附录Kinematic Characterization and Optimization of V ehicle Front-suspension Design Based on ADAMSAbstract：To improve the suspension performance and steering stability of light vehicles, we built a kinematic simulation model of a whole independent double-wishbone suspension system by using ADAMS software, created random excitations of the test platforms of respectively the left and the right wheels accordingto actual running conditions of a vehicle, and explored the changing patterns of the kinematic characteristic parameters in the process of suspension motion. The irrationality of the suspension guiding mechanism design was pointed out through simulation and analysis, and the existent problems of the guiding mechanism were optimized and calculated. The results show that all the front-wheel alignment parameters, including the camber, the toe, the caster and the inclination, only slightly change within corresponding allowable ranges in design before and after optimization.The optimization reduces the variation of the wheel-center distance from 47.01 mm toa change of 8.28 mm within the allowable range of -10 mm to 10 mm, promising an improvement of the vehicle steering stability. The optimization also confines the front-wheel sideways slippage to a much smaller change of 2.23 mm; this helps to greatly reduce the wear of tires and assure the straight running stability of the vehicle. Keywords：vehicle suspension; vehicle steering; riding qualities; independent double-wishbone suspension; kinematic characteristic parameter; wheel-center distance; front-wheel sideways slippage1 IntroductionThe function of a suspension system in a vehicle is to transmit all forces and moments exerted on the wheels to the girder frame of the vehicle, smooth the impact passing from the road surface to the vehicle body and damp the impact-caused vibration of the load carrying system. There are many different structures of vehicle suspension, of which the independent double-wishbone suspension is most extensively used. An independent double-wishbonesuspension system is usually a group of space RSSR (revolute joint - spherical joint -spherical joint - revolute joint) four-bar linkage mechanisms. Its kinematic relations are complicated, its kinematic visualization is poor, and performance analysis is very difficult. Thus, rational settings of the position parameters of the guiding mechanism are crucial to assuring good performance of the independent double-wishbone suspension. The kinematic characteristics of suspension directly influence the service performance of the vehicle, especially steering stability, ride comfort, turning ease, and tire life.In this paper, we used ADAMS software to build a kinematic analysis model of an independent double-wishbone suspension, and used the model to calculate and optimize the kinematic characteristic parameters of the suspension mechanism. The optimization results are helpful for improving the kinematic performance of suspension.2 Modeling independent double-wishbone suspensionThe performance of a suspension system is reflected by the changes of wheel alignment parameters when the wheels jump. Those changes should be kept within rational ranges to assure the designed vehicle running performance. Considering the symmetry of the left and right wheels of a vehicle, it is appropriate to study only the left or the right half of the suspension system to understand the entire mechanism, excluding the variation of WCD (wheel center distance). We established a model of the left half of an independent double-wishbone suspension system as shown in Figure 1.3 Kinematic simulation analysis of suspension modelConsidering the maximum jump height of the front wheel, we positioned the drives on the translational joints between the ground and the test platform, and imposed random displacement excitations on the wheels to simulate the operating conditions of a vehicle running on an uneven road surface.The measured road-roughness data of the left and right wheels were converted into the relationship between time and road roughness at a certain vehicle speed. The spline function CUBSPL in ADAMS was used to fit and generate displacement-time history curves of excitation. The simulation results of the suspension system before optimization are illustrated in Figure 2.The camber angle, the toe angle, the caster angle and the inclination angle change onlyslightly within the corresponding designed ranges with the wheel jumping distance. This indicates an under-steering behavior together with an automatic returnability, good steering stability and safety in a running process. However, WCD decreases from 1 849.97 mm to 1 896.98 mm and FWSS from 16.48 mm to -6.99 mm, showing remarkable variations of 47.01 mm and 23.47 mm, respectively. Changes so large in WCD and FWSS are adverse to the steering ease and straight-running stability, and cause quick wear, thus reducing tire life.For independent suspensions, the variation of WCD causes side deflection of tires and then impairs steering stability through the lateral force input. Especially when the right and the left rolling wheels deviate in the same direction, the WCD-caused lateral forces on the right and the left sides cannot be offset and thus make steering unstable. Therefore, WCD variation should be kept minimum, and is required in suspension design to be within the range from -10 mm to 10 mm when wheels jump. It is obvious that the WCD of non-optimized structure of the suspension system goes beyond this range. The structure needs modifying to suppress FWSS and the change of WCD with the wheel jumping distance.ADMAS software is a strong tool for parameter optimization and analysis. It creates a parameterization model by simulating with different values of model design variables, and then analyzes the parameterization based on the returned simulation results and the final optimization calculation of all parameters. During optimization, the program automatically adjusts design variables to obtain a minimum objective function [8-10]. To reduce tire wear and improve steering stability, the Table 1 V alues of camber angle α , toe angle θ , caster angle γ and inclination angle β before and after optimizationTable 1 The data tables of optimize the results4 ConclusionsThe whole kinematic simulation model of an independent double-wishbone suspension system built by using ADAMS software with the left and the right suspension parts under random excitations can improve the calculation precision by addressing the mutual impacts of kinematic characteristic parameters of the left and the right suspension parts under random excitations. The optimization can overcome the problem of the too large variation of WCD and overly large FWSS with the wheel jumping distance. The kinematic characteristic parameters of the suspension system reach an ideal range, demonstrating that the optimization protocol is feasible. From a practical perspective, the optimization is expected to reduce tire wear, and remarkably improve suspension performance and vehicle steering stability.Figure 1 simple picture of suspensionFigure 2 Curve with the parameters of the suspension基于ADAMS 前悬架优化设计摘要：为了提高轻型车辆性能和行驶稳定，我们使用ADAMS 软件建立一个独立双横臂悬架系统运动仿真模型，并建立随机激励的测试平台，根据车辆实际运行条件，探讨悬架的运动学特征参数的变化。