Digital Tooth Contact Analysis Of Noncircular Gear

With the development of computer and CNC machining, the designing andmachining of non-circular gear becomes increasingly easy. However, to accuratelycalculate the gear meshing process and to evaluate the transmission performanceaccording to the actual tooth of gear pair is still a vacant.In order to solve this problem,the thesis starts from tooth discrete data points, carries out curve fitting and then obtainsmathematical description of a non-circular gear,adopts the calculating the intersectionbetween curves and simulates numerically the non-circular gear driven system to buildnon-circular gear TCA cycle obtaining the whole actual cycle’s performanceparameters.Because non-circular gear tooth profile can’t be described by precise mathematicalformula as cylindrical gear, the thesis puts forward an idea that all forms of non-circulargears teeth profile can be unified expressed using sectionalized cubic spline, whichadopts discrete points as spline endpoints. At the same time, the thesis deduces thedirect conversion formula of the coefficient of cubic splines in the same profile curveduring rotation.The core of TCA process is meshing calculation of active gear teeth driving passiveones. It describes the active and passive gears’teeth shapes by two smooth sectionalizedcubic splines, respectively. Drive the active gear to an angle and calculate the meshingpassive gear’s angle, and then complete the calculation of the whole process of activegear driving the passive one. The essence of meshing calculation is iteratively judgingthe relationship of two sectionalized cubic splines, which is divided into two processes:rough judgment (geometric method) and accurate judgment (solving nonlinearequations). In order to improve the efficiency of the algorithm, the concept of cubicspline bounding rectangle is proposed. In actual condition, several pairs of gearsparticipate into meshing, according to the given error condition, meshing transmissioncalculation method of all teeth of active gear and the passive one is presented.According to the meshing points, corner values, tooth number and otherintermediate data calculated by the TCA process, the degree of coincidence, slidingcoefficient, meshing ratio, the reverse side of the gap value and other performanceparameters can be obtained, and then specific quantitative parameters evaluatingnoncircular gears can be obtained ultimately. It can shorten time for non-circular geardesign, improve the reliability of design, at the same time, it is beneficial to furtherpopularize and apply of non-circular gear.