二维轴对称摩擦制动器瞬态热弹性失稳的研究

提出考虑摩擦层闸片厚度的影响，建立二维轴对称摩擦制动器热弹性失稳的数学模型。基于扰动分析法，推导摩擦副的温度场扰动以及不同热点分布模式下的热特征平衡方程。研究临界速度和扰动增长系数的变化规律。计算摩擦面瞬态名义温度随制动时间的变化关系。分析和比较不同摩擦副厚度比、热导率、弹性模量、比热容以及热膨胀系数对系统稳定性的影响。结果表明，当热点呈反对称分布时，系统发生热弹性失稳时所需的最低临界速度远低于对称分布模式，临界速度随扰动频率的增加呈先减小后增加的变化趋势。不同扰动频率对应的扰动增长系数随滑动速度近似呈线性增加，最低临界扰动频率对应的扰动增长系数最大。当扰动频率低于临界扰动值时，温度随扰动频率的增加而增加，反之，则降低。增加摩擦副的厚度、摩擦层闸片的热导率和比热容以及减小滑动层制动盘的热导率和热膨胀系数和摩擦层闸片的弹性模量均可以提高滑动摩擦系统的稳定性。

Transient Frictionally Excited Thermoelastic Instability Analysis of Two Dimensional Axisymmetric Friction Brake

A mathematical model on thermoelastic instability(TEI) of two dimensional axisymmetric friction brake is proposed by considering the impact of friction layer’s thickness. Based on the perturbation method, temperature perturbation of the brake pair and the characteristic balance equation under different types of distribution of hot spots are respectively derived. The change rules of the critical speed and growth rate of perturbation are studied. Transient normal temperature of the frictional surface changing with time is calculated. The effects of brake pair’s different thickness ratio, thermal conductivity, elastic modulus, specific heat and thermal expansion coefficient on critical speed are analyzed and compared. The results show that the critical speed of the model whose hot spots are antisymmetrically distributed is much lower than that of symmetric mode and it will decrease firstly and then grow again with the increase of wave number. The growth rates of perturbation of different wave numbers have a approximate linear relationship with the sliding velocity. Meanwhile, the perturbation which has the lowest critical speed has the largest growth rate. For perturbations with wave number smaller than critical value, the temperature will increase，vice versa perturbations with wave number greater than critical value, the temperature will decrease. The stability of the braking system can be enhanced by increasing the thickness of the brake pair, thermal conductivity, specific heat of the friction layer and decreasing the thermal conductivity, thermal expansion coefficient of the sliding layer and the elastic modulus of the friction layer.