Research on the effect of structural and material parameters on vibrations based on quasi-static model of bearings
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(2020) 42:578
TECHNICAL PAPER
Research on the effect of structural and material parameters on vibrations based on quasi‑static model of bearings Hongchuan Cheng1 · Yimin Zhang2 · Wenjia Lu1 · Zhou Yang1 Received: 4 June 2019 / Accepted: 1 October 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract Variable compliance vibration is an inevitable source of the parametrically excited factors of rolling bearing–rotor system under the effect of only a limited number of rolling elements to carry the loads. Based on the quasi-static model of ball bearing, the mechanism of time-varying stiffness is studied and the effects of external load, rotational speed, geometric structure of the bearing and material parameters on the time-varying stiffness and relative variation of stiffness are analyzed quantitatively. Results show that load redistribution in bearing caused by the change of ball spatial position is the direct cause of the time-varying stiffness. Rotational speed, the number of balls and diameter have great effect on varying compliance vibration compared with external load and material parameters. In order to reduce the vibration, axial preload, contact angle, ball diameter and density should be appropriately increased, raceway groove curvature radius and radial load should be reduced, and the optimal number balls and rotational speed can be obtained according to the single-variable optimization method. The results provide theoretical basis for the structural design, material and manufacturing process selection. Keywords Ball bearing · Structural parameters · Material parameters · Varying compliance vibration · Time-varying stiffness · Relative variation of stiffness List of symbols F Applied load M Moment δ Bearing displacement θ Bearing misalignment N Number of rolling elements Db Ball nominal diameter dm Pitch diameter αo Free contact angle di Inner raceway contact diameter de Outer raceway contact diameter Δ Diametric clearance ρ Mass density Technical Editor: Marcelo Areias Trindade. * Yimin Zhang [email protected] Hongchuan Cheng [email protected] 1
School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China
College of Mechanical and Automotive Engineering, Zhaoqing University, Zhaoqing 526061, China
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Ki, Ke Load–deflection constant li, le Distance between ball and groove centers u Inner raceway cross section displacement vector x, y, z Bearing Cartesian coordinate system Fc Centrifugal force Mg Gyroscopic moment Qi, Qe Normal ball load δi, δe Normal contact deformation αi, αe Contact angle ωs Rotational speed of the shaft ωc Rotational speed of the cage ωR Speed of ball about its own axis ψj Azimuth angle of j-th ball λi, λe Raceway control parameters Rψj Transformation matrix β Ball attitude angle v Rolling element displacement Subscripts z Axial direction i Inner raceway r Radial direction e Outer raceway
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578
Page 2 of 24
Journal of the Brazilian Society of Mech
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