From Hertzian contact to spur gears: analyses of stresses and rolling contact fatigue

Vouaillat, Guillaume; Noyel, Jean-Philippe; Ville, Fabrice; Kléber, Xavier; Rathery, S.

doi:10.1051/meca/2019064

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…The two gears in contact are deformed by the normal load and expand into an elliptical contact area at the original contact point O, according to the Hertzian elastic contact theory [36,37]. The contact deformation is shown in Figure 8, where δ 1 and δ 2 are the shape variables of surface 1 and surface 2, respectively.…”

Section: Calculation Of Hertzian Contact Stressmentioning

confidence: 99%

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A Novel Tooth Modification Methodology for Improving the Load-Bearing Capacity of Non-Orthogonal Helical Face Gears

Jia,

Li,

2023

Machines

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This study proposes a double-crown tooth surface modification technology that improves the load-carrying capacity of non-orthogonal helical tooth surface gears. The tooth modification is determined by a modified rack-cutter, and its feed motion is related to an intentionally designed transmission error. The novelty of the tooth modification design is that the transmission error can be pre-designed. First, changing the tooth profile of the tool enables preliminary modification along the tooth profile direction; second, by modifying the interaction between the tool and the machined gear, subsequent fine adjustments are made to the contact path. This two-stage tooth modification strategy not only retains the advantages of the traditional method but also significantly improves the balance of the load distribution on the tooth surface through an original contact path modification strategy. Through systematic tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), it was verified that the new method reduces contact stress and tooth root bending stress and improves the gear’s resistance to misalignment errors. This research provides the basis and motivation for further exploring and improving this tooth profile modification technology to solve the challenges faced by more complex gear systems.

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Section: Calculation Of Hertzian Contact Stressmentioning

confidence: 99%

“…Based on the coordinates of the five pre-designed points, the restriction equation of Equation ( 35) can be written as Equation (36). (37) where…”

Section: Designation Of Intentional High-order Transmission Errormentioning

confidence: 99%

A Novel Tooth Modification Methodology for Improving the Load-Bearing Capacity of Non-Orthogonal Helical Face Gears

Jia,

Li,

2023

Machines

View full text Add to dashboard Cite

show abstract

“…They proved that the loading loaddisplacement relation still holds for δ/R as large as 0.66 with a maximum principal strain of 46.6%. Vouaillat et al [27] studied the rolling contact fatigue in spur gears taking into account the spur gear material geometry, the contact pressure fields and several parameters such as friction, sliding coefficient, load variation and roughness. A fatigue criterion based on rolling contact fatigue micro-cracks nucleation at grain boundaries is proposed.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation

et al. 2023

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In this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The EA is supplied by a constant current generating a static force and by an actuation generating a fast alternative force. The deformations between the solids in contact are supposed to be elastic and the contact is maintained. In this study, a single degree of freedom nonlinear damped oscillator under a static normal load is considered. An analytical approximate solution of this problem is obtained using the Optimal Auxiliary Functions Method (OAFM). By means of some auxiliary functions and introducing so-called convergence-control parameters, a very accurate approximate solution of the governing equation can be obtained. We need only the first iteration for this technique, applying a rigorous mathematical procedure in finding the optimal values of the convergence-control parameters. Local stability by means of the Routh-Hurwitz criteria and global stability using the Lyapunov function are also studied. It should be emphasized that the amplitude of AC excitation voltage is not considered much lower than bias voltage (in contrast to other studies). Also, the Hertzian contact coupled with EA is analytically studied for the first time in the present work. The approximate analytical solution is determined with a high accuracy on two domains. Local stability is established in five cases with some cases depending on the trace of the Jacobian matrix and of the discriminant of the characteristic equation. In the study of global stability, the estimate parameters which are components of the Lyapunov function are given in a closed form and a graphical form and therefore the Lyapunov function is well-determined.

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“…In the project, the Hertz contact theory is often used to calculate the roller's contact stress. e Hertz contact theory is also widely used in other similar structures, such as the wheel-rail contact of the train [7][8][9][10], the contact between the rolling element in the bearing and the inner and outer rings of the bearing [11,12], the calculation of the gear meshing stress [13][14][15][16][17][18], and the contact relationship between the inner and outer rings of angular contact ball bearings [19,20].…”

Section: Introductionmentioning

confidence: 99%

Analysis and Optimization of Static Contact Characteristics of Heavy-Duty Tracked Vehicle Rollers

Tian

Fang

Wang

et al. 2021

Mathematical Problems in Engineering

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The static contact characteristics of heavy-duty tracked vehicle roller and track plate contact structure are analyzed, and the influence mechanism of the roller’s shape parameters on the contact stress is studied. According to the Hertz contact theory, a mathematical model of the roller and track plate contact is established. The contact structure model is established in ANSYS software, and the simulation results are compared with the Hertz theory results to verify each other. In the parameter optimization section for the roller and track plate, based on the Hertz stress calculation formula, a new method is proposed to establish a roller and track plate Kriging model and to globally optimize the model by the genetic algorithm (GA). After that, the relationship among the track roller radius R 1 , the track roller rim radius r 1 , and the track plate rim radius r 2 is analyzed. The results show that the difference between the radius of the rim of the roller and the track plate and the radius of the roller rim both affect the maximum contact stress. Changing the plane contact into the curved surface contact can reduce the maximum contact stress by 33%. This study can provide a reference for the design and manufacture of supporting track rollers and track plates.

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From Hertzian contact to spur gears: analyses of stresses and rolling contact fatigue

Cited by 4 publications

References 27 publications

A Novel Tooth Modification Methodology for Improving the Load-Bearing Capacity of Non-Orthogonal Helical Face Gears

A Novel Tooth Modification Methodology for Improving the Load-Bearing Capacity of Non-Orthogonal Helical Face Gears

Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation

Analysis and Optimization of Static Contact Characteristics of Heavy-Duty Tracked Vehicle Rollers

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