Page 19 - 《摩擦学学报》2020年第3期

第 3 期 樊智敏, 等: 双渐开线齿轮传动的油膜刚度研究 285

1.90 0.010 5
Involute gear Involute gear
Double involute gear Double involute gear
Rolling speed, u r /(m/s) 1.80 Equivalent radius, R 2 /m 0.010 0
1.85

0.009 5
1.75

1.70 0.009 0
0 0.25 0.50 0.75 1.00 0 0.25 0.50 0.75 1.00
Normalized meshing tine, t/T Normalized meshing tine, t/T
(a) Comparison of rolling speed (b) Comparison of equivalent radius

Fig. 6 Comparison of rolling speed and equivalent radius
图 6 卷吸速度、当量曲率半径对比 4.460×10 9

Film stiffness×10 10 , K b /(N/m) 8 6 4 6.140×10 9 9 9 9 9 9 9 9 Film stiffness×10 9 , K b /(N/m) 8 6 4 6.124×10 9 9 9 9 9 9 9 9
10
10
9
6.500×10
5.780×10
5.788×10
5.420×10
5.452×10
5.060×10
5.116×10
4.780×10
4.700×10
4.340×10
4.444×10
4.108×10
3.980×10
3.772×10
3.620×10
2
2.900×10
3.100×10
0
16 1.0 3.260×10 9 9 2 0 16 1.0 3.436×10 9 9
Normalized meshing
Normalized meshing
12 0.6 0.8 12 0.6 0.8
8 0.4 8 0.4
4 0.2 Label of each segment 0.2
4
0 time, t/T of contact line, j 0 time, t/T
Label of each segment
of contact line, j
(a) Film stiffness of involute gears (b) Film stiffness of double involute gears

Fig. 7 Variations of film stiffness for two types of gears
图 7 两种齿轮油膜刚度分布规律
16 8
Involute gear 7 6 Involute gear
Film stiffness×10 10 , K b /(N/m) 10 8 6 Film stiffness×10 9 , K Z /(N/m) 5 4 3 2
14
Double involute gear
Double involute gear
12
2 4 1 0
0 0.25 0.50 0.75 1.00 0 0.25 0.50 0.75 1.00
Normalized meshing tine, t/T Normalized meshing tine, t/T
(a) Total film stiffness in meshing period (b) Film stiffness at middle position of

Fig. 8 Comparison of film stiffness for two types of gears
图 8 两种齿轮油膜刚度变化规律对比
l 对油膜刚度的影响. 其中图9(a)和图9(b)分别为 对 分阶参数 l 增大，导致双渐开线齿轮分阶区域扩
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∗
l
∗
总油膜刚度和接触线中间位置油膜刚度的影响. 大，接触线长度减小，单位线载荷增大，油膜弹性变形
由图9可知， l 变化时，总油膜刚度在啮合周期内 减小，每段名义接触线上油膜刚度增大，而 l 增大导致
∗
∗
的变化规律保持不变，总油膜刚度随 l 增大而减小；接 分阶区域扩大，最终接触线上总油膜刚度减小.
∗
触线中间位置的油膜刚度随 l 增大而增大. 图10所示为 l = 0.08时，双渐开线齿轮分阶参数
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