Dynamic optimization design of internal toothed toothed slewing bearing based on parametric multi-body dynamic model

doi:10.3785/j.issn.1006-754X.2024.03.129

Chinese Journal of Engineering Design

2024, Vol. 31

Issue (2): 168-177 DOI: 10.3785/j.issn.1006-754X.2024.03.129

Mechanical Optimization Design

Dynamic optimization design of internal toothed toothed slewing bearing based on parametric multi-body dynamic model

Wangcheng CAO(

),Jiaxuan HAN,Tingqiang YAO(

)

School of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China

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Abstract

The internal toothed slewing bearing has both the slewing bearing characteristics of rolling bearing and the gear meshing transmission characteristics. Under the action of combined load, its dynamic performance is affected by many factors, and it is easy to suffer from tooth wear or broken teeth, ring raceway wear and poor running accuracy. Considering the dynamic contact between the steel ball and the inner and outer ring raceway, the cage pocket hole and the meshing transmission between the inner ring teeth, the parametric multi-body contact dynamic model of an internal toothed slewing bearing was established. The influence of key design parameters such as radius of curvature of groove, hole diameter of cage pocket, initial contact angle and tooth displacement coefficient on the gear meshing force of slewing ring, contact force between No.1 steel ball and N1 raceway, and the axial and radial vibration displacement of the center of mass of the inner ring were analyzed. On this basis, the design of experiments (DOE) method was used to design and calculate the key design parameters of the toothed slewing bearing, and the dynamic performance of slewing bearing under the influence of multiple parameters was obtained. Combined with linear weighting method, a new multi-objective optimization function was constructed and solved by using unified dimension method and weight coefficient method, and a multivariate multi-objective optimization design method for the dynamic performance of slewing bearings was proposed, which provides a reference for the dynamic design of slewing bearings.The gear meshing force of slewing ring decreased by 49.27%, the contact force between No. 1 steel ball and N1 raceway decreased by 29.6%, the axial vibration displacement of the center of mass of the inner ring decreased by 5.41%, the radial vibration displacement of the center of mass of the inner ring decreased by 15.88%. The performance of the rotary bearing was optimized. The research results provide a reference for the dynamic design of slewing bearing.

Key words： slewing bearing multi-body dynamics experimental design dynamic optimization design multi-objective optimization

Received: 08 March 2023 Published: 26 April 2024

CLC:

TH 133.3

Corresponding Authors: Tingqiang YAO E-mail: caowangchengkust@163.com;yaotingqiang@163.com

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Cite this article:

Wangcheng CAO,Jiaxuan HAN,Tingqiang YAO. Dynamic optimization design of internal toothed toothed slewing bearing based on parametric multi-body dynamic model. Chinese Journal of Engineering Design, 2024, 31(2): 168-177.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2024.03.129 OR https://www.zjujournals.com/gcsjxb/Y2024/V31/I2/168

基于参数化多体动力学模型的内齿式回转支承动态优化设计

内齿式回转支承兼有滚动轴承的回转支承特点和齿轮啮合传动特点，在联合载荷作用下其动态性能的影响因素众多，容易出现轮齿磨损或断齿、套圈滚道磨损和运行精度变差等问题。综合考虑钢球与内外套圈滚道、保持架兜孔的动态接触作用及内齿圈轮齿间的啮合传动作用，建立了内齿式回转支承参数化多体接触动力学模型。分析了沟道曲率半径、保持架兜孔孔径、初始接触角和轮齿变位系数等关键设计参数对回转支承齿轮啮合力、1号钢球与N1滚道的接触力、内齿圈质心轴向和径向振动位移的影响规律。在此基础上，采用试验设计（design of experiment，DOE）方法，对内齿式回转支承的关键设计参数进行全因子试验设计及计算，获得了多参数影响下回转支承的动态性能。结合线性加权法，运用统一量纲法和权系数法构造新的多目标优化函数，提出了回转支承动态性能的多变量多目标优化设计方法，得到回转支承的轮齿啮合力下降了49.27%，1号钢球与N1滚道的接触力下降了29.6%，内齿圈质心轴向振动位移减小了5.41%，内齿圈质心径向位移减小了15.88%，回转支承的性能得到了优化。研究结果为回转支承的动态设计提供了参考。

关键词： 回转支承, 多体动力学, 试验设计, 动态优化设计, 多目标优化

参数	数值
滚道中心圆直径 $D l$ /mm	400
钢球直径 $D w$ /mm	25
公称外径 $D$ /mm	493
公称内径 $d$ /mm	307
总高 $H$ /mm	70
内外圈高 $H 1$ /mm	60
小齿轮齿数 $z 1$ /个	23
套端面高度 $h$ /mm	10
外圈内径 $d 1$ /mm	399
内圈外径 $D 1$ /mm	401
齿圈齿数 $Z$ /个	48
模数 $m$ /mm	6
齿宽 $b$ /mm	50
钢球数 $n$ /个	28

Table 1 Main structural parameters of slewing bearing

Fig.1 Dynamic model of parametric multi-body contact for slewing bearing

Fig.2 Schematic diagram of N1，N2，W1，W2 ring raceways

参数	钢球—内圈	钢球—外圈
接触刚度 $K / (N ? m m - 1.5)$	$1.46 × 106$	$1.48 × 106$
阻尼系数C	10	10
刚性力指数e	1.5	1.5
接触点法向穿透深度 $δ / m m$	0.1	0.1
静摩擦速度 $v s / (m m ? s - 1)$	1 000	1 000
动摩擦速度 $v d / (m m ? s - 1)$	100	100
静摩擦因数 $μ s$	0.011	0.011
动摩擦因数 $μ d$	0.011	0.011

Table 2 Parameters of multi-body contact model between steal ball and raceway

Fig.3 Schematic diagram of force between steel ball and ring raceway under different loads

Fig.4 Number of steel ball of rolling element

Fig.5 Simulation results of contact force between No.1 steel ball and N1 raceway

Table 3 Comparison of simulated, theoretical, and actual values of contact force between No.1 steel ball and N1 raceway

Fig.6 Influence of D₁ on dynamic performance of slewing bearing

Fig.7 Influence of D₂ on dynamic performance of slewing bearing

Fig.8 Influence of D₃ on dynamic performance of slewing bearing

Fig.9 Influence of D₄ on dynamic performance of slewing bearing

最优子目标函数	D₁/mm	D₂/mm	D₃/ (°)	D₄
$f 1 (x)$	13.125	25.8	55	0.6
$f 2 (x)$	13.000	25.6	55	0.6
$f 3 (x)$	12.875	25.8	55	0.4
$f 4 (x)$	13.000	25.2	40	0.6

Table 4 Design variable combination when taking optimal value of each sub objective function

处理方法	最优子目标函数	$f 1' (x)$	$f 2' (x)$	$f 3' (x)$	$f 4' (x)$
均值化	$f 1 (x)$	0.598	0.749	0.733	0.899
	$f 2 (x)$	0.601	0.748	0.729	0.893
	$f 3 (x)$	0.926	0.992	0.527	1.245
	$f 4 (x)$	0.732	0.796	1.678	0.530
极小值化	$f 1 (x)$	1.000	1.000	1.392	1.698
	$f 2 (x)$	1.004	1.000	1.385	1.685
	$f 3 (x)$	1.548	1.325	1.000	2.349
	$f 4 (x)$	1.223	1.063	3.186	1.000

Table 5 Sub objective functions values processed by unified dimension method

Table.6 Optimal design variable combination under new objective optimization function

对比项	优化前	优化后	优化率/%
$f 1 (x)$	11 708.4	5 940.22	49.27
$f 2 (x)$	1 323.41	931.621	29.60
$f 3 (x)$	0.002 59	0.002 45	5.41

Table.7 Comparison of sub objective function values before and after optimization

Fig.10 Dynamic characteristic curves of slewing bearing before and after optimization


[1]	田贵. 转盘轴承材料及其承载能力研究［D］. 合肥：合肥工业大学， 2016： 1-2. TIAN G. Study on material and carrying capacity of slewing bearing ［D］. Hefei： Hefei University of Technology，2016： 1-2.

[2]	赵健. 内齿式回转支承参数化分析与动态设计［D］. 昆明：昆明理工大学，2021： 2-3. ZHAO J. Parameterized analysis and dynamic design of internal gear slewing bearing ［D］. Kunming： Kunming University of Science and Technology， 2021： 2-3.

[3]	GLODElŽ S， POTOČNIK R， FLAŠKER J. Computational model for calculation of static capacity and lifetime of large slewing bearing's raceway ［J］. Mechanism and Machine Theory， 2012， 47： 16-30.

[4]	AMASORRAIN J， SAGARTZAZU X， DAMIÁND J. Load distribution in a four contact-point slewing bearing ［J］. Mechanism and Machine Theory， 2003， 38（6）： 479-496.

[5]	原思聪，严卫东，邹存范，等. 异形高耸塔机回转支承的接触动力学分析［J］. 机械设计， 2012， 29（9）： 61-65. doi：10.3969/j.issn.1001-2354.2012.09.013 YUAN S C， YAN W D， ZOU C F， et al. Contact dynamics analysis of slewing bearings for special-shaped tower cranes ［J］. Journal of Mechanical Design， 2012， 29（9）： 61-65. doi: 10.3969/j.issn.1001-2354.2012.09.013

[6]	王艳霜，袁倩倩. 负游隙对特大型双排四点接触球轴承载荷分布的影响［J］.机械工程学报， 2012， 48（21）： 110-115. doi：10.3901/jme.2012.21.110 WANG Y S， YUAN Q Q. Influence of negative clearance on load distribution of large-size double row four-point-contact ball bearing ［J］. Journal of Mechanical Engineering， 2012， 48（21）： 110-115. doi: 10.3901/jme.2012.21.110

[7]	罗丫，杨本梦，涂文兵. 滚动轴承保持架-滚动体接触动力学建模与接触特性［J］.航空动力学报， 2022， 38（X）： 1-9. LUO Y， YANG B M， TU W B. Dynamic modeling of the contact between cage and rolling element in rolling bearing and contact characteristics ［J］. Journal of Aerospace Power， 2022， 38（X）： 1-9.

[8]	邱明，史鹏飞，成龙，等. 四点接触球转盘轴承载荷分布的影响因素分析［J］. 河南科技大学学报， 2012， 33（5）： 49-53， 3. QIU M， SHI P F， CHENG L， et al. Analysis of influencing factors on load distribution of four-point contact ball slewing bearings ［J］. Journal of Henan University of Science and Technology， 2012， 33（5）： 49-53， 3.

[9]	ZUPAN S， PREBIL I. Carrying angle and carrying capacity of a large single row ball bearing as a function of geometry parameters of the rolling contact and the supporting structure stiffness ［J］. Mechanism and Machine Theory， 2001， 36（10）： 1087-1103.

[10]	姚廷强，王立华，刘孝保，等.变工况下角接触球轴承保持架稳定性分析［J］. 振动与冲击， 2016， 35（18）： 172-180. YAO T Q， WANG L H， LIU X B， et al. Dynamic stability analysis on the cage of ball bearing under varying working environment ［J］. Journal of Vibration and Shock， 2016， 35（18）： 172-180.

[11]	王明凯，闫柯，马帅军，等.联合载荷作用下精密角接触球轴承动态特性演变规律［J］. 航空动力学报，2022， 37（6）： 1134⁃1149. WANG M K， YAN K， MA S J， et al. Evolutionary regularity of dynamic characteristics for precision angular contact ball bearing under combined loads ［J］. Journal of Aerospace Power， 2022， 37（6）： 1134-1149.

[12]	张文虎，胡余生，邓四二，等. 高速圆柱滚子轴承保持架振动特性研究［J］. 航空动力学报， 2019， 38（22）： 85-94. ZHANG W H， HU Y S， DENG S E， et al. Cage vibration behaviors of high-speed cylindrical roller bearings ［J］. Journal of Aerospace Power， 2019， 38（22）： 85⁃94.

[13]	李芃，王敏，戚晓利，等.单排球式回转支承动态力学性能的研究［J］.振动与冲击， 2013， 31（14）： 89-93. LI P， WANG M， QI X L， al at. Dynamic mechanical properties of single-row bearings ［J］. Journal of Vibration and Shock， 2013， 31（14）： 89-93.

[14]	张义民，杨健，胡鹏，等.考虑变位系数的直齿轮啮合特性分析［J］.东北大学学报，2013， 34（9）： 1287-1291. ZHANG Y M， YANG J， HU P， al at. Meshing characteristics analysis of spur gear pair considering modification coefficient ［J］. Journal of Northeastern University， 2013， 34（9）： 1287-1291.

[15]	贾平. 偏航变桨轴承力学特性分析及结构优化设计［D］. 大连：大连理工大学，2012. JIA Ping. Mechanical performance analysis and optimization design of yaw and pitch bearing ［D］. Dalian： Dalian University of Technology， 2012.

[16]	RAO B R， TIWARI R. Optimum design of rolling element bearings using genetic algorithms ［J］. Mechanism and Machine Theory， 2006， 42（11）： 233-250.

[17]	朱琳，张刚，倪小艇，等. 风力发电机变桨轴承的力学性能分析［J］. 工业控制计算机， 2015（8）： 106-109， 112. doi：10.3969/j.issn.1001-182X.2015.08.048 ZHU L， ZHANG G， NI X T， al at. Mechanics performance analysis of wind turbine pitch bearing ［J］. Bearing， 2015（8）： 106-109， 112. doi: 10.3969/j.issn.1001-182X.2015.08.048

[18]	史朋飞. 薄壁四点接触球转盘轴承的性能分析［D］. 洛阳：河南科技大学， 2013： 24-26. SHI P F. Analysis on performances of thin-walled four point-contact ball slewing bearing ［D］. LuoYang： Henna University of Science and Technology， 2013： 24-26.

[19]	温保岗，王美令，乔留春，等. 保持架间隙对角接触球轴承振动特性的影响［J］.轴承， 2019（7）： 6-9. WEN B G， WANG M L， QIAO L C， et al. Influence of cage clearance on vibration characteristics of angular contact ball bearings ［J］. Bearing， 2019（7）： 6-9.

[20]	朱琳，张钢，倪晓艇，等. 风力发电机变桨轴承的力学性能分析［J］. 工业控制计算机， 2015， 28（8）： 106-109， 112. doi：10.3969/j.issn.1001-182X.2015.08.048 ZHU L， ZHANG G， NI X T， et al. Mechanics performance analysis of wind turbine pitch bearing ［J］. Industrial control computer， 2015， 28（8）： 106-109， 112. doi: 10.3969/j.issn.1001-182X.2015.08.048

[21]	贺新春，李兴拼，刘卫林，等. 水资源系统多目标综合评估模型与方法［J］.水利学报， 2009， 40（9）： 1033-1039. doi：10.3321/j.issn:0559-9350.2009.09.002 HE X C， LI X P， LIU W L， et al. Multi-objective comprehensive assessment model and method of water resources system ［J］. Journal of water engineering， 2009， 40（9）： 1033-1039 doi: 10.3321/j.issn:0559-9350.2009.09.002

[22]	饶江. 基于Pareto最优的悬架参数多目标优化［D］. 杭州：浙江大学， 2010. RAO J. Pareto-optimal of suspension parameters for multi-objective optimization ［D］. Hangzhou： Zhejiang University， 2010.

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