Ltd. New York Chapter IX. Drawing Dies and Drawing Methods Importance of material in drawing. Direction of metal displacement. Movement of metal structure. An Analysis of Automobile Body Die Design as Related to Die Construc- tion, Maintenance, Tryout and Production 1954 R. L. Stoothoff Fisher Body Division Hamilton, Ohio Tool and Die Design Standards 1954 Ternstedt - Columbus Division General Motors Corporation Columbus, Ohio 91 The Application of Cemented Carbide to Piercing and Blanking Dies John R. Willson 1948 Delco-Remy Division Anderson, Indiana The Collection of Data to‘Facilitate the Development of Experimental Draw Progressive Die Strips 1949 Jay D. Wisner Chevrolet Motor Division Flint, Michigan An Analysis and Definition of the Factors Affecting Deep-Drawing Operations 1952 C. E. Zimmerman Brown-Lipe-Chaplin Syracuse, New York This study investigates the factors affecting die life and on-the- job repairs connected with deep drawing of bumper guards and hub caps and initiates a program of control for testing of new drawing compounds, for the quality control checking of steel, and for the investigation are described and supported by data. Conclusions stated regarding satisfactory tolerances for bumper stock, gage variations, lubricating compounds, and stock failure and die. damage due to steel surface defects. 92 FORCE CALCULATIONS ----- Due to variations in blank thickness. Punch Diameter 2. 563 inches Cup Inside Diameter Sheet-Metal Thickness Range . 041 to . 047 Cup Outside Diameter for . 041 inches thick: 2.563 + .041 + .041 = 2.645 Cup Outside Diameter for . 047 inches thick: 2.563 + .047 + .047 = 2.657 Formula: Force 2 Pressure x Area 15 Pressure: Ultimate Tensile Strength = 40, 000 psi for dead soft No. 6 (This will give the maximum force possible to produce at the cup bottom) Area = 7(rz - r12) or fl(r22 - r12) r and r2 = Cup Outside Diameter 2 r1 2 Cup Inside Diameter 2 For . 041 inches thick: r, = 2.645 = 1.3225 2 r2 = 1.749 For .047 inches thick: r2 = 2.657 = 1.3285 2 r22 2 1.765 r1 = 2.563 = 1.2815 2 r12 = 1.642 15 92a Cline. p. 91. Op. Cit. Force for . 041 inches thick: F (40, 000) (3.14) (1.749 - 1.042) F 13, 440 lbs. or 6.72 tons Force for . 047 inches thick: F H (40,000) (3.14) (1.765 - 1.642) F 15,450 lbs. or 7.725 tons FORCE VARIATION DUE TO VARIATION IN THE BLANK THICK- NESS: (Drawing Force -- Maximum) 7.725 - 6.72 = 1.005 tons or 15,450 - 13,440 = 2,010 lbs. Average Tonnage for Average Blank Thickness of . 044 inches: 7. 22 tons Expected Error: 5 x 100 = 6.9% 7.22 93 DRAW DIE SPECIFICATIONS: 1. Punch Steel 2. 566 inches diameter. 2 Die Steel 2. 680 inches diameter. 3. Clearance . 057 inches. 4 Largest sheet-metal or blank thickness is . 047 inches. The clearance provided allows for . 010 inches of thick- ening during drawing without causing ironing or burnish- ing of the cup side wall. The normal thickening of a cup of this size and metal thickness would be approximately . 006 inches. 5. Punch steel radius 3/16 inch. 6. Die steel radius 1/16 inch. 7. Punch steel -------- 46M oil hardening tool steel. 8. Blankholder operated by pressure pins from a 13-ton air cushion. 9. Blankholder retained by block-type keepers. 10. Die steel ---------- 34M water hardening tool steel. 11. Blankholder -------- cold rolled steel with tool steel welded on the critical wearing surface. 12. Die mounted in a standard Danly die set. . Rockwell "C" Surface Finish Dle Component Hardness in Microinches Punch Steel 53. 6 13. 5 Die Steel 58. 5 31. 4 Blankholder 54. 0 37. 8 94 HAND PYROMETER SPECIFICATIONS: 1. General Electric Hand Pyrometer Type FH-l Cat. No. 8947945Gl with Fahrenheit scale. 2. Surface-type Thermocouple Cat. No. A302G2. 3. Flexible Extension Cable Cat. No. ASOOGl 34 inches long. 4. Two scales provided with temperature ranges from 0 - 500 F and from 0 - 1500 F. Least count is ten degrees. Scale is 3-1/2 inches long. 5. Weight is 1-1/2 pounds. 6. Accuracy of entire assembly is + or - 4-1/2% of the full scale. 7. Surface Tip ------- chromel-constantan thermocouple with ceramic insulation. Three inches long. 8. Automatic cold- junction compensation on both ranges counteracts the influence of ambient-temperature changes. 9. High speed response. Less than 15 seconds. 10. No preliminary adjustments necessary. 11. Tips are interchangeable without recalibration of instrument. 12. Calibrated accuracy of instrument is + or - 2%. 95 10. ll. 12. 13. 14. Press Adjustment Procedure Turn on all air pressure to the press. This involves throwing five valves . . Shut off petcocks at the two surge tanks and cushion. . Open the air valves to the three air pressure gages. . Adjust the clutch pressure to (50) psi. . Adjust the counterbalance pressure to (20) psi. . Adjust the cushion pressure to (10) psi. . Set the motor direction switch on ”forward. " Set the stroke switch on "single stroke. " . Set the Inching~Off~Run switch to "run. " Throw the switch on the control panel. Throw the main switch at the building column. Turn the electronic controls ”on. " Push the motor "start" button. After flywheel gains full speed, adjust the strokes per minute to (40). Sanborn Recorder Calibration . Connect ground lead to press piping. . Plug extension cord into 120 volt outlet. . Connect active strain gage leads to the two terminals marked R2 . (From step three and on, follow the same procedure for both vertical and circumferential strain gages.) . Connect dummy strain gage leads to the two terminals marked R1 . 96 10. 11. 12. l3. 14. 15. . Set the R-T switch on "R. " . Turn on the main power switch. . Turn on the individual channel power switches. . Turn on the motor switch. . Set the paper speed at 1. 0 mm per second. Pull up the paper drive clutch to start paper in motion. Throw the Coarse-Fine Switch to the Coarse Position, and with the attenuator at the "OFF" position, observe the position of the stylus. (It will normally be 15193;; the center of the recording chart.) Advance the Attenuator to the X100 position. Unless the bridge circuit is accidentally in balance, the stylus will be deflected upscale. Using the Resistance Balance (Res Bal) control, try to bring the stylus back towards the position it occupied when the Attenuator was at the ”OFF" position. When the minimum position is found with the Resistance Balance control, try to improve the minimum using the Capacity Balance (Cap Bal) control. Advance the Attenuator to X20 position and readjust the Resistance and Capacity Balance controls slightly, trying to bring the stylus down as close as possible to its initial position. Repeat these adjustments as the Attenuator is advanced to each succeeding position. Return the Attenuator to the "OFF" position and throw the Coarse-Fine Switch to the Fine position. Using the zero control, set the stylus (5) mm from the right hand edge of the graph for that channel. 97 16. Advance the Attenuator knob to (l) and if necessary reset the Resistance Balance slightly to bring the stylus back to the baseline position which had been selected with the zero control. If this adjustment is properly made, the Attenuator knob may be turned from one position to another without dis- turbing the stylus position. It is understood of course, that these adjustments are made with no load on the strain-sensitive elements. 17. The electrical sensitivity of the system can now be checked by pushing the Calibrating (Cal) button, and the sensitivity may be adjusted to (25) mm by using the Gain control. 18. Since the position of the Gain control may affect the baseline positions slightly it may be advisable mo- mentarily to return the attenuator to the "OFF" posi- tion to establish the baseline position, and then with the Attenuator returned to the operating level, reset the stylus to this position using the Resistance Bal- ance control. 19. The strain gage amplifier is now ready for use. Running the Experiment After the press was adjusted and the recorder calibrated, the experiment was run by the following procedure: 1. Measure the die temperature and record on the Test Data form. The temperature at the start of each sample of (50) must be at room tempera- ture. Measure the temperature hereafter only after drawing every fifth cup. 98 10. . Apply lubricant uniformly over the entire area on both sides of the blank with a paint brush. . Using the aluminum hand tongs, place the blank in the locating nest in the die. Never put the blank in the die with your hands! . Visually check the cushion pressure and strokes per minute of the press. These may have to be readjusted occasionally. . Make sure all objects are clear of the die. Then press the two "black" palm buttons to operate the press. . In an emergency, stop the press ram by pushing the single "red" palm button located between the two black palm buttons. The motor may then be stopped by pushing the "red" push button on the press control panel. . After the press stops, remove the cup with the tongs. The cup is too hot to handle at this time. . Read both the vertical and circumferential strain deflections from the Sanborn Recorder and record on the Test Data form. " I \\ \ . . It may be necessary to reset the stylus on the baseline or zero line again using the Resistance \-~ Balance control. Since the maximum sensitivity of the Recorder is being used, the bridge riiay be- ”' come slightly unbalanced. ‘~ ., ‘ a. Measure the three wall thicknesses with the deep- throat micrometer at positions A, B and C. Record _. on the Test Data form. 99 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. Wipe the cup clean and visually check for defects. 11' any occur, record on the form provided. If the defect is severe, mark the lubricant code letter, sample number and cup number on the cup. Set the cup aside for future reference. If no defects occur, discard the cup in the con- tainer provided. Repeat steps (1) through (12) for each cup. 1 After the last of the (50) cups of a sample is drawn, measure the final temperature of the die steel. ,‘ ' Shut off the press motor. “13:22. . Shut off the air to the cushion. Open the petcock at the cushion to drain off all air. This allows the blankholder to drop leaving the punch steel exposed for cleaning. Clean the punch steel, die steel and blankholder with towels and oleum. All visual traces of lubricant must be removed. Turn the air back on to the cushion and adjust as before. Repeatly measure the die temperature until room tem- perature is reached. Turn the press motor on. The setup is now ready for running the next sample of (50) parts. Note: When two samples in sequence happen to be for the same lubricant, then steps 15 to 19 and steps 21 and 22 are neglected. Step 20 must be carried out, however. 100 Temperature Measurements Average Number Lubricant Code Temperature of Letter Degrees F Cups Made A 74. 6 55 B 79. 8 200 C 75. 9 200 D 80. 1 200 E 75. 2 63 F 74. 5 47 G 75. 6 93 H 76. 4 85 J 76. 4 200 K 79. 6 200 L 79. 4 200 M 78. 8 165 101 COMPUTATION OF AVERAGE AND STANDARD DEVIATION OF FREQUENCY DISTRIBUTION --- SHORT METHOD Deviation in Cell Frequency cells from assumed origin X f d fd fd2 Totals n = Sample Size Average or Mean (SE) Average or Mean (-55) Standard Deviation ( 3) Standard Deviation ( s ) f. {d In cells from assumed origin n Assumed Origin + f; fd (Cell Interval) n In original units from true origin = £de - aid 2 n n In cell units. (5 in cell units) (cell interval) In original units. 102 COMPUTATION OF AVERAGE AND STANDARD DEVIATION OF FREQUENCY DISTRIBUTION --- SHORT METHOD Cell in Thous. ‘ 2 of an Inch f d fd id 35 5 4 20 80 34 12 3 36 108 33 18 2 36 72 ,1 32 36 1 36 36 31 48 0 0 0 'N 30 50 -1 -50 50 .i 29 25 -2 -50 100 28 6 -3 -18 54 Totals -_ _n-______z_9_0______a.__.__...i_i __10 500 SAMPLE CALCULATIONS: (Wall Thickness Position "B" Lub. "J") X- = 10 = .05 Cells from Assumed Origin 200 TrueOrigin = 31.00 + .05 = 31.05 Sigma (3) = 500 - (3‘0" 2 200 200 s = 1.58 _103 TESTS FOR SIGNIFICANCE TEST B4 Test for difference in variability ( in two samples. (Test for homogeneity) Q C“ u d, and 62 ) Standard _Deviation (Largest) .- Standard Deviation (Smallest) n1 = n2 = Sample Size (For smaller (I ) Where: n1 ‘ n2 Degrees of Freedom: Numerator DFl Sample Size (For larger (,1 ) Denominator DF2 = n2 - l 104 If "F" is less than the value from Table E, then the probability is greater than 0. 05 that the difference may occur by chance. The difference is not significant. Therefore the samples and their devia- tions are homogeneous. If "F” is greater than the value from Table E, then the proba- bility is less than 0. 05 that the difference may occur by chance. The difference is significant. Therefore the samples and their deviations are not homogeneous. FOR THIS EXPERIMENT, PROBABILITY = 0.05 HAS BEEN SET FOR CONFIDENCE. Since seven lubricants will be tested for significance, the follow— ing pairs will be checked for homogeneity of standard deviations: 3": TOTAL ---- 21 tests B-D C-D B-J C-J D-J B-K c-K D-K J-K B-L C-L D-L J-L K-L B-M C-M D-M J-M K-M L-M 105 TESTS FOR HOMOGENEITY OF STANDARD DEVIATI ONS SAMPLE CALCULATIONS: (Deflection Data) Test C-K: Lubricant C s = 3. 52 LubricantK s = 2.90 r11 = n2 2 200 DF1 = DF2 = 200 Test J-L: F =' (3.5212 = 1.47 (3.90)2 Value of F in Table E for a confidence interval of 0.05 = 1.‘ 26 F' = 1.26 F is greater than F', therefore the samples are not homogeneous. LubricantJ s = 4.52 LubricantL s = 4.35 n1 = n2 3 200 DF1 = DF2 = 200 2 . F = (4.52) = 1.08 (4.35)2 Value of F in Table E for a confidence interval of 0. 05 = 1. 26 F' a 1.26 F is less than F', therefore the samples are homogeneous. 106 2- - 1r __ _____ .1 TESTS FOR SIGNIFICAN CE TEST B2 Test for difference between two sample means (X1 and X2 ) where d. be the same for the two populations. d =.- n16.2 + n2 0': n1 + n2 - 2 Different Sample Sizes t = 3'61 - i2 01’ n1 + n2 “inz DF = n1 + n2 Same Sample Sizes t = 531 - i2 is unknown but believed to Small Probability (less than 0. 05) ........ Large Probability (more than 0. 05) 107 Significant Difference does exist Significant Difference does not exist TEST B2 t 1| Calculated value t' Value from Table C When t is greater than the value of t', then the probability is less than 0. 05 that the difference occurs due to chance. A sig- nificant difference between means does exist. When t is less than the value of t', then the probability is greater than 0. 05 that the difference occurs due to chance. A sig- nificant difference between means does not exist. SAMPLE CALCULATIONS (Wall Thickness Position "C") Test K-L LubricantK s = 1.58 if = 31.13 LubricantL s = 1.58 if = 30.57 n1=n2=200 DF=2(200-1) DF = 398 t = 31.13 - 30.57 .. 3.53 (1.58)2 + (1.53)2 200 - 1 t' = 1.96 t is greater than t', therefore a significant difference does exist between the means 108 TESTS FOR SIGNIFICANCE Test for difference between two sample means (X1 and X2) I where d is unknown and not necessarily equal for the two samples. "DZ-X t = 1 l s 2 s 2 l + 2 n1 Jrl2 Degrees of Freedom = v s 2 s 2 2 l + 2 v = -2 + n1 n2 5 2 2 s 2 2 1 2 “11 + n2 n1 + 1 n2 + 1 t = Calculated value t! Value from Table C When t is greater than the value of t', then the probability is less than 0. 05 that the difference occurs due to chance. A sig- nificant difference between means does exist. When t is less than the value of t', then the probability is greater than 0. 05 that the difference occurs due to chance. A sig- nificant difference between means does not exist. 109 SAMPLE CALCULATIONS: (Deflection) Test J-M: LubricantJ s = 4.52 if = 24.74 n = 200 LubricantM s 3.68 i = 25.66 n 148 t = 25.66 - 24.74 = 2.09 2 2 , (3.68) + (4.52) I, 148 200 g '. ((3.68)2 + (4.52)2 2 ii v = —2 + 148 200 '21 ‘ ((3.68)2)2 ((4. 62)2 )2 148 + 200 148+1 200+1 v=343 t' = 1.96 t is greater than t', therefore a significant difference does exist between the means. 110 CORRELATION CALCULATIONS ORIGINAL DATA METHOD Basic Formula Y bx + a (Regression Line) niXY ~2XZY nix2 - ((2)02 Slope b Intercept a = ELY - bix n n = Sample Size Correlation _ 2 Coefficient r =\/ a 8Y + b 5- Q - nY a Y2 - nflY-2 Correlation Coefficient Definition: A prediction of how data taken in the future will correlate or fit to the regression line found for the given data. Standard Error of Estimate (Standard Deviation) SY= 8Y2 -aiY - bEXY n Coefficient of Determination (r2) The percentage of the variance of Y that can be accounted for by predicting from X. (Per cent effec- tiveness for forecasting variance in Y using X) r2 ———«> Equal to or greater than . 50 to be useful 111 UP ##‘QT— “It" .9.- CORRELATION SAMPLE CALCULATIONS: (means) Key: X = Deflection Means Y = Wall Thickness Means £x2 ix EXY £Y 2Y2 27.75 28.47 25. 95 29. 81 27. 11 29. 37 24.74 30. 27 26. 65 31.13 27. 15 30. 57 25.66 #4 29.95 4,896.2653 185.01 5,536.8195 209.57 6,278.6511 Y = 209. 57 = 29.9386 7 -—2 Y = 896. 3198 Slope b = (7) (5, 536. 8195) - (185. 01) (209. 57) (7)(4,896.2653) — (185.01)(185.01) b Intercept a = I‘ S Y (D II - . 3279 209 57 - (- 3279)(185.01) 7 38.6050 WhenX = 0 \/(38.6050) (209. 57) + (-. 3279) (5, 536.8195) - (7) (896. 3198) . 3948 .1559 6,278.6511 - (7)(896.3198) (38.6050)(209.57) -(-.3279)(5,536.8195) \/6,278.6511 - .7294 112 7 I - 0‘“ '2-an - a» 1“. L—b [luscll l i "unnuummn 5 7 III- . 2 7 8 I'll 2 o 2 = = n. a n e d O M r I a I d a D I a V .T e S D 2 O 8 6 4 2 0 8 6 4 2 0 2 2 1 1 1.. 1. 1 >ocuzvmua in Millimeters Deflection Deflection Histogram for Lubricant "8" 113 25.95 Mean ha 2 m...» 5 o KAI 3 an = n I R dew NM «7 III 3 a mu I'll H a m I'll MM IIIIIII as lllllllll Z ,/ lllllllll 6..“ 1 .il in. ”uuuulmmmm mm lllllllllll ll'llllll'll «N mm 'Ill' «a II II a l 8 l 2 ma ha ofi 4 2 O 8 6 4 2 O 8 5 4 2 0 2 2 2 I 1 1 1 1. >ocmnomua J 10"!) bricart LL in Millimeters for tinn 114 A No Defle Deflection Histogram m .on 3 as = NH . a H MM a In. an I mm a m lllll an lllll ms llllllllll . lllllllll mm iI II .II '1 l.| "“"HHHHH . a llllll R llllll mm ll'll' 1 lllll «N A lllll mm m I'll «N l a = ON n 2 m a M S 8 .2 .4 2 0 8 6 4 2 O 8 6 4 2 0 2 2 2 .1 1 1 1 1 xocmaceca in Millimeters Deflection Deflection Histogram for Lubricant ”0” 115 ll mm vn Mn N. IIII m m IIII on IIIII IIIIIIIII a IIIII mm IIIIIII : "flu-u“ ”IHIII a IIIII a 2 .9 NN 4. IIIII a _. III'II' om n IIIIIII 3 mm Illlll 3 m a S m w I . so 3 ma vH 2 O 2 A; m” m” .M n” mw n. 6 4 n4 0 >ochUmLa Deflection in Millimeters Deflection Histogram for Lubricant ”J” 116 Deviation = 2.90 Standard 32[ .J J mm vn nn II 3 IIIII s. IIIIIIII.N 3 IIIIIIII'IIIMM IIIIIIIIIIIIWM mmmnnnnflnnuaw IIIIIIII IIIIIIII a IIIII a IIIII 3 I'll a HN ON 0H ma ha 4 2 O 8 2 2 2 1. Mu. “a... >ocmavmau 12 10 8 6 4 2 O in Millimeters 117 Deflection Deflection Histogram for Lubricant ”K" 27.15 4.35 Standard Deviation = Mean III III III I'll Illlll IIIII 'llll rl "flu““nufl Illllll Illlll' IIIIIII llllll II-I-I-I-I-I-I-III-III..- I'lll II II m“ MW m” m" up w“ m” .8 .o 4 9. Au >ocmncmaa on an hm on on fin mm «m an GA mm mm hm 0N mm VN mm mm Hm om 0H in Millimeters 118 Deflection Deflection Histogram for Lubricant ”L" mm 8 cm m I mm m = ---.Nn . mm II 3 n ma IIII 3 m m m IIIII a IIIII / IIIIII m "flunflflflfl IIIIII MM IIIIII IIIIII M II II a II a I a ma ha Mu “w ”w ”m .M m“ mw .8 ,o 4 . 9. 10 >ocmaomua in Millimeters -119 Deflection Deflection Histogram for Lubricant ”M” Frequency 55 Mean = 28.47 / 5O d— __— Standard 0 ' ' = ."3 45 eVlatlon 1 3 4O LN UI U O M U N O H U 10 —— ___p—_d—I_- 5 I'll O \‘f In 0 N (I) O. O H N n V In N N N N N N n In 7n n n in Wall Thickness in Thousandths of an Inch Wall Thickness Position ”C" Lubricant ”8” Histogram 120 55 50 Standard 45 Devsatlon = 1.69 40 H U fi fi——_———‘_ 10 5 Ill 0 in \o h- a) Cl (3 .4 (9 r1 v in \0 cu (V N N cu xx n n K» n 'uw «x Wall Thickness in Thousandths of an Inch Wall Thickness Position "C" Lubricant ”0" Histogram 121 55 5O 45 b. O U U) Frequency k) Lu U' C) N C) H U 10 Mean = 30.27 / _C—— Standard Deviation = 1.61 b— _u—fi \O B N N Well Well (I) 01 H N n V in \O N N n n n n rd m n O f‘ n Thickness in Thousandths of an Inch Thickness Position ”C" Lubricant Histogram 122 NJ” Frequency 55 Mean = 31.13 50 45 Standard Deviation = 1.58 4O 35 3O 25 20 15 h a) 0| C) 1H (V N\ v «w «5 h. m cu be cu «3 Kt «\ «i «x r» aw K\ in Wall Thickness in Thousandths of an Inch Wall Thickness Position "C" Lubricant ”K" Histogram 123 I ‘Mean 2 30.57 55 I / l/ 50 | I Standard I Deviation = 1.58 45 l 40 35 >~ 2 30 0) D 3 L 25 L1. 20 15 IIIIII 10' l 5 J 0 h» «a 04 vi - . cu xx xx «x «x xx Wall Thickness in Thousandths of an Inch Wall Thickness Position "C" Lubricant ”L” Histogram 124 Frequency 55 50 45 4O 35 50 25 20 15 10 Mean = 29.95 / / ———‘ Standard Deviation = 1.35 [x N a) O\ c3 '4 (V in v a) O\ C) .4 cu tn v xx 0: 04 04 k\ «x «x «w «x xx Wall Thickness in Thousandths of an Inch Wall Thickness Position ”8" Lubricant "8” Histogram 133 'F—‘L_ _ in. '. _ Ln - ‘aaO-jo - Frequency 55 5O 45 40 35 3O 25 20 15 10 Mean = 32.06 ————J—1 Standard' Deviation = 2.12 I I iii“ ‘ ‘0 f‘ (D OI O H N n V In to l‘ N N N N m n n In no In in In Wall Thickness in Thousandths of an Inch Wall Thickness Position "8” Lubricant ”C" Histogram 134 Frequency 55 5O 45 40 35 3O 25 20 15 10 / Mean = 31016 / Standard Deviation = 1.94 ifiiiii _" “ —' "" 33 ___- . _- 31 ___-_- 29 _- 30 _- In‘OhCDOtO “MtfitfilfiV 8 t0!" NN Wall Thickness i 2 3 32 3 Thousandths of an Inch Wall Thickness Position ”8" Lubricant ”0” Histogram 135 55 5O 45 40 Frequency m m I» LN 0 UI o w H U! 10 I Mean = 31.05 I I/ I I Standard Deviation = 1.58 I I I I I I I I I I I R R". RI .9. :74 .94 f2 3" 5“ Wall Thickness in Thousandths of an Inch Wall Thickness Position ”8” Lubricant ”J” Histogram 136 ‘.--_.___.. - ‘Mf __ - _ . o Frequency 55 5O 45 .ts O U UT U 0 10 Mean = 32.44 I I/ 1 Standard I Deviation = 1.73 I N N O U'l O H U'l 1 -- 5 (I) O\ N N In In 2 33 o r~ m cm «1 n "N n 3 34 3 Wall Thickness In Thousandths of an Inch Wall Thickness Position ”8” Lubricant ”K” Histogram 137 55 50 45 Frequency k) k: LN \fl k c: \n (3 \fl (3 H U‘ 10 Mean = 31.77 K / Deviation = 1.84 I Standard m o m n h m N N 0 O H N in V (V Kt kw «I F1 in Wall Thickness in Thousandths of an Inch Wall Thickness Position "8" Lubricant "L" Histogram 138 Frequency 55 5O 45 4O 35 3O 25 2O 15 Mean = 31.88 / / Standard I l I I Deviation = 1.70 I _— m o o H cu kw V’ rx 0 N N :0 :0 «x «x ml n n Wall Thickness In Thousandths of an Inch Wall ThiCkness Position "8” Lubricant ”M” Histogram 139 1"!“ ‘1‘. ,_____. .25.... - ....<_ !'_.'.__, ,' .l ‘ Demco-293 . .. Avg , . .‘Y’H‘N bl ll. 3. n‘"! "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIISIIIIIII“