The analysis on optimization

 [abstract] Based on the principle of multi-body system dynamics of vehicle and optimized design, the paper brought forward an approach of optimizing the main parameters and system stiffness design of suspension in vehicles, which can meet the demand of both the manipulating stability and the smoothness of vehicles. Three-dimension digital mode of twin-wishbone independent suspension and the complete vehicle was established on the virtual prototype machine, and the validity of the approach of the optimized design was validated by carrying through the emulating examinations.

1、Introduction

As the flexible link tache, suspension is a complex mechanical system composed of mass components, which affect both manipulating stability and smoothness of the complete vehicle. According to conventional methods, movement differential equations of position and state coordinate are educed in virtue of Lagrange’s equation and Newton-Euler equation. By choosing the generalized coordinate skillfully, for simple systems with few degrees of freedom simple differential equations can be educed by hand. However, as to a suspension system with more and more complicated structure and many degrees of freedom, deducing the dynamic equation by manual sign will face the very heavy algebra and differential calculation.  Meanwhile, they come to be amiss very easily. Along with the increasing of the vehicle velocity and the higher desire of manipulating stability and smoothness, the methods should be ameliorated. Multi-body system dynamics, developed in recent twenty years, provides a powerful tool to build up complex model for the systemic dynamics of vehicle. The thesis, adopting the digital virtual prototype machine technique and multi-body dynamics technique, probed into the optimized calculation of the main parameters of suspension and the matching of front and rear suspensions from such two aspects as the manipulating stability and the smoothness of the complete vehicles.

2、The mathematic model of suspension system optimized design based on the complete vehicle system dynamics

2.1 The process of optimized design

The purpose of optimizing the dynamic performance parameter design of automobile suspension system is to embody the optimum damping properties of suspension system in various driving conditions. Therefore, optimization design variables, target functions and restrict conditions should be choosed properly among the suspension system parameters, whose optimization design problems would be described as mathematic models. The parameters should be selected according with the related design request of the complete vehicle manipulate stability(considering the smoothness and other factors simultaneously ) to establish mathematic models to solve. This thesis adopts the parameterized analytical method provided by the ADAMS/ View .By firstly establishing the state variables, based on which measure function can be developed, the target of optimization is to minimize algebraic sum of the root mean square value of vertical vibration acceleration of two points, with the vehicle’s front wheel alignment parameters and suspension characteristic parameters to be used as the restrict conditions. Concrete process is showed as figure 1.

 

2.2 Establishing the design variables

During the optimization design of suspension system, the complete vehicle’s vibration should be reduced, and the running smoothness and riding comfort should be enhanced. There are nine main parameters among structure parameters of the complete vehicle suspension, which influence the vibration of the body. Considering the stiffness matching problems of front and rear suspension in the complete vehicle, we can presume and , the ideal stiffness of front and back suspension, as design variables.

Thus, we can educe the variables to be designed as follows:

2.3 Establishing the target function

The target function of suspension system optimization design is mathematic resolution of a certain performance parameter required in suspension system optimization design. This paper treats the minimum algebraic sum of the root mean square value of vertical vibratile acceleration of left and right points located in the body above the front and back axles as the target function.

Thereinto, and serve separately as root mean square value of vertical vibratile acceleration of left and right points located in the body of the vehicle  above the front and rear axle. 

2.4 Restrict conditions

The restrict conditions in suspension system optimization design mean to give necessary restrict and limitation to the range of the optimization design variables of suspension system and some performance parameters influenced greatly by the optimization design variables of suspension system. In this way, the feasibility and rationality of the result of suspension system optimization design can be ensured. The restrict conditions refered to in this paper include the structural parameters and suspension performance parameters. As to the restrict conditions of structural parameters, front wheel alignment parameters, the variation of which influence the manipulation stability, are mainly considered and can be regarded as restrict conditions. The structural parameters of suspension guide mechanism are limited by the demand of structural disposal. As to the suspension performance parameters, the matching of front and rear suspension is considered mainly.

 (1) Structural parameters’ restrict conditions

Table 1. gives the upper and lower limit values of the structural parameters , showing the way in which vehicle suspension structure influences performance of the vehicle.

table 1. the standard values and upper and lower limits of design variables

 (2) Suspension characteristic parameters’ restrict conditions

Restrict conditions of suspension characteristic serve mainly as those of stiffness matching problems in optimization design. The lateral inclination angle stiffness will dramatically influence the manipulation stability of the complete vehicle. The corresponding judging parameter is , the roll angle of the body when the lateral acceleration is 0.5g. At the same time, the dynamic earthing performance is also an important factor influencing the manipulating stability, which is concretely quantitated as ,the minimum rate of dynamic and static load between the tyres and  the ground. The symbol j can be 1 or 2, representing separately the left-front and left-back(right-front and right-back)suspensions.

Presuming ，  as left-front, left-back (or right-front ,right-back)side suspension system stiffness,  we can get relations as follows:

（3）Mathematic model

Based on the analysis above, the model of vehicle optimization analyzing system can be acquired as follows:

3、Example of engineering

The adjustment of main parameters and system stiffness of a cross-country automobile, according to the demands of inland road and the using conditions, was carried through on the basis of this thesis. The author established the virtual prototype machine for this vehicle type on the soft ware platform of ADAMS/VIEW 2005r2, and analysed the dynamic relationships between the tramping of wheel and the parameters such as the incline angle of front wheel, the toe-in angle of front wheel, the treat change, the 1/2 linear stiffness and the roll angle stiffness of suspension. All the relationships above are showed as figure 2～figure 8.By comparing with the primary suspension scheme and analysing of the disciplinarian of the diversification of many performance parameters such as the incline angle of front wheel, the toe-in angle of front wheel, king pin inward angle, caster angle, treat change quantity, linear stiffness and roll angle rate of suspension etc., according to the tramping of wheel, it can be educed as follows that:

1)  When the wheels jump about up and down, after optimizing, there is little influence upon the performance parameters such as the incline of front wheel(figure 2),the toe-in of front wheel(figure 3),king pin inward angle(figure 4), and treat change quantity(figure 5).Curves of those parameters are still identical with those of the former uncorrected performance parameters', which have already been up to the mustard on the whole.

2)  The caster angle is in the range of suspension travel. After optimizing, the diversification of which tends to be more rational than that of the primary one. Along with the increment of the upward tramping of the wheel(figure 6) , the design request is always satisfied.

3)  The changing curves of linear stiffness and roll angle rate of suspension refer to figure7 and figure8.The changing trend of suspension stiffness is gentler than that of the primary suspension. As a result, diminishing trend of suspension stiffness along with the upward jumping of the wheel can be controlled. 

4、Conclusion

(1)Based on the dynamics analysis of complete vehicle system, the paper established the calculation model of optimized design of main parameters and system stiffness of automobile suspension, which can harmonize the request of the manipulating stability and the smoothness of the complete vehicle.

(2)The author puts forward a kind of method of engineering optimization in designing suspension and the matching of system stiffness. Based on the satisfaction with the request of the smoothness of vehicles, the demand of manipulating stability is also given attention to. By optimizing the design variables, the performance of the suspension can be enhanced to some extent.

(3)It works out a sort of optimizing parameters of heavy vehicles' suspension guide mechanism, which provides theory basis for farther improvement.

 

“汽车悬架的优化分析方法及应用翻译”版权归作者所有，转载请著名出处。