Analytical Determination and Influence Analysis of Stiffness Matrix of Ball Bearing under Different Load Conditions

Abstract

Bearing stiffness, as one of the most important service characteristics for ball bearing, plays a crucial role in the bearing design and rotor dynamic analysis. To rapidly and accurately calculate the stiffness matrix of ball bearing under the arbitrary load conditions, a 5-DOF analytical model for bearing stiffness matrix analysis has been established by the ball–raceway contact analysis, implicit/explicit differential method, and matrix operations. The model has been validated comparing with the previous methods and experimental results. Based on this, the model has been used to investigate the influences of the load and operation conditions, the structural parameters variation on stiffness of ball bearing. The results show that property increasing axial preload can inhibit the attenuation of speed-varying stiffness, and the contact states between balls and raceways also have significant influence on the change in the stiffness of ball bearings. Besides, a larger curvature coefficient of inner raceway and a small curvature coefficient of outer raceway can effectively improve the stiffness of ball bearing at high speed. Therefore, the proposed method can be a useful tool in bearing optimize design and performance analysis of ball and rotor system under various load conditions.

Nonlinear dynamic analysis of ceramic bearing rotor system considering temperature variation fit clearance

“…where Fa and Fr are the external forces acting on the ceramic bearing. αij and αoj are contact angle, f1 is load factor relevant to equivalent static load P0 and rated static load C0 [30], whose value is calculated with Equation (3).…”

“…The above study has fully studied the fitting clearance of rotor system under constant temperature, but in high-speed precision instruments, temperature change is also a great influencing factor. Zhou et al [30] put forward a method to calculate bearing temperature and its distribution, and studied the influence of applied load and rotational speed on bearing temperature distribution. Bai et al [31] modeled the acoustic radiation of rotor system, and studied the acoustic radiation characteristics affected by fit clearance related to external ambient temperature, rotational speed and radial load.…”

Analysis and Experimental Research on Dynamic Characteristics of Horizontal Shaft System of Photoelectric Equipment

“…The results of the above literature show that bearing stiffness has a great influence on system characteristics. At present, the research on the dynamic characteristics of bearings mainly focuses on simple bearing structures such as deep groove ball bearings, angular contact ball bearings, and cylindrical roller bearings [5,7,8,9], but the research on the vibration transmission characteristics of complex bearing structures with multiple rows of rollers is relatively blank.…”

Comprehensive stiffness analysis of the cylindrical roller bearing for aircraft engines considering the radial clearance

“…Next, the creation of a comprehensive stiffness model of ball bearings has been studied by many researchers. Niu et al (2022) analyzed that property increasing axial preload can inhibit the attenuation of speed-varying stiffness, and the contact states between balls and raceways also have a significant influence on the change in the stiffness of ball bearings. Zhang et al (2017) proposed a new iterative algorithm on the basis of Jones' quasi-static model and stiffness analysis model and calculated the preload and stiffness of composite bearings.…”