• Journal of the Korean Society for Precision Engineering
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• v.16 no.12
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• pp.99-108
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• 1999

A four-degree-of-freedom non-linear model with time varying mesh stiffness has been developed for the dynamic analysis of spur gear trains. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover. In the model, developed several factors such as time varying mesh stiffness and damping, separation of teeth, teeth collision, various gear errors and profile modifications have been considered. Two computer programs are developed to calculate stiffness of a gear pair and transmission error and the dynamic analysis of modeled system using time integration method. Dynamic tooth and mesh forces, dynamic factors are calculated. Numerical examples have been given, which shows the time varying mesh stiffness ha a significant effect upon the dynamic tooth force and torsional vibrations.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.1
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• pp.130-136
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• 2012

Dynamic as well as static and geometric design parameters such as inertia, tooth profile, backlash and clearance can be directly considered via multi-body dynamic analysis along with contact analysis. However, it is time consuming to use finite elements for the consideration of the tooth flexibility in the multi-body dynamic analysis of gears. A computationally efficient procedure, so called, Gear Stiffness Module, is suggested to resolve this calculation time issue. The characteristics of gear tooth compliance are discussed and rotational stiffness element concept for the Gear Stiffness Module is presented. Transmission error analyses for a spur gear system are carried out to validate the reliability and efficiency of the module. Compared with the finite element model, the Gear Stiffness Module yields considerably similar results and takes only 3% of calculation time.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.224-231
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• 2006

A six-degree-of-freedom dynamic model with time-varying mesh stiffness/damping and friction has been developed for the dynamic analysis of a gear driving system. This model includes a spur gear pair, bearing, friction and prime mover. Using Newton???s method, equations of motion for the gear driving system were derived. Two computer programs are developed to calculate mesh stiffness, transmission error and friction force and analyze the dynamics of the modeled system using a time integration method. The influences of mesh stiffness/damping, bearing, and friction affecting the system were investigated by performing eigenvalue analysis and time response analysis. It is found that the reduction of the maximum peak magnitude by friction is decided according to designing the positions of pitch point and maximum peak in the responses.

• Journal of Mechanical Science and Technology
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• v.18 no.11
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• pp.1978-1988
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• 2004

Hybrid finite element analysis was used to analyze the influence of bearing stiffness on the static properties of a planetary gear system with manufacturing errors. The effects of changes in stiffness were similar for most of the manufacturing errors. State variables were most affected by the stiffness of the planet ,bearings. Floating either the sun or carrier helps to equal load sharing and minimizes the critical tooth stress. The effects of a floating sun and carrier are similar, but it is not recommended that both float, because this can induce greater critical tooth stress. Planet bearing stiffness should be optimized. Both load sharing and critical tooth stress should be considered to determine optimal bearing stiffness.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.31-36
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• 2002

Even through the problem of misalignment is of great importance, not much work has been reported in the literature on the effect of misalignment on the vibrations of the gear-bearing systems. Therefore, the nonlinear dynamic characteristics of the gear drive system due to misalignment are investigated in this work. Transmission error for helical gear and bearing nonlinear stiffness is calculated. The equation of motion of the gear drive system is modelled using the time-varying gear meshing stiffness, bearing nonlinear stiffness, and bearing pre-load due to the housing deformation. Numerical analysis lot the gear drive system show the result of misalignment effect - sub-harmonic component, bearing pre-load effect, and another nonlinear phenomenon. And the numerical analysis are verified by the experimental result.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.6
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• pp.8-14
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• 2001

We develop a method to analyze dynamic behavior off multi-stage gear train system. The example system consists of three shafts supported by ball bearings at the ends of them and two pairs of spur gear set. For exact analysis, the meshing tooth pair of gear set is modeled as spring and damper having time-dependent meshing stiffness and damping. The bearing is modeled as spring. The result of this analysis is compared to that of other model having mean mesh stiffness. The effect of the excitation force by the unbalance off rotor off motor is also analyzed. Finally, the change ova natural frequency of the whole system due to the change of an angle between three shafts is compared in each case, and from this analysis, the avoiding angle for design is advised.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.11 s.176
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• pp.111-117
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• 2005

The vibration problems associated with gear coupled rotors have been the focus of much engineering work. These systems are complex and difficult to analyze in that they have the problems associated with conventional rotors plus those additional problems associated with the gear couplings. This paper examines the problems peculiar to the gear mesh. Because of the meshing action of gears, the elasticity of the gear teeth introduces time-varying stiffness coefficients into the governing equations of motion. This means that system response must be thought of in terms of Mathieu-type equations, where multiple-frequency response occur due to the periodic coefficients. The meshing action of the gears also couples the lateral and torsional gear motions. Gear errors, such as tooth profile and spacing errors, produce forces and torque that excite the system at multiple frequencies, some of which are much higher than shaft rotational speed. To investigate how to the time-varying stiffness in the gear teeth and the gear errors act one the dynamic response of the gear coupled rotors, a three-dimensional dynamic model with lateral-tortional oscillation is developed. The harmonic balance technique is employed to solve this mathieu-type problem.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.5
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• pp.1534-1542
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• 1996

Gear vibration is caused by the mesh stiffness, gear accuracy, and assembling errors. For these reasons, helical gear has the azial, radial, and rotational vibrations. In this study, the mesh stiffness is calculated by considering the tooth bending, contact, and foundation deformations. Rotational vibration of helical gear with tooth error is modeled by the nonlidear equation of motion with single degree of freedom and is anlyzed numerically. Also, by a specially designed experimental set-up, the analysis are cross-checked and the vibration characteristics of helical gear are discussed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.12
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• pp.921-928
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• 2002

Main sources of the nitration of a gear-pair system are backlash and transmission error, the difference between required and actual rotation during gear meshing. This paper presents the nonlinear dynamic characteristics of gear motions due to the existence of backlash and periodic variation of meshing stiffness, which is assumed as a one-term harmonic component. Gear motions are classified as three types with the consideration of backlash. Each response is calculated using the harmonic balance method and confirmed by numerical integration. The responses with the increase of the rotating speed show abrupt changes in its magnitude for the variation of the preload, exciting force, and damping coefficient. The result also shows that there is a chaotic motion with some specific design parameters and operating conditions In gear diving system. Consequently the design of gear driving system with low nitration and noise requires the study on the effects of nonlinear dynamic characteristics due to stiffness variation and backlash.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.5
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• pp.489-495
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• 2016

This study focuses on a detailed ball-bearing model for spur gears. The nonlinear ball-bearing stiffness with radial clearance is derived and calculated. The bearing stiffness is used to the 3-degree-of-freedom (DOF) spur gear system model. The mode characteristics of the gear system model are analyzed and verified by performing finite-element analysis (FEA). From the results, the bearing stiffness on the radial clearance was more sensitive under low-load conditions compared to high-load conditions. The bearing stiffness significantly affected the gear dynamics in the low-frequency region, while the mesh stiffness affected the high natural frequency.