Research on mechanical characteristics of fault-free bearings based on centrifugal force and gyroscopic moment
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O R I G I NA L
Hongchuan Cheng · Yimin Zhang · Wenjia Lu · Zhou Yang
Research on mechanical characteristics of fault-free bearings based on centrifugal force and gyroscopic moment
Received: 23 November 2019 / Accepted: 17 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper presents a quasi-static model of high-speed ball bearing, and the analytical expressions of dynamic stiffness are obtained. The action mechanism of centrifugal force and gyroscopic moment and its effect on kinematic and mechanical characteristics of bearing are studied. Results show that with the increase in rotational speed, centrifugal force increases continuously, while gyroscopic moment rapidly first and then slightly. With the increase in inertial force, the inner-ring contact angles and the outer-ring contact force increase, the outer-ring contact angles and inner-ring contact force decrease, and bearing stiffness will increase in all directions, while axial load will reduce the effect of inertial force. Radial force will increase the non-uniformity of load distribution, making the difference of load carried by each ball larger, thus aggravating the instability of the system. Compared with gyroscopic moment, centrifugal force is the main factor, while ignoring both inertial forces, rotational speed no longer affects mechanical characteristics of bearings. This study provides theoretical support for the dynamic analysis of high-speed bearing rotor system. Keywords Ball bearing · Centrifugal force · Gyroscopic moment · Kinematic characteristics · Mechanical characteristics
1 Introduction Rolling bearings have the functions of supporting, guiding and positioning, drag reduction, energy saving, vibration elimination and noise reduction, etc. [1–3]. The inertial force generated by high-speed ball bearing can increase the contact force of outer ring and cause the rolling element to slide tangentially and axially, thus deteriorating the bearing force and directly affecting the working performance [4]. Therefore, it is of great significance to study the mechanism of inertial load and its effect on the mechanical properties of bearings. The period from 1850 to 1925 was an important development period of rolling bearing theory. The research of tribology and contact mechanics theory made remarkable achievements in this stage. And theoretical research can make up for the deficiencies in the traditional design concept [5–8]. Hertz [9] put forward a new method to solve the local stress and deformation of two elastic bodies when they contact at one point in 1896. He believed that a small contact area would be formed in the contact area to avoid the situation of infinite stress. Stribeck [10] derives the internal load distribution formula of rolling bearing and gives the approximate formula of the maximum load on ball. Palmgren [11] has carried out a lot of research on the bearing capacity and contact H. Cheng · W. Lu · Z. Yang School of Mechanical Engineering and Automation, Northeastern University, Shenyang 1108
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