Composite Analysis Method of Tooth Contact Load Distribution of Helical Gear

2007 ◽  
Author(s):  
Yoshikazu Miyoshi ◽  
Keiichiro Tobisawa ◽  
Kohei Saiki
Keyword(s):  
Load Distribution ◽  
Three Dimensional ◽  
Transmission Error ◽  
Contact Load ◽  
Analysis Method ◽  
Profile Error ◽  
Tooth Contact ◽  
Gear Teeth ◽  
Tooth Flank ◽  
Assembly Error

As demand for the performance improvement of automotive transmission gears increases, gear design is required that achieves high strength, low noise and high efficiency simultaneously. In addition, for high performance it is important not only to select good gear dimensions, but also to improve the tooth contact load distribution which depends on the tooth flank shape and assembly error of the gear pair. Traditional analysis methods calculate the tooth contact load distribution with integral equations that consist of the effect function of bending deflection and that of compressive deformation caused by the contact of gear teeth. However, the complicated integral equations make it difficult to instantly obtain proper results for some tooth flanks distorted by heat treatment and repetition calculation may not converge especially in light load conditions. This paper proposes a new composite analysis method which quickly calculates the tooth contact load distribution of designed or manufactured tooth flanks of helical gears in any load condition. The analytical process consists of three stages: (1) for each flank shape of a gear pair, the three-dimensional relative tooth flank shape is calculated from the actual tooth flank shape and assembly error, and the equivalent tooth profile error of the three-dimensional relative tooth flank shape is obtained by the static deflection which depends on input torque, (2) the static deflection distribution and share load on each line of contact are calculated with the obtained equivalent tooth profile error and the variable stiffness of the involute tooth pair, (3) an integral equation that consists of bending deflection and compressive contact deformation of the gear teeth is solved to obtain the tooth contact load distribution. In practical applications, the tooth contact load distribution is used to output the tooth contact pattern, tooth contact and root bending stresses, and transmission error. The prediction of tooth contact stress and transmission error contributes to the improvement of the pitting strength and gear noise of several transmissions.

Tooth Contact Analysis of Longitudinal Cycloidal-Crowned Helical Gears With Circular Arc Teeth

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Wei-Shiang Wang ◽  
Zhang-Hua Fong
Keyword(s):  
Gear Tooth ◽  
Longitudinal Direction ◽  
Transmission Error ◽  
Helical Gear ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Circular Arc ◽  
Tooth Flank ◽  
Assembly Error

This paper proposes a new type of double-crowned helical gear that can be continuously cut on a modern Cartesian-type hypoid generator with two face-hobbing head cutters and circular-arc cutter blades. The gear tooth flank is double crowned with a cycloidal curve in the longitudinal direction and a circular arc in the profile direction. To gauge the sensitivity of the transmission errors and contact patterns resulting from various assembly errors, this paper applies a tooth contact analysis technique and presents several numerical examples that show the benefit of the proposed double-crowned helical gear set. In contrast to a conventional helical involute gear, the tooth bearing and transmission error of the proposed gear set are both controllable and insensitive to gear-set assembly error.

Influence of combined assembly error and bearing elasticity on spur gear tooth contact load distribution

2011 ◽  
Vol 225 (6) ◽  
pp. 1507-1521 ◽  
Author(s):  
J Wang ◽  
D Qin ◽  
T C Lim
Keyword(s):  
Load Distribution ◽  
Gear Tooth ◽  
Contact Region ◽  
Element Model ◽  
Spur Gear ◽  
Contact Load ◽  
Tooth Contact ◽  
Contact Points ◽  
Micro Deformation ◽  
Assembly Error

A numerical method to analyse the influence of assembly error on spur gear tooth contact load distribution considering bearing elasticity is formulated. In the proposed approach, a set of transformation matrices are used to define the deviation in tooth geometry orientation from the ideal position due to the bearing elasticity and assembly error. To calculate the gear tooth deflection, the theory of contact mechanics is applied to determine the micro deformation field at the surface layer of the contact region, while the finite element model is used to represent the bulk deformation in the rest of the gear structure. An efficient search strategy for obtaining the true contact points of the deformed tooth is employed. In this strategy, the tooth contact load distribution is determined based on the smallest distance between each pair of candidate contact points within a cross-section of the mating teeth, and as well as the corresponding force and moment balance conditions. Finally, the proposed model is applied to analyse the effect of assembly errors defined at eight circumferential positions on the tooth deformation in a geared rotor system comprising of four elastic bearings.

scholarly journals A Semi-Analytical Load Distribution Model for Cycloid Drives with Tooth Profile and Longitudinal Modifications

2020 ◽  
Vol 10 (14) ◽  
pp. 4859
Author(s):  
Ting Zhang ◽  
Xuan Li ◽  
Yawen Wang ◽  
Lining Sun
Keyword(s):  
Load Distribution ◽  
Contact Stiffness ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Distribution Model ◽  
Influence Coefficient ◽  
Hertz Contact ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Analysis And Design

The current load distribution model for cycloid drives based on the Hertz contact stiffness typically assumes a two-dimensional planar problem without considering the tooth longitudinal modification effects, which fails to comply with the practical situation. In this paper, this issue is clarified by developing a semi-analytical load distribution model based on a three-dimensional and linear elastic solution. Unloaded tooth contact analysis is introduced to determine the instantaneous mesh information. The tooth compliance model considering tooth contact deformation is established by combining the Boussinesq force–displacement relationships in elastic half-space with an influence coefficient method. With this, the loads, contact patterns, and loaded transmission error are calculated by enforcing the compatibility and equilibrium conditions. Comparisons to predictions made with the assumption of Hertz contact stiffness are presented to demonstrate the effectiveness of the proposed model, which shows good agreement. At the end, the effect of tooth longitudinal modifications on load distributions is investigated along with various loading conditions. This study yields an in-depth understanding of the multi-tooth contact characteristics of cycloid drives and provides an effective tool for extensive parameter sensitivity analysis and design optimization studies.

Load Distribution in Spiral Bevel Gears

2006 ◽  
Vol 129 (2) ◽  
pp. 201-209 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Point Contact ◽  
Design Data ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Gear Teeth ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Machine Theory ◽  
Spiral Bevel

A new approach for the computerized simulation of load distribution in mismatched spiral bevel gears with point contact is presented. The loaded tooth contact is treated in a special way: it is assumed that the point contact under load spreads over a surface along the “potential” contact line (Simon, 2006, Mech. and Machine Theory, in press), which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal, instead of assuming the usually applied elliptical contact area. The bending and shearing deflections of gear teeth, the local contact deformations of mating surfaces, gear body bending and torsion, the deflections of supporting shafts, and the manufacturing and alignment errors of mating members are included. The tooth deflections of the pinion and gear teeth are calculated by the finite element method. As the equations governing the load sharing among the engaged tooth pairs and load distribution along the tooth face are nonlinear, an approximate and iterative technique is used to solve this system of equations. The method is implemented by a computer program. By using this program the load and tooth contact pressure distributions, the angular displacements of the driven gear and the stresses in the pinion and gear teeth are calculated. The influence of design data and transmitted torque on load distribution parameters and fillet stresses is investigated and discussed.

Influence of assembly error and bearing elasticity on the dynamics of spur gear pair

2015 ◽  
Vol 230 (11) ◽  
pp. 1805-1818 ◽  
Author(s):  
Jianhong Wang ◽  
Jian Wang ◽  
Teik C Lim
Keyword(s):  
Finite Element ◽  
Dynamic Behavior ◽  
Transmission Error ◽  
Spur Gear ◽  
Lumped Parameter Model ◽  
Gear Pair ◽  
Tooth Contact ◽  
Lumped Parameter ◽  
Bearing Stiffness ◽  
Assembly Error

The elasticity and geometrical errors of precision elements are one of the major factors affecting vibration responses in geared transmission systems. In this study, the influences of assembly error and bearing elasticity on the spur gear dynamic behavior are analyzed. A lumped parameter model for spur gear pair is formulated by representing the bearing elasticity with infinitesimal spring elements and tooth stiffness time function as rectangular waveform. The nonuniform tooth contact load is also considered. The severity of assembly error is assumed to be sufficiently small such that no partial loss of tooth contact occurs. A harmonic balance method is applied to the resultant second-order partial differential equation governing the gear pair dynamic behavior. The variations of dynamic transmission error and tooth contact load with respect to mesh frequency for a set of bearing stiffness are analyzed. The influences of bearing stiffness on the dynamic transmission error are also evaluated. The variation of actual cross angle, an indicator on the tooth meshing state, is examined with respect to nominal cross angle and bearing stiffness. The analysis shows that the presence of bearing elasticity and assembly error can degenerate tooth contact significantly, and hence the appropriate specifications of bearing and mesh stiffness are critical at gearbox design stage. The analysis demonstrates that the proposed lumped parameter model can provide detailed contact information like finite element model, but it avoids finite element model’s prohibitive computation burden and can be completed easily and be computed quickly.

scholarly journals Study of the tooth contact for high contact ratio spur gears with long tip relief

2019 ◽  
Vol 287 ◽  
pp. 01004
Author(s):  
José I. Pedrero ◽  
Miguel Pleguezuelos ◽  
Miryam B. Sánchez
Keyword(s):  
Load Sharing ◽  
Transmission Error ◽  
Spur Gears ◽  
Contact Ratio ◽  
Tooth Contact ◽  
Gear Teeth ◽  
Profile Modification ◽  
Static Transmission Error ◽  
Tooth Pair

Profile modifications are commonly used to avoid shocks between meshing gear teeth produced by the delay of the driven gear, and the subsequent sooner start of contact, due to the teeth deflections. A suitable tip relief at the driven tooth shifts the start of contact to the proper location at the theoretical inner point of contact. The shape of the relief governs the loading curve of the tooth pair, while the length of relief determines the intervals in which this actual loading curve differs from the theoretical one of unmodified teeth. As at least one tooth pair should be in contact at the unmodified involute profile interval, the length of modification should be smaller than the length of the intervals of two pair tooth contact; otherwise, a shock at the end of contact of the previous pair is unavoidable. However this problem does not occur for high contact ratio spur gears, in which at least two couples of teeth are in contact at any moment. In this work, a study on the load sharing and the quasi-static transmission error for high contact ratio spur gears with long profile modification has been performed, and a model for the tooth contact has been developed.

scholarly journals Load Distribution Analysis Method for Cylindrical Worm Gear Teeth

1996 ◽  
Vol 39 (3) ◽  
pp. 606-613 ◽  
Author(s):  
Katsuzo Sudoh ◽  
Yasuyuki Tanaka ◽  
Susumu Matsumoto ◽  
Yasuyoshi Tozaki
Keyword(s):  
Load Distribution ◽  
Worm Gear ◽  
Distribution Analysis ◽  
Analysis Method ◽  
Gear Teeth

Load Distribution in Cylindrical Worm Gears

2000 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Load Distribution ◽  
Gear Tooth ◽  
Point Contact ◽  
Transmission Error ◽  
Worm Gear ◽  
Gear Teeth ◽  
Total Transmission ◽  
Transmission Errors ◽  
Gear Drive ◽  
Worm Gears

Abstract A method for the determination of load sharing between the instantaneously engaged worm threads and gear teeth, for the calculation of load distribution along the teeth and transmission errors in different types of cylindrical worm gears is presented. The method covers both cases — that of the theoretical line and point contact. The bending and shearing deflections of worm thread and gear tooth, the local contact deformations of the mating surfaces, the axial deformations of worm body, gear body bending and torsion, deflections of the supporting shafts, and the manufacturing and alignment errors of worm and gear are included. Based on the real load distribution the tooth contact pressure is calculated, in the case of point contact in two different ways, and the obtained results are compared. Also, the total transmission error, consisting of the kinematical transmission error due to the mismatch of the worm gear drive and of the transmission error caused by the deflections of worm thread and gear teeth, is calculated. The method is implemented by a computer program. By using this program the influence of the type of worm gear drive and of design and manufacturing parameters on load distribution and transmission errors is investigated and discussed.

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