Dynamic Response of Toroidal Drive to Mesh Parametric Excitations

2005 ◽  
Vol 219 (9) ◽  
pp. 889-899 ◽  
Author(s):  
L Xu ◽  
H Jin ◽  
X Hao
Keyword(s):  
Dynamic Response ◽  
Three Dimensional ◽  
Forced Response ◽  
Dynamic Equations ◽  
Dynamic Factor ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Dynamic Factors ◽  
Stiffness Variation ◽  
Model Equations

In this article, a three-dimensional dynamic model of the toroidal drive is given. By the model, equations of the relative displacements between different components and the dynamic equations for the drive are obtained. Changes of the mesh stiffness are analysed and the equation of periodical time-varying mesh stiffness is presented in Fourier series form. Under neglecting nonlinear items, time-varying mesh stiffness is changed into equivalent exciting load and linear dynamic equations of the drive are obtained. Then, the analytical equations of the forced response for the drive to mesh stiffness excitation are obtained, and the equations of the dynamic factors between a planet and worm or stator are given as well. By aforementioned equations, the forced frequency responses of the drive system to mesh stiffness variation are given, the variations of dynamic response for the worm as functions of the main parameters are presented, and the dynamic factor between a planet and worm is given as a function of operating speed.

Using Dynamic Analysis for Compact Gear Design

1998 ◽  
Author(s):  
Ping-Hsun Lin ◽  
Hsiang Hsi Lin ◽  
Fred B. Oswald ◽  
Dennis P. Townsend
Keyword(s):  
Dynamic Response ◽  
Bending Strength ◽  
Three Dimensional ◽  
Spur Gear ◽  
Dynamic Factor ◽  
Operating Speed ◽  
Gear Design ◽  
Dynamic Factors ◽  
Speed Range ◽  
Response Change

Abstract This paper presents procedures for designing compact spur gear sets with the objective of minimizing the gear size. The allowable tooth stress and dynamic response are incorporated in the process to obtain a feasible design region. Various dynamic rating factors were investigated and evaluated. The constraints of contact stress limits and involute interference combined with the tooth bending strength provide the main criteria for this investigation. A three-dimensional design space involving the gear size, diametral pitch, and operating speed was developed to illustrate the optimal design of spur gear pairs. The study performed here indicates that as gears operate over a range of speeds, variations in the dynamic response change the required gear size in a trend that parallels the dynamic factor. The dynamic factors are strongly affected by the system natural frequencies. The peak values of the dynamic factor within the operating speed range significantly influence the optimal gear designs. The refined dynamic factor introduced in this study yields more compact designs than AGMA dynamic factors.

Using Dynamic Analysis for Compact Gear Design

1999 ◽  
Vol 124 (1) ◽  
pp. 91-97 ◽  
Author(s):  
Ping-Hsun Lin ◽  
Hsiang Hsi Lin ◽  
Fred B. Oswald ◽  
Dennis P. Townsend
Keyword(s):  
Dynamic Response ◽  
Bending Strength ◽  
Three Dimensional ◽  
Spur Gear ◽  
Dynamic Factor ◽  
Operating Speed ◽  
Gear Design ◽  
Dynamic Factors ◽  
Speed Range ◽  
Response Change

This paper presents procedures for designing compact spur gear sets with the objective of minimizing the gear size. The allowable tooth stress and dynamic response are incorporated in the process to obtain a feasible design region. Various dynamic rating factors were investigated and evaluated. The constraints of contact stress limits and involute interference combined with the tooth bending strength provide the main criteria for this investigation. A three-dimensional design space involving the gear size, diametral pitch, and operating speed was developed to illustrate the optimal design of spur gear pairs. The study performed here indicates that as gears operate over a range of speeds, variations in the dynamic response change the required gear size in a trend that parallels the dynamic factor. The dynamic factors are strongly affected by the system natural frequencies. The peak values of the dynamic factor within the operating speed range significantly influence the optimal gear designs. The refined dynamic factor introduced in this study yields more compact designs than AGMA dynamic factors.

Vibration-based fault diagnosis of helical gear pair with tooth surface wear considering time-varying friction coefficient under mixed EHL condition

2021 ◽  
pp. 1-16
Author(s):  
Siyu Wang ◽  
Rupeng Zhu
Keyword(s):  
Dynamic Response ◽  
Hydrodynamic Lubrication ◽  
Helical Gear ◽  
Calculation Model ◽  
Tooth Surface ◽  
Time Varying ◽  
Gear Pair ◽  
Surface Wear ◽  
Mesh Stiffness ◽  
Helical Gear Pair

Abstract Based on “slice method”, the improved time-varying mesh stiffness (TVMS) calculation model of helical gear pair with tooth surface wear is proposed, in which the effect of friction force that obtained under mixed elasto-hydrodynamic lubrication (EHL) is considered in the model. Based on the improved TVMS calculation model, the dynamic model of helical gear system is established, then the influence of tooth wear parameters on the dynamic response is studied. The results illustrate that the varying reduction extents of mesh stiffness along tooth profile under tooth surface wear, in addition, the dynamic response in time-domain and frequency-domain present significant decline in amplitude under deteriorating wear condition.

Time-varying mesh stiffness calculation for gear pairs with misalignment errors in multiple degrees of freedom based on an analytical method

2021 ◽  
pp. 095440622110392
Author(s):  
Qi Wen ◽  
Qi Chen ◽  
Qungui Du ◽  
Yong Yang
Keyword(s):  
Analytical Model ◽  
Contact Line ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Single Pair ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Position Change ◽  
Multiple Degrees Of Freedom ◽  
Effective Contact

Misalignment errors (MEs) in multiple degrees of freedom (multi-DOFs) at the mesh position will lead to a change in the time-varying mesh stiffness (TVMS) and then affect the dynamic behaviour of gear pairs. Therefore, a new, more rapid, three-dimensional analytical model for TVMS calculation for gear pairs with three rotational and three translational MEs is established in this paper, and a new solution method based on potential energy theory is presented. In addition, the correctness of the new model is verified by the finite element method (FEM). Moreover, the effective contact line, uneven distribution of mesh force on the contact line, and mesh position change are taken into account. Finally, the TVMS under different ME conditions is calculated with the new analytical model. The results showed that the different MEs have dissimilar effects on the TVMS, and the relationship between the ME and TVMS is nonlinear. In addition, the region of single-pair and double-pair teeth in contact would also change with ME.

A Static and Dynamic Model of Spiral Bevel Gears

2011 ◽  
Vol 86 ◽  
pp. 35-38
Author(s):  
Jing Wang ◽  
Joël Teixeira Alves ◽  
Michèle Guingand ◽  
Jean Pierre de Vaujany ◽  
Philippe Velex
Keyword(s):  
Dynamic Models ◽  
Three Dimensional ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Linear Distribution ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Lumped Parameter ◽  
Potential Contact ◽  
Spiral Bevel

Two three-dimensional lumped parameter dynamic models of spiral bevel gears are presented and compared. The first approach is classic and relies on a single averaged mesh stiffness element connecting the gears whereas a time-varying non-linear distribution of discrete stiffness elements over the potential contact area is used in the second model.

Calculation of Time-Varying Mesh Stiffness Affected by Load Based on FEM

2017 ◽  
Author(s):  
Qian Cheng ◽  
Yimin Shao ◽  
Jing Liu ◽  
Lei Yin ◽  
Minggang Du ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Analytical Method ◽  
Working Condition ◽  
Load Condition ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Behavior Study ◽  
Gear Transmission System ◽  
The Impact ◽  
Line Direction

Time-varying mesh stiffness (TVMS) is a key component of gear transmission system for gear dynamic response. When the machine starts working, stop working or goes into an unstable working condition, the load will be varying. In order to investigate the impact of different loads on TVMS, a numerical method based on FEM is proposed in this paper to study the effect of TVMS. The dynamic mesh forces and dynamic displacements along the action line direction at each mesh point are extracted. The calculated TVMS is validated by comprising with the TVMS calculated by the analytical method (AM). The results show that TVMS increases with the rise of input moment which can be intruded in gear dynamic behavior study under different load condition.

scholarly journals Computation Method of Gear Dynamic Response Using Experimental Strain Data and Application in Pitting Fault Analysis

2019 ◽  
Vol 11 (1) ◽  
Author(s):  
Yongzhi Qu ◽  
Haoliang Zhang ◽  
Zechao Wang ◽  
Zude Zhou
Keyword(s):  
Dynamic Response ◽  
Gear System ◽  
Dynamic Strain ◽  
Time Varying ◽  
Tooth Root ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Strain Data ◽  
Experimental Strain ◽  
Fbg Sensors

In this paper, A semi-physical method for calculating time varying mesh stiffness and the dynamic response of gear system based on experimental strain data is studied. In a previous work, it was reported that dynamic strain on gear tooth root can be measured under normal operating condition using fiber Bragg Grating (FBG) sensors. This paper aims to compute gear dynamic response using experimental strain data and give an explanation of the fault propagation process. Using the dynamic strain data from FBG sensors, a method for calculating the dynamic response of gear system is proposed. Based on the theory of potential energy and material mechanics, the relationship between the bending strain of the tooth root and the time varying mesh stiffness is established. The time varying mesh stiffness and dynamic response of healthy gear and pitted gear are then calculated respectively. The force transmission during gear mesh under the condition of surface pitting is analyzed. It is concluded that in the case of pitting fault, there will be a significant loss of torque in the power transmission process due to the loss of contact area. It is further inferred that the loss of meshing force andthedecreasing of Hertzian contact stiffness are the major contributing factors for pitting fault. In addition, the semi-analytical method of computing gear dynamic response is validated with experimental study ofacceleration signal in the perspective of dynamic response.  

Parametric Instability in Planetary Gears With Frequency-Modulated Time-Varying Mesh Stiffness

2014 ◽  
Author(s):  
Xinghui Qiu ◽  
Qinkai Han ◽  
Fulei Chu
Keyword(s):  
Parametric Instability ◽  
Operating Conditions ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Rotational Model ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Stiffness Variation ◽  
Speed Fluctuations ◽  
Gear Mesh Stiffness

A rotational model of planetary gears is developed which incorporates mesh stiffness variation and input speed fluctuations. Gear mesh stiffness is approximated by rectangle wave and different harmonic orders are considered. Because of speed fluctuations, the mesh stiffness is frequency modulated. The parametric instability associated with frequency-modulated time-varying stiffness is numerically investigated. The operating conditions leading to parametric instability are identified using Floquet theory and numerical integration. Whether the general laws derived for steady speed to suppress particular instabilities are applicable for fluctuating speed is verified. The effects of speed fluctuations on parametric instability are examined.

scholarly journals Study of the Influences of Transient Crack Propagation in a Pinion on Time-Varying Mesh Stiffness

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Youmin Hu ◽  
Jikai Fan ◽  
Jin Yu
Keyword(s):  
Potential Energy ◽  
Energy Method ◽  
Propagation Model ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Propagation Models ◽  
Material Fatigue ◽  
Stiffness Variation ◽  
Short Time ◽  
Potential Energy Method

Cracks in a cracked gear may further propagate by a tiny length in a very short time for several reasons, such as material fatigue and load fluctuations. In this paper, this dynamic process is defined as transient propagation of cracks. This research aims to calculate the time-varying mesh stiffness of gears when transient propagation of cracks arises, which has not been extensively studied in existing literatures. The transient propagation of cracks is modelled. An improved potential energy method is proposed by incorporating the propagation model into the potential energy method. The improved method can also be utilised to calculate the mesh stiffness of gears when transient propagation of cracks arises. Different transient propagation models are considered to simulate the propagation of cracks in a short amount of time. Different deterioration levels of cracks before transient propagation and different lengths and models of transient propagation are also examined. The variation rules of mesh stiffness caused by the transient propagation of cracks are summarised. The influence of the deterioration level of cracks on mesh stiffness variation when transient propagation arises is obtained. Simulation results show that the proposed method accurately calculates time-varying mesh stiffness when transient propagation of cracks arises. Furthermore, the method improves the monitoring of further propagation of cracks in gears from the perspective of time-varying mesh stiffness.

Numerical Research on Forced Response of a Compressor Rotor Row Under Inlet Distortion

2012 ◽  
Author(s):  
Zhang Zhang ◽  
Anping Hou ◽  
Wei Tuo ◽  
Aiguo Xia ◽  
Sheng Zhou
Keyword(s):  
Dynamic Response ◽  
Total Pressure ◽  
Three Dimensional ◽  
Forced Response ◽  
Vibration Response ◽  
Rotor Blades ◽  
Response Level ◽  
Blade Vibration ◽  
Inlet Distortion ◽  
Fatigue Life Analysis

Under inlet total pressure distortion, forced response of compressor blades poses a threat to aircraft propulsion system. Research on blade dynamic response is premise and basis for high-cycle fatigue life analysis. Blades of a compressor first rotor row are studied with three dimensional numerical simulation in fluid-structure coupling methods. The inlet distortion’s influence on blade aeroelastic dynamic response and flow field characteristics are analyzed. The results demonstrate that circumferential and radial total pressure distortion should be considered together in the phenomenon of actual inlet distortion induced blade vibration response. At the condition of low angle of attacks, radial distortion intensity is weak, the relation between vibration response level of rotor blades and circumferential distortion intensity is proportional. With the angle of attack increases, the vibratory stress under aerodynamic forces grows sufficiently. The radial total pressure distortion near hub increases dynamic response severity of rotor blades.

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