Digital Simulation of Impact Phenomenon in Spur Gear Systems

A digital simulation model is developed to represent a lightly loaded geared torsional system consisting of a drive unit, spur gear pair and load connected by flexible shafts. A clearance model called an Impact Pair [13] is used to represent the gear pair and includes the effects of backlash, time-varying stiffness and damping of the gear teeth and tooth-form error. Experimentally determined frequency spectra of the torsional oscillations of a gear-driven shaft have been plotted and reported on earlier [1]. Similar frequency plots are obtained from the simulation study, and data from these plots are compared with the experimental results for a variety of parameter changes including shaft speed, backlash and load. Results indicate that the simulation model portrays reasonably well the torsional behavior of the output shaft.

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Analysis of the Vibration Response of a Gearbox With Gear Tooth Faults

Dynamic Systems and Control, Parts A and B ◽

10.1115/imece2004-59224 ◽

2004 ◽

Cited By ~ 22

Author(s):

Xinhao Tian ◽

Ming J. Zuo ◽

Ken R. Fyfe

Keyword(s):

Gear Tooth ◽

Spur Gear ◽

Vibration Response ◽

Gear Pair ◽

Mesh Stiffness ◽

Gear Teeth ◽

Vibration Model ◽

Vibration Signatures ◽

Potential Energy Method ◽

The Relationship

In this study, the steady-state vibration response of a gearbox with gear tooth faults is investigated. Based on the analytical expression of the position-dependent mesh stiffness of the gear with perfect gear teeth derived with the potential energy method and the characteristics of involute gear teeth, expressions of the mesh stiffness of a gear with tooth faults such as tooth chip, tooth crack, and tooth breakage are derived. Using a coupled lateral and torsional vibration model of a one-stage spur gear pair, we have numerically solved a set of nonlinear equations and obtained typical vibration response diagrams of the gear pair with perfect gears and gears with tooth faults. This study reveals the relationship between the waveforms of the vibration and the types of local faults of the gear. These results are useful for identification of vibration signatures when there are these types of tooth faults.

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The Torque Responses in Spur Gearing

Volume 1A: 25th Biennial Mechanisms Conference ◽

10.1115/detc98/mech-5834 ◽

1998 ◽

Author(s):

Ah-Der Lin ◽

Jao-Hwa Kuang

Keyword(s):

Fourier Expansion ◽

Spur Gear ◽

Time Varying ◽

Gear Pair ◽

Contact Ratio ◽

Mesh Stiffness ◽

Frequency Spectra ◽

Stiffness Model ◽

Close Form ◽

Input Torque

Abstract In this study, the frequency spectra of a meshing spur gear pair are derived. A two-step mesh stiffness model is assumed to account for the time varying stiffness during the teeth engagement. The analytic load of this simplified gear pair system is used to derive the corresponding Fourier expansion series of the transmitted torque in close form solutions. Numerical results have shown that the frequency spectra of the transmitted torque are dominated by the mesh stiffness alternation and the contact ratio of a gear pair. Furthermore, the amplitude modulation introduced by a harmonic input torque has also been investigated.

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Numerical Simulation of Nonlinear Spur Gear Dynamics

Volume 7B: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8111 ◽

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.

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Influence of simultaneous time-varying bearing and tooth mesh stiffness fluctuations on spur gear pair vibration

Nonlinear Dynamics ◽

10.1007/s11071-019-05056-9 ◽

2019 ◽

Vol 97 (2) ◽

pp. 1403-1424 ◽

Cited By ~ 2

Author(s):

Guanghui Liu ◽

Jun Hong ◽

Robert G. Parker

Keyword(s):

Spur Gear ◽

Time Varying ◽

Gear Pair ◽

Mesh Stiffness

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The Engineering Design of Helical Spur Gear Transmission with Single Gear Pair for Electric Scooter

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.764-765.374 ◽

2015 ◽

Vol 764-765 ◽

pp. 374-378 ◽

Cited By ~ 1

Author(s):

Long Chang Hsieh ◽

Tzu Hsia Chen ◽

Hsiu Chen Tang

Keyword(s):

Engineering Design ◽

Spur Gear ◽

Gear Transmission ◽

Reduction Ratio ◽

Gear Pair ◽

Engineering Drawing ◽

Electric Scooter ◽

High Reduction ◽

Cost Of Production ◽

The Cost

Traditionally, the reduction ratio of a spur gear pair is limited to 4 ~ 7. For a spur gear transmission with reduction ratio more than 7, it is necessary to have more than two gear pairs. Consider the cost of production, this paper proposes a helical spur gear reducer with one gear pair having reduction ratio 19.25 to substitute the gear reducer with two gear pairs. Based on the involute theorem, the gear data of helical spur gear pair is obtained. According to the gear data, its corresponding engineering drawing is accomplished. This manuscript verify that one spur gear pair also can have high reduction ratio (20 ~ 30).

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The Compliance of Solid, Wide-Faced Spur Gears

Journal of Mechanical Design ◽

10.1115/1.2912651 ◽

1990 ◽

Vol 112 (4) ◽

pp. 590-595 ◽

Cited By ~ 13

Author(s):

J. H. Steward

Keyword(s):

Experimental Data ◽

Contact Line ◽

Load Distribution ◽

3D Model ◽

Spur Gear ◽

Point Load ◽

Spur Gears ◽

Line Load ◽

Gear Teeth ◽

Theoretical Results

In this paper, the requirements for an accurate 3D model of the tooth contact-line load distribution in real spur gears are summarized. The theoretical results (obtained by F.E.M.) for the point load compliance of wide-faced spur gear teeth are set out. These values compare well with experimental data obtained from tests on a large spur gear (18 mm module, 18 teeth).

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