Effect of bearing clearance on the support stiffness of deep groove ball bearings

Research has found that axial force, centrifugal force, and high-temperature bearing clearance have a significant impact on the support stiffness of deep groove ball bearings, while changes in the position of rolling elements have little effect on the support stiffness of high-temperature bearings, with a relative variation amplitude of only 0.261%. But the prerequisite for these calculation results is to assume that the actual contact angle of each rolling element is the same [5,10-11]. In fact, for deep groove contact ball high-temperature bearings subjected to radial force, axial force, and centrifugal force of rolling elements, the actual contact angle of each rolling element is different, and the calculation method is very similar to that of angular contact ball high-temperature bearings [12-14], which can be solved using a two degree of freedom "quasi rigid body model". Under the combined action of radial and axial forces, only the local contact deformation between the rolling element and the inner and outer rings is considered, and the geometric shape of the high-temperature bearing inner and outer rings as well as the rolling element remains unchanged during the force process. The solution to the problem is actually to solve an n-th degree statically indeterminate problem, where n is the number of loaded rolling elements in the rolling high-temperature bearing, which can be solved using the force method. That is, it is necessary to take the deep groove ball high-temperature bearing as the research object, establish equilibrium equations, geometric equations, and physical equations to solve simultaneously. The difference is that the initial contact angle of the deep groove ball high-temperature bearing is equal to 0.

1.2.1 Balance Equation 1) Rolling Element Balance Equation Figure 1a) shows the position of the center of the rolling element shape and the curvature center of the inner and outer raceways when not under force; Figure 1b) shows the force diagram of the rolling element when the fixed inner ring of the deep groove ball high-temperature bearing outer ring is subjected to an axial force acting to the right. Figure 1 Rolling Element Stress Diagram Due to the Centrifugal Force Fc of the Rolling Element, the Contact Angle between the Rolling Element and the Inner Ring of the High Temperature Bearing α Contact angle between iq and outer ring α The oq is different. According to the equilibrium conditions, obtain the equilibrium equation of the rolling body, namely Qiqsin α Iq Qoqsin α Oq=0Qiqcos α Iq Qoqcos α In equation oq+Fc=0 {(2): Qiq, Qoq are the forces between the qth rolling element and the inner and outer rings of the high-temperature bearing, respectively; α Iq, α Oq is the contact angle between the qth rolling element and the inner and outer rings of the high-temperature bearing; Fc is the centrifugal force. Fc=12mdm ω 2m

Interaction and influence between bearing system dynamics and tribological behavior

The high-temperature bearing system is the most common subsystem in mechanical systems, and its construction is not complex. However, studying the mechanical behavior of shaft high-temperature bearing systems involves multiple disciplines. The interaction and influence between the dynamics and tribological behavior of a shaft high-temperature bearing system under complex variable loads make simulation calculations very complex. When analyzing the dynamic problems of the shaft high-temperature bearing system, the treatment of the impact of sliding high-temperature bearings is a key issue, which has a significant impact on the calculation results. Since Stodola A proposed treating sliding high-temperature bearings as simple elastic supports [1], scholars at home and abroad have generally adopted the following methods for analysis and research: (1) Dynamic characteristic coefficient method [2-4]: under given operating conditions, high-temperature bearing structure and parameters, lubricating oil characteristics, and other conditions, by solving the Reynolds equation, the oil film pressure field and oil film force at the static equilibrium position of the system are determined. The oil film force is regarded as a function of displacement and velocity near the equilibrium point, and the dynamic characteristic coefficients of high-temperature bearings are obtained using Taylor series expansion. (2) Approximate calculation method [4-5]: For example, expressing oil film force as a function of oil film thickness or using the theory of infinitely long high-temperature bearings (or infinitely short) high-temperature bearings to obtain an approximate expression for the dynamic characteristic coefficient of high-temperature bearings. (3) Database and artificial neural network approximation method [6]: that is, solving the Reynolds equation to obtain a database of the relationship between oil film force and high-temperature bearing parameters and operating conditions, and then using interpolation theory or artificial neural network approximation to obtain the high-temperature bearing oil film force required for dynamic analysis. (4) Directly solving the Reynolds equation method [7]: that is, directly solving the Reynolds equation during dynamic calculations to obtain the high-temperature bearing oil film reaction force. These processing methods each have their own advantages and limitations, and specific problems need to be analyzed in practical applications.