多点支撑结构形变及轴系轴承承载性能分析

doi:10.12382/bgxb.2021.0575

摘要/Abstract

摘要：

为满足高功率密度传动系统对轴系轴承高承载和长寿命的指标要求,基于弹性力学理论和滚动轴承设计方法建立多点支撑轴系轴承的力学模型,通过数值计算精确获取轴系挠曲变形曲线,以及轴承载荷分布、接触角和接触应力等性能,进而分析驱动力矩和位置对轴承寿命的影响,给出轴系结构优化配置参数。研究结果表明:多点支撑轴系的挠曲变形对轴系轴承的载荷分配产生明显影响,在实际多点支撑轴系轴承性能计算中,要考虑轴系形变和轴系轴承的耦合作用,精确评估轴承寿命;从多点支撑圆柱滚子轴承最佳凸型设计角度考虑,中间列滚子轴承选择两边弧坡修型、右端滚子轴承选择全圆弧修型,有助于延长轴承使用寿命;从多点支撑球轴承80%爬坡率安全指标要求,驱动力矩为正常工况800N·m时,内沟道极限设计接触角为40.6°,外沟道极限设计接触角为44.3°;从提高轴系轴承综合寿命角度,斜齿轮作用载荷位置的调整可以起到明显效果,在段距离为41~46mm范围轴系轴承的综合寿命处于最佳区间。

关键词: 轴系轴承, 承载性能, 疲劳寿命, 挠曲变形

Abstract:

With the development of high power-density transmission systems, shafting bearings must meet higher standards such as a high load-bearing capacity and long service life. This study establishes a mechanical model for a multi-point support shafting bearing based on the theory of elasticity and the design method for rolling bearings. The deflection deformation curve of shafting, as well as the load distribution, contact angle, and contact stress of bearings, are numerically calculated. Then, the influence of driving torque and position on bearing life is analyzed, and the optimal configuration parameters of the shafting structure are given. The results show that the deflection of multi-point support shafting significantly affects the load distribution of shafting bearings. When evaluating the service life and performance of multi-point support shaft bearings, the coupling effect of shaft deflection and shafting bearing should be considered. In terms of the optimal crowning design for multi-point support cylindrical roller bearings, arc-slope crowning on both sides is selected for the middle row roller bearing, and the full crowning type is selected for the right-end roller bearing, which will help prolong the service life of the bearing. To meet the safety requirement of 80% climbing rate, when the driving torque is 800N·m under normal working conditions, the maximum design contact angle of the inner ring raceway is 40.6°, and that of the outer ring raceway is 44.3°. Adjusting the load position of helical gears can significantly prolong the service life of shafting bearings. When the distance between the ends is 41~46mm, the shafting bearings have a maximum life.

Key words: shafting bearings, loading performance, fatigue life, deflection deformation

中图分类号:

TH133.33

牛荣军, 刘越, 唐红利, 崔永存, 邓四二. 多点支撑结构形变及轴系轴承承载性能分析[J]. 兵工学报, 2023, 44(2): 615-628.

NIU Rongjun, LIU Yue, TANG Hongli, CUI Yongcun, DENG Si'er. Deformation of the Multi-point Support Structure and Loading Performance Analysis of Its Shafting Bearing[J]. Acta Armamentarii, 2023, 44(2): 615-628.

图/表 22

图1 多点支撑轴系受载力学模型

Fig.1 Mechanical model of a loaded multi-point support shaft

图2 滚动体编号及位置角定义

Fig.2 Numbering and position angles of rolling elements

图3 滚子与滚道接触关系

Fig.3 Contact relationship between roller and raceway

图4 钢球与沟道的接触关系

Fig.4 Contact relationship between steel ball and raceway

图5 多点支撑轴系轴承配置

Fig.5 Multi-point support shafting bearing configuration

表1 轴承类型和结构参数

Table 1 Parameters of bearing type and structure

类型	参数	数值
	轴承外径D/mm	100
	轴承内圈d/mm	45
	轴承宽度B/mm	25
QJ309	钢球数目Z_b	11
	设计接触角α₀/(°)	35.0
	钢球直径D_w/mm	17.462
	球列径向游隙u_Br/mm	0.035
	轴承外径D/mm	75.0
	轴承内径d/mm	30
NU2306	滚子有效长度l_e/mm	16.5
	滚子个数Z_r	13
	滚子直径D_w/mm	12.0
	滚子列径向游隙u_Rr/mm	0.030
	轴承外径D/mm	85.0
	轴承内径d/mm	45.0
NU209	滚子有效长度l_e/mm	11.633
	滚子个数Z_r	17
	滚子直径D_w/mm	11.0×2
	滚子列径向游隙u_Rr/mm	0.030

图6 多点支撑轴系形变刚性比较

Fig.6 Comparison of rigidity of multi-point support shafting

表2 刚柔性支撑轴系对轴系轴承支撑刚性的影响

Table 2 Influence of rigid and flexible shafting on support rigidity of shafting bearing

类型	T/(N·mm)	Δ_r,l/μm	Δ_a,l/μm	Θ_l/μrad	Δ_r,m/μm	Θ_m/μrad	Δ_r,r/μm	Θ_r/μrad
	400	-22.9	-0.30	-4.6	3.4	-5.6	0.78	6.9
	600	-28.7	-0.36	-6.2	4.9	-8.2	0.99	9.9
柔性轴	800	-33.6	-0.31	-7.5	6.3	-10.5	1.20	12.8
	1000	-379.0	-0.10	-8.4	7.6	-12.6	1.30	15.3
	1200	-41.9	-0.21	-9.1	8.9	-14.5	1.40	17.8
	400	3.7	-0.31		2.8		0.5
	600	5.3	-0.36		4.0		0.7
刚性轴	800	6.8	-0.32		5.1		0.9
	1000	8.2	-0.11		6.2		1.0
	1200	9.6	-0.22		7.2		1.2

图7 滚子凸型对轴承接触性能的影响

Fig.7 Effects of roller crown on contact performance

图8 滚子凸型对轴承载荷分布的影响

Fig.8 Effects of roller crown on load distribution

图9 驱动力矩对轴承承载性能的影响

Fig.9 Effects of driving torque on the bearing performance

图10 驱动力矩对轴承载荷分布的影响

Fig.10 Effects of driving torque on load distribution

图11 设计接触角对轴承接触性能的影响

Fig.11 Effects of design contact angle on bearing contact performance

图12 球轴承轴肩爬坡原理图

Fig.12 Schematic diagram of ball-bearing shoulder climbing

图13 驱动力矩对轴承爬坡率的影响

Fig.13 Effects of driving torque on climbing rate

图14 设计接触角对轴承爬坡率的影响

Fig.14 Effects of contact angle on climbing rate

图15 齿轮作用位置对支撑轴系变形刚性的影响

Fig.15 Effects of gear action position on rigidity of shafting

图16 齿轮作用位置对轴系轴承综合寿命的影响

Fig.16 Effects of gear action position on life of shafting bearing

表3 计算结果对比分析

Table 3 Comparative analysis of calculation results

参数	1号轴承		2号轴承		3号轴承
参数	仿真结果	本文结果	仿真结果	本文结果	仿真结果	本文结果
径向力/kN	2.51	2.46	7.96	8.02	0.50	0.49
轴向力/kN	-15.0	-15.1	0	0	0	0
力矩/(N·m)	-148.2	-150.0	-6.87	-6.85	1.51	1.49

图17 多点支撑轴系刚性测试原理图

Fig.17 Schematic diagram of multi-point support shafting rigidity test

图18 多点支撑轴位移量测试

Fig.18 Displacement test of multi-point support shafting

图19 多点支撑轴静态位移量结果比较

Fig.19 Comparison of static displacement results of multi-point support shafting

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