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.

scholarly journals A Method for Thermal Analysis of Spiral Bevel Gears

1996 ◽  
Vol 118 (4) ◽  
pp. 580-585 ◽  
Author(s):  
R. F. Handschuh ◽  
T. P. Kicher
Keyword(s):  
Three Dimensional ◽  
Contact Analysis ◽  
Heat Transfer Analysis ◽  
Maximum Pressure ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Finite Element Program ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

A modelling method for analyzing the three-dimensional thermal behavior of spiral bevel gears has been developed. The model surfaces are generated through application of differential geometry to the manufacturing process for face-milled spiral bevel gears. Contact on the gear surface is found by combining tooth contact analysis with three-dimensional Hertzian theory. The tooth contact analysis provides the principle curvatures and orientations of the two surfaces. This information is then used directly in the Hertzian analysis to find the contact size and maximum pressure. Heat generation during meshing is determined as a function of the applied load, sliding velocity, and coefficient of friction. Each of these factors change as the point of contact changes during meshing. A nonlinear finite element program was used to conduct the heat transfer analysis. This program permitted the time- and position-varying boundary conditions, found in operation, to be applied to a one-tooth model. An example model and analytical results are presented.

Analysis of load distribution and contact stiffness of the single-nut ball screw based on the whole rolling elements model

2019 ◽  
Vol 43 (3) ◽  
pp. 344-365 ◽  
Author(s):  
Ye Chen ◽  
Chun-yu Zhao ◽  
Si-yu Zhang ◽  
Xian-li Meng
Keyword(s):  
Load Distribution ◽  
Contact Stiffness ◽  
Structural Parameters ◽  
Contact Angles ◽  
Ball Screw ◽  
Distribution Model ◽  
Axial Stiffness ◽  
Feed System ◽  
Normal Contact ◽  
Rolling Elements

This paper aims to investigate the load distribution and contact stiffness characteristics of the single-nut ball screw pair (SNBSP). First, the transformed relationship of coordinate systems is established. Then, the whole rolling elements load distribution model of the SNBSP is presented. Based on this, the whole rolling elements contact stiffness model is obtained. Applying the Newton–Raphson iterative method to solve the model, the normal force of rolling elements and the contact angles between balls and raceway surface are determined. The calculation results are reasonably consistent with those of the half pitch model. Then, the local contact stiffness and global contact stiffness are obtained. Furthermore, the effects of axial load and structural parameters of the SNBSP on the normal contact force, contact angle, and local and global contact stiffness are discussed using numeric analysis. Finally, a dynamic model of the z-axis feed system with time-varying axial stiffness is established, and the accuracy of the model is verified by experiments.

Loaded Tooth Contact Analysis of Power-Split Gear Drives Considering Shaft Deformation and Assembly Errors

2015 ◽  
Author(s):  
Siang-Yu Ye ◽  
Shyi-Jeng Tsai
Keyword(s):  
Power Transmission ◽  
Planetary Gear ◽  
Load Sharing ◽  
Contact Analysis ◽  
Influence Coefficient ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Power Split ◽  
Loaded Tooth Contact Analysis ◽  
Compact Design

The power-split gear mechanisms is widely applied in power transmission because of the advantages of compact design, lighter weight and high power density. The load sharing and the load distribution are the important performance issues while designing the power split mechanisms. The paper propose a computerized approach based on the influence coefficient method for loaded tooth contact analysis of such the gear transmission. Not only the load sharing of the multiple contact tooth pairs and the loaded transmission errors, but also the distributed contact stresses and the corresponding contact patterns on all the engaged tooth flanks can be calculated by using the proposed LTCA approach. Some analysis results are also discussed with a study case of the first planetary stage of a compound cycloid planetary gear drive.

Stress Analysis of Spherical Gear Sets

2009 ◽  
Author(s):  
Li-Chi Chao ◽  
Chung-Biau Tsay
Keyword(s):  
Gear Tooth ◽  
Three Dimensional ◽  
Contact Analysis ◽  
Design Parameters ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Contact Points ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis ◽  
Spherical Gear

The spherical gear is a new type of gear proposed by Mitome et al. [1]. Different from that of the conventional spur or helical gear sets, the spherical gear set can allow variable shaft angles and large axial misalignments without gear interference during the gear drive meshing [1, 2]. Geometrically, the spherical gear has two types of gear tooth profiles, the concave tooth and convex tooth. In practical transmission applications, the contact situation of a spherical gear set is very complex. To obtain a more realistic simulation result, the loaded tooth contact analysis (LTCA) has been performed by employing the finite element method (FEM). According to the derived mathematical model of spherical gear tooth surfaces, an automatic meshes generation program for three-dimensional spherical gears has been developed. Beside, tooth contact analysis (TCA) of spherical gears has been performed to simulate the contact points of the spherical gear set. Furthermore, the contact stress contours of spherical gear tooth surfaces and bending stress of tooth roots have been investigated by giving the design parameters, material properties, loadings and boundary conditions of spherical gears.

scholarly journals Computer-aided design and loaded tooth contact analyses of bevel gear pair having straight teeth by different loaded torques

2020 ◽  
Vol 21 (1) ◽  
pp. 109
Author(s):  
Sándor Bodzás
Keyword(s):  
Computer Aided Design ◽  
Three Dimensional ◽  
Computer Software ◽  
Bevel Gear ◽  
Gear Pair ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Contact Points ◽  
Loaded Tooth Contact Analysis ◽  
Aided Design

The aim of this publication is to show how to integrate the designing process of straight bevel gears into a computer software so it can be further used for making the three-dimensional (CAD) model of the gear pair. During meshing the driven and the driving gears engage gradually so contact points can be mathematically determined between the element pairs according to the developed coordinate system's arrangement. With my-developed computer software, I designed a certain bevel gear pair having straight teeth. Naturally, many different types of this pair could be designed. After that Loaded Tooth Contact Analysis (LTCA) have been done − by normal stress, normal deformation and normal elastic strain parameters. The aim of the LTCA is the analysis of the connection tooth zone in mechanical aspects by different loads. If the received parameters are not appropriate, you can return to the mechanical designing process where the starting parameters of the gear could be modified. Different load torques were used to determine the established mechanical parameters of the elements.

Gear Contact Model and Loaded Tooth Contact Analysis of a Three-Dimensional, Thin-Rimmed Gear

2002 ◽  
Vol 124 (3) ◽  
pp. 511-517 ◽  
Author(s):  
Shuting LI
Keyword(s):  
Three Dimensional ◽  
Contact Analysis ◽  
Deformation Model ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Load Distributions ◽  
Dimensional Finite Element ◽  
Calculation Results ◽  
Loaded Tooth Contact Analysis ◽  
Three Dimensional Finite Element

This paper performs loaded tooth contact analysis of a three-dimensional, thin-rimmed gear (3DTRG) by presenting a method that combines the mathematical programming method with the three-dimensional, finite element method (3DFEM). Also, a face-contact and whole gear deformation model is used for the 3DTRG. 3DFEM programs for the contact analysis and strength calculation of the 3DTRG are developed successfully in a personal computer. By using this program, 3D tooth load distributions, tooth root strains and the tooth contact pattern of the 3DTRG are obtained. Calculation results are proved to be correct by experiments.

scholarly journals Transmission Performance Analysis of RV Reducers Influenced by Profile Modification and Load

2019 ◽  
Vol 9 (19) ◽  
pp. 4099 ◽  
Author(s):  
Hui Wang ◽  
Zhao-Yao Shi ◽  
Bo Yu ◽  
Hang Xu
Keyword(s):  
Contact Force ◽  
Mechanical Performance ◽  
Contact Stiffness ◽  
Impact Resistance ◽  
Torsional Stiffness ◽  
Transmission Performance ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Profile Modification ◽  
Rv Reducer

RV reducers contain multi-tooth contact characteristics, with high-impact resistance and a small backlash, and are widely used in precision transmissions, such as robot joints. The main parameters affecting the transmission performance include torsional stiffness and transmission errors (TEs). However, a cycloid tooth profile modification has a significant influence on the transmission accuracy and torsional stiffness of an RV reducer. It is important to study the multi-tooth contact characteristics caused by modifying the cycloid profile. The contact force is calculated using a single contact stiffness, inevitably affecting the accuracy of the result. Thus, a new multi-tooth contact model and a TE model of an RV reducer are proposed by dividing the contact area into several differential elements. A comparison of the contact force obtained using the finite element method and the test results of an RV reducer prototype validates the proposed models. On this basis, the influence of load on the different modification methods is studied, including a TE, the mechanical performance, and the transmission efficiency. In addition, the proposed reverse profile is particularly suitable for situations with a large clearance and torque. This study provides a reliable theoretical basis for a multi-tooth contact analysis of a cycloid profile modification.

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.

A Tooth Contact Analysis Model for Crossed Axis Helical Gears Under Load

1996 ◽  
Author(s):  
Y. Zhang ◽  
Z. Fang
Keyword(s):  
Load Distribution ◽  
Surface Deformation ◽  
Principal Direction ◽  
Tooth Surface ◽  
Analysis Model ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Helical Gears ◽  
Gear Mesh ◽  
Tooth Surfaces

Abstract This paper presents an approach for the analysis of tooth contact and load distribution of helical gears with crossed axis. The approach is based on a tooth contact model that accommodates the influence of tooth profile modifications, gear manufacturing errors and tooth surface deformation on gear mesh quality. In the approach, the tooth contact load is assumed to be distributed along the tooth surface line that coincides with the relative principal direction of the contacting tooth surfaces. The model in this paper provides a quantitative analysis on gear transmission errors, contact patterns and the load distribution of helical gears with crossed axes when the tooth surfaces are deformed under load. As a numerical example, the contact of a pair of helical gears with a small crossing angle is analyzed by the computer program that implements the approach.

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