The Optimum Modification of Tooth Profile for a Pair of Spur Gears to Make its Rotational Vibration Equal Zero

1992 ◽  
Author(s):  
Yurong Cai ◽  
Teru Hayashi
Keyword(s):  
Static Load ◽  
Tooth Profile ◽  
Parameter Study ◽  
Exact Equation ◽  
Spur Gears ◽  
Contact Ratio ◽  
Profile Error ◽  
Vibration Model ◽  
Modification Method ◽  
Rotational Vibration

Abstract This paper develops an optimum modification method of tooth profile for a pair of spur gears to make its rotational vibration become zero by using an exact vibration model. By minimizing the equivalent exciting force, which includes the effects of the static load, time-varying stiffness, and relative tooth profile error, each optimum modification curve for each gear pair with different designed contact ratios can be obtained. The magnitude and the shape of the optimum modification curve depend upon the value of the designed contact ratio ε strongly. Especially, the concave modification curve is obtained in case of ε ≤ 1.1. The effect of the optimum modification on eliminating the vibration, is verified by the numerical calculation using an exact equation of vibration. A parameter study is presented to investigate the effect of running condition.

The Linear Approximated Equation of Vibration for a Pair of Spur Gears: Theory and Experiment

1992 ◽  
Author(s):  
Yurong Cai ◽  
Teru Hayashi
Keyword(s):  
Analytical Solution ◽  
Nonlinear Equation ◽  
Linear Equation ◽  
Static Load ◽  
Time Varying ◽  
Spur Gears ◽  
Contact Ratio ◽  
Profile Error ◽  
Rotational Vibration ◽  
Set Up

Abstract The nonlinear equation for the rotational vibration of a pair of spur gears has a restriction that the analytical solution of the equation cannot be obtained. In this paper, the linear equation of vibration is derived theoretically and its physical model, i.e. the linear model of vibration is presented. The analytical solution of the linear equation, which is derived by analytical method, agrees well with the numerically calculated result by the nonlinear equation. By analyzing the analytical solution of the linear equation in detail, we clarified the relation between the waveforms of the vibration and the profile error of gear pairs, and also found that the effect of the contact ratio to the vibration is large and complex. The equivalent error, accounting for effects of the static load, the time-varying stiffness and the profile error of gear pairs, is proposed in this paper. It can be considered as promising for evaluating the profile error, because the vibration of gear pairs is excited mainly by the equivalent error. Finally, for confirming the above results, the vibration of two tested gear pairs has been measured by an experimental set-up for this purpose.

The Linear Approximated Equation of Vibration of a Pair of Spur Gears (Theory and Experiment)

1994 ◽  
Vol 116 (2) ◽  
pp. 558-564 ◽  
Author(s):  
Y. Cai ◽  
T. Hayashi
Keyword(s):  
Analytical Solution ◽  
Nonlinear Equation ◽  
Linear Equation ◽  
Static Load ◽  
Time Varying ◽  
Spur Gears ◽  
Contact Ratio ◽  
Profile Error ◽  
Rotational Vibration ◽  
Set Up

The nonlinear equation for the rotational vibration of a pair of spur gears has a restriction that the analytical solution of the equation cannot be obtained. In this paper, the linear equation of vibration is derived theoretically and its physical model, i.e., the linear model of vibration is presented. The analytical solution of the linear equation, which is derived by analytical method, agrees well with the numerically calculated result by the nonlinear equation. By analyzing the analytical solution of the linear equation in detail, we clarified the relation between the waveforms of the vibration and the profile error of gear pairs, and also found that the effect of the contact ratio to the vibration is large and complex. The equivalent error, accounting for effects of the static load, the time-varying stiffness, and the profile error of gear pairs, is proposed in this paper. It can be considered as promising for evaluating the profile error, because the vibration of gear pairs is excited mainly by the equivalent error. Finally, for confirming the above results, the vibration of two tested gear pairs has been measured by an experimental set-up for this purpose.

Influence of Tooth Profile Error on Friction Loss and Noise of Spur Gears

2003 ◽  
Vol 2003 (0) ◽  
pp. 249-250
Author(s):  
Shingo KIZAWA ◽  
Shoji HAIZUKA ◽  
Hiroshi TADOKORO
Keyword(s):  
Tooth Profile ◽  
Friction Loss ◽  
Spur Gears ◽  
Profile Error

Further Evaluation of Spur Gear Tooth Profile Designs Used in Heavily Loaded Transmissions

2011 ◽  
Author(s):  
Nihat Yıldırım ◽  
Hakan I˙s¸c¸i ◽  
Abdullah Akpolat
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Profile ◽  
Design Parameters ◽  
Preference Order ◽  
Spur Gears ◽  
Tooth Root ◽  
Contact Ratio ◽  
Practical Applications

Aerospace applications require special procedures for component design and manufacturing. Spur gears of different designs, because of their simpler geometries, are used in vital units-transmissions of helicopters and alike aerospace vehicles. In this study, performances of various profile designs of previously researched low and high contact ratio spur gears with some realistic design parameters are studied. Effects of the realistic parameters of variable tooth pair stiffness, relief shape, and adjacent pitch error on Transmission Error (TE), tooth loads and root stresses are presented; composition of these parameters determines the efficiency of the gearbox assembly. Detail of minimization of tooth root stress through optimized/proper design of relief is described. More comprehensive comparison of the gear tooth profile design cases is done to be able to guide aerospace transmission designers for practical applications with realistic parameters for each of the design cases. A preference order is done among the design cases, depending on effect of some design parameters on the results such as tooth loads, tooth root stresses, TE curves and peak-to-peak TE values.

Simulation on the Rotational Vibration of Helical Gears in Consideration of the Tooth Separation Phenomenon (A New Stiffness Function of Helical Involute Tooth Pair)

1995 ◽  
Vol 117 (3) ◽  
pp. 460-469 ◽  
Author(s):  
Y. Cai
Keyword(s):  
Helical Gear ◽  
Contact Ratio ◽  
Narrow Face ◽  
Helical Gears ◽  
Face Width ◽  
Vibration Model ◽  
Rotational Vibration ◽  
The Finite Difference Method ◽  
Vibration Time ◽  
Tooth Pair

In this paper, an exact vibration model for helical gear pairs, is developed assuming no spacing error and no shaft run-out, in consideration of nonlinear tooth separation phenomenon. Inside the model, a simple modified stiffness function, including the effect of tooth numbers and addendum modification coefficients, is proposed for a helical involute tooth pair. This new stiffness function is verified by comparing its results with theoretical calculation and experiment. The rotational vibration of helical gear pairs with comparative narrow face width is simulated clearly on a 16-bit personal computer using the finite difference method in Fortran. The total contact ratio, including transverse and overlap contact ratios, is changed in the range of 1 ≤ ε ≤ 3. As a result, the simulated vibration time waveforms and their frequency characteristics agreed precisely with Umezawa’s calculation and experiment. This simulator is also used to investigate the effect of shaft deviation and pressure angle errors on the vibration of helical gears.

Reduction of Vibration in Spur Gears by an Asymmetric Tooth Profile With High Contact Ratio

2017 ◽  
Author(s):  
Ryo Fujikawa ◽  
Kiyotaka Ikejo ◽  
Soichi Ibaraki ◽  
Kazuteru Nagamura
Keyword(s):  
Thrust Force ◽  
Spur Gear ◽  
Tooth Profile ◽  
Spur Gears ◽  
Gear Pair ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Gear Drive ◽  
Gear Drives ◽  
Helical Gear Pair

Gear drive is a mechanism transmitting a power and a motion through the teeth contact. The number of teeth in contact changes during a mesh cycle. That raises a discontinuity of the mesh stiffness, and causes a gear vibration. The discontinuity implies a direct relationship with the contact ratio of the gear pair. In general, the high contact ratio more than two decreases the discontinuity of the mesh stiffness. Therefore, the increase of the contact ratio is able to reduce the vibration and the noise in the gear drives. An adoption of a helical gear pair is a method to obtain two or more contact ratio. However, that provides a thrust force and a difficulty to machine and assemble. For a spur gear pair, though it is possible to increase the contact ratio by stretching the tooth depth, the tooth thickness may reduce or be excessively sharp at the tooth tip on the addendum circle. In this study, we designed and made a high contact ratio spur gear pair with an asymmetric tooth profile. The gear pair has a large tooth depth to increase the contact ratio, and the asymmetric tooth profile to prevent the sharpness of tooth at the tip circle. In the running test, the vibration and the noise were measured. Consequently, we succeeded in a reduction of vibration and noise in spur gear drives with the asymmetric tooth profile.

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