Calculation of optimum profile modification curve for gear pair based on complex potential method

2019 ◽  
Vol 25 (23-24) ◽  
pp. 2921-2934
Author(s):  
Quancheng Peng ◽  
Tengjiao Lin ◽  
Hesheng Lv
Keyword(s):  
Finite Element ◽  
Mixed Boundary ◽  
Transmission Error ◽  
Power Series Solution ◽  
Conformal Map ◽  
Gear Pair ◽  
Analysis Model ◽  
Profile Modification ◽  
Potential Energy Method ◽  
Optimum Profile

The optimum profile modification curve of a gear pair is usually determined according to the fluctuation minimization of static transmission error (STE). For the calculation of STE, the potential energy method dismisses the correlative tooth deflection induced by gear body elastic coupling effects, and the finite element method requires high calculation cost. In order to simultaneously obtain high calculation accuracy and efficiency, the single tooth deflection is calculated through analytical integration about the Hertz contact pressure based on the conformal map method. The correlative tooth deflection is calculated based on the power series solution of the mixed boundary problem of an elastic annulus. Via combination of deflection compatibility and the force equilibrium condition, a contact analysis model of a spur gear pair is built. Based on the model, the STE is first calculated and compared with the finite element analysis result to verify the model rationality. Then, the optimum profile modification curve which renders constant STE is calculated. For a gear pair with the obtained modification curve, fluctuation of dynamic transmission error also decreases and the optimization effect is verified.

Meshing performance of spiral bevel gear with different loads and modules considering edge contact by finite element method

2019 ◽  
Vol 43 (3) ◽  
pp. 322-332
Author(s):  
Xiangying Hou ◽  
Zongde Fang ◽  
Xuezhong Fu ◽  
Xijin Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Stress ◽  
Load Sharing ◽  
Transmission Error ◽  
Contact Forces ◽  
Gear Pair ◽  
Edge Contact ◽  
Spiral Bevel ◽  
Element Method

To analyze the edge contact of spiral bevel gears, owing to its effect on meshing performance, batch processing is performed based on a static solver and the finite element method (FEM) because of its computational speed advantage. A series of programs automatically perform the functions of modeling, analysis, and extraction of performance indexes. Starting from the entrance meshing position to the exit meshing position, a series of models was built and analyzed to describe the whole meshing process of the gear pair. For a specific gear pair, contact and bending stresses, contact stress patterns, loaded transmission errors, contact forces, and load sharing coefficients are calculated under five different load conditions and the change rules are summarized. Edge contact phenomenon occurs as the load increases to a critical value, resulting in a sharp increase in contact stress. As the load increases, the load sharing coefficient decreases gradually and the absolute value of transmission error increases, but the fluctuation of transmission error first decreases and then increases. In addition, the effect of modules is discussed and the results show that large modulus will decrease stress, contact ratio, and edge contact, but there is a certain module to minimize the fluctuation of transmission error.

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.

scholarly journals 115 Tooth Profile Modification and Transmission Error of Spur Gear Pair

2000 ◽  
Vol 2000.37 (0) ◽  
pp. 29-30
Author(s):  
Makoto TANAKA ◽  
Shigeo YANABE ◽  
Takaki KANOU ◽  
Koreaki ICHINO
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Tooth Profile ◽  
Gear Pair ◽  
Profile Modification ◽  
Tooth Profile Modification

Modeling the Nonlinear Vibration of a Spur Gear Pair

2000 ◽  
Author(s):  
R. G. Parker ◽  
S. M. Vijayakar ◽  
T. Imajou
Keyword(s):  
Finite Element ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Surface ◽  
Nonlinear Phenomena ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Time Step ◽  
Mechanics Model ◽  
Wide Range

Abstract The dynamic response of a spur gear pair is investigated using a finite element/contact mechanics model that offers significant advantages for dynamic gear analyses. The gear pair is analyzed across a wide range of operating speeds and torques. Comparisons are made to other researchers’ published experiments that reveal complex nonlinear phenomena. The nonlinearity source is contact loss of the meshing teeth, which, in contrast to the prevailing understanding, occurs even for large torques despite use of high-precision gears. A primary feature of the modeling is that dynamic mesh forces are calculated using detailed contact analysis at each time step as the gears roll through mesh; there is no need to externally specify the excitation in the form of time-varying mesh stiffness, static transmission error input, or the like. A semi-analytical model near the tooth surface is matched to a finite element solution away from the tooth surface, and the computational efficiency that results permits dynamic analysis. Two single degree of freedom models are discussed briefly. While one gives encouragingly good results, the second, which appears to have better mesh stiffness modeling, gives poor comparisons with experiments. The results indicate the sensitivity of such models to changing mesh stiffness representations.

Finite Element Analysis for Tooth Profile Modification of Gear-Box of Tracklayer

2010 ◽  
Vol 156-157 ◽  
pp. 621-624
Author(s):  
Yan Wang ◽  
Ji Sheng Ma ◽  
Hui Yong Deng ◽  
Hai Ping Liu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Contact Stress ◽  
Transmission Error ◽  
Tooth Profile ◽  
Element Analysis ◽  
Profile Modification ◽  
Tooth Profile Modification ◽  
Static Contact ◽  
Gear Box

The quasi-static contact finite element analysis of meshing gear of gear-box is computed by using MSC.Marc software, then transmission error and surface contact stress of meshing gear are computed in different tooth profile modification methods. Due to the large load fluctuation of tracklayer, the target of tooth profile modification is suggested, which is to minimize the peak value of tooth contact stress to the full, and not to increase the transmission error fluctuation of gear system.

Modeling and experimental verification on directivity of an electret cell array loudspeaker

2012 ◽  
Vol 24 (3) ◽  
pp. 326-333 ◽  
Author(s):  
Yu-Chi Chen ◽  
Wen-Ching Ko ◽  
Han-Lung Chen ◽  
Hsu-Ching Liao ◽  
Wen-Jong Wu ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Digital Control System ◽  
Analysis Model ◽  
Cell Array ◽  
Element Analysis ◽  
Finite Element Analysis Model ◽  
The Finite Element Analysis ◽  
Directivity Characteristics

We propose a model to give us a method to investigate the characteristic three-dimensional directivity in an arbitrarily configured flexible electret-based loudspeaker. In recent years, novel electret loudspeakers have attracted much interest due to their being lightweight, paper thin, and possessing excellent mid- to high-frequency responses. Increasing or decreasing the directivity of an electret loudspeaker makes it excellent for adoption to many applications, especially for directing sound to a particular area or specific audio location. Herein, we detail a novel electret loudspeaker that possesses various directivities and is based on various structures of spacers instead of having to use multichannel amplifiers and a complicated digital control system. In order to study the directivity of an electret loudspeaker based on an array structure which can be adopted for various applications, the horizontal and vertical polar directivity characteristics as a function of frequency were simulated by a finite-element analysis model. To validate the finite-element analysis model, the beam pattern of the electret loudspeaker was measured in an anechoic room. Both the simulated and experimental results are detailed in this article to validate the various assertions related to the directivity of electret cell-based smart speakers.

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