Abstract: In view of the important influence of thermal displacement on the performance of angular contact ball bearings under high-speed conditions, the calculation formula of radial thermal displacement of bearing rings is deduced, and the calculation of dynamic characteristics of high-speed angular contact ball bearings considering the influence of radial thermal displacement of rings is given. methods and corresponding procedures. The calculation results of the 7012C bearing show that the radial thermal displacement of the bearing ring, especially the inner ring, is large, which causes the radial relative displacement between the inner and outer ring channels; with the increase of the thermal displacement of the inner and outer rings of the bearing, the inner contact angle When the outer contact angle decreases, the centrifugal force of the rolling element decreases and the gyroscopic moment increases, and the contact deformation, contact stress, contact load and bearing stiffness increase significantly. Therefore, in order to make the analysis of dynamic characteristics of angular contact ball bearings more accurate and more realistic, the influence of radial thermal displacement of the ring must be taken into account.
High-speed machining technology is more and more widely used due to its advantages of high efficiency, high precision and less cutting force and cutting heat. The high-speed motorized spindle is the core component to realize high-speed machining, and its support mostly adopts high-speed angular contact ball bearings. The dynamic characteristics of the support bearing directly affect the dynamic performance and service life of the motorized spindle bearing L rotor, so it is of great significance to analyze the dynamic characteristics of the high-speed angular contact ball bearing.
Under high-speed conditions, the dynamic characteristics of angular contact ball bearings are affected by various factors such as installation, preload, rotational speed, temperature rise, load form and structural parameters. The influence of application parameters and structural parameters such as rotational speed, nominal diameter, rolling element diameter, channel curvature radius, initial contact angle, etc. on the dynamic characteristics of high-speed angular contact ball bearings is analyzed; the influence of preload on the dynamic characteristics of angular contact ball bearings is analyzed. ;According to the actual working conditions, a set of ball bearing simulation dynamics analysis software is established to analyze the dynamic characteristics of aero-engine ball bearings; The superiority of ceramic ball bearings under high speed conditions. On the basis of considering the centrifugal force and gyro moment of the rolling element. A pseudo-dynamic model of ultra-high-speed angular contact ball bearing is established. The dynamic characteristics of motorized spindle bearings under ultra-high speed conditions are analyzed. The effects of the number of rolling elements and preload on the dynamic characteristics of ball bearings are analyzed. However, with the continuous increase of the speed and power of the electric spindle, the radial thermal displacement of the inner and outer races of the bearing caused by the temperature rise has become an influential factor that cannot be ignored in the analysis of the dynamic characteristics of the electric spindle. In this paper, the radial thermal displacement of the inner and outer races of the bearing and the resulting radial thermal displacement between the inner and outer races are calculated based on the elastic mechanics theory “rolling bearing dynamics and race control theory”. The calculation method and corresponding program of the dynamic characteristics of high-speed angular contact ball bearings affected by radial thermal displacement, the influence of the radial thermal displacement of the inner and outer ring grooves on the dynamic characteristics of ball bearings is analyzed, and the theory is provided for the dynamic analysis of high-speed angular contact ball bearings. in accordance with.
1 Analysis of radial thermal displacement of inner and outer rings of bearings
1.1 Radial thermal displacement of inner and outer rings
The width of the inner and outer rings of the bearing is smaller than the diameter, and they can be regarded as thin rings symmetrical to the center of the circle when calculating the thermal displacement.#According to the theory of elasticity
1.2 Boundary condition analysis
1.2.1 Boundary conditions of bearing inner ring
The radial displacement and stress of the inner ring of the bearing and the outer surface of the main shaft satisfy the following boundary conditions;
(1) The surface stress of the inner ring channel surface and the inner hole of the main shaft is zero;
(2) The stress on the mating surface of the inner ring and the main shaft is equal;
(3) The pressure and thermal displacement of the inner ring and the main shaft on the mating surface are satisfied, which is the interference fit between the inner ring of the bearing and the main shaft (2$ is the inner diameter of the main shaft (2) 25 is the inner and outer diameter of the bearing inner ring (G>S) G>F is the thermal displacement of the inner ring of the main shaft) bearing.
1.2.2 Boundary conditions of bearing outer ring
The radial thermal displacement and thermal stress of the bearing outer ring satisfy the following boundary conditions:
(1) The thermal displacement of the outer surface of the bearing outer ring is zero
(2) The thermal stress on the surface of the outer ring raceway of the bearing is zero
1.3 Temperature distribution function of inner and outer rings of bearing
1.3.1 Temperature distribution function of bearing inner ring and main shaft
The heat dissipation condition of the inner ring is poor + it will be in thermal equilibrium soon + the inner ring can be regarded as an isothermal body * the thickness of the inner ring of the bearing is very small compared with the diameter of the mounting journal + the inner diameter of the bearing inner ring and the journal can be regarded as 2$ ) Hollow shaft with an outer diameter of 25 * According to the non-linear distribution of its temperature along the radial direction + its temperature field equation can be approximated
1.4 Example analysis
Assuming the temperature rise of the bearing and the bearing seat, the structural parameters of the bearing are shown in the table! + is the radial thermal displacement of the inner and outer rings of the bearing.
In Figure #, +G>F) G>7 and G> are the radial thermal displacement of the inner and outer ring channels of the bearing and the radial relative thermal displacement between the inner and outer ring channels, respectively. The radial thermal displacement of the inner ring channel is expressed as The expansion of the inner ring channel + and the radial thermal displacement of the outer ring channel is expressed as the contraction of the outer ring channel + Therefore + the radial relative thermal displacement between the inner and outer ring channels is the radial thermal displacement of the inner ring and the radial heat displacement of the outer ring. The sum of thermal displacements * can be seen from Figure # + is affected by the radial thermal displacement of the ring, especially the inner ring channel + the radial thermal displacement value between the inner and outer ring channels of the bearing is large + in a thermally stable state, it is as high as The influence of bearing dynamic characteristics cannot be ignored.
2 Dynamic characteristics analysis of high-speed angular contact ball bearings considering the radial thermal displacement between the inner and outer races
2.1 Basic equations
2.1.1 Deformed geometry compatibility equation
According to the outer channel control theory + in the analysis of the dynamic characteristics of the bearing + the radial relative thermal displacement between the inner and outer race channels is finally expressed as the radial relative thermal displacement of the inner race channel. The relative positional relationship between the center of curvature of the inner and outer rings of the bearing and the center of the rolling elements.
2.2 Solving basic equations
According to the above analysis, to analyze the influence of the radial thermal displacement of the inner and outer ring grooves on the dynamic characteristics of the angular contact ball bearing, it is necessary to solve the equation system composed of equations. “For such a nonlinear equation system# This paper adopts the Newton + Rafson iteration method” its calculation process.
2.3 Example analysis
In this paper, the internal dynamic characteristics of angular contact ball bearings are calculated. The bearing structure and material parameters are shown in the table! moment) contact load) contact stress and contact deformation) bearing stiffness and other dynamic characteristic parameters.
(1) Actual contact angle
The change of the contact angle between the rolling element and the inner and outer ring channels with the radial thermal displacement between the inner and outer ring channels can be seen # with the increase of the radial thermal displacement between the inner and outer ring channels# the inner contact angle decreases while the outer contact angle Increasing #Internal and external contact angles tend to be more and more equal.
(2) Centrifugal force and gyro moment of rolling element
The centrifugal force and gyro moment of the rolling elements change with the radial thermal displacement between the inner and outer ring channels. It can be seen that the centrifugal force of the rolling elements decreases slightly with the increase of the radial thermal displacement between the channels, and the gyro moment It increases slightly with the increase of the radial thermal displacement between the channels” This is mainly because the revolution and rotation speeds of the rolling elements decrease with the increase of the radial thermal displacement between the channels# and the rotation azimuth of the rolling elements It increases greatly with the increase of the radial thermal displacement between the channels.
(3) Contact deformation, contact stress and contact load
The contact deformation between the rolling element and the inner and outer ring channels, the change of contact stress and contact load with the radial thermal displacement between the inner and outer ring channels.
It can be seen that the contact deformation between the rolling element and the inner and outer rings, the contact stress and the contact load increase with the increase of the radial thermal displacement between the inner and outer ring channels# where # is the contact load, contact stress and contact between the inner ring and the rolling element The effects of deformation, etc. are greater.
(4) Bearing stiffness
The change of bearing stiffness with the radial thermal displacement between the inner and outer ring channels is shown in the figure!! “From the figure, it can be seen that the radial stiffness, axial stiffness and angular stiffness increase with the radial thermal displacement between the channels. Large and increase #where # has the greatest impact on radial stiffness.
