Optimization of Hypoid Gear Design and Tooth Contact Analysis

2017 ◽  
Author(s):  
Shouli Sun ◽  
Shilong Wang ◽  
Yawen Wang ◽  
Teik C. Lim ◽  
Baocang Zhou ◽  
...  
Keyword(s):  
Maximum Principle ◽  
Predictive Accuracy ◽  
Systems Design ◽  
Transmission Error ◽  
Design Parameters ◽  
Hypoid Gear ◽  
Normal Contact Stress ◽  
Normal Contact ◽  
Hypoid Gears ◽  
Peak Transmission

Hypoid gears are effectively used in cross axis power transmission systems. Design of hypoid gear parameters is complex and dependent on designers’ experiences. In this paper, an easy approach to design the parameters of hypoid gear to obtain the minimum of maximum principle normal contact stress and peak to peak transmission error is presented. An improved Particle Swarm Optimization (PSO) and Back Propagation (BP) algorithm is proposed to predict the stress and the transmission error if certain design parameters are given. The predictive accuracy is evaluated by Root Mean Square Error (RMSE) equation. The results show that the predictive accuracy is in reasonable agreement with the values calculated by the software [1]. Based on the prediction model, the optimization model for the design parameters of hypoid gear is established. This paper proposes a method to design a set of hypoid gears with minimum of maximum principle normal stress and peak to peak transmission error.

Simulation and Experimental Measurement of the Transmission Error of Real Hypoid Gears Under Load

2000 ◽  
Vol 122 (1) ◽  
pp. 109-122 ◽  
Author(s):  
Claude Gosselin ◽  
Thierry Guertin ◽  
Didier Remond ◽  
Yves Jean
Keyword(s):  
Measurement Data ◽  
Simulation Models ◽  
Transmission Error ◽  
Contact Analysis ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Loaded Tooth Contact Analysis ◽  
Analysis Models

The Transmission Error and Bearing Pattern of a gear set are fundamental aspects of its meshing behavior. To assess the validity of gear simulation models, the Transmission Error and Bearing Pattern of a Formate Hypoid gear set are measured under a variety of operating positions and applied loads. Measurement data are compared to simulation results of Tooth Contact Analysis and Loaded Tooth Contact Analysis models, and show excellent agreement for the considered test gear set. [S1050-0472(00)00901-6]

Optimization of Machine Tool Settings on Hypoid Gear Dynamics

2019 ◽  
Author(s):  
Chia-Ching Lin ◽  
Yawen Wang ◽  
Teik C. Lim ◽  
Weiqing Zhang
Keyword(s):  
Dynamic Response ◽  
Machine Tool ◽  
Rotor System ◽  
Design Parameters ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Tool Setting ◽  
Setting Parameters ◽  
Optimal Machine

Abstract Hypoid gears are widely used to transmit torque on cross axis shafts in a vehicle rear axle system. The dynamic responses of these hypoid geared rotor system have a significant effect on the performance of noise, vibration, and harshness (NVH) for the vehicle design. From past studies, the main source of excitation for this vibration energy comes from hypoid gear transmission error (TE). Thus, the design of hypoid gear pair with minimization of TE is one way to control the dynamic behavior of the vehicle axle system. In this paper, an approach to obtain minimum TE and improved dynamic response with optimal machine tool setting parameters for manufacturing hypoid gears is discussed. A neural network, named Feed-Forward Back Propagation (FFBP), with Particle Swarm Optimization (PSO) and Gradient Descent (GD) training algorithms are used to predict the TE. With the optimal machine tool setting parameters, a 14 degrees of freedom geared rotor system analysis is performed to verify the improvement on dynamic response aiming at minimizing the TE. A case study of a hypoid gear pair with specified design parameters and working condition is presented to validate the proposed method. The results conclude that minimization of TE, the main excitation of vehicle axle gear whine noise and vibration, with optimal machine tool setting parameters can improve the overall dynamic response. The proposed approach provides a better understanding of an optimal design hypoid gear set to minimize TE and effect on vehicle axle system dynamics.

Flank Modification Methodology for Face-Hobbing Hypoid Gears Based on Ease-Off Topography

2006 ◽  
Vol 129 (12) ◽  
pp. 1294-1302 ◽  
Author(s):  
Yi-Pei Shih ◽  
Zhang-Hua Fong
Keyword(s):  
Design Parameters ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
General Technique ◽  
Local Synthesis ◽  
Hypoid Gears ◽  
Gear Drive ◽  
Polynomial Coefficients ◽  
Spiral Bevel

The fundamental design of spiral bevel and hypoid gears is usually based on a local synthesis and a tooth contact analysis of the gear drive. Recently, however, several flank modification methodologies have been developed to reduce running noise and avoid edge contact in gear making, including modulation of tooth surfaces under predesigned transmission errors. This paper proposes such a flank modification methodology for face-hobbing spiral bevel and hypoid gears based on the ease-off topography of the gear drive. First, the established mathematical model of a universal face-hobbing hypoid gear generator is applied to investigate the ease-off deviations of the design parameters—including cutter parameters, machine settings, and the polynomial coefficients of the auxiliary flank modification motion. Subsequently, linear regression is used to modify the tooth flanks of a gear pair to approximate the optimum ease-off topography suggested by experience. The proposed method is then illustrated using a numerical example of a face-hobbing hypoid gear pair from Oerlikon’s Spiroflex cutting system. This proposed flank modification methodology can be used as a basis for developing a general technique of flank modification for similar types of gears.

Generation of Hypoid Gears on CNC Hypoid Generator

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Gear Tooth ◽  
Velocity Ratio ◽  
Transmission Error ◽  
Tooth Surface ◽  
Polynomial Functions ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Kinematic Scheme ◽  
Hypoid Gears ◽  
Fifth Order

In this study, polynomial functions of orders up to five are applied to induce variations in the cradle radial setting and the velocity ratio in the kinematic scheme of the machine tool for the generation of the pinion tooth surfaces corresponding to reduced transmission error amplitudes of a hypoid gear pair. The new CNC hypoid generators have made it possible to perform this nonlinear correction motions for the cutting of the face-milled hypoid gears. An algorithm is developed for the execution of motions on the CNC hypoid generator for the generation of face-milled hypoid gear tooth surface, based on the machine tool setting variation on the cradle-type hypoid generator induced by the optimal polynomial functions up to fifth-order. By using the corresponding computer program, the motion graphs of the CNC hypoid generator are determined for the generation of hypoid gear tooth surface, based on the optimal variation in the velocity ratio in the kinematic scheme and on the variation in the cradle radial setting on a cradle-type generator. The results presented indicate that the variation of the velocity ratio in the kinematic scheme of the hypoid generator induced by a fifth-order polynomial function resulted in a 62% reduction of the maximum transmission error of the gear pair.

Optimization of a Triangular Slot Shape in a Tire Tread Block by Using the Finite Element Analysis and MPSO

2012 ◽  
Vol 505 ◽  
pp. 424-428
Author(s):  
T. Dolwichai ◽  
J. Limtragool ◽  
S. Bureerat
Keyword(s):  
Finite Element ◽  
Tensile Test ◽  
Contact Stress ◽  
Hyperelastic Material ◽  
Design Parameters ◽  
Element Analysis ◽  
Normal Contact Stress ◽  
Normal Contact ◽  
Axial Tensile ◽  
Planar Shear

The work of this paper presents the use of MPSO which is an evolutionary optimizer. The work objective is finding the optimal shape of triangular slot in a tire tread block. The numbers of design parameters with triangular slot are 9. They are used to characterize size and position of the triangular slot in a tire tread block. The optimization methods are implemented to solve two objectives. First, the normal contact stress at contact patch region must be lowest and second, the friction contact stress at the same region must be highest. Therefore, the problem type is bi-objective optimization. The finite element analyses are simulated by modeling of tire tread block contacting to the friction surface with commercial finite element program (ANSYS). The models are simulated as compressing and sliding or braking situation. The tire tread block is modeled as hyperelastic material which used the three basic tests, i.e., uni-axial tensile test, planar shear test and equal bi-axial tensile test. The best fitted of hyperelastic material model for the work is Ogden Hyper Foam order 3th. The results of work are present as the mean of design parameters which are accepted for two objectives.

A Generalized Hypoid Gear Synthesized With Common Crown Rack Positioned Between Pinion and Gear Blanks

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Nogill Park
Keyword(s):  
Entire Range ◽  
Point Contact ◽  
Transmission Error ◽  
Gear Transmission ◽  
Speed Ratio ◽  
Neutral Position ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Pressure Angle ◽  
The Common

A new hypoid gearing using a common crown rack is introduced. The proposed hypoid gear has no unloaded gear transmission error. The common crown rack is located at a neutral position between the pinion and gear blanks. An arbitrary generating surface inclined at a pressure angle is prescribed. The proposed hypoid gearing is in point contact, fulfilling a constant speed ratio along the curved line of action. The synthesis feasibility is numerically verified for the entire range of hypoid gears, including parallel-, intersecting-, and crossed-axis gear systems. The proposed hypoid gear is compared with the hypoid gear by Gleason method and the differences between the two are discussed.

Cutter Interchangeability for Spiral-Bevel and Hypoid Gear Manufacturing

2003 ◽  
Author(s):  
Claude Gosselin ◽  
Jack Masseth ◽  
Wei Liang
Keyword(s):  
Test Case ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Manufacturing Operations ◽  
Before And After ◽  
Gear Manufacturing ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Tooth Flank Surface Topography ◽  
Flank Surface

In the manufacturing of spiral-bevel and hypoid gears, circular cutter dimensions are usually based on the desired performance of a gear set. In large manufacturing operations, where several hundred gear geometries may have been cut over the years, the necessary cutter inventory may become quite large since the cutter diameters will differ from one geometry to another, which results in used storage space and associated costs in purchasing and maintaining the cutter parts. Interchangeability of cutters is therefore of significant interest to reduce cost while maintaining approved tooth geometries. An algorithm is presented which allows the use of a different cutter, either in diameter and/or pressure angle, to obtain the same tooth flank surface topography. A test case is presented to illustrate the usefulness of the method: the OB cutter diameter of an hypoid pinion is changed from 8.9500" to 9.1000". CMM results and the comparison of the bearing patterns before and after change show excellent correlation, and indicate that the new pinion can be used in place of the original pinion without performance or quality problems. Significant cost reductions may be obtained with the application of the method.

Optimal Tooth Modifications in Hypoid Gears

2004 ◽  
Vol 127 (4) ◽  
pp. 646-655 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and optimal diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in (Simon, V., 2000, “Load Distribution in Hypoid Gears,” ASME J. Mech. Des., 122, pp. 529–535) the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the diameter of the cutter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

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