# 外文翻译--麦弗逊悬架侧载螺旋弹簧优化设计（含word版）

International Journal of Automotive Technology, Vol. 9, No. 1, pp. 29?35 (2008) DOI 10.1007/s12239?008?0004?y Copyright © 2008 KSAE 1229?9138/2008/038?04 29 OPTIMIZED DESIGN FOR A MACPHERSON STRUT SUSPENSION WITH SIDE LOAD SPRINGS J. LIU1)*, D. J. ZHUANG1), F. YU1) and L. M. LOU2) 1)State Key Laboratory of Vibration, Shock and Noise, Institute of Automotive Engineering, Shanghai Jiao Tong University, Shanghai 200030, China 2)China Spring Factory 291, Yunchuan Rd., Shanghai 200071, China (Received 23 February 2006; Revised 20 October 2006) ABSTRACT?Undesired lateral force inevitably exists in a MacPherson suspension system, which is liable to damper rod’ s side wear and promotes the damper’ s inner friction decreasing the ride performance from the suspension system. Substituting a new side load spring with curved centerline for the conventional coil spring has been proven able to solve these problems and Multi-body Dynamics combining with Finite Elements Analysis may be an efficient method in optimizing its design. Therefore, taking a passenger car as example, a detailed multi-body dynamics model for the suspension system is built to simulate forces exerted on the damper and the minimization of its lateral component is selected as the design target for the spring. When the structure optimization of the side load spring is performed using FEA software ANSYS, its vertical and lateral elastic characteristics, supported by test data, are analyzed. After importing FEA results back to the suspension system, the dynamics simulation can be performed to validate the optimization result. KEY WORDS : Multi-body system dynamics, Optimization design, MacPherson suspension, Side load spring 1. INTRODUCTION Due to its simpler structure and lower manufacture/service cost, the MacPherson strut suspension has been one of the most popular suspension systems. However, the side force FQ inevitably exists at the top of damper rod as shown in Figure 1. This side load may increase the inner friction between damper parts and result in damper rod’ s side wear. Moreover, when cars with MacPherson suspension are running on an even road, vertical vibration may be transferred to the body directly since the slight road excitation couldn’ t overcome the inner friction to operate the suspension properly. Therefore, it is very important to reduce the side load ? FQso that the optimized suspension system can protect damper parts and improve ride performance for the suspension system. The traditional solution for this side load is to incline the spring, but the install space of the suspension limits the incline angle so that the side load can not be eliminated completely. Recently, some car manufacturers adopt a new type spring with a variant centerline developed by Muhr and Schnaubelt (1989) to replace regular coil spring, which permits a spring’ s force line to deviate at an angle while the spring is pressed between two parallel planes. By designing the curvature properly, this kind of spring by itself can offset the side load so that it is named a side load spring. However, it is very difficult to directly define the stiffness from this spring’ s structure parameters since the deformation mechanism of the side load spring is still inexplicit. The design is usually based on test data so that a quicker and more economical method is demanded. Furthermore, traditional optimal design emphasizes parts instead of systems while the interactions between parts, between parts and system and between systems can greatly affect the general characteristics of a product. Therefore, the optimization of a MacPherson suspension should firstly begin from the system level. Some researchers have done much contribution for it. Figure 1. Side force exerted on piston rod.*Corresponding author. e-mail: zeh@163.com 30J. LIU, D. J. ZHUANG, F. YU and L. M. LOU In 1994, Muhr and Schnaubelt introduced side load spring’ s advantages in reducing the side force of a Mac- Pherson suspension (Wünsche and Muhr, 1994). Their research was based on physical models and the experi- mental results showed the remarkable improvement in body acceleration and damper stroke which proved the new spring’ s effect in ride comfort performance. However, their research object was only an existed side load spring and their research aim is to determine the performance character of the side load spring, while how to design a side load spring is never mentioned. In 1996, Satoshi Suzuki, Syuji Kamiya and Toshiyuki Imaizumi introduced the FEA model of side load spring to analyze the effects of structure parameters (Suzuki et al., 1996), including the number of free coils and slenderness ratio, on side load spring’ s characteristics, then discussed the arrangement of setting position of spring and tilting angle of spring seat to minimized damper’ s side force. A large number of FEA models and experiment validations are performed but their research was still limited within the analysis of performance characteristics and the design method was not involved. In 2000, Toshiyuki Imaizumi and Takashi Gotoh combined mechanical dynamics and FEA software to perform the design procedure and analysis of damper’ s friction (Gotoh and Imaizumi, 2000). In their paper, at first a FEA model for the side load spring and spring seats is built to study the effects of spring end coil angles and seat angles on side load spring’ s reaction force line. Then a new design procedure combining mechanical dynamics with FEA software was represented. At last, the authors evaluated the advantage of side load spring by comparing the reaction force axis and suspension frictions of new design with conventional springs. However, the design procedure was not represented fully and clearly, and some improvements still need to be discussed for the design procedure part of this paper, especially to design a side load spring for an existing MacPherson suspension. (1) Searching the best attach points on upper and lower seats of the scalar spring to predict the ideal force line means repeating simulation and comparison for every set of attach points, which could be substituted by an easier method. (2) How to determine the initial curvature of the spring and how to implement parameter study, especially for the curvature of spring’ s centerline is not mentioned. (3) What is the centerline of the side load spring like exactly? The paper didn’ t provided an accurate description for the side load spring’ curvature. (4) In evaluation of the suspension optimization, the comparison criteria is suspension friction which is not supported in the default MacPherson template of ADAMS/CAR module. The author may need to build a completely new model using ADAMS/CAR module or even ADAMS/View module which may cost too much time. In this paper, taking an existing passenger car as ex- ample, we proposed an easier and more detailed approach of the optimization design for MacPerson strut suspen- sion with a side load spring to reduce lateral load on the damper rod. The design flow chart is shown in Figure 2. In order to examine the forces exerted on the top mount of a damper rod, a detailed multi-body dynamics model for MacPherson front suspension system with origin coil spring is built at first, using multi-body dynamics software ADAMS/CAR. In succeeding optimization, the lateral component of the damper forces is selected as the design target for the side load spring to minimize the adverse effect of lateral force. Then the initial value of the curvature of the side load spring is derived. Subsequently, structure optimization for the side load spring is performed using Finite Element Analysis (FEA) software ANSYS, and the vertical and lateral elastic characteristics of the side load spring are analysed which are also compared with experiment data. A 2nd-order curve is obtained as the optimized curvature of the side load spring. After import- ing the FEA results to suspension system in ADAMS/CAR Figure 2. Flow chart of optimization design. OPTIMIZED DESIGN FOR A MACPHERSON STRUT SUSPENSION WITH SIDE LOAD SPRINGS31 as a Modal Neutral File (MNF), the dynamics simulations is carried out to investigate the effectiveness of the optimization design result. The consistency of vertical stiffness with original spring and the remarkable reduction in lateral force indicate that the proposed design approach is appropriate for optimi- zation of suspension systems. And the optimally design- ed side load spring can solve the lateral force problems of the MacPherson suspension and meanwhile has minimum side-influence on the original suspension stiff- ness property. 2. SUSPENSION SYSTEM SIMULATION Taking an existing passenger car as an example, a multi- body dynamics model for the MacPherson front suspen- sion system is built using ADAMS/CAR software, as shown in Figure 3. The coordination system is defined in accordance with SAE standard and the spring used is a traditional coil spring. During modeling, the dynamics parameters of the suspension system, including spring’ s stiffness and shock absorber’ s damper characteristic, are taken from experimental results, while the nonlinear characteristics of the three bushings, connecting strut top mount to car body, control arm to sub frame and sub frame to car body respectively, are also taken into account. Based on this model, a parallel wheel travel analysis is performed with the wheels moved from ?70 mm to +70 mm vertically and synchronously. The simulation results of force and the torque moment exerted on left strut’ s top mount are measured and plotted in Figure 4(a) and (b) respectively. In corresponding with the design of Side load spring, the coordination system of simulation results are changed to what uses in FEA software, e.g., the origin point is the center of spring upper coil, x axis point to the reverse of ride direction, z axis is along with the axis of spring and point upward and y axis is determined by x and z axis. From Figure 4, it can been seen that, when wheels travel, the longitudinal force component Fx is almost zero, the lateral component Fy and vertical component Fz are both approximately linear but Fz has a steeper slope. The torque moment components around z axis keeps zero, the components around the y axis are almost linear and very small, while the moment Mx around x axis is much greater and shows a strong nonlinear tendency which is certainly resulted from the components Fy and Fz. According to the force and torque simulated, the action line of desired spring force can be calculated which is the optimization target of side load spring’ s design para- meters. As shown in Figure 5, force F and torque M exerted on damper top mount can simplified to be a parallel principal force vector FO (with the same value of F) and a principal moment vector MO relating with damper moment M in form as, .(1) In equation (1), vector rTO points from the top mount of F= Fx, Fy, Fz?? M= Mx, My, Mz?? M = MO+rTOF? Figure 3. Front suspension model in ADAMS.Figure 4. Simulation results on top mount of damper rod. 32J. LIU, D. J. ZHUANG, F. YU and L. M. LOU damper (point T) to FO’ s acting point (point O). When point O moves along the action line of FO (MO), equation (1) is still available only with rTO changed. When rTO is perpendicular to FO, it is also perpendicular to the plane of F and M, then there is .(2) In equation (2), it is clear that the direction of vector v is determined by the unit vector of F and M while its value is determined by their quotient. The components of force F and torque M are available in the simulation results shown in Figure 4, therefore the action point of FO can be calculated accordingly. Since force FO is parallel to force F, the desired spring force line has the same direction with force exerted on top mount of the damper and passes point (xO, yO, zO), which can be written as, (3) or in another form as, .(4) Letting z in equation (4) respectively equal to zero and spring install height, the acting points of spring force respectively on top and bottom seats can be obtained, shown as in Figure 6(a) and (b). The structure design target of side load spring can be clearly assumed that the optimized side load spring should provide a force with a tilting angle ? determined by these two points and consistent with FO when suspension travels in order to maintain original spring’ s vertical stiffness. 3. STRUCTURE DESIGN AND VALIDATION For the original cylindrical coil spring, the main structure parameters include intermediate diameter D, free length H0, total coil number Nt, closed coil height Hc, pitch p and wire diameter d etc., which mainly determine the vertical stiffness of spring. As for side load design, another vital parameter is the curvature of spring’ s centerline which affects the deviation of spring force remarkably. 3.1. Initial Value Estimation for Centerline A spring with constant curvature centerline is a simpler type of side load spring which is easier to study and extend to spring with complex curvature. On assumption that curvature of spring centerline ? is very small, the lateral displacement of the coil during compression can be neglected. When the spring is compressed from its free height H0 to working height H, the vertical decrements on the outer and inner sides of the spring are in which and , D is the intermediate diameter, as shown in Figure 7. Within the linear domain, there is rTO= xOyOzO??T=F M? F F? -------------- - = F F ------- - M M --------- - M F ------- -?? = 1 Fx 2 Fy 2 Fz 2 ++ ---------------------------- - FyMzFzMy– FzMxFxMz– FxMyFyMx– xxO– FX -------------=y yO– FY -------------=z zO– FZ ------------ - x=x0?FX FZ -----zzO–??? y=y0?FY FZ ---- -zzO–??? ?h1= 2 ? -- - D – ?? ??arcsin ?H0 2 -------- - ?? ???H ?h2= 2 ? -- -+D ?? ??arcsin ?H0 2 -------- - ?? ???H arcsin ?H0 2 -------- - ?? ??=?H0 2 -------- - Figure 5. The principal force and moment. Figure 6. Distribution of principal vector exerted on top and bottomspring seats. OPTIMIZED DESIGN FOR A MACPHERSON STRUT SUSPENSION WITH SIDE LOAD SPRINGS33 approximately. Thus . (5) Composing corresponding vertical force on outer and inner sides as parallel forces, the magnitude of total vertical force is still as normal coil spring but its action line translates to a certain displacement .(6) According to the formula (6), the offset displacement c is in proportion with curvature of the centerline, spring’ s free length and square of intermediate diameter while having no correlation to wire-diameter. When the curvature is zero, the translation of action line vanishes as well, which matches up to normal coil springs. As for side load spring with changing curvature, the offset of spring force exerted on the bottom spring seat is cl=H tan??and the offset in section face at height z is c(z)=(H?z) tan?, , if the action line of spring passes through the centre of upper seat. Then there is c(z)=(H0?z) tan?, when the side load spring is a