Parametric Analysis of Gear Mesh and Dynamic Response of Loaded Helical Beveloid Transmission With Small Shaft Angle

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Chaosheng Song ◽  
Caichao Zhu ◽  
Teik C. Lim ◽  
Tao Peng
Keyword(s):  
Dynamic Response ◽  
Transmission Error ◽  
Load Level ◽  
Tooth Surface ◽  
Coupling Mechanism ◽  
Gear Mesh ◽  
Geometry Design ◽  
Torque Load ◽  
Shaft Angle ◽  
Mesh Characteristic

A synthesized gear mesh and dynamic model assuming line contact that is derived from a set of manufacturing parameters is formulated for analyzing the beveloid gear mesh-coupling mechanism. Using the proposed model, the effect of the dominant geometry design parameter that is the crossed angle between the first principal directions of the tooth surface curvatures (FPD-angle) on gear mesh characteristic and dynamic response is investigated. Also, the analysis of the gear mesh characteristic and dynamic response subject to torque load variation is performed. It is shown that the dynamic transmission error and dynamic mesh force worsen as the geometry FPD-angle increases for a specific torque load level. Furthermore, even though higher torque load can produce larger contact area, which is desirable, it also increases the gear mesh stiffness and transmission error that tend to aggravate dynamic response.

Influence of the backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set

2016 ◽  
Vol 231 (11) ◽  
pp. 2025-2041 ◽  
Author(s):  
Shijing Wu ◽  
Haibo Zhang ◽  
Xiaosun Wang ◽  
Zeming Peng ◽  
Kangkang Yang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Planetary Gear ◽  
Tooth Wear ◽  
Transmission Error ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Contact Ratio ◽  
The Impact

Backlash is a key internal excitation on the dynamic response of planetary gear transmission. After the gear transmission running for a long time under load torque, due to tooth wear accumulation, the backlash between the tooth surface of two mating gears increases, which results in a larger and irregular backlash. However, the increasing backlash generated by tooth accumulated wear is generally neglected in lots of dynamics analysis for epicyclic gear trains. In order to investigate the impact of backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set, in this work, first a static tooth surface wear prediction model is incorporated with a dynamic iteration methodology to get the increasing backlash generated by tooth accumulated wear for one pair of mating teeth under the condition that contact ratio equals to one. Then in order to introduce the tooth accumulated wear into dynamic model of compound planetary gear set, the backlash excitation generated by tooth accumulated wear for each meshing pair in compound planetary gear set is given under the condition that contact ratio equals to one and does not equal to one. Last, in order to investigate the impact of the increasing backlash generated by tooth accumulated wear on dynamic response of compound planetary gear set, a nonlinear lumped-parameter dynamic model of compound planetary gear set is employed to describe the dynamic relationships of gear transmission under the internal excitations generated by worn profile, meshing stiffness, transmission error, and backlash. The results indicate that the introduction of the increasing backlash generated by tooth accumulated wear makes a significant influence on the bifurcation and chaotic characteristics, dynamic response in time domain, and load sharing behavior of compound planetary gear set.

scholarly journals Meshing characteristics of a sphere–face gear pair with variable shaft angle

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985951 ◽  
Author(s):  
Lei Liu ◽  
Jinzhao Zhang
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Contact Points ◽  
Shaft Angle ◽  
Meshing Characteristics ◽  
Curvature Interference

This article presents a sphere–face gear pair by substituting the convex spherical gear for the pinion of a conventional face gear pair. The sphere–face gear pair not only maintains the advantages of the face gear pair with a longitudinally modified pinion but also allows variable shaft angles or large axial misalignments. Meshing characteristics of the proposed gear pair are studied in this article. The mathematical models of the sphere–face gear pair are derived based on machining principles. The tooth contact analysis (TCA) and curvature interference check are conducted for the sphere–face gear pair with variable shaft angles. The loaded TCA is also implemented utilizing the finite element method. The results of numerical examples show that proposed gear pair has the following features. Geometrical transmission error of constant shaft angle or varying shaft angle is zero; contact points of the sphere–face gear set with variable shaft angle are located near the centre region of face gear tooth surface; there is no curvature interference in meshing; and transmission continuity of the gear pair can be guaranteed in meshing.

Robust Optimization of Cylindrical Gear Tooth Surface Modifications Within Ranges of Torque and Misalignments

2013 ◽  
Author(s):  
Alessio Artoni ◽  
Massimo Guiggiani ◽  
Ahmet Kahraman ◽  
Jonny Harianto
Keyword(s):  
Performance Metrics ◽  
Gear Tooth ◽  
Surface Modifications ◽  
Transmission Error ◽  
Robust Design Optimization ◽  
Tooth Surface ◽  
Global Optimality ◽  
Cylindrical Gear ◽  
Geometry Design ◽  
Design Variables

Tooth surface modifications are small, micron-level intentional deviations from perfect involute geometries of spur and helical gears. Such modifications are aimed at improving contact pressure distribution, while minimizing the motion transmission error to reduce noise excitations. In actual practice, optimal modification requirements vary with the operating torque level, misalignments, and manufacturing variance. However, most gear literature has been concerned with determining optimal flank form modifications at a single design point, represented by fixed, single load and misalignment values. A new approach to the design of tooth surface modifications is proposed to handle such conditions. The problem is formulated as a robust design optimization problem, and it is solved, in conjunction with an efficient gear contact solver (LDP), by a direct search, global optimization algorithm aimed at guaranteeing global optimality of the obtained micro-geometry solutions. Several tooth surface modifications can be used as micro-geometry design variables, including profile, lead, and bias modifications. Depending on the contact solver capabilities, multiple performance metrics can be considered. The proposed method includes the capability of simultaneously and robustly handling several conflicting design objectives. In the present paper, peak contact stress and loaded transmission error amplitude are used as objective functions (to be minimized). At the end, two example optimizations are presented to demonstrate the effectiveness of the proposed method.

Mathematical Modeling and Dynamic Contact Analysis of Beveloid Gear Pairs in Marine Gearbox With Small Shaft Angle

2017 ◽  
Author(s):  
Tengjiao Lin ◽  
Hang Li ◽  
Wen Liu ◽  
Jun Zhao
Keyword(s):  
Finite Element ◽  
Dynamic Contact ◽  
Transmission Error ◽  
Parametric Modeling ◽  
Tooth Surface ◽  
Element Analysis ◽  
Solid Models ◽  
Beveloid Gears ◽  
Spatial Geometry ◽  
Shaft Angle

The research objective of this study is involute beveloid gears in marine gearbox with small shaft angle. Based on the theory of gear geometry and the generation mechanism, the mathematical models of beveloid gear pairs are derived according to the tooth surface equations of the imaginary counterpart rack. Then a parametric modeling programs of beveloid gears are developed to automatically generate exact model of tooth surface, so as to establish gear solid models. Subsequently, the assembly models are established according to the spatial geometry relation of beveloid gear pairs with intersected axis and crossed axis respectively. On this basis, the finite element models of beveloid gear pairs with intersected axis and crossed axis are established, and the dynamic contact force, dynamic stress distribution and dynamic transmission error are obtained by dynamic contact finite element analysis.

scholarly journals Experimental and Theoretical Study of Gear Dynamical Transmission Characteristic Considering Measured Manufacturing Errors

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Fang Guo ◽  
Zongde Fang
Keyword(s):  
Transmission Error ◽  
Helical Gear ◽  
Tooth Surface ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Tooth Contact Analysis ◽  
Gear Mesh ◽  
Manufacturing Errors ◽  
Tooth Modification ◽  
Helical Gear Pair

In the research of gear transmission, the vibration and noise problem has received many concerns all the times. Scholars use tooth modification technique to improve the meshing state of gearings in order to reduce the vibration and noise. However, few of researchers consider the influence of measured manufacturing errors when they do the study of tooth modification. In order to investigate the efficiency of the tooth modification in the actual project, this paper proposes a dynamic model of a helical gear pair including tooth modification and measured manufacturing errors to do a deterministic analysis on the dynamical transmission performance. In this analysis, based on the measured tooth deviation, a real tooth surface (including modification and measured tooth profile error) is fitted by a bicubic B-spline. With the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) on the real tooth surface, the loaded transmission error, tooth surface elastic deformation, and load distribution can be determined. Based on the results, the time-varying mesh stiffness and gear mesh impact are computed. Taking the loaded transmission error, measured cumulative pitch error, eccentricity error, time-varying mesh stiffness, and gear mesh impact as the internal excitations, this paper establishes a 12-degree-of-freedom (DOF) dynamic model of a helical gear pair and uses the Fourier series method to solve it. In two situations of low speed and high speed, the gear system dynamic response is analyzed in the time and frequency domains. In addition, an experiment is performed to validate the simulation results. The study shows that the proposed technique is useful and reliable for predicting the dynamic response of a gear system.

Effects of Assembly Errors on Crossed Beveloid Gear Tooth Contact and Dynamic Response

2011 ◽  
Author(s):  
Caichao Zhu ◽  
Chaosheng Song ◽  
Teik C. Lim ◽  
Tao Peng
Keyword(s):  
Dynamic Response ◽  
Gear Tooth ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Axial Position ◽  
Tooth Surface ◽  
Tooth Contact ◽  
Rigid Body Dynamic ◽  
Position Errors ◽  
Shaft Angle

It is known that the tooth flank geometry, assembly errors and the operating conditions of a gear pair have significant influence on tooth contact, load distribution and dynamic response. However, the study of the effects of assembly errors on the mesh characteristics and dynamic response for crossed beveloid gears has been limited due to the complicated geometry and time-varying mesh characteristics. In this study, three types of assembly errors including shaft angle, offset and gear axial position error are examined based on a synthesized mesh model and a three-dimensional elastically coupled rigid-body dynamic model. Also, the relation between a dominant geometry design parameter that is the crossed angle between the first principal directions of the tooth surface curvatures (FPD-angle) and the sensitivity of mesh characteristics and dynamic response subject to assembly errors is investigated. Through the sensitivity analysis with different FPD-angles, the shaft angle error is found to be the most sensitive factor affecting the mesh and dynamic behaviors of crossed beveloid gear set. On the other hand, the gear axial position errors have the least influence on the mesh characteristics and dynamic response. In most cases, the influences of assembly errors on mesh characteristics and dynamics become weaker with the increase of FPD-angle.

A Nonlinear Dynamics Bond Graph Model of Gear Transmission

2010 ◽  
Vol 139-141 ◽  
pp. 933-937
Author(s):  
Jin Yuan Tang ◽  
Hai Feng Chen ◽  
Si Yu Chen
Keyword(s):  
Nonlinear Dynamics ◽  
Graph Model ◽  
Surface Friction ◽  
Transmission Error ◽  
Bond Graph ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Time Varying ◽  
Gear Mesh ◽  
Bond Graph Modeling

A nonlinear dynamics bond graph model of gear pair is established including the time-varying stiffness, transmission error and tooth surface friction. A capacitive component C is introduced to represent the loads and tooth elastic deformation while introducing the concept of switched power junctions (SPJ) to describe time-varying gear mesh stiffness with clearance, and flow Sf represents the influences of the gear transmission error on the system dynamic equations. The tooth surface friction bond graph model involving the relationship of the relative velocity and the direction of friction are developed. According to the causal relations and the power flow, the state-space equations of the gear bond graph model are obtained. Research results show that bond graph modeling method can solve the modeling problem of the gear nonlinear dynamics.

An Analytical Study of the Effect of the Contact Ratio on the Spur Gear Dynamic Response

1999 ◽  
Vol 122 (4) ◽  
pp. 508-514 ◽  
Author(s):  
Anette Andersson
Keyword(s):  
Dynamic Response ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Contact Ratio ◽  
Constant Stiffness ◽  
Gear Mesh ◽  
Critical Rotational Speed ◽  
Stiffness Variation ◽  
Gear Mesh Stiffness

A model was used, where the total gear mesh stiffness was approximated by two constant stiffness levels, in order to analyze the influence of the contact ratio on the dynamic response of spur gears. Due to the stiffness variation there is parametric excitation of the transmission error, which generally causes tooth separation at certain critical rotational speeds. The present paper discloses a method to analytically calculate which contact ratio to use in order to avoid tooth separation near a specific critical rotational speed. [S1050-0472(00)02604-0]

Tooth Surface Modelling and Mesh Behaviors for Paralleled Beveloid Gears

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Ruihua Sun ◽  
Chaosheng Song ◽  
Caichao Zhu ◽  
Siyuan Liu ◽  
Changxu Wei
Keyword(s):  
Cone Angle ◽  
Transmission Error ◽  
Tooth Surface ◽  
Design Parameters ◽  
Tooth Contact Analysis ◽  
Geometry Design ◽  
Mesh Model ◽  
Helical Angle ◽  
Loaded Tooth Contact Analysis ◽  
Pressure Cone

Abstract This paper proposed a new tooth surface modeling method for beveloid gear based on the real cutter surface using two orthogonal variables. Then, the analytical mesh model with and without misalignments were derived and solved to study the influences of geometry design parameters on contact behaviors for paralleled beveloid gear pair. Loaded tooth contact analysis is used to validate the proposed mesh model by abaqus software, and the error is below 5%. Results suggest that the increase in pressure, cone, and helical angles enlarge the contact area for meshing without misalignments. The addendum coefficient has unsubstantial impacts on the contact behaviors. For meshing with axis error in the horizontal direction, the growth of pressure angle, cone angle, helical angle, and addendum coefficient improves the carrying capacity of single tooth. But the transmission error deteriorates with the increase in pressure, cone, and helical angles. All three types of misalignments have little influence on the size of the contact ellipse. The growth of axis errors in horizontal and vertical directions significantly increases the transmission error, but the center distance error has a little influence on the transmission precision.

Modeling of Impact Damping Effect on Hypoid Gear Dynamic Response

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Zhenghong Shi ◽  
Teik C. Lim
Keyword(s):  
Dynamic Response ◽  
Physical Parameters ◽  
Hypoid Gear ◽  
Gear Mesh ◽  
Damping Effect ◽  
Mesh Model ◽  
Torque Load ◽  
Parametric Studies ◽  
The Impact ◽  
Impact Damping

Abstract An enhanced hypoid gear mesh model that incorporates the Hertzian impact damping function is developed in this study to reveal the mechanisms of damping during gear mesh. Two types of impact damping models, namely, viscous and nonviscous type based on the first principle of mechanics, are compared to previous empirical damping models with a constant damping coefficient. Parametric studies are performed for both steady-state and transient analyses to investigate the impact damping effect under numerous load conditions or physical parameters of a meshing gear pair. Comparative study between viscous and nonviscous damping models is also performed to examine their effects on dynamic response for various load levels. It is shown that impact damping can significantly reduce the amplitude of the dynamic mesh force. Nonviscous damping has more significant effect on the dynamic response under heavy torque load due to the influence of greater elastic deformation. Furthermore, it is observed that impact damping can turn double-sided impact into single-sided impact and suppress response peaks in a certain mesh frequency range during speed ramp up.

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