Analysis of Grinding Dynamic Based on Grind Teeth Vibration Model of Spiral Bevel Gears

2014 ◽  
Vol 602-605 ◽  
pp. 176-179
Author(s):  
Miao Xin Xiao ◽  
Jian Jun Yang
Keyword(s):  
Phase Diagram ◽  
Dynamic Response ◽  
Degrees Of Freedom ◽  
Time Course ◽  
Transmission Error ◽  
Spiral Bevel Gear ◽  
Bevel Gears ◽  
Vibration Model ◽  
Braking Torque ◽  
Spiral Bevel

Starting from the fact of backlash and gear transmission error, it is established vibration model of spiral bevel gear lapping system with two degrees of freedom. Through normalized calculate, it is obtained dynamic response of lapping vibration model under different braking torque. According to the time course and the phase diagram, during the process that brake torque switch from small to big, teeth meshing, collision and disengaged alternately goes on, and with the braking torque increases to a certain value, the teeth collision disappear and then back into the complete meshing state.

Design and analysis of high contact ratio spiral bevel gears by modified curvature motion method

2017 ◽  
Vol 232 (19) ◽  
pp. 3396-3409 ◽  
Author(s):  
Yanming Mu ◽  
Zongde Fang
Keyword(s):  
Transmission Error ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Contact Ratio ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Curvature Motion ◽  
Seventh Order ◽  
Spiral Bevel ◽  
Motion Method

This paper presents a new method to design a seventh-order transmission error for high contact ratio spiral bevel gears by the modified curvature motion method to reach the purpose of reducing or eliminating gear vibration and noise. In this paper, firstly, based on the predesigned seventh-order transmission error, the polynomial coefficients of transmission error curve can be obtained. Secondly, a method named modified curvature motion method is used to generate the spiral bevel gear with the predesigned transmission error. Lastly, based on TCA and LTCA, we verify the feasibility of the modified curvature motion method to generate spiral bevel gear with seventh-order transmission error, and the meshing impact of gear set with the seventh-order and second-order function of transmission error is analyzed and compared. The results of a numerical example show that the seventh-order transmission error acquired by the modified curvature motion method can effectively reduce the meshing impact of spiral bevel gears. The tooth modification method and meshing impact analysis method can serve as a basis for developing a general technique of flank modification for spiral bevel gears.

scholarly journals Effects of Geometry Design Parameters on the Static Strength and Dynamics for Spiral Bevel Gear

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Zhiheng Feng ◽  
Chaosheng Song
Keyword(s):  
Dynamic Model ◽  
Bending Strength ◽  
Transmission Error ◽  
Design Parameters ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Geometry Design ◽  
Mesh Model ◽  
Spiral Bevel

Considering the geometry design parameters, a quasi-static mesh model of spiral bevel gears was established and the mesh characteristics were computed. Considering the time-varying effects of mesh points, mesh force, line-of-action vector, mesh stiffness, transmission error, friction force direction, and friction coefficient, a nonlinear lumped parameter dynamic model was developed for the spiral bevel gear pair. Based on the mesh model and the nonlinear dynamic model, the effects of main geometry parameters on the contact and bending strength were analyzed. Also, the effects on the dynamic mesh force and dynamic transmission error were investigated. Results show that higher value for the pressure angle, root fillet radius, and the ratio of tooth thickness tend to improve the contact and bending strength and to reduce the risk of tooth fracture. Improved gears have a better vibration performance in the targeted frequency range. Finally, bench tests for both types of spiral bevel gears were performed. Results show that the main failure mode is the tooth fracture and the life was increased a lot for the spiral bevel gears with improved geometry parameters compared to the original design.

scholarly journals Coupled Bending-Torsional Nonlinear Vibration and Bifurcation Characteristics of Spiral Bevel Gear System

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Jinli Xu ◽  
Fancong Zeng ◽  
Xingyi Su
Keyword(s):  
Nonlinear Vibration ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Global Bifurcation ◽  
Transmission Error ◽  
Bevel Gear ◽  
Gear System ◽  
Spiral Bevel Gear ◽  
Gear Backlash ◽  
Spiral Bevel

A spiral bevel gear system supported on thrust bearings considering the coupled bending-torsional nonlinear vibration is proposed and an eight degrees of freedom (8DOF) lumped parameter dynamic model of the spiral bevel gear system combined with time-varying stiffness, static transmission error, gear backlash, and bearing clearances is investigated. The spiral bevel gear system is analyzed with the equations of motion and the dynamic response is solved using the Runge-Kutta method. The effects of mesh frequency, mesh damping coefficient, load coefficient, and gear backlash are revealed, which describe the true mesh characteristics of the spiral bevel gear system. The bifurcation characteristics as jump discontinuities, periodic windows, and chaos are obtained by studying time histories, phase plane portraits, Poincaré maps, Fourier spectra, and global bifurcation diagrams of the gear system. The results presented in this study provide some useful information for engineers in designing and controlling such gear systems.

Research on Solving Method for Tooth Crest Curve of Spiral Bevel Gear under Form Milling

2010 ◽  
Vol 139-141 ◽  
pp. 1255-1259
Author(s):  
Xiu Ting Wei ◽  
Jing Cheng Liu ◽  
Qiang Du
Keyword(s):  
Coordinate System ◽  
Process Simulation ◽  
Machining Process ◽  
Geometric Transformation ◽  
Spiral Bevel Gear ◽  
Bevel Gears ◽  
Machining Process Simulation ◽  
System 2 ◽  
Spiral Bevel ◽  
Curve Equation

Combining the machining process simulation on UG NX software and the mathematically analysis, a new solving method for the tooth crest curve equation of spiral bevel gears is proposed in this paper. The steps are as follows:1) Establishing the gear blank cone equation in the original coordinate system; 2) Finding the gear convex and concave profile equations in the new coordinate system; 3) Integrating the original coordinate system and the new one through geometric transformation and then deducing the tooth crest curve equations on both sides. The equations will help calculate the cutter’s position and pose in addendum chamfering process, with the chamfer automation achieved.

scholarly journals Lubrication characteristics of gear after shot peening base on 25-pellet model

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401879065 ◽  
Author(s):  
Shuai Mo ◽  
Shengping Zhu ◽  
Guoguang Jin ◽  
Jiabei Gong ◽  
Zhanyong Feng ◽  
...  
Keyword(s):  
Shot Peening ◽  
High Speed ◽  
Target Material ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Lubrication Characteristics

High-speed heavy-load spiral bevel gears put forward high requirement for flexural strength; shot peening is a technique that greatly improves the bending fatigue strength of gears. During shot peening, a large number of fine pellets bombard the surface of the metal target material at very high speeds and let the target material undergo plastic deformation, at the same time strengthening layer is produced. Spiral bevel gear as the object of being bombarded inevitably brought the tooth surface micro-morphology changes. In this article, we aim to reveal the effect of microtopography of tooth shot peening on gear lubrication in spiral bevel gear, try to establish a reasonable description of the microscopic morphology for tooth surface by shot peening, to reveal the lubrication characteristics of spiral bevel gears after shot peening treatment based on the lubrication theory, and do comparative research on the surface lubrication characteristics of a variety of microstructures.

Nonrelative sliding of spiral bevel gear mechanism based on active design of meshing line

2018 ◽  
Vol 233 (3) ◽  
pp. 1055-1067 ◽  
Author(s):  
Zhen Chen ◽  
Ming Zeng
Keyword(s):  
Design Method ◽  
Bevel Gear ◽  
Transmission Mechanism ◽  
Tooth Surface ◽  
Design Parameters ◽  
Spiral Bevel Gear ◽  
Bevel Gears ◽  
Gear Mechanism ◽  
Active Design ◽  
Spiral Bevel

In this paper, an active design method of meshing line for a spiral bevel gear mechanism with nonrelative sliding is presented. First, the general meshing line equations for a nonrelative sliding transmission mechanism between two orthogonal axes are proposed based on the active design parameters. Then, parametric equations for contact curves on the drive and driven spiral bevel gears are deduced by coordinate transformation of the meshing line equations. Further to this, parametric equations for the tooth surface of each bevel gear are derived according to the conical spiral motion of a generatrix circle along the calculated contact curves. Finally, a set of numerical examples is presented based on two types of motion equation of the meshing points. Material prototypes are fabricated and experimentally tested to validate the kinematic performance of the functionally designed spiral bevel gear set.

Optimal Machine-Tool Settings for the Manufacture of Face-Hobbed Spiral Bevel Gears

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Contact Pressure ◽  
Optimization Problem ◽  
Transmission Error ◽  
Search Method ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Loaded Tooth Contact Analysis

In this study, an optimization methodology is proposed to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously minimize the tooth contact pressure and angular displacement error of the driven gear (the transmission error), and to reduce the sensitivity of face-hobbed spiral bevel gears to the misalignments. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors influenced by the misalignments inherent in the gear pair. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper. The targeted optimization problem is a nonlinear constrained optimization problem, belonging to the framework of nonlinear programming. In addition, the objective function and the constraints are not available analytically, but they are computable, i.e., they exist numerically through the loaded tooth contact analysis. For these reasons, a nonderivative method is selected to solve this particular optimization problem. That is the reason that the core algorithm of the proposed nonlinear programming procedure is based on a direct search method. The Hooke and Jeeves pattern search method is applied. The effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. Drastic reductions in the maximum tooth contact pressure (62%) and in the transmission errors (70%) were obtained.

Kinematical Optimization of Spiral Bevel Gears

1992 ◽  
Author(s):  
Zhang-Hua Fong ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Contact Patterns ◽  
Spiral Bevel ◽  
Kinematic Errors

Abstract Kinematical optimization and sensitivity analysis of circular-cut spiral bevel gears are investigated in this paper. Based on the Gleason spiral bevel gear generator and EPG test machine, a mathematical model is proposed to simulate the tooth contact conditions of the spiral bevel gear set. All the machine settings and assembly data are simulated by simplified parameters. The tooth contact patterns and kinematic errors are obtained by the proposed mathematical model and the tooth contact analysis techniques. Loaded tooth contact patterns are obtained by the differential geometry and the Hertz contact formulas. Tooth surface sensitivity due to the variation of machine settings is studied. The corrective machine settings can be calculated by the sensitive matrix and the linear regression method. An optimization algorithm is also developed to minimize the kinematic errors and the discontinuity of tooth meshing. According to the proposed studies, an improved procedure for development of spiral bevel gears is suggested. The results of this paper can be applied to determine the sensitivity and precision requirements in manufacturing, and improve the running quality of the spiral bevel gears. Two examples are presented to demonstrate the applications of the optimization model.

Impact analysis and vibration reduction design of spiral bevel gears

2019 ◽  
Vol 233 (3) ◽  
pp. 668-676 ◽  
Author(s):  
Yanming Mu ◽  
Zongde Fang ◽  
Wenli Li
Keyword(s):  
Impact Velocity ◽  
Optimization Method ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Load Torque ◽  
Bevel Gears ◽  
Meshing Stiffness ◽  
Polynomial Coefficients ◽  
Spiral Bevel ◽  
The Impact

To minimize the running vibration of spiral bevel gear, an optimization design method for vibration control is presented with the model of meshing impact. Firstly, based on the impact model of spiral bevel gears considering tooth deformation, the initial meshing position, meshing stiffness, and the meshing impact is studied. Secondly, the effects of load torque and rotation speed on meshing impact are analyzed. Thirdly, a mathematical model for pinion generator is built with following parameters: tool parameters, initial machine settings, and polynomial coefficients of auxiliary flank modification motion. The polynomial coefficients of the auxiliary flank modification motion are determined by optimizing the minimum impact velocity. Finally, a numerical simulation is performed. The results shows that load torque and pinion rotational speed impose significant influences on the impact. The impact velocity increases with the increase of load torque and pinion rotation speed. With load torque increasing, impact force tends to increase first and then decrease because of meshing stiffness changes, finally impact force increases dramatically due to additional load. The advantages of spiral bevel gear under the optimization of impact velocity in meshing impact are obviously. The accuracy and scientificity of the method presented in the paper for calculating the initial meshing point and meshing stiffness of complicated tooth surfaces is verified. The optimized gear obtained by the optimization method presented in the paper is also proved that owns the lowest meshing impact in the design load range. The proposed optimization method can reduce meshing impact and improve the dynamic meshing performance of spiral bevel gear. This method also can be used for optimum design of other types of gears.

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