Ma, K. and pang, S., "Interval Optimization of Uncertain Suspension Kinematics Characteristics," SAE Technical Paper 2011-01-0730, 2011, doi:10.4271/2011-01-0730.
The optimization of vehicle suspension kinematics characteristics is an important part in the chassis development. The current optimization algorithms for suspension kinematics parameters are certain optimization method. But vehicles to manufacture in large quantities are uncertainty in the structural parameters. Therefore, suspension kinematics characteristics are all uncertain parameters on vehicles.The paper explored an interval method to describe the uncertainty suspension kinematics characteristics and used improved interval Newton iteration method to optimize it. As we all know, some suspension kinematics characteristics are the curves. When the structural parameters are uncertain variables, these curves are uncertain variables curves. Thus, the paper present that uncertain suspension kinematics characteristics' curves are regarded as interval parameters curves; certainty suspension kinematics characteristic curves are regard as middle curves, suspension kinematics characteristic boundary curves are regard as interval parameters curves upper boundary curves or low boundary curves. At the same time, uncertain suspension structural parameters are also regarded as interval parameters' radius;at the same time certain suspension structural parameters are regard as interval middle value; the errors aroused by manufacture are regard as parameters' interval radius. Newton iteration method is improved used by interval method for interval optimization. The sensitivity of the single suspension kinematics curves to single structural parameter should be computed in the every iteration. The affect to uncertainty of the suspension kinematics curves should be computed too when single structural parameter error changed. After a few iterations, the reasonable structural parameters and errors can be found. At same time, the suspension kinematics uncertain curves should be controlled in the given and necessary interval.Using this interval optimization to find the proper interval variable rapidly, and find the interval optimum solution are feasible. Therefore, this interval method not only could shows the certain optimization result but also could shows the reasonable parameter error.In the example, aiming at an off-road vehicle suspension kinematics characteristics uncertain optimization problems is computed by interval optimization. Both uncertain curve of toe angle vs. wheel vertical travel and uncertain curve of camber angle vs.wheel vertical travel are optimization objective, hardpoints' coordinate and their uncertainty are uncertainty parameters. After the interval optimization, the uncertain curves would meet the design the upper boundary curves and lower boundary curve. The middle curves are the result of certain optimization, too. The interval suspension structural parameters are the desired parameters error. In conclusion, the interval optimization is useful to uncertain suspension kinematics characteristic optimization.