Multi-objective optimization of the manufacture of face-milled hypoid gears on numerical controlled machine tool

2020 ◽  
pp. 095440542097803
Author(s):  
Vilmos V Simon
Keyword(s):  
Machine Tool ◽  
Angular Displacement ◽  
Contact Stresses ◽  
Machining Process ◽  
New Method ◽  
Energy Losses ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Gear Manufacture

A new method is presented for advanced manufacture of hypoid gears on numerical controlled machine tool. The tool geometry and machine tool settings are determined to introduce the optimal tooth modifications into the teeth of hypoid gears. The goal is to reduce the maximum tooth contact stresses, angular displacement error of the driven gear, and energy losses in the oil film existing between tooth surfaces. The calculation is based on the optimal variation of machine tool settings on the classical machine tool for hypoid gear manufacture. The novelty of the method is that during the machining process of teeth surfaces, the variation of machine tool settings on the cradle-type hypoid generator is conducted by polynomial functions of fifth-order. By an algorithm, this variation of machine tool settings is transferred to the numerical controlled machine tool for hypoid gear manufacture (hypoid generator). The obtained results have shown that by applying the optimal manufacture process, considerable reductions in tooth contact stresses and angular displacement errors of the driven gear, and a moderate reduction in energy losses were obtained. Therefore, by applying this new method in practice, advanced manufacture of hypoid gears on CNC hypoid generator is made possible, resulting improved operating characteristics of the hypoid gear pair.

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]

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.

Optimal Tooth Modifications in Hypoid Gears

2003 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
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 by changing the cutter 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 [1] 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 cutter diameter 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.

Modeling Research of Hypoid Gear Based on Real Machining Process

2010 ◽  
Vol 20-23 ◽  
pp. 1429-1433
Author(s):  
Xiu Ting Wei ◽  
Jing Cheng Liu ◽  
Qiang Du
Keyword(s):  
Tooth Profile ◽  
Modeling Method ◽  
Machining Process ◽  
Transmission Ratio ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Modeling Methods ◽  
Modeling Process ◽  
Generating Method

In this paper, two modeling methods, the forming method and the generating method, for hypoid gears with two kinds of transmission ratio are discussed by simulating the actual machining process. In the generating modeling method, the tooth profile of the gear is generated by boolean algorithm step by step after creating the models of the gear blank and the cutter and then rotating around their own axis by certain degrees until the cutter is outside the gear blank completely. In contrast with the generating modeling method, the tooth profile is formed by carrying out the boolean algorithm for one time after creating the models of the gear blank and cutter seperately in the forming modeling method. Then using feature instance, all the teeth are created both in the generating modeling method and in the forming modeling method. Using the two modeling methods given in this paper, the modeling process can be shortened and the modeling precision can be improved.

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.

Machine-Tool Settings to Reduce the Sensitivity of Spiral Bevel Gears to Tooth Errors and Misalignments

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Machine Tool ◽  
Contact Pressure ◽  
Angular Displacement ◽  
Angular Position ◽  
Slight Reduction ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel

The method for loaded tooth contact analysis is applied for the investigation of the combined influence of machine-tool settings for pinion teeth finishing and misalignments of the mating members on load distribution and transmission errors in mismatched spiral bevel gears. By using the corresponding computer program, the influence of pinion’s offset and axial adjustment error, angular position error of the pinion axis, tooth spacing error, and machine-tool setting correction for pinion teeth finishing, on tooth contact pressure, tooth root stresses, and angular displacement of the driven gear member from the theoretically exact position based on the ratio of the numbers of teeth is investigated. On the basis of the obtained results, the optimal combination of machine-tool settings is determined. By the use of this set of machine-tool settings, the maximum tooth contact pressure and transmission errors can be significantly reduced. However, in some cases, by the use of appropriate machine-tool settings for the reduction of tooth contact pressure, the angular displacement of the driven gear increases. Therefore, different optimized combinations of machine-tool settings for pinion tooth finishing for the reduction of the sensitivity of gears to misalignments in regard to maximum tooth contact pressure and transmission errors should be applied. By the use of the combination of machine-tool settings to reduce the sensitivity of gears to misalignments in regard to transmission errors, a slight reduction of maximal tooth contact pressure is achieved, too.

Tooth Surface Error Correction for Face-Hobbed Hypoid Gears

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Qi Fan
Keyword(s):  
Machine Tool ◽  
Machining Process ◽  
Tooth Surface ◽  
Surface Geometry ◽  
Premature Failure ◽  
Hypoid Gears ◽  
Surface Errors ◽  
The Face ◽  
Spiral Bevel ◽  
Universal Motion

Face-hobbing is a continuous generating process employed in manufacturing spiral bevel and hypoid gears. Due to machining dynamics and tolerances of machine tools, the exact tooth surface geometry may not be obtained from the machining process using theoretical machine tool settings. Repeatable tooth surface geometric errors may be observed. The tooth surface errors will cause unfavorable displacement of tooth contact and increased transmission errors, resulting in noisy operation and premature failure due to edge contact and highly concentrated stresses. In order to eliminate the tooth surface errors and ensure precision products, a corrective machine setting technique is employed to modify the theoretical machine tool settings, compensating for the surface errors. This paper describes a method of correcting tooth surface errors for spiral bevel and hypoid gears generated by the face-hobbing process using computer numerically controlled hypoid gear generators. Polynomial representation of the universal motions of machine tool settings is considered. The corrective universal motion coefficients are determined through an optimization process with the target of minimization of the tooth surface errors. The sensitivity of the changes of the tooth surface geometry to the changes of universal motion coefficients is investigated. A numerical example of a face-hobbed hypoid pinion is presented.

Optimal Tooth Surface Modifications in Face-Hobbed Hypoid Gears

2013 ◽  
Vol 572 ◽  
pp. 351-354
Author(s):  
Simon Vilmos
Keyword(s):  
Contact Pressure ◽  
Angular Displacement ◽  
Optimization Procedure ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Loaded Tooth Contact Analysis

In this study, an optimization methodology is proposed to systematically define head-cutter geometry and machine tool settings to introduce optimal tooth modifications in face-hobbed hypoid gears. The goal of the optimization is to simultaneously minimize tooth contact pressures and angular displacement error of the driven gear, while concurrently confining the loaded contact pattern within the tooth boundaries. The proposed optimization procedure relies heavily on a loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors. The objective function and the constraints are not available analytically, but they are computable, i.e., they exist numerically through the loaded tooth contact analysis. The core algorithm of the proposed nonlinear programming procedure is based on a direct search method. Effectiveness of this optimization was demonstrated by using a face-hobbed hypoid gear example. Considerable reductions in the maximum tooth contact pressure and in the transmission errors were obtained.

Mathematical Model of Klingelnberg Cyclo-Palloid Hypoid Gear

2013 ◽  
Vol 341-342 ◽  
pp. 572-576 ◽  
Author(s):  
Jin Fu Du ◽  
Zong De Fang ◽  
Min Xu ◽  
Xing Long Zhao ◽  
Yu Min Feng
Keyword(s):  
Mathematical Model ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Tooth Surfaces ◽  
Normal Vectors

The geometry of the tooth surface is important for tooth contact analysis, load tooth contact analysis and the ease-off of gear pairs. This paper presents a mathematical model for the determination of the tooth geometry of Klingelnberg face-hobbed hypoid gears. The formulation for the generation of gear and pinion tooth surfaces and the equations for the tooth surface coordinates are provided in the paper. The surface coordinates and normal vectors are calculated and tooth surfaces and 3D tooth geometries of gear and pinion are obtained. This method may also applied to other face-hobbing gears.

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