Frictional dynamic model predictions of FZG-A10 spur gear pairs considering profile errors

2020 ◽  
pp. 135065012096297
Author(s):  
Nabih Feki ◽  
Maroua Hammami ◽  
Olfa Ksentini ◽  
Mohamed Slim Abbes ◽  
Mohamed Haddar
Keyword(s):  
Dynamic Model ◽  
Coefficient Of Friction ◽  
Power Loss ◽  
Spur Gear ◽  
Operating Conditions ◽  
Time Dependent ◽  
Nonlinear Dynamic Model ◽  
Gear Mesh ◽  
Proposed Model ◽  
Profile Errors

In this work, a nonlinear dynamic model of an FZG-A10 spur gear was investigated by taking into account for the actual time-varying gear mesh stiffness and the frictional effects between meshing gear teeth to evaluate the influence of the dynamic effects on frictional gear power loss predictions. The equations of motion of the generalized translational-torsional coupled dynamic system derived from Lagrange principle was extended compared to authors’ previous work in order to account for time dependent coefficient of friction and profile errors. The dynamic response of spur gears, computed by an iterative implicit scheme of Newmark, is changed due to the presence of coefficient of friction and profile errors. A dynamic analysis was performed and the influence of frictional effect including tooth shape deviations, in particular, was scrutinized since a time-dependent coefficient of friction is deeply related to the gear surface roughness and all parameters dependent on gears error profiles are introduced in the proposed model. The predicted meshing gear power losses with constant and local friction coefficient were compared. The influence of constant and variable profile errors considered in the local coefficient of friction formulation was also studied and their corresponding root mean square (RMS) power loss was compared to the experimental results. The results using FZG A10 spur gear pairs running under several operating conditions (different loads and speeds) validate the superiority of the proposed model against previous similar models.

Dynamic effects on spur gear pairs power loss lubricated with axle gear oils

2019 ◽  
Vol 234 (5) ◽  
pp. 1069-1084 ◽  
Author(s):  
Maroua Hammami ◽  
Nabih Feki ◽  
Olfa Ksentini ◽  
Taissir Hentati ◽  
Mohamed Slim Abbes ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Power Loss ◽  
Degrees Of Freedom ◽  
Experimental Tests ◽  
Spur Gear ◽  
Operating Conditions ◽  
Dynamic Responses ◽  
Dynamic Effects ◽  
Nonlinear Dynamic Model ◽  
Gear Oils

The dynamic model of 12-degrees-of-freedom for spur gears pair accounting for nonlinear time-varying stiffness, damping, and coefficient of friction along the path of contact obtained from experimental tests is investigated. The Newmark's integration method is used to solve the equations and obtain the dynamic responses. Elementary mass, stiffness, and damping matrices with torsional and translational coupled effects were detailed. The lens of this work is to start from a nonlinear dynamic model to evaluate the influence of dynamic effects and lubrication on meshing gears power loss for different spur gear geometries within various operating conditions. The results reveal some useful references to vibration control, dynamic design, and efficiency improvement.

Prediction of Spur Gear Mechanical Power Losses Using an EHL Model With Time-Varying Contact Parameters

2009 ◽  
Author(s):  
S. Li ◽  
A. Kahraman
Keyword(s):  
Power Loss ◽  
Normal Load ◽  
Elastohydrodynamic Lubrication ◽  
Spur Gear ◽  
Mechanical Power ◽  
Transient Pressure ◽  
Gear Mesh ◽  
Proposed Model ◽  
Time Variations ◽  
Contact Parameters

A physics-based model is proposed to predict load dependent (mechanical) power loss of spur gear pairs by using a specialized gear elastohydrodynamic lubrication (EHL) model. The EHL model includes time variations of all key contact parameters such as surface velocities, radii of curvature and normal load in their continuous forms such that a continuous analysis of a tooth contact from its root to tip can be performed. The EHL model has the capability to simulate any gear contacts represented by condition ranging from full EHL to mixed or boundary EHL conditions. Predicted transient pressure and film thickness distributions are used to determine the instantaneous as well as the overall mechanical power loss of the gear mesh. Correction factors are introduced to account for thermal effects. At the end, capabilities and accuracy of the proposed model are demonstrated by comparing its predictions to experimental data.

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.

Load-Independent Spin Power Losses of a Spur Gear Pair: Model Formulation

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
S. Seetharaman ◽  
A. Kahraman
Keyword(s):  
Power Loss ◽  
Spur Gear ◽  
Companion Paper ◽  
Total Spin ◽  
Operating Conditions ◽  
Gear Pair ◽  
Power Losses ◽  
Gear Mesh ◽  
Drag Forces ◽  
Mechanics Model

A physics-based fluid mechanics model is proposed to predict spin power losses of gear pairs due to oil churning and windage. While the model is intended to simulate oil churning losses in dip-lubricated conditions, certain components of it apply to air windage losses as well. The total spin power loss is defined as the sum of (i) power losses associated with the interactions of individual gears with the fluid, and (ii) power losses due to pumping of the oil at the gear mesh. The power losses in the first group are modeled through individual formulations for drag forces induced by the fluid on a rotating gear body along its periphery and faces, as well as for eddies formed in the cavities between adjacent teeth. Gear mesh pumping losses will be predicted analytically as the power loss due to squeezing of the lubricant, as a consequence of volume contraction of the mesh space between mating gears as they rotate. The model is applied to a unity-ratio spur gear pair to quantify the individual contributions of each power loss component to the total spin power loss. The influence of operating conditions, gear geometry parameters, and lubricant properties on spin power loss are also quantified at the end. A companion paper (Seetharaman et al., 2009, “Oil Churning Power Losses of a Gear Pair: Experiments and Model Validation,” ASME J. Tribol., 131, p. 022202) provides comparisons to experiments for validation of the proposed model.

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

2003 ◽  
Author(s):  
Rafiq Maliha ◽  
Can U. Dog˘ruer ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Dynamic Modelling ◽  
Spur Gear ◽  
Discrete Models ◽  
Nonlinear Dynamic Model ◽  
Disk System ◽  
Describing Functions ◽  
Gear Mesh ◽  
System A

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 the harmonic responses of nonlinear multi degree of freedom systems is employed for the solution. The code developed, Nonlinear Geared Rotor Dynamics (NLGRD), combines the versatility of modeling a shaft-bearing-disk system that can have any configuration, with the accuracy of an advanced nonlinear gear mesh interface model. Thus any single stage gear mesh configuration can be modeled easily and accurately. NLGRD is capable of calculating dynamic gear loads, dynamic bearing forces, bearing displacements and making modal analysis of the corresponding linear system. Theoretical results obtained by NLGRD are compared with the experimental data available in literature.

The effect of elasticity in powder metal gears on tooth loading and mean coefficient of friction

2017 ◽  
Vol 232 (11) ◽  
pp. 2023-2031 ◽  
Author(s):  
Per Lindholm ◽  
Mario Sosa ◽  
Ulf Olofsson
Keyword(s):  
Coefficient Of Friction ◽  
Loss Factor ◽  
Power Loss ◽  
Contact Length ◽  
Powder Metal ◽  
Gear Mesh ◽  
Single Tooth ◽  
The Mean ◽  
Gear Contact ◽  
Load Behavior

Powder metal gears have a lower density than conventional steel gears due to their intrinsic porosity from the manufacturing process. This also results in a lower elasticity leading to larger deformations and lower contact pressure in a gear contact. By using different modelling tools (namely FEA and available commercial software), the load behavior along the line of action is studied to compare the influence of lower elasticity with standard wrought steel elasticity for FZG-C type gears. A further step is taken analyzing this effect on the mean coefficient of friction through the recalculation of the gear mesh power loss factor. Conclusions observed are differences in load distribution and marginal differences in the gear mesh power loss factor when comparing sintered and wrought steel FZG-C type gears. Sintered steel showed a marginally longer line of action and simultaneously a decrease of the single tooth contact length when compared to wrought steel, while differences in the gear mesh power loss factor proved non-essential due to the spread in previously measured experimental data.

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.

Mathematical Modeling of a Two Spool Flow Control Servovalve Using a Pressure Control Pilot1

2002 ◽  
Vol 124 (3) ◽  
pp. 420-427 ◽  
Author(s):  
Randall T. Anderson ◽  
Perry Y. Li
Keyword(s):  
Mathematical Modeling ◽  
Flow Control ◽  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Pressure Control ◽  
Dynamic Effects ◽  
Nonlinear Dynamic Model ◽  
Two Stage ◽  
Matlab Simulink ◽  
Proposed Model

A nonlinear dynamic model for an unconventional, commercially available electrohydraulic flow control servovalve is presented. The two stage valve differs from the conventional servovalve design in that: it uses a pressure control pilot stage; the boost stage uses two spools, instead of a single spool, to meter flow into and out of the valve separately; and it does not require a feedback wire and ball. Consequently, the valve is significantly less expensive. The proposed model captures the nonlinear and dynamic effects. The model has been coded in Matlab/Simulink and experimentally validated.

scholarly journals Research on nonlinear dynamic model of spur gear pair

2021 ◽  
Vol 1820 (1) ◽  
pp. 012038
Author(s):  
Chen Zhang ◽  
Xuew Liu ◽  
Xingl Shi ◽  
Xiaom Ling
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Spur Gear ◽  
Gear Pair ◽  
Nonlinear Dynamic Model
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