Analysis of Transmission Error of Two-Stage Spur Gear Space Driving Mechanism

2018 ◽  
Vol 07 (03) ◽  
pp. 234-243
Author(s):  
建峰 马
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Driving Mechanism ◽  
Two Stage

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.

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.

Harmonic Resonance Frequency Factor of Spur Gear System and Oscillation Reduction Approaches

2007 ◽  
Author(s):  
Jianping Wang ◽  
Pengfei Li ◽  
Ziying Wu ◽  
Minghong Zhang
Keyword(s):  
Parametric Excitation ◽  
Linear Time ◽  
Primary Resonance ◽  
Frequency Factor ◽  
Multiple Scale ◽  
Transmission Error ◽  
Spur Gear ◽  
High Order ◽  
Time Varying ◽  
Harmonic Resonance

In this study, a non-linear time-varying dynamic model of a spur gear pair system is used to investigate the dynamic behavior of the system by means of multiple scale approach. Both time-varying stiffness, transmission error and tooth backlash clearance of the system are taken into account in the model. The mesh stiffness fluctuation is developed as high order Fourier series and tooth backlash clearance is fitted by high order polynomial function. The frequency factors of the system are investigated and the frequency-response equations at the case of internal and external excitation, parametric excitation and combined excitation are obtained. The peak value of the amplitude of the primary resonance, super and sub harmonic resonance and combination harmonic under internal, external and parametric excitation are researched. The approaches of vibration reduction are investigated. Finally an example is investigated using the presented process and the results indicate the sensitivity and correctness of the presented analysis approaches.

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.

A New Numerical Algorithm for Transmission Error Measurement at Gears Meshing

2012 ◽  
Vol 472-475 ◽  
pp. 1563-1567
Author(s):  
Ai Jun Xu ◽  
Xiao Zhong Deng ◽  
Jing Zhang ◽  
Kai Xu ◽  
Ju Bo Li
Keyword(s):  
Numerical Algorithm ◽  
Angular Resolution ◽  
Angular Displacement ◽  
Transmission Error ◽  
Comparison Method ◽  
Dynamic Measurement ◽  
Driving Mechanism ◽  
Error Measurement ◽  
Measurement Algorithm ◽  
Constrained Conditions

Many different methods have been developed for the measurement of transmission error (T.E.) at gears meshing. Each strategy improved the measurement performance is based on comparing the phases of sequence signals by counting the number of encoder pulses. The phase comparison method of T.E. is a dynamic measurement algorithm with lower angular resolution and many constrained conditions. This paper presents a new numerical algorithm aimed to provide the high accuracy information of instantaneous T.E. in the form of angular displacement. The analysis approach uses phase shift and demodulation technology in frequency domain to process the signals generated by encoders fixed on the both shaft of the gear driving mechanism. Finally, the algorithm is tested by simulation of gear meshing signal in Matlab software.

Low excitation spur gears with variable tip diameter

2021 ◽  
Vol 263 (5) ◽  
pp. 1275-1285
Author(s):  
Joshua Götz ◽  
Sebastian Sepp ◽  
Michael Otto ◽  
Karsten Stahl
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Low Noise ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Axial Forces ◽  
Tooth Width ◽  
Drive Trains ◽  
Static Transmission Error

One important source of noise in drive trains are transmissions. In numerous applications, it is necessary to use helical instead of spur gear stages due to increased noise requirements. Besides a superior excitation behaviour, helical gears also show additional disadvantageous effects (e.g. axial forces and tilting moments), which have to be taken into account in the design process. Thus, a low noise spur gear stage could simplify design and meet the requirements of modern mechanical drive trains. The authors explore the possibility of combining the low noise properties of helical gears with the advantageous mechanical properties of spur gears by using spur gears with variable tip diameter along the tooth width. This allows the adjustment of the total length of active lines of action at the beginning and end of contact and acts as a mesh stiffness modification. For this reason, several spur gear designs are experimentally investigated and compared with regard to their excitation behaviour. The experiments are performed on a back-to-back test rig and include quasi-static transmission error measurements under load as well as dynamic torsional vibration measurements. The results show a significant improvement of the excitation behaviour for spur gears with variable tip diameter.

scholarly journals Research on the Design and Modification of Asymmetric Spur Gear

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaohe Deng ◽  
Lin Hua ◽  
Xinghui Han
Keyword(s):  
Computer Aided Design ◽  
Design Method ◽  
Geometric Model ◽  
Simulation Method ◽  
Transmission Error ◽  
Spur Gear ◽  
Geometric Shape ◽  
Spur Gears ◽  
Gear Design ◽  
Aided Design

A design method for the geometric shape and modification of asymmetric spur gear was proposed, in which the geometric shape and modification of the gear can be obtained directly according to the rack-cutter profile. In the geometric design process of the gear, a rack-cutter with different pressure angles and fillet radius in the driving side and coast side was selected, and the generated asymmetric spur gear profiles also had different pressure angles and fillets accordingly. In the modification design of the gear, the pressure angle modification of rack-cutter was conducted firstly and then the corresponding modified involute gear profile was obtained. The geometric model of spur gears was developed using computer-aided design, and the meshing process was analyzed using finite element simulation method. Furthermore, the transmission error and load sharing ratio of unmodified and modified asymmetric spur gears were investigated. Research results showed that the proposed gear design method was feasible and desired spur gear can be obtained through one time rapid machining by the method. Asymmetric spur gear with better transmission characteristic can be obtained via involute modification.

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