A Linkage Model of Non-circular Gear Shaping and Computer Simulation Processing

A non-circular planetary gears train beating-up mechanism was proposed, the ideal kinematic curve of beating-up rockshaft was constructed and the reverse model of the pitch curve of non-circular gears was established based on the ideal kinematic curve. When the first-level non-circular gears were set as elliptical gears, the maximum swinging angle of the sley and the influence of the elliptical gears' eccentricity on the concavo-convex characteristic of the second-level non-circular gears were analyzed. Provided with a set of parameters, the pitch curves and tooth profiles of the second-level non-circular gears were determined by reverse method. The result has shown that non-circular planetary gears train beating-up mechanism can meet the requirements of beating-up process.

Continuously variable transmission (CVT) of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency. The key technology of CVT with noncircular gear has been broken through some countries, and is in the stage of deep application research. Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China, the noncircular gear CVT is still in the preliminary exploration and research stage. The linear functional noncircular gear pair, whose transmission ratio is a linear function in the working section, to realize continuously variable transmission was the research object in this paper. According to the required transmission ratio in the working section, the transmission ratio function in the non-working section was constructed by using a polynomial. And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair. In addition, for improving the stability and bearing capacity of gear transmission, the noncircular gear pair transmission with high contact ratio was designed. Furthermore, the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile, from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment. Finally, an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.

The design flexibility and transmission stability of the non-circular gears can be improved using the helical tooth scheme. Herein, a linkage model was derived for hobbing the helical non-circular gears based on the influence of the axial feed motion of the hob on the motion of the projecting rack on the gear-blank end face. This axial feed motion produces additional motion effects on the rotary axis of the gear-blank and the moving axis of the hob. Further, the accuracy of the linkage model was verified by kinematic simulations. The global convergence characteristics of the transcendental equation used for obtaining the polar angle of the pitch curve were ascertained to derive the interpolation calculation process for the linkage model-based electronic gearbox. The cause of cumulative error during the multi-turn hobbing process of the gear blank was analyzed. The error accumulation was effectively controlled by optimizing the interpolation algorithm. The hobbing experiments and meshing transmission test were conducted using the self-developed non-circular gear hobbing system to verify the effectiveness of the linkage model and interpolation algorithm.

Little research has been done so far on the development of a simplified design technique for noncircular gears. Such a technique should take into consideration various kinematic constraints that exist in the noncircular gear pitch curve design process, to obtain appropriate gearing on the basis of a given angular velocity ratio curve. It seems that no generalized design technique has yet been established. This study used design specifications such as an angular velocity ratio curve (types of curves in individual segments and their coefficients) and center distance to design a pair of noncircular gears. The center distance was kept constant. The design process for the pitch curve was obtained and extracted from various kinematic constraints. Based on thses results, We developed a design automation technique for the pitch curve for noncircular gears, with given arbitrary angular velocity ratio curve.

This paper describes a new steering mechanism proposed by one of the authors(T.E.). This steering mechanism using noncircular gears has the capability of turning a carrier with a small radius. In order to facilitate the analysis of the steering mechanism, the concept of a virtual two-wheeled vehicle was introduced. As a result of analysis made by the other author (A.A.), it was proven that the noncircular gear for the steering mechanism is an elliptical gear of which the pitch curve can be represented by a simple equation. In addition, a method to apply this mechanism to wheeled robots, such as the carrier robots used in industrial production lines, was studied. It was confirmed that the concept of the virtual two-wheeled vehicle is very useful in the design of the steering mechanism.

Noncircular face gear drive is a new type of variable transmission ratio mechanism with advantages of light weight, high interchangeability, and convenient installation. Based on its transmission principle, the excitation pattern of the time-varying instantaneous center of the noncircular face gear drive system is investigated. A torsional–lateral–axial coupled dynamic model of the noncircular face gear system is presented under the compound parametric excitations of the time-varying instantaneous center and the mesh stiffness. By using Runge–Kutta numerical integration method, the dynamic responses of the system are derived to analyze the vibration features of the noncircular face gear under compound parametric excitations and the effect of the design parameters on the coupled vibration. The analytical results indicate that there exist multifrequency components in the dynamic responses of the system, including the instantaneous center frequency f1, the meshing one f2, nf1, mf2, and mf2 ± nf1. In addition, the dynamic performance of the noncircular face gear drive can be improved by decreasing the amplitude coefficient of the instantaneous center and the mesh stiffness or increasing their mean values.

Gear Geometry and Applied Theory, second ed., F.L. Litvin, A. Fuentes. Cambridge University Press, Cambridge (2004)

Noncircular pin-cycloid transmission is proposed,which can implement variable gear ratio transmission between parallel axes. The meshing coordinate system of the noncircular pincycloid gears is set up,with the forming principle of the conjugate profile described. The tooth profile equation of the noncircular pin gear is established,then that of the cycloidal gear is derived through coordinate system transformation,based on the conjugate tooth profile theory,the circular pin gear cutting tool profile equation,and the noncircular pin gear cutting tool path and mesh equation. The parametric design of the gear pair is obtained by Matlab program. The design example of the noncircular pin-cycloid gear is achieved. And the three dimension model is established by SolidWorks. Based on the kinematics analysis of the noncircular pin-cycloid drive by Adams software,the validity of the principle and design of noncircular pin-cycloid drive is verified through the contrast analysis between the experimental and theoretical arithmetic results.

Non-circular gear systems (NCGSs) are among the most widely used transmission mechanisms in bucket wheel stacker/reclaimers (BWSRs), the performance of which depends greatly on the NCGS dynamic characteristics such as the transmission efficiency, gear vibration, and gear-teeth failure. To improve the NCGS dynamical performance, a new non-circular gear transmission system is designed based on the transmission principle of non-circular gears while taking into account the special requirements of a BWSR. The newly designed NCGS comprises a sun gear, a fixed gear, and four planetary gears. By considering the time-varying meshing stiffness and the transmission error of the NCGS, a corresponding dynamical model of the NCGS is established using the Newton's second law. The dynamic characteristics of the NCGS under different working loads and speeds are then compared and analyzed. The results show that the NCGS can reduce the working speed of the sun gear as much as possible by meeting the performance requirement of the transmission mechanism. Finally, the newly designed NCGS is shown to be capable of improving the overall BWSR performance immensely.

The profile of the pitch curve of external and internal noncircular gears, and the restricting conditions to avoid the interferences were analyzed, and the designing conditions of the mechanisms were decided. Then, the noncircular planetary gear mechanisms were synthesized as intermittent motion mechanisms, and the noncircular gear shaper was made by way of experiment and gears were cut. And then, the mechanisms were produced and the static characteristic was investigated.

In N-G-W type non-circular planetary gear strain, the planetary gear is meshed both with the center wheel and the inner gear ring. The parameters which the design of the planetary wheel system required can be received according to the three-order elliptic equation which consist of continuous smooth closed curves as the pitch curve equation of the center wheel, and on the basis of planetary gear teeths relation, the closed condition of the pitch curve and the teeth uniformly distributed in the curve. This paper studied the design process of the pitch curve on an N-G-W type internal-curve planet gear pump by a practical example.

Gear Shaving is one of the most efficient and economical ways to finish gears after gear hobbing or gear shaping. In tradition, the shaved gear can be crowning by shaving machine with the rocking mechanism. In this paper, we propose a mathematical model of a CNC shaving machine with two synchronous axes. The proposed mathematical model can be used to calculate the crowning tooth surface of the gear in parallel-shaving process.

This paper deals with experiments of the new steering mechanism which has been proposed in the first report. First of all, the elliptical gears for the steering mechanism were cut with the NC gear shaper developed by the authors, and the error of the rotational angles of the elliptical gears was measured. Then, the authors manufactured a wheeled robot for trial in order to confirm the usefulness of this steering mechanism and succeeded in controlling the wheeled robot using a TV camera for eyes. Moreover, they carried out fundamental experiments. These experiments proved that the new steering mechanism had high turning ability, and can turn the wheeled robot with the small radius.

On gear time-varying meshing stiffness calculation considering indexing feeds and processing characteristics of gear shaping processing

Chapter 2 - Conventional Manufacturing of Cylindrical Gears