HWI H WW1INUHIWIMWIWIHWIWI‘ é WI 844 AET UNIVERSITY LIBRARIES HIHHHH Hll ll H‘ H Ill 3 1293 00592 9777 H 1%fil5%84 This is to certify that the thesis entitled Measurement of Lateral and Longitudinal Vibration in Commercial Truck Shipments presented by John Rodney Antle has been accepted towards fulfillment of the requirements for Masters degree in Packaging Dr. S. Paul SZgha Major professor Date October 5, 1989 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution LIBRARY Michigan State JJniverfity H PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE} DATE DUE DATE DUE MSU Is An Affirmative Action/Equal Opportunity Institution MEASUREMENT OF LATERAL AND LONGITUDINAL VIBRATION IN COMMERCIAL TRUCK SHIPMENTS BY John Rodney Antle A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE School of Packaging 1989 m I257” ABSTRACT MEASUREMENT OF LATERAL AND LONGITUDINAL VIBRATION IN COMMERCIAL TRUCK SHIPMENTS BY John Rodney Antle The increased use of tractor trailers for Shipment of packaged products has led packaging engineers to accurately determine the nature of the shipping environment. The purpose of this study was to determine the levels of lateral and longitudinal vibration and to compare these with vertical levels measured in.the same truck trailer over various United States Highways. Four truck trailer shipments, two with light loads and two with heavy loads, were instrumented with accelerometers. Data was recorded on a multichannel FM tape recording unit. From the data acquired, Power Spectral Density plots were developed for various road conditions and then used to compare the vibration levels present at various frequencies. The results showed that below 20 Hz., lateral and longitudinal vibration levels were generally much lower than vertical levels, as expected. John Rodney Antle At frequencies above 20 Hz., the lateral and longitudinal levels were similar to the vertical vibration levels. The heavier loaded trucks showed higher lateral and longitudinal levels than the lightly loaded. ones. 'The lateral and longitudinal spectrums followed the vertical spectrums with peaks and valleys located at the same frequencies. Copyright by John Rodney Antle 1989 ACKNOWLEDGEMENTS I would like to thank my major professor 5. Paul Singh Ph.D. for his help and for the opportunities which he provided. I would also like to thank the other members of my committee, Gary J. Burgess Ph.D. who helped with questions, corrections, and photo evaluation and George E. Mase Ph.D. whose answering machine survived many calls. I also appreciate Kraft Inc. and Frito Lay Inc. for the chance to do this study. Julian J. Lee PH.D. whose computer, and fine restaurant knowledge, helped tremendously. Also Jorge Marcondes and Charles Pierce who both helped more than they know. Finally, I would like to thank all of the faculty, staff and students at the School of Packaging who helped make the last two years very enjoyable. TABLE OF CONTENTS Page LIST OF TABLES . . . . . . . . . . . . . . . . . . . Vii LIST OF FIGURES . . . . . . . . . . . . . . . . . . viii 1.0 INTRODUCTION . . . . . . . . . . . . . . . . . 1 2.0 LITERATURE REVIEW . . . . . . . . . . . . . . . 5 3.0 EXPERIMENTAL DESIGN . . . . . . . . . . . . . . 13 4.0 DATA AND RESULTS . . . . . . . . . . . . . . . 22 5.0 CONCLUSIONS AND RECOMENDATIONS . . . . . . . . 54 LIST OF REFERENCES . . . . . . . . . . . . . . . . . 58 vi LIST OF TABLES Table Page 1. Accelerometer Information . . . . . . . . . . . . 15 2. PSD Values: Smooth concrete expressway, 50 MPH, (I-90 w near Beloit, WI); Load: 7,000 lbs. . . . 44 3. PSD Values: Smooth concrete with expansion joints every 18 feet, 50 MPH, (WI-23); Load: 7, 000 lbs. . . . . . . . . . . . . . . . . . . 45 4. PSD Values: Concrete, fair condition, 50 MPH, (I-90 w near Killingly, CT); Load: 7,500 lbs. . . 46 5. PSD Values: Smooth blacktop expressway, 50 MPH, (I-9l N near Holyoke, MA); Load: 7,500 lbs. . . 47 6. PSD Values: Newly paved expressway, 55 MPH, (I- -74 w,1 hour East of Champaign, IL); Load: 40’ 000 lbs. 0 O O O O O O O I 0 O O O O O O O 0 48 7. PSD Values: Rough expressway, 55 MPH, (I-74, 90 miles West of Indianapolis, IN); Load: 40,000 lbs. 49 8. PSD Values: Smooth 2-lane road, 50 MPH, (Route 32, West of Lebanon, IN); Load: 45,000 lbs. . . 50 9. PSD Values: Rough expressway, 40 MPH uphill, (I-70 E, 30 miles East of ST. Clairsville, 0H); Load: 40,000 lbs. . . . . . . . . . . . . . . 51 10. PSD Values: Concrete expressway, 60 MPH downhill braking. (I-70 E 35 miles East of St. Clairsville 0H); Load: 40,000 lbs. . . . . . . . . . . . . 52 11. PSD Values: Concrete expressway, 60 MPH, (I—70/76 70 miles East of Pennsylvania state line); Load: 40,000 lbs. . . . . . . . . . . . . . . . . . . 53 12. Summary of Light Load . . . . . . . . . . . . . . 56 13. Summary of Heavy Load . . . . . . . . . . . . . . 57 vii LIST OF FIGURES Figure 1. Degrees of Freedom for a Moving Truck . . Location of Instrumentation for Wisconsin Frito Lay Shipment . . . . . Setup of Data Aquisition System . . . . . 5. Location of Instrumentation for Vermont Frito Lay Shipment . . . . . 6. Power Density Spectrum: analyzing equipment . 7A. Power Density Spectrum: Background noise for Lateral and Vertical 2 3. Location of Instrumentation for Kraft Shipments 4 Vibrations for Engine Noise, Truck Stationary. 7B. Power Density Spectrum: Longitudinal and Vertical Vibrations for Engine Noise, Truck Stationary. . . . . . 8A. Power Density Spectrum: Vibrations for Smooth Concrete Expressway 50 MPH Lateral and Vertical (I-90 W near Beloit, WI); Load: 7,000 lbs. 8B. Power Density Spectrum: Longitudinal and Vertical Vibrations for Smooth Concrete Expressway 50 MPH (I-90 W near Beloit, WI); Load: 7,000 lbs. . . . 9A. Power Density Spectrum: Lateral and Vertical Vibrations for Smooth Concrete with Expansion Joints every 18 Feet, 50 MPH (WI-23); Load: 7,000 lbs. . . . . . . SB. Power Density Spectrum: Longitudinal and Vertical Vibrations for Smooth Concrete with Expansion Joints every 18 Feet, 50 MPH (WI-23); Load: 7,000 lbs. . . viii Page 3 l4 19 20 21 25 26 26 34 34 35 35 ix Figure Page 10A. Power Density Spectrum: Lateral and Vertical Vibrations for Concrete, Fair Condition, 50 MPH (I-90 W near Killingly, CT); Load: 7,500 lbs. . . 36 103. Power Density Spectrum: Longitudinal and Vertical Vibrations for Concrete, Fair Condition, 50 MPH (I-90 W near Killingly, CT); Load: 7,500 lbs. . . . . . . . . . . . . . . . . . . . . . 36 11A. Power Density Spectrum: Lateral and Vertical Vibrations for Smooth Blacktop Expressway, 50 MPH, (I-9l N near Holyoke, MA); Load: 7,500 lbs. 37 11B. Power Density Spectrum: Longitudinal and Vertical Vibrations for Smooth Blacktop Expressway, 50 MPH, (I-91 N near Holyoke, MA); Load: 7,500 lbs. . . . . . . . . . . . . . . . 37 12A. Power Density Spectrum: Lateral and Vertical Vibrations for Newly Paved Expressway, 55 MPH, (I- -74 W, 1 hour east of Champaign, IL); Load: 40, 000 ibs. . . . . . . . . . . . . . . . 38 12B. Power Density Spectrum: Longitudinal and Vertical Vibrations for Newly Paved Expressway, 55 MPH, (I- -74 W, 1 hour east of Champaign, IL); Load: 40, 000 lbs. . . . . . . . . . . . . 38 13A. Power Density Spectrum: Lateral and Vertical Vibrations for Rough Expressway, 55 MPH, (I-74, 90 miles west of Indianapolis); Load: 40,000 lee O O O O O O O O O O O O O O O O O O O O O 39 13B. Power Density Spectrum: Longitudinal and Vertical Vibrations for Rough Expressway, 55 MPH, (I-74, 90 miles west of Indianapolis); Load: 40,000 lbs. . . . . . . . . . . . . . . . . . 39 14A. Power Density Spectrum: Lateral and Vertical Vibrations for Smooth 2-Lane Road, 50 MPH, (Route 32, west of Lebanon, IN); Load: 40,000 lbs. . . . . . . . . . . . . . . . . . . . . . 40 143. Power Density Spectrum: Longitudinal and Vertical Vibrations for Smooth 2-Lane Road, 50 MPH, (Route 32, west of Lebanon, IN); Load: 40,000 lbs. . . . . . . . . . . . . . . . . . 40 Figure Page 15A. Power Density Spectrum: Lateral and Vertical Vibrations for Rough Expressway, 40 MPH Uphill, (I- -70 E, 30 miles east of St. Clairsville, OH); Load: 40, 000 lbs. . . . . . . . . . . . . . 41 15B. Power Density Spectrum: Longitudinal and Vertical Vibrations for Rough Expressway, 40 MPH Uphill, (I-70 E, 30 miles east of St. Clairsville, 0H); Load: 40,000 lbs. . . . 41 16A. Power Density Spectrum: Lateral and Vertical Vibrations for Concrete Expressway, 60 MPH, Down- hill Braking. (I-70 E, 35 miles east of St. Clairsville, OH); Load: 40,000 lbs. . . . 42 16B. Power Density Spectrum: Longitudinal and Vertical Vibrations for Concrete Expressway, 60 MPH, Downhill Braking. (I-70 E, 35 miles east of St. Clairsville, OH); Load: 40,000 lbs. . . 42 17A. Power Density Spectrum: Lateral and Vertical Vibrations for Concrete Expressway, 60 MPH, (I-70/I-76, 70 miles east pf Pennsylvania State Line); Load: 40,000 lbs. . . . . . . . . . . . 43 178. Power Density Spectrum: Longitudinal and Vertical Vibrations for Concrete Expressway, 60 MPH, (I-70/I-76, 70 miles east of Pennsylvania State Line); Load: 40,000 lbs. . . . . . . . . 43 1.0 INTRODUCTION In order to design an adequate package system, it is important to know product fragility and the expected distribution environment. In many cases damage to products can be traced to various vibration forces that originate from transport systems during shipping. It is crucial to know the types and levels of these forces in order to isolate the product from them. Packaging engineers use this information, along with product fragility, to develop new package systems and to evaluate these systems in test labs. In the United States, shipment by truck is the most common and convenient method of transporting goods over land. Within the last thirty years the percentage of freight shipped by rail has decreased from 47 percent in 1950, to 29 percent in 1980. During the same time period, freight shipped by truck has increased from 26 percent in 1950 to 37 percent in 1980. (National Council of Physical Distribution Management, 1982) To completely define the movement of a truck trailer as it 2 travels over the road, six degrees of freedom are needed, Three of these are translations and three are rotations (Figure 1). For truck trailer movement, the rotational movements are normally very small and are therefore ignored in measurement studies. Among the translational movements, vertical vibration is the most severe, followed by lateral and longitudinal vibrations (Sharpe et al, 1974). Vibration movements in the lateral and longitudinal directions are attributed to: 1) Sudden accelerations produced by braking, fast turns, and fast starts. 2) Outside weather conditions, especially gusty side winds. 3) Uneven road surface profile. 4) Variation in road surface between curbside and center, due to weathering, crown, and curbs. 5) Localized concentrated loading of product inside of trailer. 6) Variation in dynamic response of individual suspension components. 7) Unequal air pressure in tires. Previous studies of vibration in trucks dealt mainly with vertical vibration with only made brief mention of lateral and longitudinal vibrations. The argument for this was that the 303,—. moire: o now 60.5on no @03qu .H enough S .n .c "meozauom m N S .x "ace—uflmcfih m 4 lateral and longitudinal components of vibrationnwere very low when compared with the vertical component and therefore did not need to be measured. (Sharpe et a1, 1974) Objectives: The purpose of this study was to measure current lateral and longitudinal vibration levels present in commercial truck- trailer systems traveling over various interstate and intercity roads in the United States. Specifically, the objectives were to: 1) Quantify the levels of lateral and longitudinal vibration over various road surfaces. 2) Compare the lateral and longitudinal levels with vertical vibration levels measured in the same truck trailer. 3) Establish the significance of lateral and longitudinal vibration levels for the truck distribution environment. 2 . 0 LITERATURE REVIEW Recent environmental measurement studies that have been done on shock and vibration levels in the truck environment have focused primarily on vertical vibration. Studies which have evaluated lateral and longitudinal vibration in more detail often involve modes of transportation other than truck. Most of these studies present results in the form of RMS acceleration, or Power Density values versus frequency. The Power Density Spectrums (PDS) are also used in lab testing to simulate the conditions found in the distribution environment (ASTM 4728). The literature review that follows will be presented in chronological order to highlight the development of the subject. Harris and Credes (1961) present tables listing the normal shock and vibration levels present in truck, tractor-trailer, and train shipments. They also provide basic shock and vibration definitions and concepts as they relate to road and rail vehicles. The environment.on.a:flatbed tractor-trailer (Foley, 1966) was 6 measured for an unloaded trailer and one with a 15 ton load. The results were presented in PSD plots for concrete and blacktop roads at speeds of 35 and 50 mph. The vertical vibration was measured at a spot 24 inches behind the location of the 15 ton load. A study by Schlue (1966), The Dynamic Environment of Spacecraft Surface Transportation, looked at the shock and vibration in vehicles used to transport spacecraft. Measurements were taken in vans driven over smooth, rough, and irregular road surfaces. It was found that: 1) Vibration levels at frequencies above 100 Hz were not significant. 2) Lateral and longitudinal vibrations were measured, but were not presented in the data because it was found that their levels were less than the levels for vertical vibrations. Preliminary Measurement and Analysis of the Vibration Environment of Common Motor Carriers (Sharpe et al, 1974) was a study conducted to find the vibration environment of common motor carriers. Some conclusions reached were: 1) It is only necessary to measureverticalvibrationsbecause they are the most severe. 2) Product testing at various PSD levels for a specified time 7 period is more desirable than testing at higher levels. These higher levels are equivalent to "worst case conditions" and may be too severe. Joint Services Highway Shock Index Project (Grier et al, 1975) was a study conducted to obtain data to be used to develop a method to determine the shock index of commercial trucks. This study resulted in: 1) A practical method, using planned payload and vehicle axle spring rates, was developed to determine the shock index of commercial trucks. 2) During highway travel, vertical accelerations were generally greater than either lateral or longitudinal accelerations and were a major component in potential damage to the cargo. 3) The percentage of maximum payload had a much greater influence on the shock index than did vehicle speed.or tire pressure. Caruso and Silver's (1976) study, Advances in Shipping Damage Prevention, compared suspension systems, rear wheel position, road conditions, amount of load, and drivers. Their findings revealed that: l) 2) 3) 4) 5) 6) PDS levels for frequencies above 50 Hz were insignificant. Different suspension types resulted in a different power density at the first peak (about 5 Hz) but beyond the second peak (about 13 Hz), the power density spectra were similar. The worst ride occurred on interstate highways at high speeds. The worst ride occurred over the rear wheels in a lightly loaded trailer The worst rides occurred when single-leaf steel suspension springs were used. Different drivers had little effect on the results. A detailed study of Australian Army trucks (Byrne and Olver, 1976) traveling on second class roads found that: l) Vibrations were highest in the vertical direction, and lowest in the longitudinal direction. 9 2) Longitudinal vibration levels were about 1/3 to 1/2, and lateral vibration about 1/2 to 3/4 that of vertical rms accelerations. Magnuson (1977 and 1988) studied the shock and vibration environment for large shipping containers with heavy loads during truck transport. His findings were: 1) The vibration.observed was random and.had.a:normal Gaussian distribution with respect to acceleration levels. 2) The highest vibration levels were generally'in the vertical direction but with significant exceptions. These exceptions were usually in the middle frequencies (120 to 240 Hz.) for spring/air suspensions and air suspension systems. Also, below 20 Hz., both the lateral and longitudinal levels were above the vertical acceleration levels in the truck with air suspension. 3) Though vertical accelerations were usually the most severe, there were exceptions unique to the vehicle and its operating conditions. 4) The type of suspension system caused little difference in vibration amplitude in shipments weighing over 15 tons. 10 A study entitled Shock and Vibration Environment in a Livestock Trailer (Turczin et al, 1980) was done to determine the shock and vibration environment on the floor of a trailer used to ship cattle. Some findings of this study were: 1) Vibration levels greater than 40 Hz were insignificant. 2) The highest vibration levels are produced in the vertical direction (peaks to 0.08 g rms). In 1983, Tevelow'summarized.many different studies done in the past 20 years. Among his conclusions were: 1) The vertical axis almost always has the highest levels of vibration. 2) Vibrations in the lateral direction are usually the lowest. 3) Vibration levels in the longitudinal axis can be as high or higher than vertical vibration levels, but this usually occurs due to resonant frequencies of the truck body. 4) Specific relationships between vertical, lateral, and longitudinal vibration levels are highly dependent upon the vehicle, and external conditions. ll Goff et al (1984) studied the effect of different suspension systems on the vibration levels in trucks. Accelerations in the rear of the truck were recorded during half-hour trips on; city and county roads, interstate freeways, bridges, and rail crossings. The three different suspension types were: 1) Fixed position air-ride tandem axle trailer. 2) Moveable leaf spring tandem axle trailer with the axle at the furthest rear position. 3) Same as 2), but the axle was positioned at the furthest front position. This study found that: A) Transient accelerations were much more severe than those generated in steady-state vibration. B) Spring leaf suspension with wheels forward resulted in the roughest ride. C) Air-ride suspension caused the greatest amplification of vibration inputs by the load. 12 Goodwin and Holland (1987) studied the distribution environment of two different modes of shipment between Rochester, NY, and Los Angeles, CA. These modes were; Trailer on a Flat Car (TOFC), and Container in a well Car (CIWC). Data was analyzed and presented in terms of PDS. 3 . 0 EXPERIMENTAL DESIGN To gather the necessary data for this study four separate truck shipments were monitored to measure the respective vibration levels present in each of the shipping environments. The following four shipments were sponsored by the two major food companies listed. 1) Champaign, IL to Lehigh Valley, PA (Kraft Inc.) 2) Palmyra, PA to Decatur, GA (Kraft Inc.) 3) Beloit, WI to Orangeville, WI (Frito Lay Inc.) 4) Killingly, CT to Burlington, VT (Frito Lay Inc.) To monitor the truck shipments, piezoelectric accelerometers were used, one for lateral motion, one for longitudinal motion, and two for vertical motion. Micro-dot cables were used to connect the accelerometers to Kistler (model 5112) signal conditioners and a Teac XR-310 cassette data recorder was used to record the output from the signal conditioners. The tapes used by the Teac recorder can record more than 5 hours of data each. Figure 2 shows the setup of the environmental measurement system used and Table 1 describes the sensor types and their sensitivity values. 13 Teac XII-319 Data Recorder [2.21 11W" Accelerometer: Figure 2. l3 lh D.C. Power Sapply Oscilloscope Audlo Channel Kletler Slgnel Condltlone Setup of Data Aquisition System 15 Table 1. Accelerometer Information Serial Number Manufacturer Model Sensitivity 14310 PCB 302-A02 10.07 mv/g 14311 PCB 302-A02 9.96 mv/g 14312 PCB 302-A02 10.00 mv/g 14644 PCB 302-A02 10.01 mv/g 16 SHIPMENT A: Champaign, IL to Lehigh Valley, PA 797 total miles February, 1988. Champaign to route 32 (near Crawfordsville, IN) I-74 Route 32 to Lebanon, IN I-65 5 Lebanon to Indianapolis I-465 E Indianapolis to Pennsylvania state line I-70 Pennsylvania turnpike to Carlisle, PA I-76 Carlisle to Lehigh Valley, PA I-81 Trailer: 47 feet x 90 inches (width) x 108 inches (height) Tandem axle Leaf spring suspension Load: pallets of mayonnaise in glass quarts, of approximately 40,000 pounds total weight. Instrumentation: (See Figure 3) Accelerometer positions: 2 vertical (front and rear) 1 lateral (left side 12 feet from door, 80 inches above floor) 1 longitudinal (right side of nose, 79 inches above floor) SHIPMENT B: Palmyra, PA to Decatur, GA 716 total miles February, 1988 Palmyra to I-81 US-422 I-81 (near Carlisle) to I-77 S I-81 I-77 S to Charlotte, NC I-77 S Charlotte to Greenville, SC I-85 Greenville to Decatur, GA I-85 S Trailer: 47 feet x 90 inches (width) x 108 inches (height) Tandem axle Leaf spring suspension Load: pallets of crackers, approximately 30,000 pounds total weight Instrumentation: (See Figure 3) Accelerometer positions: 2 vertical (front and rear) 1 lateral (left side 12 feet from door, 80 inches above floor) 17 1 longitudinal (right side of nose, 79 inches above floor) SHIPMENT C: Beloit, WI to Orangville, WI October 1988. Beloit to Madison I-90 W Madison to Richland Center US-l4 Richland Center to Dodgeville US-l4 Dodgeville to Avon US-151 Avon to Monroe WI-23/WI-11 Monroe to Orangeville WI-26 Trailer: 47 feet x 96 inches (width) x 162 inches (height); drop-frame Tandem rear axle on trailer Single rear axle on tractor Leaf spring suspension Load: 1,000 cases of product, break bulk, approximately 7,000 pounds Instrumentation: (See Figure 4) cover) Accelerometer positions: 2 vertical (front and rear) 1 lateral (left side, over center line of axles, 60 inches above floor) 1 longitudinal (forward face of left wheel well SHIPMENT D: Killingly, CT to Burlington, VT December 1988. Killingly to Massachusetts turnpike I-52/I-395 Massachusetts turnpike to Holyoke, MA I-90 Holyoke to Brattleboro, VT I-91 Brattleboro to Lebanon, VT I-91 Lebenon to route 7 I-89 Route 7 to Burlington, VT I-89 Trailer: 46 feet x 96 inches (width) x 162 inches (height); low-frame Tandem axle trailer Tandem axle tractor Load: 1,100 cases of product, break bulk, approximately 7,500 pounds Instrumentation: (See Figure 5) 18 Accelerometer positions: 2 vertical (front and rear) 1 lateral (left side, 3 feet forward of rear doors, 60 inches above floor) 1 longitudinal (center line of trainer on front bulkhead, 1 foot above floor) 19 eucoaeuxm uuoux new coauoucoasuuocm up cowuoooa .n enough 23:30... ..o~eEo.o.ooo< c2653 .83....5 5:265 .223 $563.93.. acme—35m as euaum 52303: new cowuouceaouuucn mo condos .e «an»: 93:30.. couoEoce_ooo< 20 Q a. ...._../._/- ...... I a 5:955 \ .mo_to> c2355 $563.96.. / / 5.353 .823 21 ucoaeusm .34 cuff.» ucoEo> new ecuuoucguuecu uo cowuooon .m was»: 93:30.. 33:33.02; \fl \\HH \\ . THREE» ........ Hull‘s 8 e cozee>\.\ \a _ E > 356333.." _ m N I 5:955 .23.... 4.0 DATA AND RESULTS There are two methodologies of producing simulated varying vibration levels, these are: 1) Time Domain 2) Frequency Domain The concept of Time Domain is to exactly reproduce a segment of the distribution system. This method has several short comings which limit its application in the area of distribution simulation for the purpose of package development (Singh, Young, 1988). Frequency Domain uses random vibration to simulate the distribution, and is making a significant contribution in this area (Tustin, 1984). The Frequency Demand method was chosen for this study, and a brief description of its workings follows. The vibration data recorded on tape was analyzed using a Schlumberger 1209 Random Vibration Analyzer/Controller and printed on a Team TP-35 Video Hard Copy Printer. The random vibration analyzer preforms a Spectral analysis on the tape recorded data, and produces a Power Density Value for each component frequency of the spectrum. The Power Density Value is calculated as: 22 2. P.D. =5; (RMS). / N (at a given frequency) 1 l (4.1) where (RMS) i is the Root Mean Square acceleration value measured in g's at any instant within a band width BW of frequencies and N is the number of instants sampled. The corresponding P.D. is then plotted against the center frequency of the bandwidth. The plot describing the Power Density versus frequency is called the Power Density Spectrum (PDS). Statistically, the Power Density at a given frequency is the .variance about a mean value of zero acceleration. Based on the probabilities associated with Normal Distribution, the acceleration levels associated with any of the component frequencies of the complex wave form can be predicted as follows: Accelerations within + or - l P.D. values occur 68.3 % of the time Accelerations within + or - 2 P.D. values occur 95.4 % of the time Accelerations within + or - 3 P.D. values occur 99.7 % of the time Trailer Vibration: Figure 6 shows the background noise levels for the recording and analyzing equipment. The levels for this spectrum are no greater than 1 * 10 -6. The spike at 60Hz. is the result of the line current which operates at 60 cycles per second. Figure 7A shows the vertical and lateral vibration levels in the truck trailer caused by engine vibration and Figure 7B shows engine vibration levels in the longitudinal and vertical directions. The peaks in these spectrums occur at similar frequencies, 32 and 50-60 Hz., and have similar levels. Tables 2 through 11 show the Power Density values at specific frequencies for the various road conditions that were encountered. Figures 8A through 17B show the Power Density Spectrums that were developed from these same road sections. (Tables 2 through 11 and Figures 6 through 17B are located at the end of this section to preserve continuity) What follows is a brief summary of each Table and corresponding Figures. It is important to note that the height above the floor of the accelerometers which measure lateral vibrations is extremely important. The top of the trailer will experience more sideways movement than will the floor of the trailer. This fact must be taken into account if comparisons to other studies are made. 25 1C“) E-OG PSD \ 92/“: \\/\V(p-F\‘ A L“ 1 E1 2 1 FREQUENCY (Hz) 100 Figure 6. Power Density Spectrum Background Noise for Analyzing Equipment 26 10 5.03 I ha PSD \ f2" ’1 ‘1 s’le “’ ’ " 13 E. 1 FREQUENCY (Hz) 100 Figure 7A. Power Density Spectrum: Lateral and Vertical Vibrations for Engine Noise, Truck Stationary 2.33 H PF- I PSD ‘ m 93le l W l I l l . | E ' 51:2. LsheouemflLLY (Hz) 1 .00 Figure 73. Power Density Spectrum: Lateral and Vertical Vibrations for Engine Noise, Truck Stationery 27 Figure 8A.shows lateral vibrations and.vertical.vibrations for a trailer traveling 50 MPH on a smooth concrete expressway with a 7,000 lb. load. The vertical vibration spectrum shows peaks at 4-5 Hz, and again at 15, 20, and 30 Hz. The 4-5 Hz peak corresponds to the suspension system of trailer, while the higher frequency'peaks correspond to the trailer structure natural frequencies. The lateral spectrum has peaks at 12, 17, and 28 Hz. Figure 8B shows longitudinal vibrations and vertical vibrations for the same road segment as above. The longitudinal spectrum shows a long rise from 14 to 20 Hz, and a peak in the 50 Hz. area. These levels are usually 10 times lower than the vertical levels at the same frequency Figure 9A shows lateral and vertical vibration spectrums for a trailer with a 7,000 lb. load traveling 50 MPH on a smooth concrete road with expansion joints every 18 ft. The vertical spectrum shows a major peak from 3-5 Hz. and another smaller peak from 43-50 Hz. The lateral spectrum has peaks in the 11- 12 Hz region, and again at 17-20 Hz. Figure 9B shows longitudinal and vertical spectrums for the same road segment with no peaks in the longitudinal vibrations. Figure 10A shows lateral and vertical spectrums for a trailer with a 7,500 lb. load traveling on a concrete expressway that is in fair condition. Again, the vertical spectrum shows the first peak to be at the lightly loaded trailer's suspension 28 natural frequency of 3-4 Hz. Another peak is located in the 15-25 Hz region, which corresponds to the trailer structure natural frequency. Other peaks at 52, 61, and 70 Hz. are the result of the road irregularities being transmitted to the trailer structure. The lateral spectrum shows peaks at 8 Hz. , from 14-27 Hz., and from 55 to 70 Hz. In Figure 10B, the longitudinal vibration spectrum indicates a long rise from 13 to 23 Hz. similar to the vertical spectrum. IFigure 11A is the spectrum for a lightly loaded truck trailer carrying, 7,500 lbs. and traveling over a smooth blacktop expressway at 50 MPH. The levels are much lower throughout the frequency range, due to the new road surface. The vertical spectrum shows the normal suspension and structure natural frequencies at 3 to 5 Hz. and at 15 and 23 Hz. Other peaks at 40, 50 ,60, 70, and 80 Hz. are again most likely the result of engine vibration and the vibration of the trailer body panels. The lateral spectrum shows little excitement until 13 Hz. and again at 23 Hz. and then follows the vertical spectrum in peaks as well as levels. In Figure 11B, the longitudinal spectrum reveals peaks at 16 and 23 Hz. Here too, the spectrum looks very similar to the vertical spectrum. Figures 8A through 113 are all for lightly loaded trailers (7,000 to 7,500 lbs.). Because of this, differences in these spectra can largely' be attributed. to different external 29 conditions, while similarities are representative of a lightly loaded trailer. The first peak for these four spectra occurs between 4 to 5 Hz. which is the natural frequency for the trailer. Due to the large displacement of the trailer floor, _ high vibration levels at these frequencies occur and can result in product damage. This occurs in the vertical vibration, (Figures 9A and B) where the vehicle speed and distance between expansion joints matches the 4 Hz. natural frequency of the trailer suspension. A smooth road (Figure 11A and B) results in the vibration levels at these frequencies being lower by a factor of 1,000, as can be seen by comparing the two PSD plots. For lateral and longitudinal vibrations, the first peak occurs above 10 Hz. and the overall RMS levels are generally much less in the l to 10 Hz. range. Beyond 10 Hz. the lateral and longitudinal spectrums look very similar to the vertical spectrum, and the RMS levels are about the same. The exception to this being in Figures 8A and 9A, where a lateral peak at 11 Hz. is substantially greater than the vertical level. Figure 12A is a spectrum for a heavily loaded truck trailer carrying 45,000 lbs. and traveling at 55 MPH on a newly paved expressway. The first peak is at a lower frequency than previous spectrums, 3 Hz. versus 4 or 5 Hz., because this 30 trailer has a much heaver load. Again the peak at 8 Hz. is from the trailer structure, and other peaks at 30 Hz. and beyond are again the result of the drive train and frame members. The longitudinal spectrumlin Figure 12B shows a peak at 9 Hz. and a substantial peak at 22 Hz. The large peak, at 22 Hz. is the result of the drive train, while the peak at 9 Hz. is also from the trailer structure. Figures 13A and 13B are spectra for a heavily loaded truck traveling 55 MPH on a rough expressway. The vertical spectrum reveals peaks at 3 Hz. from the suspension of the trailer and another peak at 22 Hz. from the trailer structure. The lateral spectrum shows a peak at 8 Hz. and a large peak at 14 Hz. The longitudinal vibrations in Figure 13B show peaks at 3 and 9 Hz., and a large peak at 16 Hz. Figure 14A is the spectrum from a heavy loaded truck carrying 45,000 lbs. traveling on a two lane road at 50 MPH. Again, the first peak in the vertical structure is in the 3 to 4 Hz. range, indicating a heavy load, and other peaks at 20 and 30 Hz. are from the trailer structure. The lateral spectrum shows a hump in the 6-8 Hz. band, which can be attributed to sway from the loaded suspension. A second large peak in the 14 to 18 Hz. band is the result of waves in the 2-lane road. Figure 14B for longitudinal vibrations, reveals a peak at 9 Hz. and a larger peak at 20 Hz. The first peak is the trailer structure, while the peak at 20 Hz. is the result of for and aft pitching, due to the variations in the surface of the 2— 31 lane road. Figure 15A is a spectrum for a heavily loaded truck carrying 45,000 lbs. and traveling uphill at 40 MPH on a rough expressway. The vertical spectrum again shows the normal peak in the 3 to 4 Hz. band. A second smaller peak is at 8 Hz., while a long peak spans the 15 to 22 Hz. range. A final peak is located at 30 Hz. The spectrum for lateral vibrations shows a large peak at 15 Hz., another peak at 24 Hz., and other peaks at 50, 62, and 80 Hz. In Figure 15B, the spectrum for longitudinal vibration, a hump appears from 3 to 4 Hz., and a peak at 9 Hz. Another peak appears at 20 Hz., which corresponds to pitching from the road conditions. Figure 16A is spectrum for a heavy truck, 45,000 lbs., on an expressway going downhill with its brakes applied. The spectrum for vertical vibration again shows the familiar suspension hump at 3-4 Hz. and structural peaks at 22 and 30 Hz. The lateral spectrum shows a peak from 7 to 8 Hz., another long peak from 13 to 23 Hz., and a peak at 45 Hz. Figure 16B shows the longitudinal vibrations to peak at 9 Hz. and again from 18 to 23 Hz. These peaks are from similar causes as previously stated. Figure 17A are the vertical and lateral spectra for a heavily loaded truck traveling at 60 MPH downhill on an expressway. The peaks for the vertical spectrum are located at 3-4 Hz. and at 25 Hz. The spectrum for lateral vibrations contains a peak at 8 Hz., a large peak at 15 Hz., and another peak at 25, 45, 32 and 80 Hz. Longitudinal vibrations in Figure 17B, show peaks at 9 Hz. and from 20 to 23 Hz. Figures 12A through 17B are for a heavily loaded truck trailer (40,000 lbs.), so differences in these spectrums versus the spectrums for the lightly loaded truck trailer are expected. The vertical spectrum shows a shift in the first peak from 4- 5 Hz. down to 3 Hz. indicating a reduction in natural frequency if the suspension This is caused by the increase in the weight of the load that is being transported. A second peak appears at 8 Hz. and a third in the 20 to 30 Hz. range. The peak which appears at 8 Hz. is pmobably caused by the lowering of the trailer structure, due to the increased load. The peaks in the 20 to 30 Hz areas fall within the natural frequency of trailer's tires. The lateral spectra for the heavily loaded truck trailer (Figures 12A through 17A) show two pronounced peaks, at 7-8 Hz., and again from 13 to 23 Hz. The peak at 7-8 Hz., not present in the lighter shipments, has an RMS level equal to the vertical vibration spectrum. The peak in the 13 to 23 Hz range is of greater magnitude than the vertical vibration peak in same frequency range. The longitudinal vibration spectra, (Figures 12B to 17B) for the heavily loaded truck, also are different than the similar 33 spectrums developed from the lightly loaded trailer (Figures 8B to 11B). The most noticeable difference in these spectra is the frequency at which the first peak occurs. The hump in the 3-4 Hz. range, which was not present in the Frito Lay shipments, results from the tractor and trailer pitching fore and aft. This motion does not occur in the lighter shipments because spring deflection is small, therefore movement is restricted. Above 10 Hz. the longitudinal spectrum closely follows the vertical spectrum, with levels equal, to or slightly above that of the vertical, in the 20 Hz. band. 34 1 O E-OQ 1 FREQUENCY (H2) 1 00 Figure 8A. Power Density Spectrum: Lateral and Vertical Vibrations for Smooth Concrete Expressway 50 MPH (1-90 W Near Beloit, WI); Loads 7,000 lbs. ----- Lateral Vertical ‘ l l | .l .01 -— H J . .001/ N V .... PSD - . a‘ 93m: - ”NM ,I I—‘fi-‘Tv—l .1 | 1° 3 5'09, mecuencYu-m 100 Figure 83. Power Density Spectra: Longitudinal and Vertical Vibrations for Seooth Concrete Expressway 50 MPH (1-90 W near Beloit, WI): Load: 7,000 lbs. ..-..-- Longitudinal Vertical 35 1 I /\ l .1 H”\\ .01 ’ - W ' "' -1--qb-‘~ A, \ VJ . .001 PSD 92in 1 0 5°09 1 FREQUENCY (Hz) 100 Figure 9A. Power Density Spectrum: Lateral and Vertical Vibrations for Smooth Concrete with Expansion Joints Every 18 Feet, 50 MPH (VI-23); Load: 7.000 lbs. ----- Lateral Vertical 1 , 1 I A l | | .01 .. .001 ALH‘ " "Mi ‘ P80 :3le T7 T 10' L i a 3.. . H i 1 5'09, meoueucvmz: 100 Figure 9!: Power Density Spectrum: Longitudinal and Vertical Vibrations for Smooth Concrete with Expansion Joints Every 18 Feet, 50 MPH (HI-23): Load: 7,000 lbs. ..-.—-- Longitudinal Vertical 36 1 .1 .01 .001 Ne‘ Pi“ ' H70“: --__ b 9 [H2 Ob--‘.~ “y’H H W" -- E 63 ' 1 FREQUENCY (Hz) 100 Figure 10A. Power Density Spectrum: Lateral and Vertical Vibrations for Concrete, Fair Condition, 50 MPH (1-90 W Near Killingly, CT); Load: 7.500 lbs. ---- Lateral Vertical 1 .1 .01 r”’F__- .001 7K .. PSD 91le ' I I ‘| c---------‘..'em! 1C) ' )4L_1_ . 3°09, FREQUENCY (Hz) ,00 Figure 103. Power Density Spectrum: Longitudinal and Vertical Vibrations for Concrete, Fair Condition, 50 MPH (I-9O Near Killingly, CT): Load: 7,500 lbs. Longitudinal Vertical ” 37 1 .1 .01 .001 _____ PSD ______./ \ M A 92/": ----”‘ VT ’7 g th I‘ “I V Aer: -’ ........L ‘-..-’ 1O E-OS 1 FREQUENCY (Hz) 100 Figure 11A. Power Density Spectrum: Lateral and Vertical Vibrations for Smooth Blacktop Expressway, 50 MPH, (1-91 N near Holyoke, MA); Load: 7,500 lbs. ----- Lateral Vertical 1 .1 .01 .001 __ FNSIW’ _______,,.qp—- \N" 1327’*3 "T i’ F, V ncccosbcoqp-.i-1rw4 i‘1l - l 1 I l. l i l l ‘0 [I ‘3') t 1 '11) 509‘ FREQUENCY (Hz) 100 Figure 113. Power Density Spectrum: Longitudinal and Vertical Vibrations for Smooth blacktop Expressway, 50 MPH (I-9l N near Holyoke, MA); Load: 7,500 lbs. Longitudinal Vertical 38 .001 P50 2 Sig/Hill {H u- : ’1 1 O 5'09, FREQUENCY (Hz) .00 Figure 12A. Power Density Spectrum: Lateral and Vertical Vibrations for Newly Paved Expressway, 55 MPH, (1-74 W, 1 Hour East of Champaign, IL); Load: 40,000 lbs. ----- Lateral Vertical I J | .001 :;;:::’T‘E‘t ' 1 1 I "+CJLN d, ‘ “ D PSD 93in | V II I l l :l ii I l llll .. ielll“ ' lllllll 5“: FREQUENCY (Hz) .00 Figure 123. Power Density Spectrum: Longitudinal and Vertical Vibrations for Newly Paved Expressway, 55 MPH, (1-74 V, l Hour East of Champaign, IL); Load: 40,000 lbs. -—---- Longitudinal Vertical 39 1 1 I .01 ——Ir4 [,2- ‘L .001 A {L .‘ I ' PSD __ '1 'x'\ . \ 92in "' = 1 10 509 1 - DEMAND] FREQ (Hz) 100 Figure 13A. Power Density Spectrum: Lateral and Vertical Vibrations for Rough Expressway, 55 MPH, (1-74, 90 Miles West of Indianapolis); Load: 40,000 lbs. ----- Lateral Vertical .1 .01 .001 , L” \ 4 ‘ PSD _‘-‘ \ ‘ 93le 1’ 1" 8.091 DEMAND] FREQ (H21 100 Figure 133. Power Density Spectrum: Longitudinal and Vertical Vibrations for Lough Expressway, 55 MPH, (1-74, 90 Miles Heat of Indianapolis); Load: 40,000 lbs. ..-._—- Longitudinal Vertical 40 1 .1 .01 "' I .001 ——— I I ‘ ( PSD M "2 ’ ’ I 92/”; .----qp--.-dl” I ‘3 5:0 . 1 FWRELXJEHKDY’(FDD 10:) Figure 14A. Power Density Spectrum: Lateral and Vertical Vibrations for Smooth Z-Lane Road, 50 MPH, (Route 32, Heat of Lebanon, IN); Load: 40,000 lbs. ----- Lateral Vertical 1 .l .01 F1!!! ’3’": ~~--l,v = ‘ I 1O terms 1 IRRECINHNCN'(HB) 1‘”; Figure 143. Power Density Spectrum: Longitudinal and Vertical Vibrations for Smooth 2-Lane Road, 50 MPH, (Route 32, West of Lebanon, IN); Load: 40,000 lbs. ..-.—-- Longitudinal Vertical 41 ' I .1 .01 ii“ 001 \ ’LME 'q e I PSD wfl 4" ."' ‘ a 92/": b--~~“‘o‘P-¢~~"I 1‘) 5°09 1 F$HKIJEhKrY(PhD 100 Figure 15A. Power Density Spectrum: Lateral and Vertical Vibrations for Rough Expressway, 60 MP8 Uphill, (I-7O E, 30 Miles East of St. Clairsville, 08); Load: 40,000 lbs. ----- Lateral Vertical 1 .1 l l .01 .001 — .- Pso AP‘R C 93qu __--Jr’ "‘1 .. 1 1 L 9°“: FaeouemM-m too figure 15!. Power Density Spectrum: Longitudinal and vertical Vibrations for Rough Expressway, 40 HPH Uphill, (1-70 E, 30 Miles East of St. Clairsville, 08); Load: 40,000 lbs. ..-_——- Longitudinal Vertical \ 42 1 n g I z I | | .1 i I g I .01 . ._\ i 1.0.”1’.‘ 5 ~001:::::=’flt”l ‘V : d l V I .4' t}\) PSD : \LF ’ » fl ‘ - 92m: ----._-.5__‘ j \j I ."3 as: 1 FREIXJEDK?((}hfl 100. Figure 16A. Power Density Spectrum: Lateral and Vertical Vibrations for Concrete Expressway, 60 MPH, Downhill Braking, (1-70 B, 35 Miles East of St. Clairsville, 08); Load: 50,000 lbs. ---- Lateral Vertical 1 .1 l .01 .00174 \V | | P80 >215 4L 1 .A 01“ b - ‘; ‘ 92/"! ..‘- 1 4 6.000 53 40 > 1 > 1 5 5,000 40 30 > 1 > 1 6 1,000 15 15 2 2 7 600 23 40 4 7 8 300 20 40 '7 l3 9 60 S3 9 88 15 10 50 200 9 400 18 20 2,000 2.000 100 100 S 30 1,500 400 150 27 10 40 100 300 so 300 so 50 250 300 530 120 212 60 130 loo 100 77 77 70 100 60 30 60 30 80 20 SO 30 250 150 90 10 lo 6 100 60 100 10 13 10 130 o. 100 45 Table 3 . PSD values: Snooth concrete with expansion joints every 20 feet, 50 MPB, (WI-23); Load: 7,000 lbs. Freq. Power Density value (*10 -6) Percentage of (Hz) _ vertical "'"mVJJE; """ £5 {£5 """ {J 5;. """""" 1:; (.1??mean ' ".1- ------- 2 “.500 ........ 4 73.0.0- ...... 1. :3-0-0 -------------- 1 .7-2 ---------- E: 2"- 2 9,000 5,000 1,100 $6 12 3 150,000 3,000 1,700 2 l 4 600,000 2,500 3,000 > 1 > 1 5 150,000 1,700 1,300 1 > 1 6 10,000 1,100 1,500 11 15 7 9, 000 1 ,100 1,700 12 19 8 l3 , 000 3 ,000 f 2, 500 23 19 9 4, 000 5,300 1, 500 133 38 10 2 , 500 20 , 000 1 , 500 800 60 20 10 , 000 10 , 000 4 , 300 100 43 30 4, 300 9,000 4, 300 209 100 40 10,000 4,000 3,300 40 33 50 10,000 4, 300 4 ,300 43 43 60 2, 500 3,000 3 ,000 120 120 70 5,300 1,700 2,000 32 38 80 4,000 1,500 1,300 38 33 90 1,500 1,100 2,300 73 153 100 1,300 1,000 1,300 77 100 46 Table 4. PSD values: Concrete, fair condition, 50 MPB, (1-90 w near Killingly, C'l'; Load: 7,500 lbs. Freq. Power Density value (*10 -6) Percentage of ‘ (82) . vertical "'"m'ir'ér'é'iZJ """ E; €55 ""155; """"""" 1:; ;;r.;1.----fo-n-g.:- --1 ......... 400 ........... 53 ----------- 6 --------------- l3 ----------- {~- 2 1,700 30 6 2 > 1 3 5,300 20 5 > 1 > 1 4 6,000 13 4 > 1 > 1 5 2,300 13 5 > 1 > 1 6 430 17 6 4 l 7 130 53 6 41 3 8 130 200 20 154 15 9 150 130 28 87 19 10 40 90 25 225 63 20 400 300 130 75 33 30 43 60 15 140 35 40 43 60 20 140 47 so no 40 13 36 , 12 60 113 113 100 100 89 70 300 100 30 33 10 80 150 S3 40 35 27 90 100 40 30 40 30 100 30 40 30 133 100 47 Table 5. PSD values: Smooth blacktop expressway, 50 MP3, (21-91 N near Holyoke, MA); Load: 7,500 lbs. Freq. Power Density value ('10 -6) (Hz) . “$33351“ --------.;;r.€i.;;1. .... 1.: {Jr-{1' "“156; ----------- I: 13;: ""1669...- "I -------- 1 .3'0 ----------- 4 '6' """"""" 6. """""""""" 3 ’1' """"""" 5 "- 2 150 25 6 17 4 3 300 10 4 3 1 4 500 5 3 1 > 1 s 500 s 4 1 > 1 6 130 4 3 3 3 7 so 13 6 26 12 a 53 40 1o 75 19 9 60 53 1o 83 17 1o 9 so 6 556 67 20 so 15 53 17 59 30 25 15 1o 60 4o 40 25 10 1o 40 40 so 200 ' 200 13 100 _ 7 60 130 300 30 231 23 70 140 100 100 71 71 so 40 30 3o 75 75 so 100 30 10 3o 10 100 60 100 25 167 42 48 Table 6. PSD values: Newly paved expressway, 55 MP8, ”-74 W, 1 hour east of Champaign, IL); Load 40,000 lbs. Percentage of (32) . vertical --------Ve-;t:i.c:1- '''' 1.: 1:121. "’72:; . """""""" 1: {61.51- “-1.3119- ." --1 ......... 100 ----------- 20 ---------- 11 ---------------- 20' --------- 13:- 2' 1,000 10 10 1 1 3 2,500 9 43 > 1 2 4 1,300 10 43 > 1 3 s 250 13 10 s 4 6 63 25 1s 40 24 7 130 100 17 77 13 a 20 270 60 1,350 300 9 53 4o 90 75 170 10 13 s 17 41 131 20 17 600 600 3,529 3,529 30 . 1000 60 3o 6 3 40 130 300 150 231 115 so 150 I 110 100 73 ' 67 60 100 100 53 100 53 70 100 600 100 600 100 so 17 40 10 23s 59 90 53 90 10 ' 170 19 100 60 170 60 283 100 49 Table 7. PSD Values: Rough expressway, 55 MPH, (1-74: 90 miles west of Indianapolis, IN); Load: 40,000 lbs. Freq. Power Density value (‘10 -6) Percentage of (Hz) vertical """'"V€:¥1§f"m€§€§£{'56; """""" E.” {$.11 ""1656." "I """"" 9’ 0.0 """""" 9 "o """"" 6 6' """"""" 1 'o' """"" 7 --- 2 6,300 100 170 2 3 3 20,000 100 600 > 1 3 4 10,000 60 530 > 1 S 5 1,000 53 100 5 10 6 400 43 10 11 3 7 300 300 100 100 33 8 400 $30 300 133 75 9 300 100 600 33 200 10 110 53 100 48 91 20 4,000 3,000 2,000 75 50 30 1,100 150 100 14 9 40 600 1,000 300 167 50 50 250 600 300 240 120 60 300 $30 200 177 67 70 300 900 170 300 57 80 200 300 100 150 50 90 600 530 53 88 9 100 ’ 200 300 60 150 30 50 Table 8. PSD Values: Smooth 2-1ane road, 50 m, (route 32 west of Lebanon, 18); Load: 40,000 lbs. Freq. Power Density value (’10 -6) (82) ”3333321“ """"Ve}'€1:§{ """ L: :35 ""136; . """""" z: {551 ""136; ." "1 --------- 1 50 ........... 5 .3 ---------- 4 .3 --------------- 3 .5 .......... 2 .9." 2 530 30 25 6 5 3 2,500 33 53 1 2 4 2,000 30 60 2 3 5 200 60 13 30 7 6 100 170 15 170 15 7 100 250 33 - 250 33 8 150 170 150 2 113 100 9 53 30 200 57 377 10 1s 25 33 167 220 20 600 1000 1,100 167 183 30 1,500 100 53 7 5 40 100 330 60 330 60 50 40 150 90 375 ' 225 60 200 . 170 170 85 85 70 100 530 30 530 30 80 30 100 17 333 57 90 300 300 17 100 6 100 40 200 20 500 50 51 Table 9. PSD Values: Rough eXpressway, 40 MPH uphill, (1-70 B 30 miles east of St. Clairsville, 08); Load: 40,000 lbs. «m P7326221“ " " ' " "7.16:5 """ 6: 2:1“ 1...... """ 1 25;." ”-1- ......... 2 .5-0 ----------- 6 .3 ---------- 2 .5 ---------------- 2 .5 --------- 1 .0.-- 2 1,500 27 30 2 2 3 9,000 60 250 > 1 3 4 6,000 53 300 > 1 5 5 600 27 93 S 16 6 300 33 60 11 20 7 400 100 S3 25 13 8 900 170 300 19 33 9 400 100 530 25 133 10 100 33 100 33 100 20 1,300 3,000 2,000 231 154 30 600 100 100 17 17 40 300 900 200 300 67 50 300 ' 900 530 300 ‘ 177 60 200 200 170 100 85 70 100 400 40 400 40 80 60 1,000 100 1,667 167 90 100 300 30 300 30 100 60 90 25 150 42 52 Table 10. PSD Values: Concrete expressway, 60 MPH, downhill- braking, (1-70 3 35 miles east of St. Clairsville, 08): Load: 40,000 lbs. Freq. Power Density value (*10 -6) (82) “1:333:31“ -----..--.v.;r.;1:; ..... 1: 6:5 .... 1: {inmmmiffieru 1669." “-1-.- --------- 2. 5.0 ----------- 5 .3 .......... 5- 3 ----------------- 2 .1 ........ 2. 1.-- 2 1 ,000 40 20 4 2 3 2 , 500 27 100 1 4 4 2 , 500 27 110 1 4 5 530 17 40 3 7 6 150 30 25 20 17 7 170 250 27 147 16 8 250 300 100 120 40 9 60 53 110 33 133 10 17 15 53 88 312 20 500 2 ,700 500 450 100 30 1 , 300 100 53 8 4 00 1 ,000 I 530 150 S3 15 50 250 500 250 200 100 50 170 300 170 175 100 70 250 600 30 200 12 80 100 330 40 330 40 90 100 400 17 400 17 100 30 90 20 300 57 53 Table 11. PSD‘Values: Concrete expressway, 60 MPH, (1-70/1-76, {gamiles east of Pennsylvania state line): Load 40,000 Freq. Power Density'value (*lO -6) Percentage of (82) vertical ""W'TJEJQQE """ 11' .213""'I.T.§f ' ‘ {$675.3 """ 1’ 563'." "1 ......... 2 70 ----------- 2 7: __ 33 H“— — J ...... 1 .0 ........ 1 .2." 2 l,500 40 33 3 2 3 9,500 90 170 > 1 2 4 9,000 90 250 1 3 5 1,000 60 95 6 10 6 300 53 33 18 11 7 150 20 40 13 27 8 170 400 170 235 100 9 130 100 200 77 154 10 40 10 40 25 100 20 400 2,000 1,000 500 250 30 1,000 150 40 15 4 40 170 300 95 176 S6 50 90 300 33 333 37 60 100 250 100 250 100 70 90 300 33 333 37 80 40 900 53 2,500 133 90 100 530 10 530 10 100 30 100 10 333 33 5.0 CONCLUSIONS AND RECOMMENDATIONS The following conclusions can be drawn from this study: 1) Generally, the levels of lateral and longitudinal vibration in commercial truck shipments are mmch less than the vertical vibrations in the same trailer at frequencies below 10 Hz. 2) At frequencies greater than 10 Hz. the lateral and longitudinal spectrums have contours very similar to that of the vertical spectrum. 3) The levels of vertical, lateral, and longitudinal vibration at frequencies above 20 Hz. are very similar. 4) The displacement at frequencies above 20 Hz., where lateral and longitudinal levels are generally highest, are much less than the displacement at lower frequencies. The RMS displacement necessary to produce 1 g RMS at 3 Hz. is 1.1 inches. The RMS displacement necessary to produce 1 g RMS at 20 Hz. is 0.02 inches. 54 55 This number can be calculated by using the following formula: A (in inches) = A“ a * 386.4 (5.1) (27 f) Where A is the amplitude (displacement), acc is the acceleration, f is the frequency, From this formula it is evident that for a given acceleration, the amplitude (displacement) is inversely proportional to the square of the frequency. The substantial difference in amplitudes at different frequencies is why low frequency vibrations are more damaging to most products. Tables 12 and 13 have been included to help summarize this study. They show frequency bands for peaks, RMS acceleration levels, and the causes of the peaks. Table 12. Frequency Average 9's (1:145) Cause of vibration Frequency Average 9'5 (RMS) Cause of vibration _ Frequency Average 9'8 (1:145) Cause of vibration 56 Summary of a Light Load 15-25 Hz. 0.035 g's Structure 33-60 Hz. 0.04 g's Drivetrain 4-5 Hz. 0.028 g's Suspension 12-20 Hz. 0.11 g's Structure 40-60 Hz. 0.037 g's Drivetrain 4-5 HZ. 0.023 g's 15-25 Hz. 0.033 g's Structure 50-70'Hz. 0.033 g's IDrivetrain 57 Table 13 . Smary of a Heavy Load Vertical . Lateral Longitudinal Frequency 3-4 Hz. 3-4 Hz. 3-4 Hz Average g's (R148) .089 g's .007 g's .042 g's Cause of vibration Suspension Suspension Suspension Frequency 15-30 Hz. 15-25 Hz. 15-25 Hz. Average g's (RMS) .031 g's .055 g's .040 g's Cause of vibration Structure Structure Structure Frequency 50-70 Hz. 50-70 Hz. 50-70 Hz. Average I ° g's (RMS) .014 g's .041 g's .018 g's Cause of vibration Drivetrain Drivetrain Drivetrain LIST OF REFERENCES Slected ASTM Standards on Packaging, American Society for Testing and Materials, 1987 Brandenburg, R.K. and. Lee, J.J., Fundaments of Packaging Dynamics, MTS Systems Corporation, 1985. - Foley J.T. , Preliminary Analysis of Data Obtained in the Joint Army/AEC/Sandia Test of Truck _Transport Environment, Shock and Vibration Bulletin 35, Part 5, 1966. Foley J .T. , The Environment Experienced by Cargo on a Flatbed Tractor-Trailer _. Combination, Sandia Laboratories, SC-RR-66- 667, 1966. Goff, J.w.; Grebe, J.; Twede, D. and Townsend, T., You'll Never See It From The Road, Technical Report # 26, School of Packaging, Michigan State University, 1984. Goodwin, D.L., and Holland, R.R., Shock and Vibration Dynamics of Intermodel Distribution Environment - Trailer on a Flat Car, Container in a Well Car, 1987. Harris, C. M., and C. E. Crede, Shock and Vibration Handbook, Vol. 3, Mo Graw Hill Book Company; NY, 1961. Magnuson, C. F., Shock and vibration Environments for Largg Shipping Container During Truck Transpgrt, (Part 1), Sandia Laboratories, SAND 77-1110, 1977. Magnuson, C. F., Shock and Vibration Environments of Large Shipping Container Durirg Truck Transport, (Part 2), Sandia Laboratories, SAND 78-0337, Nuclear Regulatory Commission, NUREG/CR-0128, 1978 National Council of Physical Distribution Management, WM 1982 Sharpe, w. N., Jr.; Kusza, T. J.; Sherman, P. w., and J. C. Goff, Preliminary'Measurement and Analysis of the Vibration Environment of Common Motor Carriers, Shock and Vibration Bulletin 44, Part 4, 1974. 58 59 Singh, s. P., and Young, D. E., Measurement and Analysis Technimles Used to Simulate the Shipping Enviroments. Presented at the Winter Meeting, American Society of of Mechanical Engineers. Tevelow, F. L., The Military Lgstical Transportation Vibration Environment: Its Characterization and Relevance to MIL-STD Fuze Vibration Testing, 0.5. Army Electronics Research and Development Command, Harry Dimond Laboratories, 1983. Thomsom, W. T., Theory of Vibration With Application, 3rd Ed., Prentice Hall, 1988. Turczyn, M. T.; Stevens, D. G., And Camp, T. H., Shock and Vibration Environmth in a Livestock Trailer, Shock and Vibration Bulletin 50, Part 2, 91-101, 1980. Tusyin, W., and Mercado, R., Random ‘Vibration in Perspective. 1984 TQTE UNIV. LIBRQRIES HICHIGQN s IIIIIIIIIIIIIIIIII II 3129 3005929777