This article considers vertical vibration of a two-axle automobile in spatial model (full-car model) where wheel separation and road deformation are taken into account. The automobile with dependent suspensions is modeled as a spatial vibration system with three masses and seven degrees of freedom. The deformed road is modeled as an elastic rectangular plate which has uniform thickness, lies on the Kelvin’s visco-elastic ground and is simply supported at all edges. The phenomenon of wheel separation is taken into account by introducing four contact state parameters (each per a wheel) into the differential equations of motion. The change in dimensions of the contact areas is also regarded by generating relations among the contact forces, the wheel geometries and their vertical deformations. The differential equations of motion of the automobile-road coupled system where exists a partial differential equation are transformed into a set of all ordinary differential equations by applying the Bubnov–Galerkin’s method. Some illustrating results obtained from consideration are also given in the article. The results confirm the need of regard to the wheel separation. The effect of movement velocity on the dynamic responses and the total time of losing contact in case of taking wheel separation are also considered.

本文在考虑车轮分离和道路变形的空间模型（整车模型）中考虑了两轴汽车的垂直振动。具有独立悬架的汽车被建模为具有三个质量和七个自由度的空间振动系统。变形的道路被建模为一个弹性矩形板，它具有均匀的厚度，位于开尔文粘弹性地面上，并且在所有边缘都得到简单的支撑。通过在运动微分方程中引入四个接触状态参数（每个每个车轮）来考虑车轮分离现象。接触区域尺寸的变化也可以通过接触力、车轮几何形状及其垂直变形之间的关系来考虑。通过应用Bubnov-Galerkin 方法，将存在偏微分方程的汽车-道路耦合系统的运动微分方程转化为一组所有常微分方程。文章中还给出了一些说明从考虑中获得的结果。结果证实需要考虑车轮分离。还考虑了运动速度对动态响应的影响以及在车轮分离的情况下失去接触的总时间。