基于虚拟激励法的汽车行驶平顺性仿真
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摘要
虚拟激励法是我国学者近年提出来的一套精确、高效的随机振动计算方法,通过构造虚拟激励,使计算步骤大大简化,却仍保持了理论上的精确性。虚拟激励法已在许多工程领域得到应用,但在汽车领域尚未得到良好的推广。因此,将虚拟激励法应用到汽车行驶平顺性评价中,具有十分重要的意义。
围绕这一主题,本文进行了如下工作:对虚拟激励法的基本思想、理论公式进行了研究,以简单、易于理解的方式论述了单自由度线性系统虚拟激励法的理论,为多自由度线性系统虚拟激励法的应用奠定了理论基础。以1/2汽车6自由度系统振动模型为研究对象,应用实模态虚拟激励法求得了系统响应量的功率谱密度,并与功率谱分析法求得的仿真结果进行了对比,结果表明,由于采用比例阻尼或振型阻尼而忽略了模态阻尼非对角线上的元素,实模态虚拟激励法的仿真结果存在着一定的误差。因此,应用复模态虚拟激励法再次求得了系统响应量的功率谱密度,通过与功率谱分析法作比较,结果表明系统振动响应量的功率谱密度仿真曲线可以完全吻合。这充分说明了应用复模态虚拟激法求解行驶平顺性问题的可行性与精确性,为虚拟激励法在高自由度系统振动模型中的应用打下了基础。以空间汽车11自由度系统振动模型为研究对象,基于复模态虚拟激励法求解了系统响应量的功率谱密度,获得了更为精确的仿真结果。最后,开发了基于虚拟激励法的汽车行驶平顺性仿真软件。
研究表明,基于虚拟激励法的汽车行驶平顺性仿真是一种有效且精确的方法,在行驶平顺性分析领域有着广泛的应用前景。
With the rapid development of national economy, the overall construction of expressway network and the great improvement of people’s living standard, automobiles have gradually come into people’s life and work, and become an indispensable means of transportation. Automobile ride comfort is one of the most important capability guideline. The quality of automobile ride comfort influences not only people’s comfortableness, efficiency of work and healthiness, but also influences the automobile’s power and economic performance and handling and stability. Therefore the investigation to improve automobile ride comfort is attached more and more attention.
The pseudo excitation method(PEM) is a precision and highly efficient algorithm for random vibration proposed by Pro J.H.Lin. Especially when calculating the high degree of freedom(DOF)model’s random dynamical response, it can greatly predigest the calculating step and still keep theoretically accuracy. The pseudo excitation method has been applied and further developed in many engineering fields, and solved many problems. But few people apply this method in automobile field. This article is for the purpose of applying PEM in automobile ride comfort. Main content of this article is as follows:
(1) Aiming at the description of theory of PEM wasn’t systemic anciently, from the single DOF linearity system, its basic theory of the single DOF linearity system has been elucidated. Research of PEM of the single DOF linearity system, constructing method of pseudo excitation has been elucidated by the simple and easy understanding way, at the same time, the basic formula and derivative relations of PEM have been showed. Researching of the multi-DOF linearity system, the basic theory of the real mode and the complex mode has been described. Using the theory can translate the multi-DOF linearity system into the single DOF linearity system. Thereby, the theory of PEM of the multi-DOF linearity system has been constructed completely.
(2) After study of six DOF vibration model of 1/2 automobile, the mechanics and mathematics model have been summarized. The road excitation of the above model has been confirmed. Based on the road excitation model, the pseudo excitation of the road has been constructed. First of all, using the real-mode PEM, power spectrum density of three responses(perpendicular acceleration of body, dynamic flexibility of suspension, relatively dynamic load of wheel)have been acquired. Due to the traditional power spectrum analytical method is mature in theory, a contrast between the traditional power spectrum analytical method and the real-mode PEM has been made. The results show that there exist errors under the real mode condition, because neglecting the damp of non-diagonal elements. So the following work is discussing of the plural-mode PEM. Using the plural-mode PEM, power spectrum density of three responses has been acquired. A contrast between the traditional power spectrum analytical method and the plural-mode PEM has been made. The results show that the curve can absolutely inosculate. Therefore the plural-mode PEM has the feasibility and accuracy when applied to automobile ride comfort.
(3) After study of eleven DOF vibration model of tridimensional automobile, the mechanics and mathematics model have been constructed, and the method of calculating system static load has been confirmed. The four-wheel road excitation has been confirmed. Based on the above road excitation model, the pseudo excitation of the road has been constructed using the road surface spectrum matrix’s character pair. Power spectrum density of three responses has been acquired based on the plural-mode PEM.
(4) Based on GUI of MATLAB, the software of evaluating of automobile ride comfort based on PEM has been developed. This software includes three parts: simulation of responses of vibration model of 1/2 automobile, simulation of responses of vibration model of tridimensional automobile, evaluating of automobile ride comfort. Simulation curves of power spectrum density of responses and the results of evaluating of automobile ride comfort can be acquired by inputting vehicle parameter, road surface type and vehicle velocity. The operation of the software is simple and convenient.
This paper tries to apply PEM to the analysis of automobile ride comfort, the results show that the feasibility and accuracy of the method. PEM will have a wide application in the automobile ride comfort analysis.
围绕这一主题,本文进行了如下工作:对虚拟激励法的基本思想、理论公式进行了研究,以简单、易于理解的方式论述了单自由度线性系统虚拟激励法的理论,为多自由度线性系统虚拟激励法的应用奠定了理论基础。以1/2汽车6自由度系统振动模型为研究对象,应用实模态虚拟激励法求得了系统响应量的功率谱密度,并与功率谱分析法求得的仿真结果进行了对比,结果表明,由于采用比例阻尼或振型阻尼而忽略了模态阻尼非对角线上的元素,实模态虚拟激励法的仿真结果存在着一定的误差。因此,应用复模态虚拟激励法再次求得了系统响应量的功率谱密度,通过与功率谱分析法作比较,结果表明系统振动响应量的功率谱密度仿真曲线可以完全吻合。这充分说明了应用复模态虚拟激法求解行驶平顺性问题的可行性与精确性,为虚拟激励法在高自由度系统振动模型中的应用打下了基础。以空间汽车11自由度系统振动模型为研究对象,基于复模态虚拟激励法求解了系统响应量的功率谱密度,获得了更为精确的仿真结果。最后,开发了基于虚拟激励法的汽车行驶平顺性仿真软件。
研究表明,基于虚拟激励法的汽车行驶平顺性仿真是一种有效且精确的方法,在行驶平顺性分析领域有着广泛的应用前景。
With the rapid development of national economy, the overall construction of expressway network and the great improvement of people’s living standard, automobiles have gradually come into people’s life and work, and become an indispensable means of transportation. Automobile ride comfort is one of the most important capability guideline. The quality of automobile ride comfort influences not only people’s comfortableness, efficiency of work and healthiness, but also influences the automobile’s power and economic performance and handling and stability. Therefore the investigation to improve automobile ride comfort is attached more and more attention.
The pseudo excitation method(PEM) is a precision and highly efficient algorithm for random vibration proposed by Pro J.H.Lin. Especially when calculating the high degree of freedom(DOF)model’s random dynamical response, it can greatly predigest the calculating step and still keep theoretically accuracy. The pseudo excitation method has been applied and further developed in many engineering fields, and solved many problems. But few people apply this method in automobile field. This article is for the purpose of applying PEM in automobile ride comfort. Main content of this article is as follows:
(1) Aiming at the description of theory of PEM wasn’t systemic anciently, from the single DOF linearity system, its basic theory of the single DOF linearity system has been elucidated. Research of PEM of the single DOF linearity system, constructing method of pseudo excitation has been elucidated by the simple and easy understanding way, at the same time, the basic formula and derivative relations of PEM have been showed. Researching of the multi-DOF linearity system, the basic theory of the real mode and the complex mode has been described. Using the theory can translate the multi-DOF linearity system into the single DOF linearity system. Thereby, the theory of PEM of the multi-DOF linearity system has been constructed completely.
(2) After study of six DOF vibration model of 1/2 automobile, the mechanics and mathematics model have been summarized. The road excitation of the above model has been confirmed. Based on the road excitation model, the pseudo excitation of the road has been constructed. First of all, using the real-mode PEM, power spectrum density of three responses(perpendicular acceleration of body, dynamic flexibility of suspension, relatively dynamic load of wheel)have been acquired. Due to the traditional power spectrum analytical method is mature in theory, a contrast between the traditional power spectrum analytical method and the real-mode PEM has been made. The results show that there exist errors under the real mode condition, because neglecting the damp of non-diagonal elements. So the following work is discussing of the plural-mode PEM. Using the plural-mode PEM, power spectrum density of three responses has been acquired. A contrast between the traditional power spectrum analytical method and the plural-mode PEM has been made. The results show that the curve can absolutely inosculate. Therefore the plural-mode PEM has the feasibility and accuracy when applied to automobile ride comfort.
(3) After study of eleven DOF vibration model of tridimensional automobile, the mechanics and mathematics model have been constructed, and the method of calculating system static load has been confirmed. The four-wheel road excitation has been confirmed. Based on the above road excitation model, the pseudo excitation of the road has been constructed using the road surface spectrum matrix’s character pair. Power spectrum density of three responses has been acquired based on the plural-mode PEM.
(4) Based on GUI of MATLAB, the software of evaluating of automobile ride comfort based on PEM has been developed. This software includes three parts: simulation of responses of vibration model of 1/2 automobile, simulation of responses of vibration model of tridimensional automobile, evaluating of automobile ride comfort. Simulation curves of power spectrum density of responses and the results of evaluating of automobile ride comfort can be acquired by inputting vehicle parameter, road surface type and vehicle velocity. The operation of the software is simple and convenient.
This paper tries to apply PEM to the analysis of automobile ride comfort, the results show that the feasibility and accuracy of the method. PEM will have a wide application in the automobile ride comfort analysis.
引文
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