Tooth Profile Of Non-circular Gear Research Articles

Tooth Profile Construction and Experimental Verification of Non-Circular Gear Based on Double Arc Active Design

The double arc pitch curve is a novel way for creating a non-circular gear tooth profile. Aiming at the problems of the rounding of non-integer teeth and the nonlinear equation system in the construction of double circular arc tooth profile, an active design method based on planetary gear transmission kinematics and gear-meshing theory is proposed. By studying the double arc pitch curve of the three engagement positions, combined with the uniform theory of the relative curvature of surfaces, the distribution characteristics of the solution of the nonlinear equation system are analyzed in depth, leading to the optimal solution of the characteristic parameter values of the pitch curve. Combined with UG modeling and ADAMS motion simulation, the gear engagement force and the angular velocity of the planetary gear around the center are compared and analyzed in the case of integer tooth ratio and non-integer tooth profile. The results show that the engagement force of the gear pair constructed by integer teeth is reduced by about 17%. The optimal combination of the numbers of teeth is determined by orthogonal experiments, on which trial production and hydraulic load tests are based. The results reveal that the torque of the product at a rated speed is about 2.6% higher than that of foreign prototypes, which verifies the effectiveness of the design method proposed in this paper.

A Novel Curve for the Generation of the Non-circular Gear Tooth Profile

This paper presents a novel curve generated by a point attached to an ellipse as it rolls without slipping along a datum line of rack cutter. A mathematical model of the non-circular gear profile has been developed based on the theory of gearing. The effect of an axial ratio l (the ratio of the lengths of the major and minor axes of the ellipse) and the position of the point KR, at which the novel curve starts to generate on the tooth shape and the undercut of the non-circular gear pair is also taken into consideration. A numerical program developed from the mathematical model has been proposed for the calculation and design of the non-circular gears (NCGs). Case studies are presented to show the steps of tooth shape design and to examine the geometrical profile of the NCGs in relation to design parameters of the rack cutter etc. From that, the axial ration l and position of the point KR on the generating ellipse ƩE can be selected for each specific case in order to design the appropriate profiles of the NCGs. On that basis, an experiment to determine the gear ratio of the NCGs pair based on the meshing between gears has manufactured.

Design of a Noncircular Planetary Gear Mechanism for Hydraulic Motor

Given the design difficulty and poor accuracy of tooth profile of noncircular gear used in noncircular gear hydraulic motor, it is proposed to reduce the design difficulty and improve the design accuracy by using arc-shaped pitch curve instead of noncircular pitch curve with continuously varying curvature. Based on the geometric relationship and transmission relationship of the noncircular planetary gear mechanism, a nonlinear programming model is constructed for the circular arc-shaped pitch curve. By solving the nonlinear programming model, a noncircular planetary gear mechanism with a modulus of m = 1.5 is designed. The noncircular gear mechanism with the arc-shaped pitch curve was machined and installed in a hydraulic motor, and an efficiency comparison experiment was conducted with a high-order elliptical noncircular gear mechanism with a continuously varying curvature. The experiment shows that the efficiency of the two noncircular gear mechanisms is basically the same, and the best speed range is 100–400 rpm. The noncircular planetary gear mechanism with an arc-shaped pitch curve designed in this paper has reasonable structure, correct transmission relationship, and simple design method, which shows that the design method proposed in this paper has a good engineering application value.

Method for generating non-circular gear with addendum modification and its application in transplanting mechanism

With a focus on the design of tooth profiles of non-circular gears with addendum modifications that conform to the given complex transmission ratio curves and based on a series of discrete point sets on the pitch curves, the criteria for tooth profile distortion and undercut in non-circular gears were proposed. With the constraint of no tooth profile distortion and undercut, the addendum modification coefficient was introduced into the calculation of the distorted and undercut segments of the tooth profile of a non-circular gear, and the addendum modification coefficient of each contact point of the non-circular gear was obtained. Based on the generating principle for gear shaping with gear cutters, a theoretical model for calculating the tooth profile of non-circular gears with addendum modification was derived. The cutting and radial feeding motions of the pinion cutter were ignored, and only the meshing motion was considered. The involute tooth profiles of the pinion cutter enveloped the tooth profile of the non-circular gear. 3D automatic non-circular gear model generation software was developed, which was a secondary development product of the software UG. A non-circular gear in a rice potted seedling transplanting mechanism was designed, and the transplanter was developed and tested. The test results showed that the designed tooth profile of non-circular gear achieved the variable transmission ratios required by the transplanting mechanism. When the transplanting efficiencies were 140 plants/min, 160 plants/min and 180 plants/min, the transplanter completed the rice potted seedling transplanting operation with high quality. Keywords: non-circular gear; tooth profile generation; addendum modification coefficient; enveloping characteristics; transplanting mechanism DOI: 10.25165/j.ijabe.20201306.5659 Citation: Zhou M L, Yang Y C, Wei M X, Yin D Q. Method for generating non-circular gear with addendum modification and its application in transplanting mechanism. Int J Agric & Biol Eng, 2020; 13(6): 68–75.

Error Detection and Classification of Tangential Radial Single Machining of Non-Circular Gear

The studies on non-circular gear cutting and using errors were generally based on theory of cylindrical gear errors, and the similarities and differences between cylindrical gear and non-circular gear were combined to study the change rule of non-circular gear contacting line and obtained corresponding conclusions. In this paper, from a different perspective, by starting from the non-circular gear engagement principle, on the basis of analyzing the concrete geometric error conditions, new type tooth profile algorithm routine is reasonably modified, and needed non-circular gear tooth profile error contrast figure is obtained. Furthermore, theoretical derivation is carried out by incorporating analytical method and contacting line incremental method, validity of computer simulation is verified, a reasonable classification method is proposed based on the characterization of the error characteristic code in the general case, Summed up the error genetic map which possess enormous significance to direct practice generation[1].

Analogue simulation and analysis of non-circular gear reentry error

The studies on non-circular gear cutting and using errors were generally based on theory of cylindrical gear errors, and the similarities and differences between cylindrical gear and non-circular gear were combined to study the change rule of non-circular gear contacting line and obtained corresponding conclusions. In this paper, from a different perspective, by starting from the non-circular gear engagement principle, on the basis of analyzing the concrete geometric error conditions, new type tooth profile algorithm routine is reasonably modified, and needed non-circular gear tooth profile error contrast figure is obtained. Furthermore, theoretical derivation is carried out by incorporating analytical method and contacting line incremental method, validity of computer simulation is verified, and the characterization of the tangential error characteristic code is obtained, Summed up the error sources for error genetic which possess enormous significance to direct practice generation.

Numerical Algorithm of Tooth Profile of Noncircular Gear Pair

According to the generating method theory, noncircular gear with all convex pitch curve can be processed by generating, author designed noncircular gear tooth profile, described a method of precisely calculating noncircular gear tooth profile. And proposed automatically optimizes the noncircular gear tooth profile meshing curve part separately by the identical rack cutting tool different side envelope. Through rack cutting tool along two gear center of rotation segment deviation pitch curve change modified quantity to avoid tooth undercut, realization nonzero modified. The driving gear and the driven gear tooth profile meshing curve part separately by the identical rack cutting tool different side envelope, guarantees when meshing zero clearance. The noncircular gear machined by this method has been used in real machine, which verifies the feasibility of the method.

The Research on Three-Dimensional Model of Non-Circular Gear

According to the principles of engagement and the mathematical model of non-circular gear tooth profile, the tooth profile of non-circular gear is draw. Then the three-dimensional model of the non-circular gear is created in Pro/E three-dimensional software to provide the basis for a non-circular gear motion analysis, dynamic analysis and finite element analysis.

Study on the Method of Expressing the Pitch Curve of Non-Circular Gear Based on NURBS Curve

In order to express the pitch curve of non-circular gear conveniently in a uniform way, which would lessen the complexity of calculating the tooth profile of non-circular gear, the authors propose a curve fitting method of NURBS curve with the least data points based on the fitting of NURBS curve. This method is used to express the pitch curve of non-circular gear, and the specific solution model and detailed calculation procedure are presented. In addition, a method to select data points inhomogeneously and appropriately using non-uniform factor of selecting points is proposed. Two design examples are introduced to testify the validity of this expression method.

The Design of Noncircular Gear of Constant Pressure Angle and the Realization of Its Wire-Electrode Cutting

This paper brings forward a new type of the tooth profile of noncircular gear—constant pressure angle involute tooth profile, and realizes its wire-electrode cutting. By the design of CAD and CAM, this paper shortens the design time of the noncircular gear and improved the design accuracy of the noncircular gear. By the research of the constant pressure angle involute tooth profile of noncircular gear, this paper has improved the transmission accuracy of the noncircular gear. By the research of the technology of wire-electrode cutting, this paper has improved the manufacturing accuracy of the noncircular gear.

3D Mesh Generation for Static Stress Determination in Spiral Noncircular Gears Used for Torque Balancing

Standard procedures available for evaluating gear fillet stresses are targeted to circular gears where little information is available about noncircular gears. In this paper, a mesh generation algorithm is presented for the discretization of gear tooth profiles of noncircular gear elements for static stress evaluation using FEM (Finite Element Method). The procedure assumes that the noncircular gear tooth profile is known. Delimiting a tooth domain from the gear structure and subdividing it into sectors, the gear tooth mesh is generated by mapping pregenerated patterns into the sectors. The discretized tooth domain is used in conjunction with the FEM to obtain stresses within the tooth fillet region. For comparison, this procedure was applied to determine the stress distribution in circular gears and rectangular beams. The results were in complete agreement with existing analytical solutions. An illustrating example is presented where a noncircular gear pair is introduced to eliminate the speed and torque fluctuation that exists in an electrical generator when an I.C. engine is used as the power source for the generator. The maximum fillet Von Mises stress is calculated for each angular position of the noncircular gear pair.