Effect of static transmission error on dynamic responses of spiral bevel gears

The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the spiral bevel gear model were adopted,where the static transmission error was expressed in two patterns as predesigned parabolic function and sine function of transmission errors.The dynamic response,bifurcation map,time domain response,phase curve and Poincare map were obtained by applying the explicit Runge-Kutta integration routine with variable-step.A comparative study was carried out and some profound phenomena were detected.The results show that there are many different kinds of tooth rattling phenomena at low speed.With the increase of speed,the system enters into stable motion without any rattling in the region(0.72,1.64),which indicates that the system with predesigned parabolic function of transmission error has preferable capability at high speed.

Optimal Load Balancing Leveling Method for Multi-leg Flexible Platforms

The working platforms supported with multiple extensible legs must be leveled before they come into operation.Although the supporting stiffness and reliability of the platform are improved with the increasing number of the supporting legs,the increased overdetermination of the multi-leg platform systems leads to leveling coupling problem among legs and virtual leg problem in which some of the supporting legs bear zero or quasi zero loads.These problems make it quite complex and time consuming to level such a multi-leg platform.Based on rigid body kinematics,an approximate equation is formulated to rapidly calculate the leg extension for leveling a rigid platform,then a proportional speed control strategy is proposed to reduce the unexpected platform distortion and leveling coupling between supporting legs.Taking both the load coupling between supporting legs and the elastic flexibility of the working platform into consideration,an optimal balancing legs’ loads(OBLL) model is firstly put forward to deal with the traditional virtual leg problem.By taking advantage of the concept of supporting stiffness matrix,a coupling extension method(CEM) is developed to solve this OBLL problem for multi-leg flexible platform.At the end,with the concept of supporting stiffness matrix and static transmissibility matrix,an optimal load balancing leveling method is proposed to achieve geometric leveling and legs’ loads balancing simultaneously.Three numerical examples are given out to illustrate the performance of proposed methods.This paper proposes a method which can effectively quantify all of the legs’ extension at the same time,achieve geometric leveling and legs’ loads balancing simultaneously.By using the proposed methods,the stability,precision and efficiency of auto-leveling control process can be improved.

Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic

In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.

A cascade model of information processing and encoding for retinal prosthesis

Retinal prosthesis offers a potential treatment for individuals suffering from photoreceptor degeneration diseases.Establishing biological retinal models and simulating how the biological retina convert incoming light signal into spike trains that can be properly decoded by the brain is a key issue.Some retinal models have been presented,ranking from structural models inspired by the layered architecture to functional models originated from a set of specific physiological phenomena.However,Most of these focus on stimulus image compression,edge detection and reconstruction,but do not generate spike trains corresponding to visual image.In this study,based on stateof-the-art retinal physiological mechanism,including effective visual information extraction,static nonlinear rectification of biological systems and neurons Poisson coding,a cascade model of the retina including the out plexiform layer for information processing and the inner plexiform layer for information encoding was brought forward,which integrates both anatomic connections and functional computations of retina.Using MATLAB software,spike trains corresponding to stimulus image were numerically computed by four steps：linear spatiotemporal filtering,static nonlinear rectification,radial sampling and then Poisson spike generation.The simulated results suggested that such a cascade model could recreate visual information processing and encoding functionalities of the retina,which is helpful in developing artificial retina for the retinally blind.