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受径向力滚动轴承摩擦力矩的测试和函数拟合

清华大学 辅仁网/2017-07-07

受径向力滚动轴承摩擦力矩的测试和函数拟合
陶润,侯之超()
Measurement and curve fitting of the friction torque of rolling bearings subjected to radial loads
Run TAO,Zhichao HOU()
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China

摘要:
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摘要该文展示了一种可以测定径向受力滚动轴承稳态摩擦力矩的方法和测试设备,并用以测量某乘用车发动机前端附件传动系统中典型滚动轴承在不同径向力和转速下的摩擦力矩。基于最小二乘法应用多种函数对摩擦力矩与转速之间的关系进行拟合,依据相关系数和显著性水平选定了最优拟合函数,进而得到了摩擦力矩与转速、径向力之间的经验公式。与试验数据的对比显示,所拟合公式比Palmgren公式具有更高的精度。该测试方法可直接用于其他工程领域中的滚动轴承摩擦力矩的测试。拟合方法与拟合公式对滚动轴承摩擦力矩的表征具有参考意义。

关键词 滚动轴承,径向力,摩擦力矩,数据拟合,发动机前端附件皮带传动
Abstract:A device is developed to measure the friction torque of rolling bearings subjected to radial loads while running at steady speeds. The friction torques are measured at various speeds and radial loads for typical rolling bearings used in an engine front end accessory belt drive of a passenger vehicle. The least squares method is used to fit the friction torque and the rotational speed with the optimal function chosen according to the correlation coefficient and significance level. A set of empirical formulae are then derived for the friction torque in terms of both the rotational speed and the radial load. The expressions are more accurate than the Palmgren formula. The test method can be applied to measure the friction torque of rolling bearings used in other fields as a valuable method to characterize the torque characteristics.

Key wordsrolling bearingradial loadingfriction torquedata fittingengine front end accessory belt drive
收稿日期: 2013-09-30 出版日期: 2015-03-17
引用本文:
陶润,侯之超. 受径向力滚动轴承摩擦力矩的测试和函数拟合[J]. 清华大学学报(自然科学版), 2014, 54(6): 744-749.
Run TAO,Zhichao HOU. Measurement and curve fitting of the friction torque of rolling bearings subjected to radial loads. Journal of Tsinghua University(Science and Technology), 2014, 54(6): 744-749.
链接本文:
http://jst.tsinghuajournals.com/CN/ http://jst.tsinghuajournals.com/CN/Y2014/V54/I6/744


图表:
轴承受力示意图
测试装置的构成
测试原理图
基于干扰力矩的旋转刚度辨识
力矩增量随外伸臂位移的变化关系
某乘用车的发动机前端附件皮带传动系统
6203轴承的实测摩擦力矩
6203轴承摩擦力矩的曲线拟合(径向载荷为1 500N)
序号 函数 拟合公式 相关系数R2
1 对数函数 y=25.81·lnx+96.9 0.664
2 幂函数 y=100x0.377 0.684
3 指数函数 y=41.69e1.19x 0.753
4 一次多项式 y=82.43x+36.58 0.748
5 二次多项式 y=45.67x2+45.67x+42.25 0.754
6 三次多项式 y=-461x3+623.5x2-165.8x+63.25 0.771
7 四次多项式 y=-477.5x4+323.5x3+185.1x2-69.9x+56.49 0.772
8 五次多项式 y=733.6x5-1965x4+1450x3-207.1x2-8.129x+53.03 0.772


基于不同函数得到的6203轴承摩擦力矩计算式
转速/(r·min-1) σ/(N·mm)
载荷100 N 载荷500 N 载荷1 000 N 载荷1 500 N 载荷2 000 N
1 500 0.3 3.9 4.5 8.8 12.7
2 900 2.3 3.0 6.7 6.6 10.4
4 350 3.2 2.9 7.8 8.6 10.4
5 050 2.1 7.1 10.0 9.0 5.9
5 770 5.4 3.4 9.6 11.0 17.8


6203轴承摩擦力矩的标准差σ
6203轴承摩擦力矩的曲线拟合
载荷/N 1 500 r/min 2 900 r/min 4 340 r/min 5 770 r/min 7 060 r/min
Ti/(N·mm) τ/% Ti/(N·mm) τ/% Ti/(N·mm) τ/% Ti/(N·mm) τ/% Ti/(N·mm) τ/%
100 4.9 71.7 7.0 77.0 8.9 77.8 10.5 78.0 11.8 80.3
500 9.5 69.5 11.6 70.1 13.4 69.9 15.0 71.6 16.4 74.4
1 000 15.2 59.6 17.3 60.8 19.1 65.3 20.7 68.7 22.1 69.6
1 500 20.9 57.5 23.0 57.2 24.8 62.9 26.4 69.2 27.8 71.5
2 000 26.6 53.3 28.7 53.5 30.5 57.3 32.1 68.0 33.5


6203轴承摩擦力矩(Palmgren公式计算)及其误差


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