Non-circular Gear Dynamic Characteristics

Non-circular gear is mainly used in variable transmission between parallel axes. In recent years, with the rapid development of the computer and NC technology, more and more non-circular gears are applied in industry, and gradually are present to some high power and high speed applications. Therefore, deep understanding of dynamic characteristics of non-circular gears appear very necessary.But nowadays, few researches about dynamics of non-circular gear are studied. In the current research, some time-varying factors such as pressure angle and contact ratio are ignored, and tooth deformation is lumped along the common tangent direction of the pitch curves, not along the normal direction of meshing tooth profile. It will make an important difference from the actual dynamic characteristics of non-circular gear. In view of these facts, this paper is devoted to the establishment of the more actual dynamic model of non-circular gear, the solution of the corresponding model and the analysis of dynamic characteristics of non-circular gear.From the basic gear theory, by a comprehensive consideration of the time-varying normal of meshing tooth profile and radius vector of pitch curve which are only particularly found in non-circular gears, the relationships of tooth profile equation, pressure angle, contact ratio and polar angle are established. By analyzing tensional vibration model of non-circular gear, differential equations of general non-circular gear dynamics which takes time-varying meshing stiffness and inertia into count is achieved. Supposing that input torque and resistance torque are constant, a solution method of Piecewise linear approximation is proposed. And analytical solution is instead of numerical solution in equation simplified from the above differential equations, it reduces the system computation greatly. Meanwhile, by letting non-circular gear pair equivalent to circular gear pair, mean stiffness of single tooth of non-circular gear is solved. Through introducing parameterized contact ratio, composite stiffness at any meshing location is obtained. Furthermore, a detailed program flow chart of dynamics calculation of non-circular gear is given. Then, elliptic gear and oval gear which represent two categories of non-circular gear are studied. Effects of some factors such as speed of rotation, damping, addendum, modulus, face width, input torque, eccentricity on the dynamic characteristics of non-circular gear are discussed. And an optimization method of dynamic characteristics is tried by adjusting contact ratio. An approach to predicting main peak of vibration response spectrum is also proposed. With comparative analysis, it is found the method is feasible.In addition, the above dynamics model and analysis method are general, and the non-circular gears studied are representative, so the analysis method and research conclusions are applicable to dynamic analysis of universal non-circular gears.