Effect of Tooth Contact and Gear Dimensions on Transmission Errors of Loaded Hypoid Gears

1991 ◽  
Vol 113 (2) ◽  
pp. 182-187 ◽  
Author(s):  
M. Sugimoto ◽  
N. Maruyama ◽  
A. Nakayama ◽  
N. Hitomi
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Surface ◽  
Alignment Error ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Module Design ◽  
Transmission Errors ◽  
Loaded State ◽  
Final Drive

The effect of the tooth contact and alignment error of the hypoid gear assembly on transmission error was investigated with a new measuring apparatus which can measure the transmission errors of loaded hypoid gears assembled into a final drive unit. Measurements indicate that transmission error predictions made with the TCA and LTCA — analytical tools developed by Gleason Works for a no-load and loaded state, respectively — have sufficient accuracy when actual data on the gear tooth surface and alignment error of the gear assembly are used in the calculations. A systematic examination has also been made of the effects of tooth contact and gear assembly alignment error on transmission error on the basis of the LTCA calculations. It was found that the transmission errors relative to the applied load varied not only according to the tooth contact but also the no-load transmission error of the gears. This relationship was also examined by taking into account the effects of the gear dimensions. It was confirmed through calculation and experiment that a small module design was effective in reducing transmission error.

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.

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.

Investigation of tooth contact deviations from the plane of action and their effects on gear transmission error

2005 ◽  
Vol 219 (5) ◽  
pp. 501-509 ◽  
Author(s):  
C H Wink ◽  
A L Serpa
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Contact Analysis ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Tooth Contact ◽  
Helical Gears ◽  
Influence Coefficients ◽  
Manufacturing Errors ◽  
Tooth Surfaces

In this paper tooth contact deviations from the plane of action and their effects on gear transmission error are investigated. Tooth contact deviations come from intentional modification of involute tooth surfaces such as tip and root profile relief; manufacturing errors such as adjacent pitch error, profile errors, misalignment and lead errors; and tooth elastic deflections under load, for example, bending and local contact deflections. Those deviations are usually neglected on gear tooth contact models. A procedure to calculate the static transmission error of spur and helical gears under loading is proposed. In the proposed procedure, contact analysis is carried out on the whole tooth surface, eliminating the usual assumption that tooth contact occurs only on the plane of action. Lead and profile modifications, manufacturing errors and tooth elastic deflections are considered in the calculation procedure. The method of influence coefficients is employed to calculate the tooth elastic deflections. Load distribution on gear meshing is determined using an iterative-incremental method. Results of some numerical examples of spur and helical gears are analysed and discussed. The results indicate that the tooth contact deviations from the plane of action can lead to imprecision on the gear transmission error calculation if they are not take into account. Therefore, the proposed procedure provides a more accurate calculation methodology of gear transmission error, since a global contact analysis is done.

Crowned Spur Gears: Methods for Generation and Tooth Contact Analysis—Part I: Basic Concepts, Generation of the Pinion Tooth Surface by a Plane

1988 ◽  
Vol 110 (3) ◽  
pp. 337-342 ◽  
Author(s):  
F. L. Litvin ◽  
J. Zhang ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Numerical Results ◽  
Degree Of Freedom ◽  
Tooth Surface ◽  
Spur Gears ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Basic Concepts

A topology of crowned spur pinion tooth surface that reduces the level of transmission errors due to misalignment is proposed. The geometry of the deviated pinion tooth surface and regular gear tooth surface, along with tooth contact analysis is discussed. Generation of the deviated pinion tooth surface by a plane whose motion is controlled by a five-degree-of-freedom system is proposed. Numerical results are included and indicate that transmission errors remain low as the gears are misaligned.

An Ease-Off Based Method for Loaded Tooth Contact Analysis of Hypoid Gears Having Local and Global Surface Deviations

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
M. Kolivand ◽  
A. Kahraman
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Surface Deviations ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

Actual hypoid gear tooth surfaces do deviate from the theoretical ones either globally due to manufacturing errors or locally due to reasons such as tooth surface wear. A practical methodology based on ease-off topography is proposed here for loaded tooth contact analysis of hypoid gears having both local and global deviations. This methodology defines the theoretical pinion and gear tooth surfaces from the machine settings and cutter parameters, and constructs the surfaces of the theoretical ease-off and roll angle to compute for the unloaded contact analysis. This theoretical ease-off topography is modified based on tooth surface deviations and is used to perform a loaded tooth contact analysis according to a semi-analytical method proposed earlier. At the end, two examples, a face-milled hypoid gear set having local deviations and a face-hobbed one having global deviations, are analyzed to demonstrate the effectiveness of the proposed methodology in quantifying the effect of such deviations on the load distribution and the loaded motion transmission error.

The Influence of Gear Hobbing on Worm Gear Characteristics

2007 ◽  
Vol 129 (5) ◽  
pp. 919-925 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Machine Tool ◽  
Gear Tooth ◽  
Theoretical Background ◽  
Worm Gear ◽  
Tooth Surface ◽  
Design Parameters ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Gear Hobbing

In this paper, a method is presented for the determination of the differences between the worm gear tooth surface processed by an oversized hob of finite number of teeth or by a flying tool, and the theoretically required gear tooth surface. The influence of hob oversize and machine tool settings on tooth contact pressure and transmission errors is determined. The full geometry and kinematics of gear tooth processing by an oversized hob or by a flying tool is included. The theoretical background is implemented by a computer program. By using this program, the influence of relevant design parameters of the worm gear set and the hob and of machine tool settings on processed gear tooth errors and on loaded tooth contact of the worm gear pair is investigated and discussed.

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.

The TCA of Hypoid Gears Based on MATLAB

2012 ◽  
Vol 190-191 ◽  
pp. 213-217
Author(s):  
Miao Xin Xiao ◽  
Hua Ru Yan
Keyword(s):  
Present Situation ◽  
Transmission Error ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Graphic Display ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Calculation Process ◽  
Mathematical Calculation

The present situation of the tooth contact analysis (TCA) and the application of MATLAB to the tooth contact analysis (TCA) is introduced briefly in this paper. The tooth surface equation of the big gear and pinion is established by powerful mathematical calculation and graphic display of MATLAB, at the same time transmission error and contact path is obtained. The calculation process is simplified and the operation precision of TCA is improved than before.

Tooth Contact Analysis of Face Gear Drive Modified by a Grinding Worm

2010 ◽  
Vol 139-141 ◽  
pp. 1154-1157 ◽  
Author(s):  
Hui Guo ◽  
Ning Zhao ◽  
Hao Gao
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Alignment Error ◽  
Contact Ratio ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Gear Drive ◽  
Bearing Contact

This paper proposes a modification method for tooth surface of face gear drive with a grinding worm on a numerical grinding machine. The surface equation of grinding worm is derived, and the coordinate System of generating the worm is established. Tooth contact analysis (TCA) is performed to investigate the performance of face gear drive before and after modification, and the alignment error is considered. This method can obtain a more stable bearing contact in contrast to the method by increasing tooth number of shaper. The longitudinal bearing contact on the face-gear tooth surface has been obtained which will increase the contact ratio. By modification the edge contact at surface edges of the gears can be avoided and the modification magnitude can be controlled freely.

Sign in / Sign up

Export Citation Format

Share Document