Longitudinal creep force properties of wheel and rail under short-pitch corrugation state
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摘要: 为了对具有简谐波形的钢轨短波波磨进行分组与分析轮轨非稳态滚动接触的纵向蠕滑力特性, 引入了波磨深度指数与波长比, 采用Kalker三维滚动接触理论计算了车轮的纵向蠕滑力, 并与采用稳态滚动理论计算结果进行了对比, 使用频率响应的系统辨识法对纵向蠕滑力的波动分量进行了拟合, 在短波波磨等深度指数条件下, 用波长比的二阶传递函数描述了轮轨纵向蠕滑力的波动分量与稳态理论波动分量之间的关系, 使用传递函数, 由稳态纵向蠕滑力的波动分量计算了非稳态纵向蠕滑力的波动分量, 进而计算了非稳态的纵向蠕滑力。计算结果表明: 在小蠕滑条件下, 由Kalker三维滚动接触理论计算出的纵向蠕滑力的波动分量随着波长比的变化产生明显的幅值衰减和相位滞后, 波长比越大, 幅值衰减越大, 相位滞后越多, 而稳态滚动理论的计算结果与波长比无关。由传递函数和Kalker数值理论计算的纵向蠕滑力的时域波形、频域幅值谱和相位谱相同。Abstract: Shallowness factor and wavelength ratio were induced to group sinusoidal short-pitch corrugations with simple harmonic waveforms and to analyze the properties of longitudinal wheel/rail creep forces for unsteady state rolling contact, the longitudinal creep forces due to sinusoidal short-pitch corrugations were calculated by Kalker 3D rolling contact theory, and the calculation result was compared with the calculation result from steady rolling contact theory. The system identification method of frequency response was used to fit the fluctuating part of unsteady longitudinal creep force. The relationship of fluctuating parts for unsteady state and steady state longitudinal creep forces was described as two order transfer function of wavelength ratio when sinusoidal short-pitch corrugations had same shallowness factor. The fluctuating part of unsteady longitudinal creep force was calculated according to the fluctuating part of steady longitudinal creep force, thereout, the unsteady longitudinal creep force was calculated. Calculation result shows that under small creep condition, the fluctuating part of unsteady longitudinal creep force decreases in amplitude and phase lag with the growth of wavelength ratio. The bigger wavelength ratio is, the smaller amplitude is, and the more phase lag is. However, the result from steady state theory is independent of wavelength ratio. For unsteady longitudinal creep forces calculated by the transfer function and Kalker 3D rolling contact theory, the waveforms in time domain, the amplitudes and phase spectrums in frequency domain are accordant.
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图 2 同波长不同深度的波磨
Figure 2. Corrugation waveforms with equal wavelength and different shallowness factors
图 3 等深度波磨的幅值和波长关系
Figure 3. Relationship between amplitudes and wavelengths of corrugations with equal shallowness factor
图 6 α为5.0时的短波波磨的纵向蠕滑力
Figure 6. Longitudinal creep forces under short-pitch corrugations when α is 5.0
图 7 α为10.0时短波波磨的纵向蠕滑力
Figure 7. Longitudinal creep forces under short-pitch corrugations when α is 10.0
图 8 纵向蠕滑力的Nyquist图和传递函数
Figure 8. Nyquist figures and transfer functions of longitudinal creep forces
图 9 等深度多频段波磨的纵向蠕滑力
Figure 9. Longitudinal creep forces of multi-frequency corrugations with equal shallowness factor
图 10 不等深度多频段波磨的纵向蠕滑力
Figure 10. Longitudinal creep forces of multi-frequency corrugations with different shallowness factors
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