scholarly journals Nonlinear Vibration of Gears With Tooth Surface Modifications

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Tugan Eritenel ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Gear Tooth ◽  
A Priori ◽  
Surface Modifications ◽  
Element Model ◽  
Transmission Error ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Partial Contact

This work provides an analytical solution for the nonlinear vibration of gear pairs that exhibit partial and total contact loss. Partial contact loss is where parts of contact lines lose contact although other parts remain in contact. The gear tooth surface modifications admit an arbitrary combination of profile and lead modifications. Modifications are a source of partial contact loss. The analysis also applies for total contact loss. Unlike models in the literature that are excited by static transmission error or time-varying mesh stiffness, the excitation and the nonlinearity are not a priori specified. Instead, the force-deflection function of the gear pair is provided by an independent source, such as a finite element model or Hertz contact formula. The manipulation of the single-degree-of-freedom oscillator equation of motion yields the excitation and the nonlinearity that arise from Fourier and Taylor series expansions of the force-deflection function. These expansions capture the essential contact behavior that includes tooth profile and lead modifications as well as the bending and shear flexibility of the gear teeth and gear blanks. The method of multiple scales gives the steady-state dynamic response in terms of a frequency-amplitude relation. Comparisons with gear vibration experiments and simulations from the literature that include spur and helical gears with tooth profile and lead modifications verify the method.

Nonlinear Vibration of Gear Pairs With Tooth Surface Modifications at Primary Resonance Using a Perturbation Method

2011 ◽  
Author(s):  
Tugan Eritenel ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Vibration ◽  
Half Space ◽  
Multiple Scales ◽  
Gear Tooth ◽  
Primary Resonance ◽  
Surface Modifications ◽  
Element Model ◽  
Elastic Behavior ◽  
Tooth Surface ◽  
Contact Vibrations

An analytical solution for the nonlinear vibration of gear pairs that exhibit partial and total contact loss is found. The gear teeth can have arbitrary tooth surface modifications. Such modifications and dynamic displacements separate parts of gear tooth surface otherwise designed to be in contact. This is partial contact loss. The excitation and the nonlinearity are not specified but are found from the force-deflection function of the gear pair, which comes from independent analysis, such as a finite element model. Fourier and Taylor series expansions of the force-deflection function capture the flexibility, nonlinearity, and the excitation in a few coefficients. The gear elastic behavior includes Hertz contact, bending, and shear. The nonlinearity arises chiefly from tooth surface modifications due to the dependence of contact upon the instantaneous dynamic mesh force. Although this work focuses on gear pairs with tooth surface modifications, the physical system from which the force-deflection function comes is not limited to gear pairs. Sphere/half-space contact vibrations are also analyzed. The dynamic frequency-amplitude relation at the steady-state is found using the method of multiple scales. Comparisons with experiments from the literature on gear vibrations and sphere/half-space contact vibrations verify the method.

Robust Optimization of Cylindrical Gear Tooth Surface Modifications Within Ranges of Torque and Misalignments

2013 ◽  
Author(s):  
Alessio Artoni ◽  
Massimo Guiggiani ◽  
Ahmet Kahraman ◽  
Jonny Harianto
Keyword(s):  
Performance Metrics ◽  
Gear Tooth ◽  
Surface Modifications ◽  
Transmission Error ◽  
Robust Design Optimization ◽  
Tooth Surface ◽  
Global Optimality ◽  
Cylindrical Gear ◽  
Geometry Design ◽  
Design Variables

Tooth surface modifications are small, micron-level intentional deviations from perfect involute geometries of spur and helical gears. Such modifications are aimed at improving contact pressure distribution, while minimizing the motion transmission error to reduce noise excitations. In actual practice, optimal modification requirements vary with the operating torque level, misalignments, and manufacturing variance. However, most gear literature has been concerned with determining optimal flank form modifications at a single design point, represented by fixed, single load and misalignment values. A new approach to the design of tooth surface modifications is proposed to handle such conditions. The problem is formulated as a robust design optimization problem, and it is solved, in conjunction with an efficient gear contact solver (LDP), by a direct search, global optimization algorithm aimed at guaranteeing global optimality of the obtained micro-geometry solutions. Several tooth surface modifications can be used as micro-geometry design variables, including profile, lead, and bias modifications. Depending on the contact solver capabilities, multiple performance metrics can be considered. The proposed method includes the capability of simultaneously and robustly handling several conflicting design objectives. In the present paper, peak contact stress and loaded transmission error amplitude are used as objective functions (to be minimized). At the end, two example optimizations are presented to demonstrate the effectiveness of the proposed method.

Robust Optimization of Cylindrical Gear Tooth Surface Modifications Within Ranges of Torque and Misalignments

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Alessio Artoni ◽  
Massimo Guiggiani ◽  
Ahmet Kahraman ◽  
Jonny Harianto
Keyword(s):  
Performance Metrics ◽  
Gear Tooth ◽  
Surface Modifications ◽  
Transmission Error ◽  
Robust Design Optimization ◽  
Tooth Surface ◽  
Global Optimality ◽  
Cylindrical Gear ◽  
Design Variables ◽  
Gear Contact

Tooth surface modifications are small, micron-level intentional deviations from perfect involute geometries of spur and helical gears. Such modifications are aimed at improving contact pressure distribution, while minimizing the motion transmission error to reduce noise excitations. In actual practice, optimal modification requirements vary with the operating torque level, misalignments, and manufacturing variance. However, most gear literature has been concerned with determining optimal flank form modifications at a single design point, represented by fixed, single load and misalignment values. A new approach to the design of tooth surface modifications is proposed to handle such conditions. The problem is formulated as a robust design optimization problem, and it is solved, in conjunction with an efficient gear contact solver (Load Distribution Program (LDP)), by a direct search, global optimization algorithm aimed at guaranteeing global optimality of the obtained microgeometry solutions. Several tooth surface modifications can be used as microgeometry design variables, including profile, lead, and bias modifications. Depending on the contact solver capabilities, multiple performance metrics can be considered. The proposed method includes the capability of simultaneously and robustly handling several conflicting design objectives. In the present paper, peak contact stress and loaded transmission error amplitude are used as objective functions (to be minimized). At the end, two example optimizations are presented to demonstrate the effectiveness of the proposed method.

Modeling of surface roughness in a novel magnetorheological gear profile finishing process

2020 ◽  
pp. 095440622097826
Author(s):  
Ravi Datt Yadav ◽  
Anant Kumar Singh ◽  
Kunal Arora
Keyword(s):  
Surface Roughness ◽  
Gear Tooth ◽  
Surface Characteristics ◽  
Spur Gear ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Magnetic Flux Density ◽  
Element Analysis ◽  
Finishing Process ◽  
Gear Profile

Fine finishing of spur gears reduces the vibrations and noise and upsurges the service life of two mating gears. A new magnetorheological gear profile finishing (MRGPF) process is utilized for the fine finishing of spur gear teeth profile surfaces. In the present study, the development of a theoretical mathematical model for the prediction of change in surface roughness during the MRGPF process is done. The present MRGPF is a controllable process with the magnitude of the magnetic field, therefore, the effect of magnetic flux density (MFD) on the gear tooth profile has been analyzed using an analytical approach. Theoretically calculated MFD is validated experimentally and with the finite element analysis. To understand the finishing process mechanism, the different forces acting on the gear surface has been investigated. For the validation of the present roughness model, three sets of finishing cycle experimentations have been performed on the spur gear profile by the MRGPF process. The surface roughness of the spur gear tooth surface after experimentation was measured using Mitutoyo SJ-400 surftest and is equated with the values of theoretically calculated surface roughness. The results show the close agreement which ranges from −7.69% to 2.85% for the same number of finishing cycles. To study the surface characteristics of the finished spur gear tooth profile surface, scanning electron microscopy is used. The present developed theoretical model for surface roughness during the MRGPF process predicts the finishing performance with cycle time, improvement in the surface quality, and functional application of the gears.

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

2017 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Deepak Sah ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Gear Tooth ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Transmission Error ◽  
Sound Level ◽  
Tooth Surface ◽  
Surface Error ◽  
Planetary Gear Trains ◽  
Tooth Stiffness ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

scholarly journals Meshing characteristics of a sphere–face gear pair with variable shaft angle

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985951 ◽  
Author(s):  
Lei Liu ◽  
Jinzhao Zhang
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Contact Points ◽  
Shaft Angle ◽  
Meshing Characteristics ◽  
Curvature Interference

This article presents a sphere–face gear pair by substituting the convex spherical gear for the pinion of a conventional face gear pair. The sphere–face gear pair not only maintains the advantages of the face gear pair with a longitudinally modified pinion but also allows variable shaft angles or large axial misalignments. Meshing characteristics of the proposed gear pair are studied in this article. The mathematical models of the sphere–face gear pair are derived based on machining principles. The tooth contact analysis (TCA) and curvature interference check are conducted for the sphere–face gear pair with variable shaft angles. The loaded TCA is also implemented utilizing the finite element method. The results of numerical examples show that proposed gear pair has the following features. Geometrical transmission error of constant shaft angle or varying shaft angle is zero; contact points of the sphere–face gear set with variable shaft angle are located near the centre region of face gear tooth surface; there is no curvature interference in meshing; and transmission continuity of the gear pair can be guaranteed in meshing.

Study on Design Method of the Double Arc Gear Hobs

2013 ◽  
Vol 823 ◽  
pp. 257-260
Author(s):  
Jie Wu ◽  
Jia Quan Wang
Keyword(s):  
Design Method ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Engineering Practice ◽  
Approximate Design ◽  
Circular Arc ◽  
Running Performance ◽  
Engagement Theory ◽  
Gear Rack

This article find that one of the effecting the double circular arc gear s running performance is the double circular arc gear tooth profile precision, through analysis to the running-in properties of double arc gear. The problems about tooth profile precision of gear hobs caused by the current profiling theory and approximate design method of gear hobs are analyzed. In the design of circular arc gear hob, use the space engagement theory, can eliminating the tooth error. Acquiring the equation of hobs basic of worm tooth surface by analytical and calculation that the establishment of basic gear rack and worm of hob meshing. The hob not only eliminate the tooth profile error in manufacturing, but also improve the running performance of double circular arc gear, and provides the theory evidence for engineering practice.

The Deformation Analysis on Tooth Profiles with Electroplated CBN Hard Gear-Honing-Tools

2012 ◽  
Vol 426 ◽  
pp. 159-162 ◽  
Author(s):  
Man Dong Zhang ◽  
H.H. Zhao ◽  
Ming Lv
Keyword(s):  
Gear Tooth ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Deformation Analysis ◽  
Normal Deformation ◽  
Gear Honing ◽  
Important Means ◽  
Profile Errors ◽  
Tooth Profile Errors ◽  
Exact Analytical Method

Using electroplating CBN hard gear-honing-tools with standard involute, the vicinity of the workpiece tooth pitch circle will be a “mid concave” error, the root of the tooth will be a “dig root” error generally. For the formation factors of the error are more complex, it is difficult to calculate errors with an exact analytical method. To this end, by using Pro/E and ANSYS software, the contact analysis of electroplating CBN hard honing process was simulated. The honed tooth surface normal deformation analysis was the important means to determine extent of tooth profile error, through the normal deformation analysis based on simulation results, the location and extent of normal deformation was determined. Practice shows that the location and extent of the normal deformation has been a certain relationship with processing gear tooth profile errors. It is provided a theoretical basis to make the gear-honing tooth surface modification as possible.

Influence of Tooth Profile Deviations on Helical Gear Wear

2004 ◽  
Vol 127 (4) ◽  
pp. 656-663 ◽  
Author(s):  
A. Kahraman ◽  
P. Bajpai ◽  
N. E. Anderson
Keyword(s):  
Gear Tooth ◽  
Helical Gear ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Surface Wear ◽  
Mechanics Model ◽  
Surface Slopes ◽  
Tooth Surfaces ◽  
Computation Algorithm ◽  
Gear Contact

In this study, a surface wear prediction model for helical gears pairs is employed to investigate the influence of tooth profile deviations in the form of intentional tooth profile modifications or manufacturing errors on gear tooth surface wear. The wear model combines a finite-element-based gear contact mechanics model that predicts contact pressures, a sliding distance computation algorithm, and Archard’s wear formulation to predict wear of the contacting tooth surfaces. Typical helical gear tooth modifications are parameterized by an involute crown, a lead crown, and an involute slope. The influence of these parameters on surface wear are studied within typical tolerance ranges achievable using hob/shave process. The results indicate that wear is related to the combined modification parameters of a gear pair rather than individual gear parameters. At the end, a design formula is proposed that relates the mismatch of contacting surface slopes to the maximum initial wear rate.

scholarly journals A Novel Approach to Calculating the Transmission Accuracy of a Cycloid-Pin Gear Pair Based on Error Tooth Surfaces

2021 ◽  
Vol 11 (18) ◽  
pp. 8671
Author(s):  
Chang Liu ◽  
Wankai Shi ◽  
Lang Xu ◽  
Kun Liu
Keyword(s):  
Transmission Error ◽  
Tooth Profile ◽  
Tolerance Allocation ◽  
Tooth Surface ◽  
Gear Pair ◽  
Eccentric Load ◽  
Novel Approach ◽  
Manufacturing Errors ◽  
Tooth Surfaces ◽  
Theoretical Analyses

Transmission error (TE) and backlash are important parameters used to evaluate the transmission accuracy of cycloid-pin drives. Existing calculation methods are mostly based on two-dimensional tooth profile models, and these methods ignore the influence of some abnormal meshing phenomena caused by profile modifications (PMs), manufacturing errors (MEs), and assembly errors (AEs), such as the instantaneous mesh-apart of tooth pairs and the eccentric load on the tooth surface. To fill this gap, a novel approach to accurately calculating the TE and backlash of a cycloid-pin gear pair based on the error tooth surfaces is proposed, and its feasibility and effectiveness are validated by comparison with the theoretical analyses and the results from the literature. Based on this, the effects of the PMs, MEs, and AEs on the transmission accuracy are studied, which will be helpful in optimizing the tooth profile design of a cycloid gear and the tolerance allocation during the installation of a gear pair. The proposed method is also expected to provide accurate error excitation data for the dynamic analysis of cycloid-pin drives.

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