The influence of preload and speed on bearing temperature

During the working process of the spindle system, the higher the speed, the more heat generated by the bearing. Excessive heat affects the speed, stiffness and accuracy of the spindle system. In the steady state, the frictional heat of the bearing will diffuse through heat transfer. Therefore, the temperature distribution is a measure of the heat transfer capacity, design level, speed and accuracy of the spindle unit. The calculation of the frictional heat of the bearing and the heat transfer model of the spindle bearing are the basis of the temperature calculation.

The main shaft bearing contact load refers to the contact force between the bearing ball and the inner and outer rings of the bearing. The calculation of the bearing contact angle and contact force is the basis for analyzing bearing heat and deformation. In order to analyze the influence of the bearing preload and speed on the dynamic characteristics of the bearing, it is also essential to study the relationship between the preload, the speed and the bearing contact angle and contact load.

1. Bearing contact angle change and axial displacement in static preload state

Under the action of preload, the contact deformation of the spindle bearing will cause axial displacement of the inner and outer rings of the bearing. At the same time, the contact angle of the bearing will also change. It is the inner and outer rings of the spindle bearing under the combined action of radial, axial and moment loads. The displacement of each ball and the azimuth angle of each ball can be known from the geometric relationship. When there is no load, the distance between the centers of curvature of the inner and outer ring channels is:

Under the combined load, the distance between the centers of curvature of the inner and outer races increases with the increase in contact deformation. The line BD between the centers of curvature of the race passes through the center of the sphere. When the bearing rotates, the centrifugal force makes the center of the ball When moving outwards, at the same time, the centrifugal displacement of the inner ring channel and the thermal displacement of the components caused by frictional heat make the center of the ball deviate from the line BD of the center of curvature of the channel, and the contact angles of the inner and outer rings are no longer equal. Assuming that the center of curvature of the outer ring channel is fixed, the center of curvature of the inner ring channel can move relatively. .

Pre-tightening is a specific state of stress. There are mainly two pre-tightening methods for rolling bearings: one is constant pressure pre-tightening, and the other is positioning pre-tightening. Under constant pressure preloading, the inner and outer rings can produce axial displacement, but its axial load is always constant; under positioning preload, even if it is subjected to other loads, the axial displacement of the inner and outer rings is approximately unchanged.

2. Bearing friction

The friction of the bearing is the sum of the resistance to movement of the components inside the bearing when the inner and outer rings rotate relatively. It can be divided into five categories according to the mechanism and location of impedance.

1) Pure rolling friction caused by elastic hysteresis

The rolling elements roll along the surface of the raceway under load, and the material under the contact surface will be elastically deformed. After the contact is eliminated, the main part of the elastic deformation is restored. However, when the load increases, the deformation corresponding to a given stress is always smaller than the deformation when the load decreases. This is called elastic hysteresis. It reflects the energy loss of Shiding, which is manifested as rolling friction resistance.

This part of the energy helps the rolling elements to overcome the resistance and continue to roll forward. However, due to elastic hysteresis, the energy released by elastic recovery at the back of the contact area is always less than the energy lost due to elastic deformation at the front of the contact area. The difference between the two is the energy converted when the rolling friction torque is overcome and the work is done.

2) Microscopic sliding friction that occurs in the contact area between the ring and the rolling element

When the rolling element is rolling, the surface linear velocity of a certain point on the surface is proportional to the distance (radius) from that point to the axis. Since the contact surface is a curved surface, the distance from each point of the contact surface to the axis of rotation of the rolling element is not equal, and the linear velocity of each point is not equal. Therefore, pure rolling occurs only at two points, and occurs on the middle and both sides of the contact surface. Differential sliding in the opposite direction. Because the contact area is very small, the linear velocity difference of each point is very small. It is called micro-differential sliding friction.

(3) Spin sliding friction

In angular contact ball bearings, once there is an axial load, the steel ball may generate a spin motion relative to the raceway around the normal line of the contact surface. The resulting sliding friction is called spin sliding friction. Because the contact area between the ball and the raceway is small, the relative sliding linear velocity caused by the spin is not large, and this type of friction is also microscopic sliding friction.

(4) Macroscopic sliding friction

The rolling element is not an ideal pure rolling motion. For various reasons, the movement of the rolling elements on the raceway is often a kind of continuous rolling and sliding movement. The friction caused by the macroscopic slippage of the rolling elements on the inner and outer raceways and the friction caused by the sliding contact parts in the bearing are collectively called macroscopic sliding friction. The macroscopic slippage of the rolling elements on the inner and outer raceways is related to many factors such as the structural parameters of the bearing, speed, load and lubricant viscosity, and there is no effective calculation method at present.

(5) Friction loss of lubricant

The friction loss of lubricant consists of two parts. Part of it is caused by the internal frictional resistance of the lubricating oil film. The other part is the agitation resistance loss of the lubricant that the rolling elements and cages receive when they rotate. Whether it is an elasto-hydrodynamic oil film or a sliding dynamic pressure oil film, the thickness of the oil film is on the order of micrometers, and the area of the contact area is small, so the volume of lubricant that actually plays a lubricating role in the contact area is often less than a few cubic millimeters. Most of the lubricant in the bearing splashes and collides under the agitation of the moving components, resulting in agitation resistance. The friction loss of lubricant is mainly agitation friction loss. Excessive lubricant will cause great agitation resistance, resulting in excessive temperature rise of the bearing. For grease lubrication, it is recommended not to exceed 1/3 of the free space volume in the bearing. Studies have shown that under the conditions of proper oil injection and grease lubrication, the rolling and sliding friction loss of the bearing accounts for 20% to 30% of the total friction loss; The stirring friction loss of the lubricant accounts for 50%~60%; the friction loss of the seal ring accounts for 10%~30%. The current research results on the friction mechanism of rolling bearings cannot provide engineers with accurate theoretical values of the losses caused by various types of friction under given operating conditions.

3. The heat transfer method of the spindle bearing

In classical thermodynamics, there are three main ways of transferring heat: heat conduction, heat convection and heat radiation.

(1) Theoretical basis of heat conduction

Heat conduction refers to the transfer of heat from the high temperature part to the low temperature part of the object when there is a temperature difference inside the object, or when objects of different temperatures are in contact with each other, the heat is transferred from a higher temperature object to a lower temperature object in contact with it transfer. From a microscopic point of view: the process of heat conduction is a process of heat transfer that only relies on the thermal motion of microscopic particles such as molecules, atoms, and free electrons when there is no relative displacement between various parts of the object. The existence of temperature difference is a necessary condition for heat conduction. Since there is no temperature difference on the isothermal surface, heat conduction only occurs between different isothermal surfaces, that is, from the high temperature isothermal surface along its normal direction to the low temperature isothermal surface.

(2) Theoretical basis of thermal convection

Thermal convection refers to the heat exchange caused by relative motion of various parts of fluids at different temperatures. The convection heat transfer, which is widely mentioned in engineering, refers to the heat transfer process between the fluid and the solid wall in contact with it. It is the result of the combined effects of heat conduction and heat convection. The main factor that determines the intensity of heat transfer is the movement of convection. The salient feature of thermal convection is that the transfer of energy from one point in space to another is achieved by the displacement of the fluid itself. Convection is divided into natural convection and forced convection: when there is a temperature difference in the fluid, the density of the fluid changes with temperature, which causes the flow of the fluid, which is usually called natural convection; the flow generated by the fluid dependent on external force is called Forced convection. In a fluid, if there is a temperature difference between the various parts to cause heat conduction, it will inevitably produce natural convection due to the difference in density of each part. Therefore, heat conduction and convection in the fluid always occur at the same time, unless the fluid is located The space is very small and convective motion cannot be formed. Only then will there be pure heat conduction.

(3) Theoretical basis of thermal radiation

Thermal radiation refers to the way an object emits visible and invisible rays to transfer heat due to its own temperature. The heat radiation process has the following characteristics: heat radiation does not rely on the contact of substances to transfer heat and can be transmitted in a vacuum; the radiation heat exchange process is accompanied by the conversion of energy forms: as long as the temperature of the object is higher than zero, it is constantly outward It emits thermal radiation, and at the same time, it continuously absorbs the thermal radiation emitted by other objects around it. The combined result of radiation and absorption results in the heat transfer between objects in the form of heat radiation, that is, the process of radiation heat exchange. The higher the temperature of the object, the more heat radiated per unit time