Abstract
Thermal deformation caused by temperature rise affects the contact status of bearings in motorized spindles. In turn, the change in the contact status will affect the temperature rise and thermal deformation of the system. However, the latter has been rarely focused on in the previous literature. Therefore, a thermal network model of motorized spindle is enhanced by considering the thermal–mechanical coupling effect. Then, an iterative method is presented to solve the coupled equations, and a temperature test rig of the motorized spindle is set up to verify the proposed model. The predicted results by the proposed model are compared with the experimental results and the predicted results by the previous model. The relative error between the predicted and experimental results at two test points decreases by 9.56% and 3.44%, respectively, after considering the thermal–mechanical coupling effect. The temperature changes the contact angle and contact load of the bearings, thereby causing changes in frictional heat and temperature field. Such changes cause the difference between the proposed and previous models. The comparison with the experimental results shows that the proposed model with thermal–mechanical coupling effect can obtain a more accurate temperature field than the previous model.
Highlights
Motorized spindle is a core functional component of computer numerical control (CNC)
As the bases of calculation for the temperature in the spindle system, a thermal–dynamic model of bearings was established by Palmgren [4] and the frictional heat of bearings was calculated by Jones [5]
The temperature in the spindle system was determined through the finite difference model (FDM) by Harris [6], but the thermal deformation of the spindle system was not included in their model
Summary
As an important part of the motorized spindle, the built-in permanent magnet synchronous motor has the characteristics of high efficiency, small volume, light weight, and low temperature rise. Where δz denotes the relative axial displacement caused by the bearing preload; Ri represents the radius of curvature in the bearing inner raceway; θx and θy are the relative angular displacement of the bearing in x and y directions, respectively; Ψj denotes the position angle of the ball; ua in bearings 1 and 2 is determined using Eq (27a), and that in bearings 3 and 4 is calculated using Eq (27b). Where Kij and Koj denote the load deformation coefficients in the bearing; αij and αoj are the contact angles between ball j and the inner raceway or outer raceway, respectively; Mgj and Fcj represent the gyroscopic moment and centrifugal force on ball j, respectively. An iterative algorithm is provided to solve the coupled equations
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