Bifurcation Analysis of a Quarter Car Vehicle System

四分之一車輛動力學系統的分岔分析

童林軍(Lin-Jun Tong) ； 曾威(Wei Zeng)

《中國機械工程學刊》 40卷4期 (2019/08) Pp. 423-429

摘要

A systematic analysis of the effects of nonlinear, hysteretic, tire damping and stiffness forces, on the nonlinear, dynamic response of a two degrees of freedom, quarter-car suspension system. The dynamics of the system were evaluated through analysis of dynamic trajectories, power spectra, Poincare maps, bifurcation maps and frequency responses, respectively. The quasi-periodic solution for the twisting of the natural frequency was detected, and the coexistence of quasi-periodic and periodic solutions, due to the fold bifurcation, was also observed. Two resonances were found in the frequency response. The first resonance is the main resonance due to the lower natural frequency, and the second resonance is a subharmonic resonance of the higher natural frequency. The tire damping, combined with excitation amplitude and frequency, strongly impacted the dynamic characteristics. The results presented in this study provide a better understanding of the operating conditions under which undesirable dynamic motion takes place in a quarter-car system, and would therefore serve as a useful source of reference for engineers interested in designing and controlling such systems to extend the expected lives of automobiles.

關鍵字

quasi-periodic ； nonlinear hysteretic damping ； frequency response ； bifurcation

並列摘要

基於二自由度1/4車輛懸掛系統，系統的分析了輪胎非線性、遲滯效應、阻尼和剛度對車輛非線性動力學響應的影響。以動態跡線、功率頻譜、Poincare映射圖、分岔圖和頻率响應為指标，分析了系統動力學性能，得到了扭轉固有頻率的准週期解，發現了由於鞍結分叉點導致的准週期解與週期性解的共存現象。通過頻率响應分析發現了兩處共振：第一處共振是由於固有頻率較低而導致的主共振；第二處共振為高固有頻率的次諧波共振。同時，發現輪胎阻尼、激勵的幅值與頻率對動力學性能影響極大。研究結果將有利於分析1/4車輛動力學系統在出現不良動態時的實際運行工况，可為同類系統設計人員延長汽車服役期提供有益的參攷。