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RUCK SUSPENSION SYSTEM OPTIMIZATION
INTRODUCTION
Truck suspension systems, hardware innovations for improvements, analytical investigations to improve design, techniques for testing, and computer simulation to predict performance have been described in numerous previous technical papers. Many of these investigators have been seeking, in some sense, that elusive design which might be termed an optimum suspension system. The difficulty associated with obtaining an optimal design is primarily due to the difficulty of determining the operating environment (input) and a realistic figure of merit or criterion for optimization (output).
The fundamental purpose of a vehicle suspension system is to act as a vibration isolation system between the frame, chassis, passengers, and cargo, and the vibratory input caused by road or terrain irregularities. The lack of a firm deterministic definition of the profile to which a vehicle is subjected throughout its lifetime requires a statistical approach, that of random vibration. The author and others, for example ,have previously made some progress in the statistical definition of the input. It appears that a fairly realistic approximation of road or cross-country terrain can be made by assuming a white (equal probability of all frequencies) Gaussian distribution for the slope (or first special derivative). This can then be converted to a temporal input for vehicle vibration studies by accounting for the speed of the vehicle and the interrelations associated with following in-line wheels.
The measure of the vibratory response or output usually associated with random vibration is mean square acceleration. Studies have indicated that the proper frequency domain weighting of mean square acceleration to account for human resonances can yield a criterion which correlates with the subjective sensation of human comfort . Sinusoidal and random test specifications for components and cargo, for example, are usually associated with acceleration levels. From the standpoint of component fatigue failure there are indications that arms measurement of stress will yield a realistic criterion in a random environment.
Thus, it appears that a properly identified random input together with the proper selection of a mean square output might be used as a technique for optimization of truck suspension systems.
The author has recently completed a study to develop some of the fundamental relationships necessary for optimization of vibration isolation systems subjected to random inputs and the practical numerical techniques required. This paper presents some of the results of that study applied to the redesign of a particular truck suspension system.
OPTIMIZATION
Before exploring the procedures employed to achieve an improved design of a specific vehicle suspension system, it is of interest to briefly explore the modern concepts of optimization and systems analysis. From an engineering point of view, the techniques employed in the design of systems can be grouped into two classifications: synthesis and analysis .
The synthesis of a system implies only a minimum amount of information about a system and the normal definition is that of the input and functional requirements or optimization criteria. Based upon this information the best possible system is synthesized to meet the optimal objective. From the standpoint of systems subjected to random inputs, the rudiments of the synthesis techniques were first introduced by Wiener [9] and further developed by Newton, Gould, and Kaiser [10]. An application of synthesis techniques to vehicle suspensions was presented by Bender, Karnopp, and Paul in 1967 [1 l]. The difficulty with this technique is that it normally results in an active suspension based upon servomechanisms. Carried to the extreme this might result in a highly elaborate servo system including surface profile sensors to predict the existence of bumps prior to contact and initiate proper preventive action. While this type of suspension system may be of interest for some types of special purpose vehicles, and may even be commonplace in the future, it is not practical for present commercial or military trucks. The cost and complexity, the inherent maintainability and reliability problems, the desire to conserve weight and space for cargo, and other limitations preclude the use of synthesis techniques in the current state-of-the-art truck suspension design. The practical use of the synthesis approach is the establishment of an ultimate optimum level for the performance of a particular configuration in a particular environment which can be used as a basis for the comparison of more practical alternates.
In contrast to the synthesis approach more definitive information is necessary for the analysis approach. Normally the system configuration together with a description of the inputs and the output criteria are required in order to perform analysis. A parameter variation is then undertaken to determine the sensitivity of the output criterion as a function of each of the design parameters and/or combinations of design parameters. With this information an optimal combination of design parameters is sought either through formal optimization procedures [8] or through trial and error methods. The procedures for the application of the analysis approach, coupled with limited field testing, to improve the suspension design of an existing vehicle are described in the remainder of this paper.
PROCEDURE
The problem of interest is the improvement of the suspension system in a prototype truck. Since the actual hardware was in existence, in this case, the procedure consisted of actual field tests coupled with computer simulation. Instrumented field tests were undertaken to establish a baseline and to compare parameter variations that could easily be explored in hardware. The instrumentation results were augmented by the subjective impressions of trained suspension engineers. A mathematical model of the truck was developed simultaneously with the field testing, and results were compared to establish the validity of the model. A mathematical parameter search was then undertaken to seek the optimum suspension parameters. The results of the field-testing and computer simulation were then used to design an improved suspension for the truck.
DESCRIPTION O F THE VEHICLE
The vehicle was a large military tractor semitrailer combination called the Heavy Equipment Transporter (HET). The development of the HET consisted of a joint effort between the United States and the Federal Republic of Germany. Joint concept studies were initiated in November 1965 by the Joint Task Force consisting of Chrysler Corp. in the United States, and Krupp and Faun in Germany. The result of these studies was a concept consisting of an 8 × 8 tractor and a four-axle semitrailer. During the Phase III Development Contract with the same three firms, the concept and detailed design advanced to the hardware status with the fabrication and assembly of prototype vehicles. Differences in the national requirements resulted in variations between the United States and German versions.
The vehicle of interest is the United States version shown in Fig. 1 with a M60A1 E2Main Battle Tank as a payload. Three United States engineering test units were constructed and each tested for 20,000 miles of operation over a combination of primary roads, secondary roads, and cross-country terrain. The trailer passed all tests and has recently been designated the M747.
The tractor, the XM746, required modifications as a result of the engineering tests. While the suspension system performed adequately and there was no necessity for change, the opportunity afforded by other design modifications resulted in a program to modify the suspension for ride improvement. Thus the interest in this program was that of minor modifications in the tractor suspension only. The success of the trailer suspension dictated no changes in that area and the success of the tractor hardware precluded major modifications which could result in substantial requalification of a radically different suspension design. Two additional Advanced Production Engineering (APE) tractors were designed and constructed. One of these, the APE-l, was used for the test program at the U.S. Army Aberdeen Proving Ground Grounds. The HET tractor-semitrailer combination has an overall length of 732 in., an overall width of 137 in. reducible to about 120 in., and an overall height of 119 in. The combination curb weight is 77,400 lb, and it is designed for a payload of I05,000 lb, resulting in a gross vehicle weight of 182,400 lb. The axle loads in the fully loaded condition are below 25,000 lb. The vehicle is powered by a 600 SAE h.p. diesel engine which gives an engine governed top speed of 38.5 m.p.h. The vehicle can ford up to 5ftwithout preparation and negotiate a 31.5 % ramp with full payload. The vehicle has a26-ft long flat cargo deck with room for any tracked vehicle as well as wheeled vehicles or general cargo.
The 600 h.p. diesel engine is coupled to a power shift converter-type transmission and a transfer case. All four axles are driven, and numbers 1 and 2 also steer. The tractor has an overall length of 332 in. The suspension, shown in Fig. 2, is a spring and link version with 18 × 22.5, 20 ply rating tires. Each set of axles, 1 and 2, and 3and 4, form a bogie arrangement. The axles in each set are interconnected with a longitudinal taper leaf spring on each side of the vehicle which is free to pivot at the center frame attachment point. Each axle is separately constrained by a parallelogram link arrangement. The ends of the spring are free to slide longitudinally in blocks provided in each axle. The only damping is the inherent friction, and no shocks were provided in the original APE-1 vehicle. Heavy-duty power steering is provided with an axle-driven auxiliary pump as a safety feature. Full air brakes are used with an automatic load-sensitive control to adjust the balance in braking level. Failsafe units included in the brake system. Continuous braking is achieved by a transmission mounted retarder which is electrically connected with the semitrailer service brakes for simultaneous activation. Dual winches with a 60,000-1b capacity each are provided and a self-recovery capability is achieved by being able to fair-lead the right winch cable forward.
The semitrailer has an overall length of 513 in. with four no powered axles, equipped with dual 15 × 19.5, 14 ply rating wide base tires. The front two axles are an unsprung walking beam arrangement and the rear set of axles incorporate air springs which do not have equalization, but are provided with a lift system for use when driving without a payload. All axles are equipped wilts full air brakes, and failsafe devices are provided on two axles. Simple rear-mounted one-piece aluminum ramps are provided with an 18 deg ramp angle. Winch cable guides in the goose-neck allow the winching on and off of disabled payloads.
RESULTS
The results of the suspension optimization are summarized below in four different sections:
Test result
s1. The combination of soft front springs, lower tire pressure, and shock absorbers allowed speeds up to 180% of the standard vehicle speed on rough secondary roads.2. A decrease in tire pressure provides a decrease in both frame and wheelacceleration.3. The addition of shock absorbers reduces the wheel acceleration by more than50% and allows only small improvements in frame acceleration.4. Wheel travel was not a contributing factor to the riding quality of the standard vehicle.
Linear model results
I. Optimum damping parameters were achieved for a given vehicle speed. The optimum value varied slightly with speed.2. Optimum spring rates could be defined as a function of the severity of the course, the vehicle speed, and the probability of exceeding the allowable jounce travel (bottoming out).3. The rear wheels (axles 3 and 4) contributed more to the frame acceleration than the front wheels, and optimization of the rear spring showed substantial improvement.
Nonlinear model results
1. A small amount of suspension friction is beneficial in the absence of shockabsorbers.2. When optimum shock absorbers are selected suspension friction is detrimental.3. The linear model probability of bottoming out yielded results similar to the nonlinear jounce stops.4. Tire surface separation did not significantly affect the optimum values.
New vehicle design
A new vehicle design has been defined as shown by Table 8. This vehicle has been built and at the time of this writing is being tested at the Aberdeen Proving Grounds. Initial results are very favorable and show substantial ride improvements. The criteria for the final configuration, as summarized in Table 8, are:1. Lower tire pressures as far as possible consistent with tire wear, heat buildup, and load ratings.2. Increase jounces travel by 1 in. with new curvature to the springs.3. Reduce spring rates consistent with the optimum value for 5 in. jounce travel on cross-country courses at 8 m.p.h.4. Provide shock absorbers at all wheel locations with damping coefficients selected from available items consistent with optimum values on cross-country travel at 18m.p.h.5. Reduce interleaf friction in the design of the new springs.
CONCLUSIONS
It is possible to optimize the parameters in a given suspension configuration. This optimization is a function of the course severity and the vehicle speed. Interactions of parameter changes must be taken into account since optimum damping is a function of spring rate, etc. Relatively simple vehicle models yield realistic optimum suspension parameters even though all attributes of the vehicle dynamics are not taken into account.
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