To investigate the cage stability of high-speed oil-lubricated angular contact ball bearings, a dynamic model of cages is developed on the basis of Gupta’s and Meeks’ work. The model can simulate the cage motion under oil lubrication with all six degrees of freedom. Particularly, the model introduces oil-film damping and hysteresis damping, and deals with the collision contact as imperfect elastic contact. In addition, the effects of inner ring rotational speed, the ratio of pocket clearance to guiding clearance and applied load on the cage stability are investigated by simulating the cage motion with the model. The results can provide a theoretical basis for the design of ball bearing parameters.
A new product conceptual design approach is put forward based on Hopfield neural networks models. By research on the mechanisms of Hopfield neural networks, the associative simulation approaches are proposed. The approach is given by Hebb learning law, Hopfield neural networks and crossover and mutation.The calculating models and the calculating formulas for the conceptual design are put forward. Finally, an example for the conceptual design of a solar energy lamp is given.The better results are obtained in the conceptual design.
This paper develops a five degrees of freedom(5-DOF) model for aeroengine spindle dual-rotor system dynamic analysis.In this system,the dual rotors are supported on two angular contact ball bearings and two deep groove ball bearings,one of the latter-mentioned bearings works as the inter-shaft bearing.Driven by respective motors,the dual rotors have different co-rotating speeds.The proposed model mathematically formulates the nonlinear displacements,elastic deflections and contact forces of bearings with consideration of 5-DOF and coupling of dual rotors.The nonlinear equations of motions of dual rotors with 5-DOF are solved using Runge-Kutta-Fehlberg algorithm.In order to investigate the effect of the introduced 5-DOF and nonlinear dy-namic bearing model,we compare the proposed model with two models:the 3-DOF model of this system only considering three translational degrees of freedom(Gupta,1993,rotational freedom is neglected);the 5-DOF model where the deep groove ball bearings are simplified as linear elastic spring(Guskov,2007).The simulation results verify Gupta's prediction(1993) and show that the rotational freedom of rotors and nonlinear dynamic model of bearings have great effect on the system dynamic simula-tion.The quantitative results are given as well.
It is a complicated problem for the bottom-to-top adaptive conceptual design of complicated products between structure and function. Reliable theories demand to be found in order to determine whether the structure accords with the requirement of design. For the requirement generally is dynamic variety as time passes, new requirements will come, and some initial requirements can no longer be used. The number of product requirements, the gene length expressing requirements, the structure of the product, and the correlation matrix are varied with individuation of customer requirements of the product. By researching on the calculation mechanisms of dynamic variety, the approaches of gene expression and variable length gene expression are proposed. According to the diversity of structure selection in conceptual design and mutual relations between structure and function as well as structure and structure, the correlation matrixes between structure and function as well as structure and structure are defined. By the approach of making the sum of the elements of correlation matrix maximum, the mathematical models of multi-object optimization for structure design are provided based on variable requirements. An improved genetic algorithm called segment genetic algorithm is proposed based on optimization preservation simple genetic algorithm. The models of multi-object optimization are calculated by the segment genetic algorithm and hybrid genetic algorithm. An example for the conceptual design of a washing machine is given to show that the proposed method is able to realize the optimization structure design fitting for variable requirements. In addition, the proposed approach can provide good Pareto optimization solutions, and the individuation customer requirements for structures of products are able to be resolved effectively.
