基于弹性迟滞理论的轮胎滚动阻力解析模型构建

Analytical model of tire rolling resistance based on elastic hysteresis theory

为了降低轮胎滚动能量损失,该文提出一种新型轮胎滚动阻力解析模型。分析轮胎滚动阻力产生的机理,考虑材料的弹性迟滞特点,定义非线性弹性力和非线性阻尼力构建轮胎垂向复合回复力公式,搭建特定试验进行模型参数辨识。根据刷子模型将轮胎接地部分化简为两部分：一部分为接地中心到刷毛单元开始接触地面的加载区域;另一部分为接地中心到刷毛单元离开地面的卸载区域。然后分别对参数辨识得到的加载和卸载曲线在相应区域内积分并求和,获得轮胎滚动阻力矩解析模型。根据ISO 28580标准对轮胎滚动阻力进行测试,结果表明：轮胎滚动阻力随速度（10~120 km/h）和垂向负载（6~25 kN）的增大而增大;试验结果与解析值在相同的工况条件下变化趋势基本一致,从而验证了模型的有效性。新型滚动阻力模型的提出有助于轮胎的结构优化。

With the situation of the global power shortage and the increasing demand for the fuel, it becomes an important subject for the tire researchers to reduce energy consumption of tire and improve tire’s energy efficiency. In the field of the interaction mechanism between the tire and the road, a calculation model of the energy consumption of the tire is very meaningful, and it is restricted by multiple conditions, such as the tire temperature, the material properties and the friction conditions. The tire’s friction force develops from the contact region. In the process of tire rolling, the forces generate periodical stress spectrum whose frequency lies on the tire’s rolling velocity. The periodical stress causes energy loss according to the size and the material property of the tire. The parameter identification of the proposed model in this paper could be carried out through specific experiments, which possessed the variation characteristics for the vertical loading and velocity of the tire through the horizontal motion of the sine guide rail and the load of the guide rod, and the equipment consisted of guide pulley, guide rod, sine guide rail, tire and supporting structure. The brush model assumes that the slide rate develops from the relative displacement of the tread between the wheel hub and the road. The tread is supposed to be elastic brush adhered to the stiff wheel hub. The wheel hub can neither stretch nor shrink, yet deformations may occur in every small elastic brush. Using the brush model to simplify the interaction relationship between the tires and the ground, the contact patch is divided into two parts：the first is loading part which ranges from the starting contact point to the central of the contact region, and the elastic force fits the loading curve of tire’s compound restoring force;the second is unloading part which ranges from the central of the contact region to the end contact point, and the elastic force fits the unloading curve of tire’s compound restoring force. The analytical model of tire rolling resistance can be obtained by the integral within the two contact parts for the loading curve function and unloading curve function, which is the main innovation of this paper. In the end, by defining the velocity and the load as the test variables, the effectiveness of the proposed analytical model was verified by the experiments of the rolling resistance measurement in accordance with the standard of ISO 28580. The results showed that the rolling resistance of the tire increased with the increasing of speed （10-120 km/h） and vertical load （6-25 kN）;and change trend of the test result was consistent with that of the analytical value under the same condition. The new model of rolling resistance proposed in this paper is helpful to structure optimization of the tire.