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I I I I I I .I I I- I I I I I . I I I . II I. . I I I I . - I I . I I .r o I II. I I I I III“ I~ 0' . I I I ll V I I IIIII'III I I I. . (III-I, L. W m W WWW a 3 1293 01072 7646 w-u'l'qls This is to certify that the thesis entitled An Analysis of Suspension Media Used in Automotive Vehicles - a. ' "“‘presente’d by , - : -. Amir Mohamed Mirsepasy has been accepted towards fulfillment of the requirements for ALL degree in _M_!_E_1____ Major professor Date March 1, 1956 0-169 PLACE IN RETURN BOX to remove this checkoutfiom your record. TO AVOID FINES Mum on or before date duo. DATE DUE DATE DUE DATE DUE (if 1, v ' t aw Ho .‘1 ‘91.:in AN ANALYSIS OF SUSPENSION MEDIA USED IN AUTOMOTIVE VEHICLES by Amir Mohamed Mirsepasy M A THESIS Submitted to the School of Graduate Studies of 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 1955 THFSIS ACKNOWLEDGEMENTS The author extends his sincere thanks and appreciation to Dr. Louis L. Otto, the major Professor of the Automotive Option, Mechanical Engineering Department of Michigan State University, under whose supervision, assistance, and valuable guidance this work was done. The writer also wishes to thank the Applied Mechanics Department for the facilities they provided for carrying out the necessary eXperimental operations. 11 VITA The author was born in Tehran, Iran, January 8, 1926. He attended grade and high school in Tabriz, a northern city in Iran, and was graduated in June 19hh. In September 19hh, he passed the open competitive entrance examination for the College of Engineering in the University of Tehran. After the first year of basics he chose the Electro- Mechanical option, with Automotive as his fourth year minor. He had his two terms of working eXperience, necessary for the degree of Engineering, with two different companies (a well drilling company in northern Iran, and the Anglo-Iranian Oil Company). He graduated in September l9h8, with an engineering degree in Electro-Mechanical, (this college offers the Bachelor of Science degree, and the "Engineering" degree with a rating higher than B.Sc., and attained by those students with superior scholastic records). Soon after graduation he was employed by the Anglo- Iranian Oil Company (October l9h8), as a transportation engineer until June 1953, with an interruption of eighteen months for military services, during which he served in the Engineering division as a second lieutenant, in charge of a border Brigade power plant. From July 195% until August 195%, he worked with Iran- America Sanitary and Health Cooperation, as the head of the iii iv Transportation Division and Installation engineer. In September 195%, he came to the United States to continue his studies and is now a candidate for the degree of Master of Science in Mechanical Engineering at Michigan State University. ABSTRACT Suspension systems for automotive vehicles create many problems concerned with spring materials and spring config- urations. This thesis discusses these problems as they relate to the materials or media used as the "spring," or elastic distortion member. The introduction discusses the vibration problems involved in suspensions, and develops the general solutions obtained for the fundamental mathemat- ical relations. The next parts deal with the types and characteristics of suspension systems employing four differ- ent materials as their main medium--these are steel, rubber, air, and liquid. The part on "Steel as a Suspension Medium" includes three different types mostly used in automotive field, (leaf spring, coil, and torsion bar); necessary design formulas for each case are given. In the case of the torsion bar the new system developed by the Packard Division of the Studebaker-Packard Corporation is described as well as its automatic-leveling system. The section on rubber explains the various types of material shapes and loadings introduced in practice, and in a few cases stress-strain calculations are also given. The third medium considered is air. The characteristics of this type of spring are compared with those of a steel spring; the analysis and illustration of an air suspension V vi system now in production is also included. Data and curves obtained from a series of experiments carried out on two different sizes of pneumatic spring boosters are also shown at the end of this section. The next section, a discussion on liquid springs, covers the characteristics of fluids as applied in practice, and also the difficulties involved in producing this type of Spring. In this part a hydro-pneumatic system used on pas- senger cars is described, as well as the liquid springs deve10ped and used by Wales-Strippit Company. A The last part of this paper deals with various types of dampers, with theoretical calculations for each type, (viscous, coulomb, solid, and hydraulic). The calculation procedure for equivalent damping efficiency is also shown. TABLE OF CONTENTS Page Introduction: A brief discussion on automotive suspension systems and their requirements . . . . . . . . . . . . . . I Part I - Vibration Problems Concerned with Suspension Systems . . . . . . . . . . . . . . . . . . . 9 Part II - Steel as a Suspension Medium . . . . . . . . 2% A. Laminated Leaf Springs . . . . . . . . . 2% B. Coil Springs . . . . . . . . . . . . . . . 31 C. Torsion Bar Springs . . . . . . . . . . . 35 Part III - Rubber as a Suspension Medium . . . . . . . h2 Part IV - Air as a Suspension Medium . . . . . . . . . 50 Part V - Use of Liquid as a SuSpension Medium . . . . . 71 Part VI - A Discussion of Vibration Dampers . . . . . . 77 Conclusion . . . . . . . . . . . . . . . . . . . . . . 86 Bibliography . . . . . . . . . . . . . . . . . . . . . 89 Vii INTRODUCTION A mechanical Spring is defined as an elastic body whose primary function is to deflect or distort under the applica- tion of a load, and which recovers its original shape when released after being distorted. Most material bodies are elastic to some extent, and will be distorted under load, but in cases in which they are not primarily designed for the purpose of elastic deflection they will not be considered as springs. The automotive vehicle is directly concerned with the use of springs as a means of maintaining wheel to ground contact over uneven surfaces, and as a means of cushioning the vehicle and its contents from the shocks created by rapid travel over bumps and irregularities. This paper is concerned with the applicability of various spring materials to the problem of automotive vehicle suSpen- sion. The main factors involved in the application of any given spring material to this problem are: (1) energy absorp- tion ability per pound of spring material; (2) ability to conform to the space limitations imposed by vehicle dimensions; (3) variations of Spring rate with change in initial load; (h) degree of internal friction under dynamic loading. The materials which have been most frequently used for automotive vehicle springs are steel, air, and rubber. Liquid springs are at present under consideration. 1 Each vehicle manufacturer has established his own stand- ards for ride control and spring action. The Society of Automotive Engineers has an Activity Committee which is endeavoring to establish standard procedures and instrumen- tation for several "standard" ride control and car vibration tests. The several "standards" thus established differ appre- ciably from one another, and to some degree are empirical in nature. Early ride control theories assailed rate of change of velocity as a cause of passenger discomfort, but experiments dwith reduced rates showed that low rate of velocity change, like the slow roll of a ship at sea, can beacause of passenger discomfort. Through the ages the average human's internal organs have become accustomed to the motion which arises from walking at the rate of two or three miles an hour with approximately a 30 inch step. Converting two miles an hour to steps per minute, gives a rate of 70.h oscillations per minute and three miles per hour converts to a rate of 105.6 oscillations per minute. This concept was presented in 1923 before the Insti- tution of Automotive Engineers. Most contemporary pleasure cars are designed with a suspension frequency of 60 to 90 oscillations per minute. The automotive industry has found that any frequency appre- ciably lower than 60 causes nausea for some passengers and unsatisfactory vehicle control. Any appreciably higher number of oscillations per minute than 90 produces a hard, jarring ride. Any change of mass in a body affects the kinetic energy of that body: 2 K.E. : ET. 2% As the body weight decreases, its ability to resist force without changing its equilbrium position is decreased. An obvious example of this would be the comparison of a ride in an empty truck with conventional Springs with the ride produced by this same truck when fully loaded. Desirable Eeatuges of a Suspension System The most desirable type of suSpension system is one that keeps the same number of oscillations per minute regard- less of the load. This insures a comfortable ride whether the vehicle is full or empty. Another feature of an ideal vehicle suSpension is its ability to provide the necessary mechanism to reduce the amplitude of the successive motion cycles of the chassis caused by stored energy in the suSpension and moving parts. An ideal suspension system should also have a minimum amount of friction. This is necessary for two reasons: static friction is greater than the friction of motion and varies with the physical and lubrication conditions of the surfaces. With a large amount of friction, small movements of the unsprung portion of the vehicle are transmitted almost lin- early to the Sprung mass because the heavy static friction must be overcome before even a slight flexing of the resilient means occurs. When larger movements of the unsprung mass occur, heavy friction at the beginning of the movement causes appreciable transmission to the sprung mass, resulting in a high rate of acceleration, or lurch. Spring rates and mass distribution are the major factors controlling the rotation of the sprung mass of a vehicle about its center of gravity, as will be discussed in the next part. The combination of distributed mass and elastic suspension is usually referred to as the mass-elastic system. Suitable damping is an important item which is necessary to control the motion of the Sprung mass. The oscillation frequency of the mass Should be kept within a range which causes the least disturbance to the human body as previously mentioned; (pitch and bounce frequencies are least disturbing), this range normally is covered by frequencies of 70 to 100 c.p.m. Professor J. G. Guest, in his paper (1926) to I.A.E. outlines a mathematical analysis of a mass-elastic system for an automobile and arrives at the conclusion that the best ride is obtained when the ratio of mass constant to elastic constant equals unity. Elastic Constant = H - LU (See Figure l) L._._2.\__ " where, H2 2 \/ --@ si_. A.B. in which: 1- -A- '4: A : rear spring rate l° = front spring rate A : distance from center of gravity of sprung mass to center of rear spring. B : distance from center of gravity of sprung mass to .center of front Spring. L : distance from center of gravity to plane of axis of oscillation. U : distance that spring must be raised to be unloaded (initial displacement). (See page 6.) The mass constant of the system is represented by KQ-P’LZ: where K is the radius of gyration of the sprung mass. EXperiments carried out by Messrs. James, Churchill, and Ullery on six different cars gave results depending on type of Spring, shock absorber, stabilizer, et cetera. It was noted that good-riding cars had lower frequencies about points P and Q (Figure l) and particularly about Q. Rotation about point Q produces pitching of the vehicle, most notice- able to the front seat occupants. It was also shown by these tests that the ride is of high quality when the ratio of mass Plane of axis of .. oscillation i f1.” .J (A p,,-. . ‘ - i . w_ . 5i (”aplane of wheel centers 1‘ C I . fl . T C ‘ - 5-- ., ...s.. A CsG “:4 u V . . Figure l constant to elastic constant is close to unity. By plotting the data obtained, they concluded that the actual effective spring rates of the front and rear Springs do not by them- selves alone control the comfort of the ride. The safety of the passengers and the operator is another item of primary importance in a vehicle's suspension system. Steering, car control, and suspension are interrelated so that one cannot be discussed without the other. Steering is understood to mean "the control that the driver exercises over the direction of travel of the vehicle," and is used to cause the vehicle to travel in the desired direction with safety and ease. This control, exercised by the driver, is concerned with the linkage, the suspension and the tires. The ideal suspension has the important job of keeping the axle in proper position with respect to the chassis. Axles should move up or down only with reSpect to the body. Lateral, longitudinal, or torsional movements are to be avoided. Any of these three may have an unfavorable effect on the ride, tire wear, steering geometry, and vehicle control. Among the different characteristics necessary for a satisfactory suspension medium, the ability to store energy at various frequencies is of primary importance. This ability is a function of the "elastic limit" of the material. A high elastic limit enables the material to undergo higher deflections through any given number of cycles without any appreciable permanent deflection. Materials used for Springs should have stable physical properties against temperature, humidity, corrosion, et cetera, and should be relatively free from a need for periodic maintenance operations. An intelligent solution to the problem of the selection and application of a Spring material can have an important effect on the initial cost, the ride, the safety, and the reliability of an automotive vehicle. PART I VIBRATION PROBLEMS CONCERNED WITH SUSPENSION SYSTEMS Whenever an elastic system, free from impressed forces, is distrubed from its equilibrium position, a free vibration will take place. The system in this case will vibrate at its natural frequency and its amplitude will gradually diminish with time by reason of energy dissipated by the motion. .When calculating the natural frequency of a system, the presence of any damping effect is neglected as the definition of free vibration requires this assumption. In order to be able to calculate the natural frequency of various systems, an analysis of the system into simpler systems will be essential. The calculations for a few prin- cipal cases are deveIOped in the following pages. Theoretical approach to the vibration characteristics of a simple system which is more or less similar to the sus- pension systems used in automotive vehicles is as follows. A mass M suspended from a spring (coil) with a negligible mass (Figure 2) constitutes a simple vibrating system. The position of the mass is Specified by a single value of X, therefore, the system has only one degree of freedom. In its equilibrium position, the gravitational force w acting on the mass is balanced by the spring force KA where K is 9 10 the spring stiffness and L: is the static deflection of the “3“" Spring. When the mass is dis- placed a distance X from its ‘,< equilibrium position and S] released, the unbalanced force W t ‘x and acceleration are related L————J by Newton's Law of motion. (Neglecting friction) Figure 2 2 2 . - m d x 3 2 F 2 -K.X or 51.}... .3. 12232... - 0 Therefore, the natural frequency of the system will be: 211 Remembering that, K : W = E m m db 45 the natural frequency becomes a function of statical deflec- tion: A are“ The period of oscillation can be determined as: TL?! . ' l’ ._ ,4 .. [7‘ ~— Another case which is similar to what is used in the automotive field as a "Spring nest" can be schematically simplified as in Figure 3. ‘ .../.€. / C“) 1”?“ r’“ < ” \ h " —;i’{ r 7> , , ‘~ '0‘) $325223 ::I\5 , f 1 I i _3 (a) (b) a» Figure 3 In finding the natural frequency of such a system, remembering that in practice points A, B, and C are super- imposed on each other, spring stiffnesses will be added together so the natural frequency of the system will be: /' - g g; M, f/f‘ m ,. - q- J 256 v ’71 In case of Springs in series, however, this addition will be as follows: (Figure H) r) C (as the sum of displacement per unit weight) so the frequency, / ” 2 I ‘ " 32/1: f'i"3+/];A// The other case which some- times is applicable to Special ‘Jg,< systems is the combination of fir~ I two springs in parallel with a t r’ K? non—symmetric load location . ,,3 such as Figure 5. In this case the load is divided so [ n1 I that AP is applied to K :7 b. 1 and éfaE- to K2, the deflec- Figure 4 tion at point P is therefore the sum of deflections due to " '9... /_,-_/'/'/’ each one of the Springs, which I :1_ will be for a unit load: l3 A _ I if. d I ,______. d 6 - - (.7: ¢)A; a {-5 __ (72+élll'k (av-6)]; 9: +4 .. .4. K (4 $525,): Ml dz 6" 7r " “' z ’5 Another slightly different case which might be applied to torsion bar systems deals with angular oscillation. Suppose a disk mass with a moment of inertia of J is attached to a slender bar of torsional stiffness K = Torque__ (See Figure 6) £9 rad. torsion which is assumed to be a linear proportion; when the bar is twisted and released, the unbalanced torque about the axis of rotation is equal to the mass moment of inertia multiplied by the angular acceleration. TLxfl 1% Since the restoring torque of the shaft acting on the disk is -v(§‘ , the equation of motion becomes: (G’Iis the angular acceleration) As previously shown, the frequency of oscillation for a motion of this equation will be: ifizhnnkgzl; ,I‘! - ,1... m. 5212‘ V J K Figure 6 One other way to approach all of the previously mentioned cases is the conservation of energy method (in which the sum of kinetic and potential energy with respect to time is con- sidered to remain constant). Damped Vibration: In case of damped vibration, however, the equation of motion will have a third term concerned with the damping force, such as: md‘r: vine, “14-3,:A2: :20 (15" d5 Trix fl ... . is a,F.iEE.LIJl y , 2!. cuff-Hr" 15 in which case the damping force is a function of velocity of oscillation. Three different phases of damped vibration can be shown by the results obtained from the solution of such a differential equation as shown in Figures 7-a, b, c, depend- ing on the rate of damping relative to the spring constants. A detailed discussion on various types of dampers and their characteristics is given in Part VI of this paper. Figure 7-a -Jr Figure 7-b Figure 7-c 16 Air Spriggs Whenever air is used as the spring medium, together with a nonéflexible container, the approach for natural frequency is slightly different. First of all this medium enables a system to have a very low natural frequency with zero static deflection. Secondly, with this type of spring, the body is supported by air pressure and in many cases such springs are used for leveling too. The behavior of the air can be deter- mined by assuming a bellows as a piston and cylinder of area A, and letting the pressure and volume of the air in the equilibrium and displaced positions to be PO, V0 and P, V, respectively. The following gas law for the adiabatic change holds: X r /".l/ : PJ/ where $E:,Ai¢ is the ratio of specific heats (for air). Differentiating with respect to the displacement x, the following equation is obtained: ’ ”(any - 3 ~99!” JV ax 4/9: Since the volume corresponding to any x is: &/'::(&3 '”/4.E7r9 ‘1§< _4,;4 dz l7 and as Spring stiffness K is equal to force per unit of displacement: ‘2 __(9( f) mag/.8 _ 21.9.4 0. .436.) dx— lg” 56 This equation indicates that the stiffness of the air Spring is dependent on the displacement and hence is non-linear. However, the oscillatory deflection x is generally quite small and the stiffness can be approximated by the equation: ‘9 1" o'Iy’oxtf GNU 6 l "I j . A-' I : - f I .. _: ’ V r ,p ’I Z, t g) v) a This indicates that a very soft Spring is possible by in- creasing the volume Vo of the system by means of a connecting tank. The pressure PO required is established by the weight W and the area A of each bellow used. For damping purposes a throttle valve should be placed in the air line. The equation for the natural frequency then can be written: at: A, .2. /l 3 7.: r" u rcu;._t:3:’ ' ‘ {:43 A - I _' lf‘lf’ilci’o/ . C, n" // 2,2237 [5 V ———_3 18 Vehicle Suspension The automobile represents a complex system with many degrees of freedom. (Figure 8). Nevertheless, it can be simplified to the figure shown here: h—u-‘——~ . - ‘IQ ”' "A? ‘ ? «I 5,7” l I i l Ifécfi/ \\ m J L~ C >- Figure 15 The torsional resisting moment is: 5.! zsvza" c 2 By equating the applied moment to the resisting moment, .3 /AZ'=:/£24é?’:: £54355? ~flfléfizyda’:5, 5 .-.- 222 7:43 the mean radius of coil where: R the radius of wire Cl P axial load applied Figure lé-a 33 It; can be seen that another item neglected here is the effect of‘ direct shear stress due to axial load P. (Figure lé-a) By considering two neighboring sections and their rela- tive rotation, and also the axial load the resultant stress will. be: 5: fix 72a3 where K, known as Wahl's correction factor, is: .. 4C-l o6/5 .. ' K“ 477+ "’5‘“ and where C: 22-- is t he spring index . The exact theory, however, employing the theory of elasticity, results in: 2P2 —. Iéma :: '3 .<; " 7Z6! Where the correction factor: 19:1”. 1.1.1., ,3 l / + “—- /é> (géi-l By comparing the two correction factors mentioned above (Plotting against Spring index C) we come to the conclusion that: 31+ 1. The value of K is larger than the corresponding value of C so the approximate theory is on the safe side. K and G are so close that at C as small as 2 their [‘0 difference is only 2%. 3. The approximate theory is Simpler and is sufficiently accurate for practical use. The deflection for an axially loaded spring is given by: g .. 024-36%” etc/4 the coil radius at zero load where: r n = number of active turns G 2 modulus of rigidity ( 112 d 2 the diameter of wire ;-”"_‘;?:::<= ‘~ Figure 16-h By using the theory of elasticity again, the resultant formula will be: .3 §::: 7p'$,-— ~%’<94z;2 011? - ’,(é ._ I, 1. «1 c' . d The factor 9” depends on the initial pitch angle x0 (Figure lé-b). The value of ’7? usually calculated for a f ratio of 2.6 (which applies approximately for most spring steels) varies depending on the various values of ::( and 0 n jfl_’ ‘ ' total extension ”6' m; turns x initial coil Maia; (it is assumed that spring ends are free to rotate). When ends are fixed, the amount of: 9p :91" C: """ bin 6:9 ’ — J ‘— L05“, le'nc‘f-bincg 'ACQCascg-éajcf .7. {1 61; and this value can be obtained by plotting deflection against: .0 (3E0 n The theoretical equation of motion and frequency, whether it is a damped or free system, is dicussed in Part I. C. Iorsion Bars Although the torsion bar suspension system has been common in European practice for many years, it has not found much favor in the United States, probably because of its higher cost and design complexity. However, the following are among the major advantages to be mentioned here: l. Space saving, essential in today's passenger car design (mostly European cars). (It has been claimed by General Motors Firebird designers that the choice 36 of this type of suspension was mainly because of the above reasoning.) 2. Cleaner installation at the front. 3. An excellent boulevard ride. An element of novelty for what it is worth from an advertising standpoint. The problem of cost has been answered to a great degree by the use of necessary automation employed in production techniques. The General Motors Firebird torsion bar, which is an extremely clean and simple installation, is moderately stressed, maximum fiber stress being around 9,000 PSI. The shaft was machined all over but not pre-set. It is desirable to make the bars as light as possible, consistant with loading. The higher the allowable maximum fiber stress, the smaller the diameter of the bar and the lighter will be the entire assembly. The maximum stress is believed not to be more than 130,000 PSI, although there are bars stressed to lh0,000 PSI for military vehicle purposes, and some others even higher than lh0,000 PSI. Design and Calculation: For a straight round bar subject to a torsion moment Mt about its axis, the torsion stress 9' is given by Simple equation: MM: /«7::4£2 CVR/ 57-:: ,.. t r' 726/3 37 rad; from which: . /'.7l5 : y: 7- The angular deflection g? , in radians, of a round bar of length 4: under a torque /Q§ is: cp = 8.421414- 72' 44' Q where G is the torsional modulus of elasticity. The energy stored in a torsion rod can be obtained by computing the amount of: d .2’-- .£./k7. (a 1. /zigfifié_f1. ‘ - - Z, I 72 c5 4%! and by substituting the value of: 67.3 x4. 3 '8 ._.. :7" As we get the result of: 6 /— ’5 Z. 4&7 1. 4 f. ‘where ./33 “‘(Z . The torsional modulus U7:: ...7: (:1 (Z. 5 J 'v '. b/ in which z‘33 Poisson's ratio (for most materials ,A3 may be taken .3) which gives a modulus of “a: {f: c‘ . ('1) yield point ;2; can be taken as fé» times the tension point .O , the shearing \u 38 1" C3. , (from the Shear energy theory) thus 25,2vciz ; the static load now can be obtained by equating the allowable stress to the stress at the yield point: The vibration of a rod under an applied torque is Shown in the first part of this paper. A general illustration of a torsion rod assembly in a vehicle suspension can be as shown in Figure 17. Torsion 6"" Figure 17 The Packard Motor Car Company has a new arrangement of a torsion bar suspension system together with an automatic leveling device which enables the vehicle to maintain a constant level altitude. This system is the only system in which the front and rear wheel suspensions are connected together. The two main torsion bars, which run from front to the rear, are one inch in diameter, 111 inches long, of SAE5160 39 steel, precision rolled without any further finishing. They have forged hexes at each end. The ends fit into broached hex holes in levers mounted on needle bearings in a bracket. The front end bracket is attached to the front cross member and the rear brackets are welded to the frame. Torque arms and transverse stabilizer rods are used on the rear axle to control lateral and longitudinal movement, and all bushings are rubber mounted. The bars are stressed to a maximum of 130,000 PSI during full simultaneous bottoming at front and rear wheels, although this rarely happens in service. Bars are wound up during installation about 120 degrees. In ad- dition, two compensator bars are used which enable the sus- pension to keep the chassis level for all usual passenger loads. These two short compensator torsion bars are attached to the rear axle and frame. An electric motor, gear reduction and linkage is utilized for winding these bars in either direction to raise or lower the rear of the vehicle under control of a sensing means for telling when the car is not level. The control switch of the electric motor is actuated by means of sensing lever located on the long left rod on a node point close to the middle bearing. When the car is level, even though its vertical height changes, the nodal point does not rotate, so the lever does not act on the switch. If, however, the rear of the car is low or high, the lever will be moved to the right or the left respectively, which in turn MO will activate the electric circuit on the small electric motor, causing the short bars to be wound or unwound which will raise or lower the rear end of the car. Bimetal relays are used in the electric switch circuit, so that instanta- neous connections will not actuate the motor. However, when the brakes are applied, the power to the motor circuit is cut out, so that the rise of the rear end would not actuate the system. A dash switch is also provided to cut out the compensator action when changing tires. Individual wheel rates are 66 lb./in. in front and 69 lb./in. at rear. This is low compared to the equivalent standard suspension rates. Pitch frequency is approximately MO C.P.M. and bounce frequency approximately 5% C.P.M. with h.5 passenger load. Roll stability is higher than that of standard cars because of the combined Spring rates act on body in roll. The following is a sketch of the system described above: (See Figure 18) \T'l mfim Figure 18 Front Stabilizer Main Torsion Bar (left) Leveling Switch Control Rod Reduction Gear Box and Electric Motor Torque Arm (Rear Axle, left) Leveling Torsion Rod (left) Rear Stabilizer Link Node Point of Rod #1 7 PART III RUBBER AS A SUSPENSION MEDIUM For a long time it has been the conviction of engineers in rubber industries that rubber can be compounded, designed and engineered into suspension systems of various equipment including automobiles, buses, trucks, trailers, airplanes, and railway cars. Today, apparently the stage is set for some really constructive work since automotive engineers are now more receptive to rubber as a suspension medium. Rubber as the elastic element offers a wide variety of basic functional forms which can be classified as follows: A. Straight loading: 1. Compression (Figure 19,20) a. Block b. Column c. Special Shape 2. Shear distortion a. Plate sandwich (Figure 22) b. Coaxial-bushing sandwich (Figure 23) 3. Tension distortion B. Torsional loading: 1. Compression distortion a. Rotating cylindrical b. Rotating disc 2. Shear distortion H2 l*3 a. Torsilastic (Figure 26) b. Lord c. Robertson 3. Rotating plate sandwich (Figure 25) H. Rotating conical The following Sketches are illustrating these various types: Figure 19 Figure 20 Direct Compression Block Direct Compression Hr’fl/"TL .— ---\ | Figure 21 Figure 22 Distorsion Compression Shear Distorsion (plate sandwich) Figure 23 Coaxial Sandwich Bushing ? .i r -" Figure 25 Shear Distortion Sandwich Figure 23 Tortional Elements Figure 26 Torsilastic (Goodrich) (used in twin coach buses with automatic leveling device) an Compared to spring steel, rubber in some ways is a more adaptable medium as a basis for design. For example, spring steel is limited to about 2% elastic deformation. Futhermore, steel Springs are quite limited in the physical shapes that may be used as springs and are limited to Simple bending and torsion members. Spring rubber on the other hand has an elastic deformation with recovery of 600 to 800%. It can be distorted enormously in many ways or directions, offering the suspension designer a great assortment of linkages and load compoundings. The following table Shows a good compar- ison of spring rubber with other spring forms as regards to stored energy. In.-Lb. of Energy Per rin orm Lb._of Spging _ Leaf Spring 300 - #00 Helical Round Wire Coil Spring 700 - 1100 Torsion Bar Springs 1000 - 1500 Volute Springs 500 - 1000 Rubber Spring in Shear 2000 - H000 Rubber in shear has a non-linear stress-strain relation which fits the requirements of a suspension system very well. (See Part I, page 23, ). Rubber used in compression usually produces a strongly non-linear Spring because of distortions and changes of effective area during deflection. As a result, this type of suspension has found increasing application as a vibration isolator for machinery, flexible mountings, et cetera. M6 The fundamental principles of design and calculation of rubber springs by available methods are only approximate. Among the reasons for variations between the predicted and actual behavior of such springs are the following: 1. Variations in elastic or shear moduli occur among different rubber compounds even though of the same hardness reading. In the case of compression springs of rubber, friction between compressed surfaces may vary through wide limits thus affecting the behavior of the spring. Where rubber pads are bonded to steel plates, such variations will not occur however. The static and dynamic moduli of elasticity will differ. In general, rubber springs are deflected by rela- tively large amounts, and such deflections are more difficult to calculate accurately. In case of compression slabs the following empirical method was developed by J. Smith, taking as a basis an aver- age of a considerable number of tests. The following notation is used: n is percentage deflec- tion of a slab of rubber at a given unit pressure; A is the sectional area of Slab; B is the ratio of length of slab to width; h is the thickness; E is the modulus of elasticity of the rubber used; E0 is the modulus of elasticity of rubber 47 having 55 durometer hardness; n0 is the percentage deflection of a 1 inch cube of 55 durometer hardness rubber; nO may be taken from the average curve of mean load - deflection of SIlCh a rubber versus unit pressure Lb/sq. in. Then the empirical expression for percentage compression of rubber slab is: . ‘56 fl_ not, (45/__ " f ”H 4%.; In the case of a Simple shear Spring such as is shown 11: Figure 27, assuming that the Shear angle K in radians is Pstportional to shear stress arui inversely proportional to the modulus of rigidity G (according to Smith, this assumption gives a better agreement between theory and practice). Then the Shear Stress ‘3': 2; and (Y: 2% radians, where A is the sectional I -~ "P Figure 27 area of each pad, factor 2 is used because of two pads are subjected to the load P; (the modulus of rigidity G depends on the durometer hardness of the rubber and may be estimated from the curve of modulus or rigidity versus durometer hardness). To calculate us deflection S , if the shear angle X is known, 8:.- A-Iém 3’, ( 3' will be figured from the above equations). In case of cylindrical shear springs such as those shown in Figures 28-29, in most practical cases where A. z-‘<4’ the shear stress will be: ,0 27: ’76 l - and the deflection will be: : _ ,. . n __ a 72 he; ’4: In this case, a similar type which is sometimes used is called constant stress, for which the deflection formula is: p ( a: (f; "' 67/12”: 5-— In which 3': _____.f:..__ cnrh ‘ \g ’45,. ,2 ~ r ‘Vrgi— ‘v’ LL' .1; I Figure 28 “9 p K 1 1:: \Ul , A , ’1...— ',, ho ' “A Figure 29 For cylindrical torsion with constant length h (Figure 30) the Shear stress f=g7 and obviously the maximum 6/ ‘* shear stress ‘3'": ”7)_ , and for small angles of LIZK‘A. deflection: " . 5.. 6) _ [/17 4,7 f; a " ’7‘: ’56 ”‘32: “a” 1 //f t . /‘° S .= 3 ,9‘ ”i , Figure 30 PART IV AIR AS A SUSPENSION MEDIUM The use of air as a medium in suspension systems is a reasonably new development considered for production. As in the case of any other new product, the designer had to make certain that the new development would be able to produce all requirements needed for a better system, so it was neces- sary to submit the air suspension system to a series of rigorous tests. This system was tested on different types of vehicles, such as coaches, city and highway commercial vehicles, and was compared with similar conventional suspen- sion systems under the same conditions. The air suspension system is arranged with many differ- ent combinations as far as bellows arrangement and axle positioning is concerned. In most of these systems a level- ing valve is introduced which controls the flow of compressed air to and from the bellows, and many different designs were tested before a practical device was obtained. A complete air suspension system was revealed by General Motors in 1953. The durability and service of the various units involved in this system were tested by General Motors Truck and Coach Division on a total mileage of 50,000 on a Belgian Block road. The test was carried out on eight different types of vehicles. 50 Studies were also made of the effect of the system on steer- ing, braking, roadability and tire life. In the General Motors' design air is contained in four air beams, two for each axle, and two rubberized nylon cord bellows are mounted below each one of the air beams to serve as the deflection media. As mentioned before, rubber is used in most parts of air suspension systems because of its high flexibility and other favorable characteristics. There is no metal to metal contact between the axle and chassis. (Figure 31) Compressed air is supplied to a leveling valve which, :in turn, meters it to the suSpension system. This medium lies a very desirable characteristic in its instant response tca the slightest vibration, especially in the high frequency Iwanges, because there is no friction to overcome with com- pressed air. It also has, what is called, a progressive rate C317 deflection. This is shown on Figure 32 in which the rate C317 deflection at different ranges of load is plotted against the load. Frequency of a leaf spring at different loads is I>3uotted and compared in Figure 33 with the frequency of an 811 1' Spring . Another advantage of this system is its relative com- IDELctness, which enables the vehicle to have a shorter turning I-‘<“=i<:lius. This is important, especially in the case of city c(Benches. This system employs radius rods to bear the task of keeping the axles positioned properly as designed. (Figure 31) 52 Figure 31 “8‘ .Zéa/ajkw?§2 _ -— _—_—-——- t s be ‘5 $5 3.3 ‘H Q X i . 9 u" «60 ‘55“, ‘ gigoo AZUg’AAS. Figure 32 242;. axe/w. \ ( \ \996' \‘531 \q ’1’}- j/V'. \_3 [M lbs. 4 Figure 33 O\\J'l :0) M H Air Inlet Inlet Valve Seal Arm Check Valve Link \0 03\l 100 11. Figure 3h Needle Valve Arm Shaft Exhaust Valve Bellow Air Beam 5% Low maintenance cost is another advantage of this system. Spring replacement is eliminated, since there is no metal fatigue. This system is noiseless, because all joints are rubber bushings with no lubrication required, and long life can be expected because of good absorptivity of Shocks. Leveligg'Valve. The most critical component of this system is the leveling valve. General Motors uses three valves mounted on each frame. Their function mainly is to maintain the correct riding clearance between body and axles. A gradual increase in weight causes the bellows to flex and the loaded body settles towards the axle. As this happens, the axle connecting link rises and forces the arm (A) to rotate in a clockwise manner as shown in Figure 3%. This rotation forces the inlet valve upward, the exhaust valve remains in a closed position, and the air from the auxiliary air tank rushes through the air inlet. Its pressure forces open the check valve and rushes down the air feed line through the air beam into the bellows. The bellows eXpand and the increased air pressure returns the vehicle body to its original position. Conversely, as the load is decreased gradually, the body of the vehicle rises and this causes the connecting link to lower and the arm to rotate in counterclockwise motion and this, in turn, forces the exhaust valve open while the inlet valve remains locked. The compressed air in the ex- panded bellows, discovering an outlet, rushes through the air feed line, past the exhaust valve, and out the exhaust port, 55 so the bellows deflate and return the body to its original position with respect to the axles. This arrangement results in constant frequency and the same riding quality regardless of whether the vehicle is loaded or unloaded. Figure 35 shows deflection characteristics on a transit coach equipped with one pair of rear bellows. S4 \; ‘aL - If Q 6&9”: \ a 3.. av ’4» e 5 5 i —A 0 am 60” I'm ‘ Koaa/ (6.5. Deflection characteristic of 51 Passenger G. M. Coach (Equipped with one pair of real bellows) Figure 35 The important factor in the leveling valve is that it never admits or exhausts air except when the load is changed gradually, normal movements of the axles which occur when the coach is moving over rough road have no effect on the leveling valve. This is accomplished by means of a damping device. Most of the quick road Shocks are absorbed by rubber bellows. 56 In air suspension system, radius rods maintain the positions of each axle against lateral, longitudinal and torsional movements. These torque rods are equipped with rubber bushings. Rods are mounted in a fore and aft direc- tion above and below each axle so that they absorb all kinds of forces, such as longitudinal, driving, and braking. General Tire and Rubber Company has developed an air suspension system which employs long air bags connected to a compressed air tank. The eXperiment on a 66 inch trailer air bellows, made by this company, Figure 36, Shows a deflection vs load curve (Figure 37) for a change of air pressure in the bellows. Figure 37 Note that the Spring rate (slope of line drawn tangent to the h1.8 Psig curve at 6 in. height) which is applied to 57 two wheels is h500 lbs. at the design height of 6 in. Most leaf Spring installations are more than double this figure, or 5000 lbs. per wheel, thus, even when a vehicle is fully loaded, the air spring has a decided spring rate advantage over conventional springing. Air Springs Made by_"Air Lift" Company A series of experiments to determine spring rates were carried out on two different units of Pneumatic Spring Boosters made by "Air Lift" Manufacturing Company of Lansing, Michigan. The data and curves for various characteristics of the units were obtained and are discussed in this part. (Figure 39) The "Air Lift," as it is called by the manufacturer, is a combination of rubber, air, and steel as far as the medium is concerned. The bellows, or air bag which is the major part of both of the units can be inflated up to any definite pressure through the valve furnished at one end. This results in a considerable change in spring rate as a whole. The coil spring is used mainly as a container of the air bag. Accord- ing to the manufacturer, the initial air bag pressure should not be less than M Psi, and for safety it should not be more than 12 Psi. The following table gives the required inner pressure when used on passenger cars overloaded at the rear end. 58 Rear Wheel Overload Lbs. Initial Pressl Psi 50 h 100 6 150 8 200 10 250 12 In making the spring rate tests on the "Air Lifts" the air bag pressure was started from 2 Psi and carried in steps up to 16 Psi. In each of the eight steps the deflection and force were measured, and in few cases the hysteresis curve was also obtained, (Figures hl-h2). The first measurements were obtained with the air bag at atmospheric pressure, to obtain the stiffness of the unit itself (including coil spring and non-inflated air bag). In the case of the smaller unit (F-lOO), the 4m“ was 10.75 in. (see Figure 38) and the minimum height due to deflection was 7.75 in. There- fore a maximum deflection of 3 in. was obtained. The re- quired force was measured every .5 inches of deflection. Figure 38 Tables 1, 2, 3, h, S, 6, 7, and 8 are shown on the following pages, and the results are illustrated graphically in Figures 38-h0-h1-h2. The starting heights were the same in all cases. 59 Initial height 10.g5 in. Height of base a, l .9 Thickness of upper flange .2 Total length .6775 Air Lift Assembly F-IOQ (1) Atmospheric Initial Pressure Height Force Lbs. Deflection Force Lbs. Inner Inches Increasing Inches Decreasing Pressure PSIg 10.75 - - - 10.25 76 .5 5h 9.75 1H7 1.0 110 9.25 200 1.5 152 8.75 265 2.0 22% 8.25 non-uniform deflection results See Figure M1. (2) 2 PSI Intitial Inner Pressure Height Force Lbs. Deflection Force Lbs. Inner Inches Increasing Inches Decreasing Pressure PSIg 10.75 - - -3 10.25 92 .5 73 9.75 160 l. 120 9.25 236 1.5 180 8.75 31h 2. 275 8.25 532 2.5 532 non-uniform deflection (3) h Lbs./Sq.In. Initial Inner Pressure 60 _.._._. Height Force Lbs. Deflection Force Lbs. Inner Inches Increasing Inches Decreasing Pressure PSIg 10075 - - " l. 9.75 123 1.0 - 8 9.25 150 1.5 - 10.5 8075 330 2.0 - 15.1 8.25 532 2.5 21 (h) 6 Lbs./Sq. In. Initial Inner Pressure Height Force Lbs. Deflection Force Lbs. Inner Inches Increasing Inches Decreasing Pressure PSIg 10.75 - - -10 6 10.25 98 .5 76 7.6 9.75 18“ 1.0 132 10. 9.25 265 1.5 320 13.h 8.75 370 2.0 370 18.2 (5) 8 PSI Initial Inner Pressure Height Force Lbs. Deflection Force Lbs. Inner Inches Increasing Inches Decreasing Pressure PSIg 10075 - " 'l‘} 8 10.25 10M .5 80 9.h 9.75 19M 1 . 139 13 9.25 28% 1.5 210 15.5 8.75 H10 2 350 20.2 8.25 620 2.5 620 23. I 61 (6) 10 PSI Initial Pressure Height Force Lbs. Deflection Force Lbs. Inner Inches Increasing Inches Decreasing Pressure PSIg 10075 at): - - 10 10.25 1 0 .5 110 12 9.75 230 1.0 183 15 9.25 27 1.5 266 19 8.75 61 2. 908 29.3 8.25 66h 2. 66M 32 Note: Initial force to restore the initial height is 35 psig- —___ (7) l2 PSIg Initial Inner Pressure Height Force Lbs. Deflection Force Lbs. Inner Inches Increasing Inches Decreasing Pressure PSIg 10075 - - - 1.2 10.25 105 .5 75 1h.2 9.75 198 1.0 lh5 17.1 9.25 305 1.5 320 21.5 8.75 5H0 2.0 380 27.5 8.25 686' 2.5 620 31 (8) 1% PSI Initial Pressure I Height Force Lbs. Deflection Force Lbs. Inner Inches Increasing Inches Decreasing Pressure PSIg 10.75 h 0 - 1% 10.25 180 .5 75 16 9.75 278 1.0 19% 19,5 9.25 388 1.5 228 2% 8.75 581 2.0 3 75 30.h 8.25 759 2.5 590 38.8 7.75 1H2h 3.0 1350 52 62 (9) 16 PSI Inner Pressure Height Force Lbs. Deflection Force Lbs. Inner Inches Increasing Inches Decreasing Pressure PSIg 10.75 92 0 71 16 10.25 195 .5 158 17.9 9.75 280 1.0 228 22.2 9.25 922 1.5 326 27.5 8.75 58% 2. 500 39.2 8.25 832 2.5 720 85.2 7.75 1961 3. 1h61 5 .8 (10) Coil Spring Deflection Data (Container): Height Force Inches Lbs. 5. 0 8.8 18 Initial Height was h.g 36 53‘ inches. 3. 3.3 60 Curve illustrated in 2. 78 Figure MO. 2.3 92 63 75 e / " I l /‘ [Orce .133, E ; I . I / ar . -700 J/ J _,./, 3 2 fly 4a 02/: W .W CC/"/~5P/’/Og A/QZ/FT 52,,57 5005/9.»— y’mfit Fl/oo 151-0: V5 Def/6J0” of Var/I9 v: lflI/‘Ia/ //7//a//an [Dressy/25 ( 74y. 39 j 64 A} Z}// ._ {jar/W 537 005/92) 5,6,7 # F: /m I [mamas/(0.7 23' 927 ,4“ 1;; "Egg-2:15.: . ,r VI \ rflorce - 427767/‘06/6/73 7.32:5. 50:9 /5, Zoo» /00 .. / z 042/7. m [M fib' / .. J”... é‘yfld/m€$AV/C /:/’ 6.315. ("221753 c}. . " o I 00)} fr. mo Ar 63; 455 V3, [Jeféec‘en 65 The following data were taken from the test on the larger size of "Air Lift" A-100. height 1”,”: 12.22 and minimum of 4”,.” = 6.22 inches which is a deflection of six inches. The coil spring alone was subjected to the deflection test and the following tables and curves were obtained. (Table l). The other tables and curves were obtained for different initial pressures inside the air bag. The (Figure 83). The initial i .Ai i... _ ,]._.. Figure #3 starting height was the same in call cases. TABLE I Coil Spring Only - Initial Height 17.78 Inches Deflection Force Inches Lbs. 1.0 102 2.0 200 3.0 292 1+.0 378 5.0 M68 6.0 5h0 7.0 618 8.0 7190 9.0 802 10.0 882 11.0 980 I TABLE II 2 PSIg Initial Inner Pressure Deflection Increasing Decreasing Inner in Force Lbs. Force Lbs. Pressure Inches PSIg 0 600 580 2 1 7h0 715 3.3 2 880 8h0 9.5 a 1050 1000 6.7 1270 1185 10 5 1965 1h65 15 TABLE III M PSIg Initial Inner Pressure Deflection Increasing Decreasing Inner in Force Lbs. . Force Lbs. Pressure Inches PSIg 0 620 610 h 1 800 770 5.1 2 950 910 68 3 1100 1065 9.1 h 1290 1235 13 5 1580 15 0 18 5.h9 1700 1700 29.5 TABLE IV 6 PSIg Initial Inner Pressure —‘ Deflection Increasing Decreasing Inner in Force Lbs. Force Lbs. Pressure Inches PSIg 0 6h0 620 6 1 820 800 7.7 2 1000 960 9.7 3 1150 1120 12.h h 1320 1320 16.6 5 1620 1590 22.h 5. 1860 1860 28.8 TABLE V 8 PSIg Initial Inner Pressure Deflection Increasing Decreasing Inner in Force Lbs. Force Lbs. Pressure Inches PSIg 0 660 625 8 1 880 890 10 2 1020 998 12.2 3 1200 1160 13 h 1385 1360 19 5 1675 1690 25.8 5.59 1870 1870 37.8 TABLE VI 10 PSIg Initial Inner Pressure Deflection Increasing Decreasing Inner in Force Lbs. Force Lbs. Pressure Inches PSIg 0 682 - 10 1 885 865 12.2 2 1080 1005 15 3 1230 1180 18 h 1h00 13h0 23.1 5 1650 1590 30.2 6 2280 2280 — TABLE VII 12 PSIg Initial Inner Pressure Deflection Increasing Decreasing Inner in Force Lbs. Force Lbs. Pressure _¥Inches PSIg 0 690 - 12 1 920 - 19.8 2 1120 1195 17.9 3 1280 1222 21.96 A 1960 1900 26.8 5 1720 16h0 36.1 6 2380 2380 M2. 1h PSIg Initial Inner Pressure ~m- M TABLE VIII 68 Deflection Increasing Decreasing Inner in Force Lbs. Force Lbs. Pressure Inches PSIg 0 790 680 11+ 1 980 915 17.5 2 1150 1080 21.1 3 1350 1230 2h.8 5 1890 1770 36.6 6 2320 2320 51.8 TABLE IX 16 PSIg Initial Inner Pressure Deflection Increasing Decreasing Inner in Force Lbs. Force Lbs. Pressure Inches PSIg 0 800 - 16 l 1030 - 19 2 1220 - 21.5 3 11+L+0 - 21+ 9 1638 - 31 5 1950 - M7 6 2660 53 v— --wwc—np -p. .. 69 Force“ 11115 0- 2 : i a :6 a r A. [a #— oa/Z In W ( r7744 ) Def/226m of 602/ Jpn/73 oéne m 14% {3 m am/ 8 U /Q‘) ‘sl / M K“ / X ’5‘” / / ’11?!) A500 ( 743. 45 ) 41f [If/gj/f/y (5.... __ ‘ 4562'” MI? #34400 //M farce Ks. Def/e ch‘a/w (Ina/6051773 - decays/(.9) Var/‘04! /n/°//’o//?7/b/Abn Prefix/r55. 60° 1 / z 3 4 7 De/kc/ion IN. 2% sq §> 40 ‘ / ”a t v‘ 30) g /, 1 20 {I Q I s (6 Zaw /0 J / 0 i 2 3 3 5‘ I M in 11V. / at» am/ 4. mo I . . 4 \0. (21,17 6) / N / '3 a \ I I Q g9 '0 / / fi / my » | / , 4’ / 123$ / / / I , / [fr [/4 Jar/37W fluor- ’ M/ r .4400 / I farce VJ. aflxfi'afl 4/ / Var/aw: /}7/9‘/a//0m wares, / / / 60¢ ‘ / 6% 7 a 3 7‘ —- s a 99M //7 [M (297-47) PART V USE OF LIQUIDS AS A SUSPENSION MEDIUM Liquid is a comparatively new medium for use in suspen- ssion systems, though it has been commonly used in damping cievices such as shock absorbers. Liquid springs, at today's stage of development, have \Jery few advantages and numerous disadvantages compared to sateel or air springs. Comparing this type of spring with the conventional sateel Spring, it has been shown that the frequency of the Iliquid spring is much higher than that of the steel spring. flDhis is because of the extremely small mass of the piston member. The energy absorption range, as compared to the steel 53pring, is also very high, as shown in Figure M9, for 5 in. Cieflection due to a force of 8500 lbs., the energy absorption an5 about 21,250 in.-1b. This characteristic might be advan- 1:ageous whenever the system is used for heavy load application As the force per unit of deflection is very high, the Ilse of a levering system is always necessary to get a desir- This, however, is a dis- eable spring rate for the vehicle. Rate .advantage, due to the cost and complexity encountered. <3f deflection in this type of spring is around 2000 lb./in. 71 72 (tuith the liquids used today), and the comparison of the sxize of the unit with a steel coil spring, having the same Irate of deflection, shows that it occupies only one-third (bf the volume of the latter. This space saving could make :it very convenient for installation on heavy vehicles. Quite a few disadvantages are apparent in design and rnaintenance problems, some of which are listed as follows: 1. Problems involved in design of high pressure chambers as far as material, cost and weight are concerned. 2. Sealing difficulties at high pressure together with close tolerances desired. 3. Problem of producing a desirable frequency for the system by means of a levering system. A. Maintenance and repair difficulties especially in field operation. Among the suspension systems employing liquid as a part c>f the medium, the system employed by the Citroen Motor Car Clompany of France is described here. It is in reality a klydropneumatic design which completely replaces the rear ssuspension system. Citroen uses this system as optional eequipment on the company's six cylinder sedan, and applies :it to the rear wheels only. Each rear wheel is mounted on an oscillating bar and lincorporates a gas filled sphere. The weight of the car and 1She influence of the road shocks act on a cylinder filled 73 with liquid under pressure. The connecting rod of the piston in the cylinder is mounted on a slide on the under position of the body. The piston compresses the gas contained in the sphere by means of liquid acting on a diaphragm within the sphere. The liquid, which is of the nature of that used in hydraulic brakes, is delivered under pressure and passes through calibrated holes to assure the absorption of shocks. (Figure 88) The liquid pump is installed under the hood and consists of a compact seven-piston pump, driven by a belt from camshaft pulley with the same speed. A fluid tank is also installed under the hood. A regulator valve, operated by accumulator pressure (which has a higher pressure than that of the line), provides constant liquid pressure in the cylinder whatever the engine speed might be. The weight of the system is practically the same as the torsion bar used on the same type of vehicle, but cost is obviously higher. An auxiliary advantage of this system is that the higher pressure of the accumulator is used for jacking the vehicle up by means of a three-way valve in the trunk compartment which connects the accumulator line to the cylinder. This can be done without having run the engine for quite a length of time; but in order to build up pressure again a run of 15 seconds of the engine is enough. Road tests revealed a high degree of riding comfort and there were no short wave vibrations. 0n winding road, there 71, was little tendency for the passenger to be moved laterally. As mentioned before, the above system is not a pure liquid system. The first type of spring using only liquid as the medium, was introduced by George Dowty of England in 19M5, using silicones and fluorocarbons as the spring medium. This system is also combined with a dampening valve. é) €3€3C3 . :9 q; I, Q0 a 1.1 i @7 Q\l . I, (‘2 ~// Compressed gas chamber Liquid separated by diaphragm Three-way valve (two ways connection at each position) Accumulator Pump Regulator (operated by accumulator pressure) Check valves (one way only) Reservoir Chassis frame rail Spherical re se r'volr Roll stabilizer bar HOOCDQ®\.n-F'WR)H FHA Figure M8 75 The first liquid suspension attempt in the United States was on a heavy vehicle, and was installed by Wales Strippit Company in 1953. For this vehicle a unit of 8500 lb.-force capacity with a stroke of 5 inches was used. (Figure M9) The liquid had a compressibility of 12% at 20,000 psi. The schematic design and deflection curve is shown in Figure 89. 8500 Farcev .16. [1 1K 3000 Zone loco l r 1.0 2.0 .20 4-0 JKraée in inc-63$ Figure M9 Another unit also designed by the same company later, was proposed for installation on light vehicles. This unit can be levered to a stroke of 2.3 in. The Figure 50 illus- trates the schematic design of this unit. The spring rate in the following unit (Figure 50) is about 2000 lb. per in. of deflection and the ultimate pres- sure of the liquid is about 180,000 psi. The problem of lubrication is another important factor in case of liquid springs, since liquids of high 76 Figure 50 compressibility are not good lubricants at extremely high pressures. The presence of very high pressure makes it important that any sealing material be backed with well designed structural members. It is also obvious that the life of any sealing material will be increased when the length of the travel is decreased. EXperience with suitable seals shows that leakage will be held to nil for a seal clearance of .001 to .002 of an inch. I As a conclusion, the direct action of levered liquid springs, as they are now known, is suited only for heavy ‘vehicle applications. PART VI A DISCUSSION OF VIBRATION DAMPERS There are several types of damping which effect the motions of a vehicle body. In this discussion some of the more important types will be covered. 1. Coulomb damping. This is the mathematicians' ideal- ization of dry-friction damping. It is defined as a constant resistance to motion, regardless of relative velocity. It is approximately found in practice as the result of rubbing between two dry surfaces. It is also present in liquid dampers when a relief valve is used in the system. The equation of friction in this case will be: F=r~N where l‘ is the coefficient of friction (kinetic) and N the normal force. This type of friction generally predominates in damped free vibration during the final stages of the motion when other types of damping become negligible. As the above equation shows, the frictional force is independent of the displacement and, therefore, in a harmonic oscillation the decay of amplitude due to above force can be determined by considering energy dissipation. 77 78 Assuming a body with mass m, oscillating in the X direction, using a spring of stiffness K, and providing only coulomb damping is present, the change in kinetic energy of the system will be equal to the amount of work done (assume only a half cycle). (Figure 51) I x \ K Figure 51 .Xo being the initial amplitude, b the change in.amplitude per half cycle: 2.4 “18.2-(fi-6f]: Fm, x043) Therefore, during a R- , _ _ --.V If~\.\‘ F complete cycle the decay ‘ \\\\, \\\,§? I I“ \\ will be: h F/ ‘R\ J/?\\\\\\\ and the oscillation will i )\’// decay linearly as shown , 3,- here in Figure 52. Figure 52 2. Yiscoug damping. This type of damping is character- ized by a resisting force which is linearly proportional to the velocity of motion. It is found where there is a rela- tive motion between two well lubricated surfaces, and where 79 a viscous liquid is forced through a relatively long passage of small cross-sectional area. In this case, as with any other type, damping is associ- ated with energy dissipation. The resisting force is propor- tional to the velocity of motion: F = -C V' Conventional automotive shock absorbers are based on this basic relation. For free vibration of a spring-mass system with viscous damping as shown by Figure 53, the equation of motion becomes: rn:z7—— c: " /<:c _" DC ’ c K h') 7 Figure 53 Assuming a solution of exponential form, such as eSt, the above differential equation can be written as: (52+—;C,,—5+/7,”5—) c5530 The solution of this equation gives three different answers, each one of which contains the quantity 3.2% it (2”?) ‘ 25' 80 Evaluation of the answers results in two cases of non-oscil- lating motion and one of decaying oscillating motion. The following is the procedure used to analyse each case: Remembering: ZV/f/T) :: q, , V7.7? : a) ’71 .- and also, % - 3 C the answers of the last equation will be: 5,, =[—-3-t/5—2:]w. If the radical is real (§>/ ), S1 and 52 are negative, the equation of motion will be the sum of two decaying exponentials and aperiodic, such as: g 5't x :fle ”(+593 /\ t (See Figure 58) Figure 5% When :5 : 1, radical becomes zero, the equation of motion .7.) a will be in form of: 95:644-803 " aperiodic. , which is also This is called critically damped motion. (See Figure 55) 81 When §035" ,2 TI \§ lXSFn?’ ‘ ’\\ l I in . Figure 56 The frequency of motion will be: / 6:272 "3'2 “4» which is lower than.ag’, the natural frequency of the system. As the equation of motion indicates, the decaying envelope 82 of the oscillation is the curve of: ‘Sfagfié 2:)(4 3. Hydraulic damping. In this type of damping the resisting force is proportional to the second power of velocity, therefore, the equation of the friction force will be expressed by: £3 /E-:: If 67'95’ Assuming harmonic motion, 3C .1 --X. Caswg Then, in determining the work absorbed by such a damper in one complete cycle: +X. W: -—Z 61sz 'X o and by substitution, Figure 57 83 Compgzigon of vagious dampers and equivalents, In order to be able to evaluate various dampers, viscous damping is taken as the base of comparison. For example, if the rela- tive damping efficiency of a system such as the one already mentioned is to be determined, the amount of work per cycle should be equated to the amount of work per cycle of a vis- cous damper, considering that the amount of work per cycle for a viscous damper is: .AV‘:-— 73gz’ so the equation will be: ac ouxz _. 2 3 a? O ’94“) X0 and therefore, the equivalent damping efficiency of a hydraulic damper is: —§—Q—wx eg’3775 ° A. Solid dgmping. ‘Whenever a damping force is propor- tional to the diSplacement and independent of frequency the system is called a solid damper. This is mostly the case with structural members and the force equation will be in the form of: Fz-X/q/X 8h I'a non-dimensional factor and K spring stiffness. Although damped oscillations are never really harmonic, in this case only, (since 3’ for structural material is small) the motion during one cycle can be assumed harmonic and work equation will be: 2’ AW: 72%; x. = 77: wrx. Experiment indicates that in this case energy dissipa- tion is independent of frequency and proportional to the square of the amplitude, which means the above equation is based on a Justifiable assumption. ' In general, a convenient way to determine the amount of damping present in a system is to measure the rate of decay of oscillation. Usually the natural logarithm of the ratio of two successive amplitudes is: 5:47): 2 In the case of oscillatory motion the equation of amplitude is: QC :: Xe—jw,,55m( #32 6041+ c?) and, 5;,,(//_ gzwflg+¢) is equal to 1.0 at each peak, 85 "3%é 3w," 7 therefore, 5’ =4, :———’- :47 6’ 3a),(:j+‘7) : 1,, 6 :: fwm é 2 6’ This is called "logarithmic decrement." Remembering: Effl:.__":§321_1_ W'- “‘6 The logarithmic decrement will be: s- i”? from which the damping factor of the system can be calculated. CONCLUSION When comparing the types of springs discussed in this paper from different points of view, such as energy absorption per pound of material used, spatial problems, load and deflec- tion characteristics, and material-production problems, as well as inherent damping efficiency as put in the table below, the conclusion is apparent that no particular type of spring is superior in all respects to the others. a o Q) m H E U) 4.) m +> s o w o 94H GT! 0 0H :4 O :>.o+2 '60 >> +J O > >5 PH") Q +3 U) U) «P HP-H (U C. HOD-H .0 p. H u—IOH O HES-a <: o .4 wfi0)m r1e4 wivim Hr! nap mp nap m >143 (6.0 COCO-10 -H 0 $80 GD 1203:: or-I m Roam A :3 {403:6 cu Fatm u +1 aficih m'd «4:39 H (DI-H (U H 0') C5 +3 O U) (U CD so as own my was > mIz 01m (:00 2:0. goo «m __._ I ' 7 Leaf ’ |+ b. 5 I 2 I 5 .:r I I | I . h I co Steel Coil I 3 2 I 3 I 2 (5 I I I I I . cn Torsion 2 X I 3 5 I h (J I ‘ . U Rubber I l X i 2 1 II 6 (3 ‘ I 2:: Air I x I 3 1 h I 1 I (G .3' Liquid 6 1 6 6 3 .33 (Numbers indicate the degree of superiority, with l as highest.) X - Indicates multiple answers (can be given according to the condition to be met). 86 87 If each of the factors listed in the tabular columns is given equal weight a numerical average of the factors may be made. This average is shown in the last column on the right. This weighing of the various factors would place air springs as most preferable, with rubber next in order. Coil or torsion bar springs are next and are of approximately equal merit. Leaf springs are fifth, with liquid springs last. A survey of present practice indicates that these factors are not weighed equally, and that other advantages and disadvantages besides those listed in the tabular com- parison are important in choosing the type of spring to be used. Present American automobiles use coil springs at the front and leaf springs at the rear with few exceptions. Longitudinal torsion bars are used on one make and two makes use coil springs front and rear. The commercial vehicle field uses leaf springs almost exclusively, with only one manufacturer producing an appre- ciable number of torsion bar suspensions. Air suspensions and rubber suspensions have not as yet progressed much beyond the experimental stage in public acceptance. The ability of the leaf spring to act as a positioning member as well as a spring, coupled with its ease of fabrica- tion and its relatively low cost have counterbalanced its linear spring rate, its unpredictable damping characteristics, and its low energy absorption per pound of weight. The use of coil springs for front wheel suspensions became necessary 88 when spring rates dropped to a point so low that the leaf spring could no longer function effectively as a positioning member. The ability of a spring system to provide a non-linear spring rate with change in deflection is quite important for vehicles whose unloaded weight is a small proportion of their loaded weight. Trucks have this characteristic, and to a lesser extent, so do very small automobiles. The use of air or rubber springs, or non-linear adaptations of mechanical springs, could make it possible for the unloaded truck to have nearly as smooth a ride as the same truck when loaded, or for a small light car to have nearly the same ride with one passenger as it does with four. The choice of the spring medium to be used on future vehicles will be based on the factors discussed in this thesis, but the relative weighing of the various factors will change from time to time as new techniques and new cost factors are developed. I n. ! .n BIBLIOGRAPHY "Fundamentals of Suspension," H. E. Churchill, P. G. Hykes, and M. Z. Delp, Studebaker Corp., S.A.E. Annual Meeting March, 19h6. "Liquid Springs in Vehicle Suspensions," Paul H. Taylor, Wales-Strippit Corporation, S.A.E. Annual Meeting, January, 1955. (S.A.E. Journal, December, 1955) Literature on Suspension Systems: S.A.E. Journal, January, 1938, 19M6, 195%; Automotive Industries, July, 195%, December, 195%. Mechanical Springs, A. M. Wahl, Westinghouse Electric Company, Canton, Ohio. Mechanical Vibrations, Thompson, New York: Prentice-Hall. "Packard Torsion-Level Suspension," McFarland, Studebaker- Packard Corp., Automotive Industries, October, 1955. "Rubber Suspension," J. E. Hale, Firestone Tire and Rubber Company, S.A.E. Journal, 19h6. "Trends in Commercial Vehicle Suspension," N. Hendricson, S.A.E. Journal, March, 1939. "What Motor Cars Can Be," 3. Stout, S.A.E. Journal, January, 1930. 89 "Iifl‘tlflflfufluumumm IWWMHIHIIHIEITW ES 7646