Study on transmission error of double circular arc spiral bevel gears for nutation drive based on assembly errors and different loads

2019 ◽  
Vol 83 (3) ◽  
pp. 481-490
Author(s):  
Yongwu Cai ◽  
Ligang Yao ◽  
Jiaxin Ding ◽  
Simin Ouyang ◽  
Jun Zhang
Keyword(s):  
Transmission Error ◽  
Circular Arc ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

scholarly journals Dynamic modal analysis of double-sided meshing nutation drive with double circular arc spiral bevel gears

2020 ◽  
Vol 11 (1) ◽  
pp. 115-123
Author(s):  
Zheng Lin ◽  
Ligang Yao ◽  
Zhiyu Xie
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Transmission Error ◽  
Drive System ◽  
Nonlinear Dynamic Model ◽  
Circular Arc ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Meshing Stiffness ◽  
Spiral Bevel

Abstract. In order to reduce the vibration of the double-sided meshing nutation drive with double circular arc spiral bevel gears, the dynamic modal of the nutation system is analyzed. The bending-torsional-axial coupling nonlinear dynamic model of the double-sided meshing nutation drive system with time-varying meshing stiffness, meshing damping, transmission error and tooth backlash is established, and the equation of motion of the system is derived. The natural frequencies and corresponding modal modes of the nutation system are calculated, and the effects of the average meshing stiffness of gears and the bearing support stiffness of nutation gears on the modal of the system are analyzed. The modal analysis of double circular arc spiral bevel gears is carried out, and the ten order natural frequencies and their corresponding modes are obtained. The results show that the nutation drive system and the double circular arc spiral bevel gears do not resonate during transmission.

Mathematical Modeling and Simulation of the External and Internal Double Circular-Arc Spiral Bevel Gears for the Nutation Drive

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Ligang Yao ◽  
Bing Gu ◽  
Shujuan Haung ◽  
Guowu Wei ◽  
Jian S. Dai
Keyword(s):  
Mathematical Modeling ◽  
Numerical Control ◽  
Tooth Surface ◽  
Circular Arc ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Nc Simulation ◽  
Helical Angle ◽  
Nc Milling ◽  
Spiral Bevel

The purpose of this paper is to propose a pair of external and internal spiral bevel gears with double circular-arc in the nutation drive. Based on the movement of nutation, this paper develops equations of the tooth profiles for the gear set, leading to the mathematical modeling of the spiral bevel gear with a constant helical angle gear alignment curve, enabling the tooth surface to be generated, and permitting the theoretical contacting lines to be produced in light of the meshing function. Simulation and verification are carried out to prove the mathematical equations. Numerical control (NC) simulation of machining the external and internal double circular-arc spiral bevel gears is developed, and the spiral gears were manufactured on a NC milling machine. The prototype of the nutation drive is illustrated in the case study at the end of this paper.

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.

Computerized Design and FE Simulation of Meshing of Involute Spiral Bevel Gears with Alignment Errors

2011 ◽  
Vol 199-200 ◽  
pp. 386-391 ◽  
Author(s):  
Ben Wang ◽  
Lin Hua
Keyword(s):  
Fe Simulation ◽  
Transmission Error ◽  
Load Carrying Capacity ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Load Carrying ◽  
Contact Models ◽  
Stress Transmission ◽  
Spiral Bevel ◽  
Alignment Errors

Influence of alignment errors on the meshing of involute spiral bevel gears using FEM is investigated in this paper. 3D geometrical models of involute spiral bevel gear drive are computationally designed and the reliable non-linear finite element contact models are also developed. Furthermore, based on the valid 3D FE models, simulations of meshing of loaded spiral bevel gears with four types of alignment errors are performed. The influence of four types of alignment errors on contact stress, transmission error and shift of path of contact has been discussed in detail. The results demonstrate that the alignment errors have different degrees of adverse effects on the load-carrying capacity and the smoothness of transmission. Therefore, the study provides useful reference for the modification design and the assembling of spiral bevel gears in practice.

scholarly journals Theoretical and Experimental Study on Contact Characteristics of Spiral Bevel Gears under Quasi-Static and Large Loading Conditions

2020 ◽  
Vol 10 (15) ◽  
pp. 5109 ◽  
Author(s):  
Yimeng Fu ◽  
Yaobing Zhuo ◽  
Xiaojun Zhou ◽  
Bowen Wan ◽  
Haoliang Lv ◽  
...  
Keyword(s):  
Finite Element ◽  
Performance Test ◽  
Element Model ◽  
Transmission Error ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Transition Surface ◽  
Spiral Bevel

The precise mathematical model for the tooth surface and transition surface of spiral bevel gears is derived. Taking a pair of spiral bevel gears of a heavy vehicle as an example of calculation and analysis, a finite element model of spiral bevel gears transmission system is established. Through the finite element tooth contact analysis under quasi-static loading and high loading condition, the influences of torque on the root stress distribution, contact stress, and transmission error are discussed, and the results are compared with the empirical formula results. Finally, a contact performance test bench of spiral bevel gear pair is developed, then the root bending stress, contact pattern, and transmission error tests are carried out. These experiment results are compared with analyzed ones, which showed a good agreement.

Manufacture Parameter Design of SMG Spiral Bevel Gears Based on Local Synthesis and Transmission Error Optimization

2010 ◽  
Vol 29-32 ◽  
pp. 2319-2326
Author(s):  
Guang Lei Liu ◽  
Hong Wei Fan ◽  
Ping Jiang
Keyword(s):  
Error Function ◽  
Transmission Error ◽  
Parameter Design ◽  
Optimization Approach ◽  
Tooth Contact Analysis ◽  
Local Synthesis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Bearing Contact ◽  
Spiral Bevel

An optimization approach for manufacture parameter design of the SGM spiral bevel gears with modified tooth geometry is proposed. The approach is accomplished by application of local synthesis, tooth contact analysis (TCA) and dual-objective optimization of transmission error function. A computer program to obtain a set of manufacture parameters based on the proposed theory is developed and illustrated with an example. The proposed method provides a set of machine-tool settings for pinion NC-grinding which ensures: (i) a localized bearing contact pattern less sensitive to misalignments, (ii) a parabolic transmission error function to reduce vibration and noise in mesh.

An Extremum Principle for Computation of the Zone of Tooth Contact and Generalized Transmission Error of Spiral Bevel Gears

1988 ◽  
Vol 110 (2) ◽  
pp. 211-220 ◽  
Author(s):  
W. D. Mark
Keyword(s):  
Computational Procedure ◽  
Transmission Error ◽  
Error Component ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
True Values ◽  
Method Of Steepest Descent ◽  
Three Components

For a given set of forces transmitted by the gears, each of the three components of the generalized transmission error of spiral bevel gears is shown to be stationary with respect to small independent variations in the positions of the endpoints of the lines of tooth contact about their true values. The tangential generalized transmission error component is shown to take on a minimum value at the true endpoint positions. A computational procedure based on the method of steepest descent is described for computing the true line of contact endpoint positions and the three components of the generalized transmission error. A method for computing the Fourier series coefficients of the tooth meshing harmonics of the three generalized transmission error components also is provided.

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