An Efficient Hybrid Analytical-Computational Method for Nonlinear Vibration of Spur Gear Pairs

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Xiang Dai ◽  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Nonlinear Vibration ◽  
Spur Gear ◽  
Computational Method ◽  
Tooth Surface ◽  
Dynamic Force ◽  
Finite Element Analyses ◽  
Gear Teeth ◽  
Lumped Parameter

This work develops a hybrid analytical-computational (HAC) method for nonlinear dynamic response in spur gear pairs. The formulation adopts a contact model developed in (Eritenel, T., and Parker, R. G., 2013, “Nonlinear Vibration of Gears With Tooth Surface Modifications,” ASME J. Vib. Acoust., 135(5), p. 051005) where the dynamic force at the mating gear teeth is determined from precalculated static results based on the instantaneous mesh deflection and position in the mesh cycle. The HAC method merges this calculation of the contact force based on an underlying finite element static analysis into a numerical integration of an analytical vibration model. The gear translational and rotational vibrations are calculated from a lumped-parameter analytical model where the crucial dynamic mesh force is calculated using a force-deflection function (FDF) that is generated from a series of static finite element analyses performed before the dynamic calculations. Incomplete tooth contact and partial contact loss are captured by the static finite element analyses and included in the FDF, as are tooth modifications. In contrast to typical lumped-parameter models elastic deformations of the gear teeth, including the tooth root strains and contact stresses, are calculated. Accelerating gears and transient situations can be analyzed. Comparisons with finite element calculations and available experiments validate the HAC model in predicting the dynamic response of spur gear pairs, including for resonant gear speeds when high amplitude vibrations are excited and contact loss occurs. The HAC model is five orders of magnitude faster than the underlying finite element code with almost no loss of accuracy.

Nonlinear Vibration of Single-Walled Carbon Nanotubes Under Magnetic Field by Stochastic Finite Element Method

2016 ◽  
Vol 16 (08) ◽  
pp. 1550046 ◽  
Author(s):  
T.-P. Chang
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Response ◽  
Nonlinear Vibration ◽  
Longitudinal Magnetic Field ◽  
Small Scale ◽  
Stochastic Finite Element Method ◽  
Single Walled Carbon ◽  
Statistical Dynamic

In the present study, we investigate the statistical nonlinear dynamic behaviors of a single-walled carbon nanotube (SWCNT) subjected to a longitudinal magnetic field by considering the effect of geometric nonlinearity. We consider both the Young’s modulus of elasticity and mass density of the SWCNT as stochastic with respect to the position to actually characterize the random material properties of the SWCNT. In addition, we use the theory of nonlocal elasticity to investigate the small scale effect on the nonlinear vibration of the SWCNT. By using the Hamilton’s principle, the nonlinear governing equations of the SWCNT subjected to a longitudinal magnetic field are derived. We utilize the stochastic finite element method along with the perturbation technique to compute the statistical response of the SWCNT. Some statistical dynamic response of the SWCNT, such as the mean values and standard deviations of the midpoint deflections, are computed and checked by the Monte Carlo simulation, besides, the effects of the small scale coefficients, magnetic field and the elastic stiffness of matrix on the statistical dynamic response of the SWCNT are studied and discussed.

A Frequency Domain Finite Element Approach for Three-Dimensional Gear Dynamics

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker ◽  
Sandeep M. Vijayakar
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Frequency Domain ◽  
Dynamic Models ◽  
Three Dimensional ◽  
Static Solution ◽  
System Level ◽  
Element Formulation ◽  
Lumped Parameter ◽  
Element Approach

A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides an accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.

Influence of assembly error and bearing elasticity on the dynamics of spur gear pair

2015 ◽  
Vol 230 (11) ◽  
pp. 1805-1818 ◽  
Author(s):  
Jianhong Wang ◽  
Jian Wang ◽  
Teik C Lim
Keyword(s):  
Finite Element ◽  
Dynamic Behavior ◽  
Transmission Error ◽  
Spur Gear ◽  
Lumped Parameter Model ◽  
Gear Pair ◽  
Tooth Contact ◽  
Lumped Parameter ◽  
Bearing Stiffness ◽  
Assembly Error

The elasticity and geometrical errors of precision elements are one of the major factors affecting vibration responses in geared transmission systems. In this study, the influences of assembly error and bearing elasticity on the spur gear dynamic behavior are analyzed. A lumped parameter model for spur gear pair is formulated by representing the bearing elasticity with infinitesimal spring elements and tooth stiffness time function as rectangular waveform. The nonuniform tooth contact load is also considered. The severity of assembly error is assumed to be sufficiently small such that no partial loss of tooth contact occurs. A harmonic balance method is applied to the resultant second-order partial differential equation governing the gear pair dynamic behavior. The variations of dynamic transmission error and tooth contact load with respect to mesh frequency for a set of bearing stiffness are analyzed. The influences of bearing stiffness on the dynamic transmission error are also evaluated. The variation of actual cross angle, an indicator on the tooth meshing state, is examined with respect to nominal cross angle and bearing stiffness. The analysis shows that the presence of bearing elasticity and assembly error can degenerate tooth contact significantly, and hence the appropriate specifications of bearing and mesh stiffness are critical at gearbox design stage. The analysis demonstrates that the proposed lumped parameter model can provide detailed contact information like finite element model, but it avoids finite element model’s prohibitive computation burden and can be completed easily and be computed quickly.

Evaluation of spur gear mesh compliance using the finite element method

1999 ◽  
Vol 213 (6) ◽  
pp. 569-579 ◽  
Author(s):  
M H Arafa ◽  
M M Megahed
Keyword(s):  
Finite Element ◽  
Experimental Methods ◽  
Spur Gear ◽  
Spur Gears ◽  
The Finite Element Method ◽  
Mesh Stiffness ◽  
Fe Modelling ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Gear Mesh Stiffness

This paper presents a finite element (FE) modelling technique to evaluate the mesh compliance of spur gears. Contact between the engaging teeth is simulated through the use of gap elements. Analysis is performed on several gear combinations and the variation in tooth compliance along the contact location is presented in a non-dimensional form. Results are compared with earlier predictions based on analytical, numerical and experimental methods. Load sharing among the mating gear teeth is discussed, and the overall gear mesh stiffness together with its cyclic variation along the path of contact is evaluated.

A Fast Finite Element Based Methodology to Predict the Temperature Field in a Thermoplastic Spur Gear Drive

2017 ◽  
Author(s):  
V. Roda-Casanova ◽  
F. Sanchez-Marin ◽  
A. Porras-Vazquez
Keyword(s):  
Finite Element ◽  
Temperature Field ◽  
Mechanical Response ◽  
Error Function ◽  
Transmission Error ◽  
Spur Gear ◽  
Temperature Variations ◽  
Gear Teeth ◽  
Gear Drives ◽  
Plastic Gears

Plastic gears bring some interesting advantages compared to metal gears. However, they also have some drawbacks, many of them related to the dependency of their mechanical properties with the temperature. Among other reasons, the friction between the gear teeth causes a heat flux that heats the gears and produces temperature variations within the gear geometries. These temperature variations have effects on the mechanical response of the gears, that must be taken into account when designing plastic gear drives. In this work, two different finite element models have been proposed to perform heating contact analysis, that is a coupled thermal-stress analysis that takes into account the heating produced by friction and the non-linear properties of the material. As a result of these models, the temperature field of the gears can be determined at any running time, as well as other interesting results, such as the transmission error function or the instantaneous power loss.

scholarly journals An Analysis of the Surface Geometric Structure and Geometric Accuracy of Cylindrical Gear Teeth Manufactured with the Direct Metal Laser Sintering (DMLS) Method

2019 ◽  
Author(s):  
Jadwiga Małgorzata Pisula ◽  
Grzegorz Budzik ◽  
Łukasz Przeszłowski
Keyword(s):  
Surface Roughness ◽  
Geometric Structure ◽  
Gear Tooth ◽  
Spur Gear ◽  
Laser Sintering ◽  
Tooth Surface ◽  
Direct Metal Laser Sintering ◽  
Cylindrical Gear ◽  
Sand Blasting ◽  
Gear Teeth

This paper presents findings concerning the accuracy of the geometry of cylindrical spur gear teeth manufactured with the direct metal laser sintering (DMLS) method. In addition, the results of the evaluation of the tooth surface geometric structure are presented in the form of selected two-dimensional and three-dimensional surface roughness parameters. An analysis of the accuracy of the fabricated gear teeth was performed after gear sand-blasting and gear tooth milling processes. Surface roughness was measured before and after sand-blasting and gear tooth milling. The test gear wheel was manufactured from GP1 high-chromium stainless steel on an EOS M270 machine.

Time-varying stiffness model of spur gear considering the effect of surface morphology characteristics

2018 ◽  
Vol 233 (2) ◽  
pp. 242-253 ◽  
Author(s):  
Zhifeng Liu ◽  
Tao Zhang ◽  
Yongsheng Zhao ◽  
Shuxin Bi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Roughness Parameter ◽  
Spur Gear ◽  
Contact Model ◽  
Tooth Surface ◽  
Mesh Stiffness ◽  
Stiffness Model ◽  
Input Torque ◽  
Element Method

The nonuniform cantilever beam and Hertzian contact model have been widely used to derive the mesh stiffness of spur gear assuming that the contact surface is absolutely frictionless. However, studies have confirmed that machined surfaces are rough in microscale and can be simulated by the Weierstrass–Mandelbort function. In order to get a reasonable and precise mesh stiffness model, the M-B contact model and finite element method are combined to express the local contact stiffness Kh. Through the simulation and comparison, the analytical finite element method is proved to be consistent with the traditional models and introduces the roughness parameters of machined tooth surface into the meshing process. Furthermore, the results also show that it is advantageous to improve the total mesh stiffness by increasing the fractal dimension D and input torque T as well as decreasing the roughness parameter G. In this paper, a relationship is built between the total mesh stiffness of gear sets with tooth surface characters and input torque, which can be a guidance in the design of the tooth surface parameters and the choice of the processing method in the future.

Sign in / Sign up

Export Citation Format

Share Document