Numerical Simulation of Nonlinear Spur Gear Dynamics

1999 ◽  
Author(s):  
Nagaraj K. Arakere ◽  
C. Nataraj
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Spur Gear ◽  
Journal Bearings ◽  
Accurate Estimation ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Gear Mesh Stiffness

Abstract An analytical investigation of the nonlinear dynamics of a high-speed spur-gear pair supported on journal bearings is presented. Dynamic tooth loads result from the interaction between periodic variation of gear mesh stiffness, involute tooth profile errors and gear rotor dynamics. Accurate estimation of dynamic tooth loads, as the gear teeth engage and disengage, is critical for fatigue life estimation. Load-deflection characteristics of a spur gear mesh and the periodically varying gear mesh stiffness is developed using a finite element model. Relative displacement between the gear teeth (transmission error) due to tooth deflection along the line of action is evaluated. The coupled torsional-lateral vibrations of a spur-gear pair supported on journal bearings is modeled as a six degree of freedom system. The time dependent radial and tangential forces acting on the gear shaft supported on journal bearings is evaluated. Short bearing theory is used for modeling the journal bearing dynamics. The resulting nonlinear equations of motion are numerically integrated to obtain gear and pinion whirl orbits due to unbalance excitation and dynamic tooth load variation. Dynamic tooth loads are compared with the mean load due to torque transmission.

Evaluation of spur gear mesh compliance using the finite element method

1999 ◽  
Vol 213 (6) ◽  
pp. 569-579 ◽  
Author(s):  
M H Arafa ◽  
M M Megahed
Keyword(s):  
Finite Element ◽  
Experimental Methods ◽  
Spur Gear ◽  
Spur Gears ◽  
The Finite Element Method ◽  
Mesh Stiffness ◽  
Fe Modelling ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Gear Mesh Stiffness

This paper presents a finite element (FE) modelling technique to evaluate the mesh compliance of spur gears. Contact between the engaging teeth is simulated through the use of gap elements. Analysis is performed on several gear combinations and the variation in tooth compliance along the contact location is presented in a non-dimensional form. Results are compared with earlier predictions based on analytical, numerical and experimental methods. Load sharing among the mating gear teeth is discussed, and the overall gear mesh stiffness together with its cyclic variation along the path of contact is evaluated.

scholarly journals Improvement on Meshing Stiffness Algorithms of Gear with Peeling

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 609
Author(s):  
Lingli Cui ◽  
Tongtong Liu ◽  
Jinfeng Huang ◽  
Huaqing Wang
Keyword(s):  
Simulation Analysis ◽  
Gear Tooth ◽  
Gear Wheel ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Involute Gears ◽  
Gear Mesh Stiffness ◽  
Meshing Process

This paper investigates the effect of a gear tooth peeling on meshing stiffness of involute gears. The tooth of the gear wheel is symmetric about the axis, and its symmetry will change after the gear spalling, and its meshing stiffness will also change during the meshing process. On this basis, an analytical model was developed, and based on the energy method a meshing stiffness algorithm for the complete meshing process of single gear teeth with peeling gears was proposed. According to the influence of the change of meshing point relative to the peeling position on the meshing stiffness, this algorithm calculates its stiffness separately. The influence of the peeling sizes on mesh stiffness is studied by simulation analysis. As a very important parameter, the study of gear mesh stiffness is of great significance to the monitoring of working conditions and the prevention of sudden failure of the gear box system.

An Energy-Based Load Distribution Approach for the Application of Gear Mesh Stiffness on Elastic Bodies

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Faysal Andary ◽  
Joerg Berroth ◽  
Georg Jacobs
Keyword(s):  
Degrees Of Freedom ◽  
Design Method ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Elastic Bodies ◽  
Single Tooth ◽  
Traditional Approaches ◽  
Energy Based Design ◽  
Gear Mesh Stiffness

This study introduces a new potential energy-based design method for simplifying elastic gear bodies in low- to mid-range frequency applications by bridging over the gear teeth with external stiffness elements. The advantage of the introduced method over more traditional approaches, which are either based on rigid gears or on replacing the teeth, is that the complex gear body and its dynamic behavior are preserved, albeit with fewer degrees of freedom. The method is demonstrated on a gear by replacing a single tooth under load and then validated numerically against a typical flexible gear model. The simulation results show good accuracy within the chosen frequency range and with a clear reduction in calculation time compared to the unreduced model. Furthermore, the extension and optimization potential of the results is discussed.

Vibration of High-Speed Compliant Gear Pairs

2016 ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
High Speed ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
System Structure ◽  
Vibration Modes ◽  
Mesh Stiffness ◽  
Nodal Diameter ◽  
Gear Teeth ◽  
Wide Range ◽  
System Coupling

This study analytically investigates the vibration of high-speed, compliant gear pairs using a model consisting of coupled, spinning, elastic rings. The gears are elastically coupled by a space-fixed, discrete stiffness element that represents the contacting gear teeth. Hamilton’s principle is used to derive the nonlinear governing equations of motion and boundary conditions. These equations are linearized for small vibrations about the steady equilibrium due to rotation. The equations are cast in operator form, which exemplifies their gyroscopic system structure. The eigenvalue problem is discretized using Galerkin’s method. The natural frequencies and vibration modes for an example aerospace gear pair are numerically calculated for a wide-range of rotation speeds. The system coupling leads to multiple eigenvalue veering regions as the gear rotation speed varies. Highly coupled vibration modes that have meaningful deflection in the discrete mesh stiffness occur within a set frequency band. The vibration modes within this band have distinct nodal diameter components that evolve with rotation speed.

Dynamic Analysis of a Spur Geared Rotor-Bearing System with Nonlinear Gear Mesh Stiffness

2014 ◽  
Vol 945-949 ◽  
pp. 853-861 ◽  
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Element Model ◽  
Dynamic Responses ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Lagrange’S Equation ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The gear mesh stiffnesses have been regarded as constants in most previous models of geared rotor-bearing systems. In this paper, a dynamic analysis of a spur geared rotor-bearing system with nonlinear gear mesh stiffness is presented. The nonlinear gear mesh stiffness is accounted for by bending, fillet-foundation and contact deflections of gear teeth. A finite element model of the geared rotor-bearing system is developed, the equations of motion are obtained by applying Lagrange’s equation, and the dynamic responses are computed by using the fourth-order Runge-Kutta numerical method. Numerical results indicate that the proposed gear mesh stiffness provides a realistic dynamic response for spur geared rotor-bearing system.

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.

Prediction of Spur Gear Mesh Stiffness Associated with the Tooth Corrosion

2015 ◽  
Vol 799-800 ◽  
pp. 570-575
Author(s):  
Zheng Min Qing Li ◽  
Qing Bin Zhao ◽  
Xiao Zhen Li
Keyword(s):  
Spur Gear ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Gear Drive ◽  
Corrosion Effect ◽  
Proposed Model ◽  
Stiffness Model ◽  
The Stability ◽  
Gear Drives ◽  
Gear Mesh Stiffness

In this study, a mesh stiffness model of spur gear drives considering the tooth corrosion effect, which is based on Ishikawa model, is proposed. The fidelity of mesh stiffness based on the proposed model is checked by comparing the result with a benchmark result from the reference and the effect of the tooth corrosion on mesh stiffness is analyzed. The prediction indicates mesh stiffness is insensitive to the tooth corrosion, but this conclusion has a signification for assessing the stability of inherent properties of a spur gear drive when the tooth corrosion is produced.

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