Research on Partial Slip Contact Behaviors Under Temperature Effects
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摘要:
针对不同温度装配件间接触界面的局部滑移问题，建立了三维稳态热弹性局部滑移接触的半解析求解模型。基于热弹性理论与热传导方程，构建了半空间受热流载荷和力载荷作用下的频响函数并建立了相应的影响系数矩阵。借助离散卷积-快速Fourier变换等数学工具，实现了针对高温压头与热弹性半空间局部滑移接触问题的高效求解。接触界面间的热量传递满足Fourier热传导定律，并且黏/滑状态由Coulomb定律确定。基于该半解析模型分析了不同荷载及温差对表面法向压力分布、摩擦力分布、刚体位移及接触区黏/滑演化行为的影响。研究结果表明，当法向荷载和切向荷载一定时，温差的上升会导致接触区域的减小，引起接触面法向压力及摩擦力的峰值增大，并且会显著影响黏着区与滑移区的分布情况。
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关键词:
- 热弹性接触 /
- 局部滑移 /
- 半解析法 /
- 离散卷积-快速Fourier变换 /
- 共轭梯度法
Abstract:Aimed at the partial slip problem of contact interface between assemblies at different temperatures, a semi-analytical model for 3D steady-state thermoelastic partial slip contact was established. Based on the thermoelastic theory and the heat conduction equation, the frequency response functions of the half space under heat flux and force load were given, and the corresponding influence coefficients were established. With the discrete convolution and fast Fourier transform (DC-FFT), the partial contact between the rigid high-temperature indenter and the thermoelastic half space was efficiently solved. The heat conduction behavior was assumed to follow Fourier’s law, and the stick/slip state on the contact interface was determined under Coulomb’s law. Based on this semi-analytical model, the effects of external loads and temperature differences on the surface pressure distribution, the friction distribution, the rigid body displacement, and the stick/slip evolution behaviors, were analyzed in detail. The numerical results show that, the increase of the temperature difference will lead to a decrease of the contact area, result in an increase of the peak values of the normal pressure and the friction, and significantly influence the regions of the stick zone and the slip zone.
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图 4 半解析法向压力p沿x轴方向的分布与Hertz解析解的对比
Figure 4. Comparison between the distribution of semi-analytical normal pressure p along the x-axis and the Hertz analytical solution
图 5 切向力
${q_x}$ 沿x轴方向的分布Figure 5. The distribution of tangential force
${q_x}$ along the x-axis
图 6 不同温差、切向荷载下，无量纲切向力沿x轴方向的分布：(a)
${F_x} = 0.3\mu _f P$ ；(b)${F_x} = 0.9\mu _f P$ Figure 6. Distributions of the dimensionless tangential force along the x-axis under different temperature rises and tangential loads: (a)
${F_x} = 0.3\mu _f P$ ; (b)${F_x} = 0.9\mu _f P$ 
图 7 不同温差、切向荷载下，无量纲法向压力沿x轴方向的分布：(a)
${F_x} = 0.3\mu _fP$ ；(b)${F_x} = 0.9\mu _fP$ Figure 7. Distributions of the dimensionless normal pressure along the x-axis under different temperature rises and tangential loads: (a)
${F_x} = 0.3\mu _fP$ ; (b)${F_x} = 0.9\mu _f P$ 
图 8 300 ℃温差下不同切向荷载作用下法向压力沿x轴方向的分布
Figure 8. Distributions of the normal pressure along the x-axis under different tangential loads at a temperature rise of 300 ℃
图 9 不同温差下刚体位移与切向荷载的关系
Figure 9. Relationships between the rigid body displacement and the tangential load at different temperatures rises
图 10 不同切向荷载下黏/滑比与温差的关系
Figure 10. Relationships between the stick/slip ratio and the temperature under different tangential loads
表 1 模型参数
Table 1. Model parameters
model parameter value normal load $P/{\rm{N}}$ 20 tangential load ${F_x}/{\rm{N}}$ $\left( {0 \sim 0.9} \right) \times {\mu _f}P$ tangential load ${F_y}/{\rm{N}}$ 0 friction coefficient ${\mu _f}$ 0.3 ball radius $R/{\rm{mm}}$ 18 maximum Hertzian pressure ${p_{\max } }/{\rm{MPa}}$ 907 elastic half space modulus $E/{\rm{GPa}}$ 210 Poisson’s ratio of elastic half space $\nu $ 0.3 thermal expansion in coefficient elastic half space K $2.0 \times {10^{ - 5}}$ elastic half space heat transfer coefficien $Q/({{\text{W}}/ {({\text{m}} \cdot {\text{K}})}}$) 60 
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