Multi-objective optimization design algorithm of dynamic and thermal performances of high speed spindle bearing
A multi-objective optimization design algorithm model for dynamic and thermal properties analysis of high speed spindle bearing is constructed. Stiffness of bearing can be obtained by solving equilibrium equations of inner ring of bearing. Heat generation of the high speed ball bearing is studied by analyzing the local friction in the bearing considering coupling of dynamic properties, a new model for evaluating bearing temperature is set up treating the contact surfaces between rolling elements and raceways as moving heat sources. Based on this model, multi-objective optimization of stiffness and temperature rising of high speed spindle bearings are studied. Pareto-optimal solution of high speed spindle bearing are given.
Prediction of thermo-elastic behavior in a spindle–bearing system considering bearing surroundings
Abstract This paper presents a simulation method based on system dynamics to establish a comprehensive prediction model for the thermal and mechanical behavior of a spindle–bearing system in consideration of bearing surroundings such as assembly tolerance, geometric dimension, cooling conditions, operating conditions and thermal deformation. By introducing a lumped element into the system, not only mechanical properties but also thermal behaviors can be readily examined and predicted. The most important behavior in the spindle–bearing system is the bearing pressure, which determines the spindle characteristics and friction moment. In this study three different simplified assemblies are investigated. One is the bearing inner race–shaft subassembly that includes a negative assembly clearance, and another is the outer race–housing assembly that includes a positive assembly clearance. The third is the entire system that is composed of a rolling element bearing, an inner race–shaft subassembly and an outer race subassembly. The two subassemblies are coupled by rolling elements in which the frictional moment and heat generation vary with the assembly clearance and thermal deformation of the bearing surroundings. The new method can be applied to spindle cooling as well as the optimal thermal and mechanical design of the spindle–bearing system for various surrounding conditions. Furthermore, on the basis of the proposed model, the effect of steel and ceramic bearing materials on the thermo-elastic behavior of the spindle system was investigated.
Non-linear dynamic analysis of a flexible rotor supported on porous oil journal bearings
Abstract In the present paper, the non-linear dynamic analysis of a flexible rotor with a rigid disk under unbalance excitation mounted on porous oil journal bearings at the two ends is carried out. The system equation of motion is obtained by finite element formulation of Timoshenko beam and the disk. The non-linear oil-film forces are calculated from the solution of the modified Reynolds equation simultaneously with Darcy’s equation. The system equation of motion is then solved by the Wilson-θ method. Bifurcation diagrams, Poincare maps, time response, journal trajectories, FFT-spectrum, etc. are obtained to study the non-linear dynamics of the rotor-bearing system. The effect of various non-dimensional rotor-bearing parameters on the bifurcation characteristics of the system is studied. It is shown that the system undergoes Hopf bifurcation as the speed increases. Further, slenderness ratio, material properties of the rotor, ratio of disk mass to shaft mass and permeability of the porous bush are shown to have profound effect on the bifurcation characteristics of the rotor-bearing system.