Comparison on torsional mesh stiffness and contact ratio of involute internal gear and high contact ratio internal gear

2019 ◽  
Vol 234 (7) ◽  
pp. 1423-1437
Author(s):  
Yanzhong Wang ◽  
Delong Dou ◽  
E Shiyuan ◽  
Jianjun Wang
Keyword(s):  
Spur Gear ◽  
Finite Element Models ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Gear Drive ◽  
Single Tooth ◽  
Dimensional Finite Element ◽  
Internal Gear ◽  
Tooth Pair ◽  
Input Torque

The mesh stiffness and contact ratio of gear drive are very important factors which have a great impact on the dynamic load. Contact ratio also affects the fluctuation and the mode of change of the mesh stiffness. In this research, a novel high contact ratio internal gear with a circular arc contact path is introduced. However, the irregular tooth profile of non-involute gear usually causes the numerical calculation to be more complex. To get the torsional mesh stiffness of a pair of internal spur gear, the two-dimensional finite element models of involute internal gear and high contact ratio internal gear are presented and compared. In addition, the influence of input torque on torsional mesh stiffness and contact ratio are analyzed. The mesh stiffness of a single tooth pair and the effect of different engagement positions on mesh stiffness are obtained and compared. Finally, experimental measurement of contact ratio is established by strain gauge technique. It is shown that the torsional mesh stiffness increases with the increase of input torque, and the greater the contact ratio, the smoother the gear drive.

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.

The Torque Responses in Spur Gearing

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.

Design and Analysis of Asymmetrical Spur Gear Drive for Automobile Gear Box Application

2014 ◽  
Vol 592-594 ◽  
pp. 2277-2281 ◽  
Author(s):  
Rama Thirumurgan ◽  
Clement Christy C. Deepak
Keyword(s):  
Motor Vehicle ◽  
Gear Tooth ◽  
Load Sharing ◽  
Spur Gear ◽  
Mesh Stiffness ◽  
Gear Drive ◽  
Contact Points ◽  
Actual Load ◽  
Gear Box ◽  
Sharing Behavior

This work mainly aims to explore the actual load, fillet and contact stresses induced during a mesh cycle in a spur gear tooth. As the mesh stiffness differs at different contact points along the path of contact, it significantly affects the load sharing between the simultaneously meshed contact pairs hence stresses. Comparative study has been made between existing symmetric spur gear pair used in light motor vehicle gear box and asymmetric spur gear. Finite element multi pair contact model has been used to explore the load sharing behavior and related stresses in this work.

Formulation for an optimal design problem of spur gear drive and its global optimization

2012 ◽  
Vol 227 (8) ◽  
pp. 1804-1817 ◽  
Author(s):  
Zhong Wan ◽  
ShaoJun Zhang
Keyword(s):  
Global Optimization ◽  
Optimal Design ◽  
Design Problem ◽  
Optimization Method ◽  
Spur Gear ◽  
Global Optimization Method ◽  
Contact Ratio ◽  
Gear Drive ◽  
Variable Space ◽  
Global Optimal

In this article, an optimal design problem of spur gear drive with a fixed load factor is formulated as a nonlinear optimization model. Three methods are presented to find the globally optimal design scheme on the structure of the spur gear pair. By suitable variable transformation, the constructed model is first converted into a linear program with mixed variables. By developing an algorithm of global optimization for solving a binary linear programming with mixed variables, all global optimal solutions are found for the original design problem. Taking into account the modification of the contact ratio factors, a specific global optimization method is provided to optimize the design of spur gear drive with soft tooth flank in a continuous variable space. On the basis of enumeration of the discrete variables and utilization of the monotonicity in the optimal model, another global optimization method is designed to search for the global optimal solutions in the mixed variable space, which does not depend upon whether the modification of contact ratio factor exists or not. Case studies are employed to demonstrate the validity and practicability of the constructed model and the proposed methods.

scholarly journals Practical Optimal Design on Two Stage Spur Gears Train Using Nature Inspired Algorithms

2019 ◽  
Vol 8 (6) ◽  
pp. 4073-4081
Keyword(s):  
Power Transmission ◽  
Spur Gear ◽  
Contact Ratio ◽  
Two Stage ◽  
Gear Drive ◽  
Mechanical Constraints ◽  
Design Variables ◽  
Accurate Design ◽  
Power Transmission Systems ◽  
Nature Inspired Algorithms

The accurate design of spur gear drive has a tremendous impact on size, weight, transmission and machine performance. Also, the demand for lighter gears is high in power transmission systems, as they save material and energy. Hence this paper presents an enhanced method to solve a two stage spur gear optimization problem. It consists of a mathematical model with a nonlinear objective function and 11 constraints. A two stage spur gear is considered. To obtain minimum volume of spur gear drive is objective of the problem. The considered design variables are: Module, number of teeth, base width of the gears and, shaft diameter and power. Besides considering regular mechanical constraints based on American Gear Manufacturers Association (AGMA) requisites, six more additional critical constraints on contact ratio, load carrying capacity, power loss, root not cut, no involute interference and line of action are imposed on the drive. Nature inspired optimization algorithms, namely, Simulated Annealing (SA), Firefly (FA) and MATLAB solver fmincon are used to find solution in MATLAB environment. Simulation results are analyzed, compared with literature and validated

Prediction of Spur Gear Mesh Stiffness Associated with the Tooth Corrosion

2015 ◽  
Vol 799-800 ◽  
pp. 570-575
Author(s):  
Zheng Min Qing Li ◽  
Qing Bin Zhao ◽  
Xiao Zhen Li
Keyword(s):  
Spur Gear ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Gear Drive ◽  
Corrosion Effect ◽  
Proposed Model ◽  
Stiffness Model ◽  
The Stability ◽  
Gear Drives ◽  
Gear Mesh Stiffness

In this study, a mesh stiffness model of spur gear drives considering the tooth corrosion effect, which is based on Ishikawa model, is proposed. The fidelity of mesh stiffness based on the proposed model is checked by comparing the result with a benchmark result from the reference and the effect of the tooth corrosion on mesh stiffness is analyzed. The prediction indicates mesh stiffness is insensitive to the tooth corrosion, but this conclusion has a signification for assessing the stability of inherent properties of a spur gear drive when the tooth corrosion is produced.

Studies on the Dynamic Performance of a Spur Gear With Hollow Teeth

1992 ◽  
Author(s):  
A. Ramamohana Rao ◽  
B. Srinivasulu
Keyword(s):  
Damping Ratio ◽  
Dynamic Performance ◽  
Spur Gear ◽  
Dynamic Loads ◽  
Response Analysis ◽  
Spur Gears ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Direction Parallel ◽  
Gear Teeth

Abstract Performance of spur gears largely depends on the magnitude and nature of variation of dynamic loads occuring between mating teeth. Variable tooth mesh stiffness is one of the primary sources causing parametric excitations resulting in dynamic loads. The usual method of varying the mesh stiffness to reduce dynamic loads is to use high contact ratio and profile modified gears. In this paper, a new type of tooth design to improve the dynamic performance of spur gears is presented. In this, a through hole is drilled in each tooth in a direction parallel to the gear axis. The diameter of the hole and its position on the tooth centre line are variable. Such a gear is called a hollow gear. Dynamic analysis is carried out for the mesh of hollow pinions mating with solid gears. The results are compared with solid pinions (no holes in teeth) meshing with solid gears. Finite element method is used for the analysis. For estimation of the dynamic load variation in hollow-solid and solid-solid gear meshes, a model incorporating the varying mesh stiffness and damping of gear teeth is used. Governing differential equations are solved using unconditionally stable Newmark-beta algorithm. The dynamic loads obtained are used as an input time varying loads for the determination of dynamic fillet and hole stress response of solid and hollow gear teeth whichever is applicable. Modal superposition technique is used for transient response analysis. The study shows that for the same damping ratio, dynamic loads in hollow-solid meshes are nearly the same as in a solid-solid mesh. In reality, the dynamic loads in a hollow-solid mesh are less than a solid-solid mesh due to its inherent higher material damping.

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.

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