滚动轴承支撑下转子系统的耦合故障动力学

doi:10.19596/j.cnki.1001-246x.8503

摘要/Abstract

摘要：

研究含波纹度滚动轴承支撑下裂纹转子系统发生碰摩故障时的动力学特性。建立滚动轴承内外圈表面的波纹模型，采用综合模型描述转子轴系的呼吸型裂纹，研究转子系统与定子碰摩的非线性动力学特性。根据拉格朗日方程建立四自由度含波纹度滚动轴承支撑下裂纹-碰摩转子系统动力学方程，采用四阶Runge-Kutta方法进行数值求解，研究波纹度幅值、波纹数、轴承间隙及偏心量等参数对系统非线性特性的影响。结果表明：在低转速区间，随着波纹度最大幅值的增大，系统振动响应逐渐混乱，间谐波数量以及幅值随之增大，且逐渐出现连续特征谱。随着转速的逐渐增大且到达临界转速后横向位移随着轴承间隙的增大逐渐减小，随着偏心量的增大逐渐增大。到达超临界转速后，转子系统呈现出较强的非线性特征，横向位移随着最大幅值的增大而逐渐增大，振动响应随着偏心量的增大由混沌运动转变为周期1运动和拟周期运动。大轴承间隙下，系统在低转速区随着轴承间隙的增大而趋于稳定，在超高转速区则一直处于混沌运动中。波纹数与滚珠个数一致的系统相比不一致的系统在低转速区更加稳定，超临界转速区更加混乱。

关键词: 波纹度滚动轴承, 转子, 非线性动力学, 裂纹, 碰摩

Abstract:

Dynamic characteristics of a cracked rotor system supported by corrugated rolling bearing is studied. A ripple model of inner and outer ring surface of rolling bearing is established, in which the respiratory crack of rotor shaft system is described with a comprehensive model. The nonlinear dynamic characteristics of rub impact between rotor system and stator is studied. With Lagrange equation, dynamic equation of crack rub impact rotor system supported by four degree of freedom rolling bearing with waviness is established. A fourth-order Runge Kutta method is used to solve the equation numerically. Effects of parameters such as waviness amplitude, waviness number, bearing clearance and eccentricity on nonlinear characteristics of the system are studied. It shows that in low speed range, with the increase of the maximum amplitude of waviness, the vibration response of the system is gradually chaotic, the number and amplitude of interharmonics increase, and the continuous characteristic spectrum appears gradually. The lateral displacement decreases with the increase of bearing clearance and increases with the increase of eccentricity after reaching a critical speed. After reaching the supercritical speed, the rotor system presents strong nonlinear characteristics. The lateral displacement increases gradually with the increase of the maximum amplitude, and the vibration response changes from chaotic motion to periodic 1 motion and quasi periodic motion with the increase of eccentricity. Under the condition of large bearing clearance, the system tends to be stable with the increase of bearing clearance in a low speed region, while it is in chaotic motion in the ultra-high speed region. Compared with a system with same number of corrugations and balls, a inconsistent system is more stable in the low speed region and more chaotic in the supercritical speed region.

Key words: waviness rolling bearing, rotor, nonlinear dynamics, crackle, rubbing

余登亮, 南国防, 姜珊, 宋传冲. 滚动轴承支撑下转子系统的耦合故障动力学[J]. 计算物理, 2022, 39(6): 733-743.

Dengliang YU, Guofang NAN, Shan JIANG, Chuanchong SONG. Coupling Fault Dynamics of Rotor System Supported by Rolling Bearing[J]. Chinese Journal of Computational Physics, 2022, 39(6): 733-743.

图/表 16

图1 含内外波纹故障的滚动轴承示意图

Fig.1 A schematic of rolling bearing with internal and external ripple fault

图2 碰摩力模型示意图

Fig.2 A schematic of rub impact force model

图3 裂纹轴横截面示意图

Fig.3 A cross section of crack shaft

图4 耦合故障转子系统示意图

Fig.4 A schematic of coupling fault rotor system

表1 系统主要参数

Table 1 Main parameters of the system

参数	值
轴承处集中质量m₁/kg	4
轮盘处集中质量m₂/kg	32.1
无裂纹转轴刚度k/(N·m^-1)	2.5 × 10⁷
轴承阻尼c₁/(N·m·s^-1)	1 050
圆盘阻尼c₂/(N·m·s^-1)	2 100
摩擦系数f	0.1
定子径向刚度k_r/(N·m^-1)	3.5 × 10⁷
转定子间隙δ/m	2 × 10^-5
偏心量e/m	1 × 10^-5
最大幅值A/m	1 × 10^-6
波纹数N_w	8

图5 不同最大幅值下系统振动响应分岔图(a) A=1 × 10-6 m; (b) A=3 × 10-6 m; (c) A=4 × 10-6 m

Fig.5 Bifurcation diagrams of system vibration response under different maximum amplitudes (a) A=1 × 10-6 m; (b) A=3 × 10-6 m; (c) A=4 × 10-6 m

图6 不同最大幅值下系统振动响应频谱瀑布图(a) A=1 × 10-6 m; (b) A=3 × 10-6 m; (c) A=4 × 10-6 m

Fig.6 Spectrum waterfalls of system vibration response under different maximum amplitudes (a) A=1 × 10-6 m; (b) A=3 × 10-6 m; (c) A=4 × 10-6 m

图7 ω = 1350 rad ·s-1、A = 1 × 10-6 m时耦合故障系统(a) 时间历程、(b) 频谱及(c) Poincaré截面

Fig.7 (a) Time history, (b) spectrum and (c) Poincaré section of coupled fault system at ω = 1350 rad ·s-1, A = 1 × 10-6 m

图8 ω = 350 rad ·s-1时不同最大幅值的耦合故障转子系统频谱(a) A = 1 × 10-6 m; (b) A = 3 × 10-6 m; (c) A = 4 × 10-6 m

Fig.8 Spectrum diagrams of a coupled fault rotor system with different maximum amplitudes at ω = 350 rad ·s-1 (a) A = 1 × 10-6 m; (b) A = 3 × 10-6 m; (c) A = 4 × 10-6 m

图9 不同波纹数下系统振动响应分岔图(a) Nw = 7; (b) Nw = 9; (c) Nw = 10

Fig.9 Bifurcation diagrams of system vibration response under ripple numbers (a) Nw = 7; (b) Nw = 9; (c) Nw = 10

图10 不同波纹数下系统振动响应频谱瀑布图(a) Nw = 7; (b) Nw = 9; (c) Nw = 10

Fig.10 Waterfalls of system vibration response spectrum under ripple numbers (a) Nw = 7; (b) Nw = 9; (c) Nw = 10

图11 ω = 1450 rad ·s-1、Nw = 10时耦合故障转子系统(a) 时间历程、(b) 轴心轨迹、(c) 频谱和(d) Poincaré截面

Fig.11 Time history, (b) axis trajectory, (c) spectrum and (d) Poincaré section diagram of coupled fault rotor system at ω = 1 450 rad ·s-1 and Nw = 10

图12 不同轴承间隙下系统振动响应分岔图(a) r = 20 × 10-6 m; (b) r = 30 × 10-6 m; (c) r = 40 × 10-6 m

Fig.12 Bifurcation diagrams of system vibration response under different bearing clearance (a) r = 20 × 10-6 m; (b) r = 30 × 10-6 m; (c) r = 40 × 10-6 m

图13 不同轴承间隙下系统振动响应频谱瀑布图(a) r = 20 × 10-6 m; (b) r = 30 × 10-6 m; (c) r = 40 × 10-6 m

Fig.13 Spectrum waterfalls of system vibration response under different bearing clearances (a) r = 20 × 10-6 m; (b) r = 30 × 10-6 m; (c) r = 40 × 10-6 m

图14 不同偏心量时的系统振动响应分岔图(a) e = 2 × 10-5 m; (b) e = 3 × 10-5 m; (c) e = 5 × 10-5 m

Fig.14 Bifurcation diagrams of system vibration response under different eccentricity (a) e = 2 × 10-5 m; (b) e = 3 × 10-5 m; (c) e = 5 × 10-5 m

图15 不同偏心量时的系统振动响应频谱瀑布图(a) e = 2 × 10-5 m; (b) e = 3 × 10-5 m; (c) e = 5 × 10-5 m

Fig.15 Spectrum waterfalls of system vibration response under different eccentricity (a) e = 2 × 10-5 m; (b) e = 3 × 10-5 m; (c) e = 5 × 10-5 m

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