scholarly journals Transmission Error Analysis and Disturbance Optimization of Two-Stage Spur Gear Space Driven Mechanism with Large Inertia Load

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Jianfeng Ma ◽  
Chao Li ◽  
Lingli Cui
Keyword(s):  
Dynamic Model ◽  
Model Space ◽  
Transmission Error ◽  
Spur Gear ◽  
Gear System ◽  
Variable Load ◽  
Driving Mechanism ◽  
Nonlinear Dynamic Model ◽  
Profile Error ◽  
Two Stage

For the nonlinear disturbance actual issues of the model space drive mechanism two-stage spur gear system, a nonlinear dynamic model of 14-DOF (degree of freedom) two-stage spur gear with time-varying stiffness and damping was established. This model has been developed previously by the authors to access the large inertia on the dynamic response of spur gear space driving mechanism, and its effectiveness was proved by a motion simulation experiment. In this paper, the profile error (PE) and the index error (IE) were enhanced in the dynamic model. The effects of profile error, index error, and variable load torque on transmission error (TE) were analyzed, while the optimization was proposed according to the analyzed result. The peak-to-peak value of the optimized load transmission error (LTE) was reduced by 60.7%, which improved the transmission accuracy and reduced the phenomenon of disturbance. The research of nonlinear dynamical model of two-stage spur gear and the TE of the large inertia load were enriched, which provided an important reference for the actual design of the gear system.

scholarly journals Experimental study on transmission error of space-driven gear system under large inertia load

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985695 ◽  
Author(s):  
Jianfeng Ma ◽  
Chao Li ◽  
Jia Liu ◽  
Dongxing Cao ◽  
Jinfeng Huang
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Dominant Role ◽  
Transmission Error ◽  
Spur Gear ◽  
Gear System ◽  
Experimental Results ◽  
Normal Operation ◽  
Driving Mechanism ◽  
Set Up

There is a nonlinear disturbance problem in the operation of large inertia load space-driving mechanism, which seriously affects the normal operation of the system. A 14 degree-of-freedom nonlinear time-varying dynamic model was established for a two-stage spur gear system. The dynamic equations were solved numerically based on the Runge–Kutta method. The correctness of the dynamic model was verified through experiments. In the author’s previous research, the transmission error and dynamic response of gear system was analyzed. After the establishment of the dynamic model, a comparative analysis of the load response under different inertia was performed to illustrate the importance of studying large inertia loads. A large inertia load transmission error experimental device was set up to collect and process the transmission error data under different load inertia and different speeds. Comparing experimental results with numerical results, the correctness of the numerical model was verified, and the reasons for the differences between the two were explained. The analysis of the experimental results shows that for the transmission error of large inertia load gear transmission system, the influence of stiffness excitation on the transmission error amplitude is dominant. For the high-speed gear system, the pitch error plays a dominant role.

scholarly journals Dynamic Response Analysis of Spur Gear System with Backlash

2021 ◽  
Vol 276 ◽  
pp. 01012
Author(s):  
Chao Li ◽  
Jigang Wang
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Transmission Error ◽  
Spur Gear ◽  
Gear System ◽  
Response Analysis ◽  
Response Curves ◽  
Nonlinear Dynamic Response ◽  
Dynamic Response Analysis ◽  
Return Difference

There are few studies on space-driven gear systems in the existing literature. In this paper, a spacedriven two-stage spur gear system is taken as the research object, and a 10 DOF dynamic model is established. A nonlinear dynamic response analysis was performed. The backlash was introduced into the dynamic model, and the time-varying stiffness was corrected to make the theoretical model closer to reality. By comparing two kinds of dynamic response curves with and without return difference, it was illustrated that the influence of return difference on dynamic transmission error in a gear system. The results obtained in this paper provide a reference and basis for subsequent research.

Rocking vibration and dynamic characteristics of a two-stage spur and bevel gear transmitting system

2016 ◽  
Vol 231 (24) ◽  
pp. 4528-4547 ◽  
Author(s):  
Haiyan Yan ◽  
Siyu Chen ◽  
Jinyuan Tang
Keyword(s):  
Dynamic Model ◽  
Transmission Error ◽  
Spur Gear ◽  
Bevel Gear ◽  
Mode Shapes ◽  
Gear Pair ◽  
Tooth Contact Analysis ◽  
Two Stage ◽  
Rocking Motion ◽  
Gyroscopic Effects

In this study, theoretical analysis is performed in order to investigate the nonlinear vibration response of the two-stage spur and straight bevel gears transmitting system. The system dynamic model of the transmitting system is considered in detail. The tooth contact analysis results are obtained through calculation and the dynamic model with time-varying stiffness, and backlash for both gear pair is built. The natural frequencies, mode shapes, and critical speed for the transmitting system with gyroscopic effects are calculated. The results show that the whirling motion due to the second shaft may be the main factor of vibration for the transmitting system and the lateral–torsional–axial vibration dominate the overall system vibration. Many critical characteristics cannot be represented in the transmission error, especially when the rocking and other freedoms are considered in the gear transmitting system. The rocking motion will be excited due to the coupled effect of bevel gear pair, which may be also the reason for the catastrophic damage of the thin web spur gear.

scholarly journals A Coupled Torsional-Transition Nonlinear Vibration and Dynamic Model of a Two-Stage Helical Gearbox Reducer for Electric Vehicles

2020 ◽  
Vol 2020 ◽  
pp. 1-25
Author(s):  
Abdulhameed M. Y. Al-Tayari ◽  
Siyu Chen ◽  
Zhou Sun
Keyword(s):  
Dynamic Model ◽  
Lyapunov Exponents ◽  
Electric Vehicles ◽  
Degrees Of Freedom ◽  
Transmission Error ◽  
Torsional Stiffness ◽  
Nonlinear Phenomena ◽  
Nonlinear Dynamic Model ◽  
Two Stage ◽  
Torsional Transition

A coupled torsional-transition nonlinear dynamic model of a two-stage helical gear (TSHG) reduction system for electric vehicles (EVs) is presented in this paper. The model consists of 16 degrees of freedom (DOF), which includes factors such as the nonlinearity of backlash, time-varying mesh stiffness (TVMS), mesh damping, supporting bearings, static transmission error (STE), and the torsional damping and stiffness of the intermediate shaft, in which the fourth-order Runge–Kutta numerical integration method was applied to solve the differential equations. With the help of bifurcation diagrams, time-domain histories diagrams, amplitude-frequency spectrums, phase plane diagrams, Poincaré maps, root-mean-square (RMS) curves, peak-peak values (PPVs), and Lyapunov exponents, the effects of pinion rotational speed, backlash, torsional stiffness, and torque fluctuation on the dynamic behavior of TSHG system are investigated. The stability properties of steady-state responses are investigated using Lyapunov exponents. The results reveal various types of dynamic evolution mechanisms and nonlinear phenomena such as periodic-one responses, quasiperiodic responses, jumps phenomena, and chaotic responses. The research presents useful results and information to vibration control and dynamic design of the TSHG transmission system used in EVs.

Nonlinear Dynamic Modeling of Gear-Shaft-Disk-Bearing Systems Using Finite Elements and Describing Functions

2003 ◽  
Vol 126 (3) ◽  
pp. 534-541 ◽  
Author(s):  
Rafiq Maliha ◽  
Can U. Dogˇruer ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Degree Of Freedom ◽  
Discrete Models ◽  
Nonlinear Dynamic Model ◽  
Disk System ◽  
Gear Mesh

This study presents a new nonlinear dynamic model for a gear-shaft-disk-bearing system. A nonlinear dynamic model of a spur gear pair is coupled with linear finite element models of shafts carrying them, and with discrete models of bearings and disks. The nonlinear elasticity term resulting from backlash is expressed by a describing function, and a method developed in previous studies to determine multi harmonic responses of nonlinear multi-degree-of-freedom systems is employed for the solution. The excitations considered in the model are external static torque and internal excitation caused by mesh stiffness variation, gear errors and gear tooth profile modifications. The model suggested and the solution method presented combine the versatility of modeling a shaft-bearing-disk system that can have any configuration without a limitation to the total degree of freedom, with the accuracy of a nonlinear gear mesh interface model that allows to predict jumps and double solutions in frequency response. Thus any single stage gear mesh configuration can be modeled easily and accurately. With the model developed it is possible to calculate dynamic gear loads, dynamic bearing forces, dynamic transmission error and bearing displacements. Theoretical results obtained by using the method suggested are compared with the experimental data available in literature, as well as with the theoretical values calculated by employing a previously developed nonlinear single degree of freedom model.

scholarly journals An implicit algorithm for the dynamic study of nonlinear vibration of spur gear system with backlash

2018 ◽  
Vol 19 (3) ◽  
pp. 310 ◽  
Author(s):  
Youssef Hilali ◽  
Bouazza Braikat ◽  
Hassane Lahmam ◽  
Noureddine Damil
Keyword(s):  
Continuation Method ◽  
Time Discretization ◽  
Contact Problems ◽  
Spur Gear ◽  
Gear System ◽  
Two Stage ◽  
Math Model ◽  
Newmark Scheme ◽  
Regularization Techniques ◽  
Taylor Series Expansions

In this work, we propose some regularization techniques to adapt the implicit high order algorithm based on the coupling of the asymptotic numerical methods (ANM) (Cochelin et al., Méthode Asymptotique Numérique, Hermès-Lavoisier, Paris, 2007; Mottaqui et al., Comput. Methods Appl. Mech. Eng. 199 (2010) 1701–1709; Mottaqui et al., Math. Model. Nat. Phenom. 5 (2010) 16–22) and the implicit Newmark scheme for solving the non-linear problem of dynamic model of a two-stage spur gear system with backlash. The regularization technique is used to overcome the numerical difficulties of singularities existing in the considered problem as in the contact problems (Abichou et al., Comput. Methods Appl. Mech. Eng. 191 (2002) 5795–5810; Aggoune et al., J. Comput. Appl. Math. 168 (2004) 1–9). This algorithm combines a time discretization technique, a homotopy method, Taylor series expansions technique and a continuation method. The performance and effectiveness of this algorithm will be illustrated on two examples of one-stage and two-stage gears with spur teeth. The obtained results are compared with those obtained by the Newton–Raphson method coupled with the implicit Newmark scheme.

scholarly journals Rattle dynamics of noncircular face gear under multifrequency parametric excitation

2021 ◽  
Vol 12 (1) ◽  
pp. 361-373
Author(s):  
Dawei Liu ◽  
Zhenzhen Lv ◽  
Guohao Zhao
Keyword(s):  
Dynamic Model ◽  
Parametric Excitation ◽  
Nonlinear Dynamic ◽  
Velocity Ratio ◽  
Harmonic Balance Method ◽  
Transmission Error ◽  
Dynamic Responses ◽  
Discrete Fourier Transformation ◽  
Nonlinear Dynamic Model ◽  
Face Gear

Abstract. A noncircular face gear (NFG) conjugated with a pinion is a new type of face gear which can transmit variable velocity ratio and in which two time-varying excitations exist, namely the meshing stiffness excitation and instantaneous center excitation. Considering the tooth backlash, static transmission error and multifrequency parametric excitation, a nonlinear dynamic model of the NFG pair is presented. Based on the harmonic balance method and discrete Fourier transformation, a semi-analytic approach for the nonlinear dynamic model is given to analyze the dynamic behaviors of the NFG. Results demonstrate that, with increase in the eccentric ratio, input velocity and error amplitude, the NFG will undergo a non-rattle, unilateral rattle and bilateral rattle state in succession, and a jump phenomenon will appear in the dynamic responses when the rattle state of the gears is transformed from unilateral rattle to bilateral rattle.

Bifurcation and Chaos of a Spur Gear Transmission System With Non-Uniform Wear

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Zhibo Geng ◽  
Ke Xiao ◽  
Junyang Li ◽  
Jiaxu Wang
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Operating Time ◽  
Spur Gear ◽  
Gear Transmission ◽  
Nonlinear Dynamic Model ◽  
Gear Backlash ◽  
Gear Transmission System ◽  
Nonlinear Dynamic Characteristics

Abstract In this study, a nonlinear dynamic model of a spur gear transmission system with non-uniform wear is proposed to analyze the interaction between surface wear and nonlinear dynamic characteristics. A quasi-static non-uniform wear model is presented, with consideration of the effects of operating time on mesh stiffness and gear backlash. Furthermore, a nonlinear dynamic model with six degrees-of-freedom is established considering surface friction, time-varying gear backlash, time-varying mesh stiffness, and eccentricity, and the Runge–Kutta method applied to solve this model. The bifurcation and chaos in the proposed dynamic model with the change of the operating time and the excitation frequency are investigated by bifurcation and spectrum waterfall diagrams to analyze the bifurcation characteristics and the dimensionless mesh force. It is found that surface wear is generated with a change in operating time and affects the nonlinear dynamic characteristics of the spur gear system. This study provides a better understanding of nonlinear dynamic characteristics of gear transmission systems operating under actual conditions.

scholarly journals Dynamic Model of Spur Gear Pair with Modulation Internal Excitation

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Wang ◽  
Lei Zhang ◽  
Yuan-Qing Luo ◽  
Chang-Zheng Chen
Keyword(s):  
Dynamic Model ◽  
Transmission Error ◽  
Spur Gear ◽  
Experimental Result ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Internal Excitation ◽  
Modulation Sideband

In the actual measurements, vibration and noise spectrum of gear pair often exhibits sidebands around the gear mesh harmonic orders. In this study, a nonlinear time-varying dynamic model of spur gear pair was established to predict the modulation sidebands caused by the AM-FM modulation internal excitation. Here, backlash, modulation time-varying mesh stiffness, and modulation transmission error are considered. Then the undamped natural mode was studied. Numerical simulation was made to reveal the dynamic characteristic of a spur gear under modulation condition. The internal excitation was shown to exhibit obvious modulation sideband because of the modulation time-varying mesh stiffness and modulation transmission error. The Runge-Kutta method was used to solve the equations for analyzing the dynamic characteristics with the effect of modulation internal excitation. The result revealed that the response under modulation excitation exhibited obvious modulation sideband. The response under nonmodulation condition was also calculated for comparison. In addition, an experiment was done to verify the prediction of the modulation sidebands. The calculated result was consistent with the experimental result.

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