Comparative analysis of numerical methods for the determination of contact pattern of spiral bevel gears

2018 ◽  
Vol 90 (2) ◽  
pp. 359-367 ◽  
Author(s):  
Adam Marciniec ◽  
Jacek Pacana ◽  
Jadwiga Malgorzata Pisula ◽  
Pawel Fudali
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Load Condition ◽  
Contact Analysis ◽  
Bevel Gear ◽  
Contact Pattern ◽  
Tooth Contact Analysis ◽  
Content Type ◽  
The Mathematical Model

Purpose This paper aims to present a comparison of numerical methods for determining the contact pattern of Gleason-type bevel gears. The mathematical model of tooth contact analysis and the finite element method were taken into consideration. Conclusions have been drawn regarding the usefulness of the considered methods and the compatibility of results. The object of the analysis was a bevel gear characterised by an 18:43 gear ratio and arc tooth line, and manufactured according to the spiral generated modified-roll method. Design/methodology/approach The mathematical model of tooth contact analysis consists of both the mathematical model of tooth generating and the mathematical model of operating gear set. The first model is used to generate tooth flanks of the pinion and the ring gear in the form of grids of points. Then, such tooth surfaces are used for the tooth contact analysis performed with the other model. It corresponds to the no-load gear meshing condition. The finite element method model was built on the basis of the same tooth flanks obtained with the former model. The commercial finite element method software Abaqus was used to perform two instances of the contact analysis: a very light load, corresponding to the former no-load condition, and the operating load condition. The results obtained using the two models, in the form of the contact pattern for no-load condition, were compared. The effect of heavy load on contact pattern position, shape and size was shown and discussed. Findings The mathematical models correctly reproduce the shape, position and size of the contact pattern; thus, they can be reliably used to assess the quality of the bevel gear at the early stage of its design. Practical implications Determination of the correct geometry of the flank surfaces of the gear and pinion teeth through the observation of contact pattern is a fundamental step in designing of a new aircraft bevel gear. Originality/value A possibility of the independent use of the mathematical analysis of the contact pattern has been shown, which, thanks to the compatibility of the results, does not have to be verified experimentally.

scholarly journals Frictional Tooth Contact Analysis along Line of Action of a Spur Gear Using Finite Element Method

2014 ◽  
Vol 5 ◽  
pp. 1801-1809 ◽  
Author(s):  
Santosh Patil ◽  
Saravanan Karuppanan ◽  
Ivana Atanasovska ◽  
Azmi A. Wahab
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spur Gear ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Element Method

A Material Selection Method Based on Finite Element Method

2014 ◽  
Vol 887-888 ◽  
pp. 1013-1016
Author(s):  
Sheng Bin Wu ◽  
Xiao Bao Liu
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Material Selection ◽  
Selection Method ◽  
Structure Design ◽  
The Finite Element Method ◽  
The Mathematical Model ◽  
Selection Of ◽  
Element Method

A new method for material selection in structure design based on the theory of the finite element method was presented. The method made material selection and structure design working at the same time. The mathematical model was established based on the finite element method. Finally, the material selection of an excavator's boom was verified, the results show that the proposed method is effective and feasible.

Finite Element Analysis of High - Pressure Grinding Mill

2011 ◽  
Vol 314-316 ◽  
pp. 675-681
Author(s):  
Yi Liu ◽  
Ji Shun Li
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
High Pressure ◽  
Fem Simulation ◽  
Element Analysis ◽  
Important Index ◽  
Set Up ◽  
The Mathematical Model ◽  
Grinding Mill

The stress distribution of the high - pressure grinding roller is an important index of the grinding mill design. A simulation model of high - pressure grinding roller is created by means of finite element method (FEM), utilizing the FEM software ANSYS. At first, the paper calculated the pressure of the high - pressure grinding roller by the grinding materiel mathematical model. Secondly, a physical model is set up material characteristics is defined and the areas are meshed, then the border conditions are established, finally loading and solving are made. The result of the FEM simulation indicated the mathematical model of the grinding materiel is rational.

Dynamic States Specific Analysis for Belt Conveyor Based on FDM

2013 ◽  
Vol 278-280 ◽  
pp. 27-30
Author(s):  
Xiao Shen ◽  
Qun Wang ◽  
Zhou Yu Fu ◽  
Shuo Wei Bai ◽  
Zhao Yang Sun
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Mathematical Method ◽  
Finite Element ◽  
Continuous Model ◽  
Belt Conveyor ◽  
Specific Analysis ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Dynamic States

There are two common research methods on the dynamic states model of belt conveyor in China at present. The mathematical model is built by finite element method then it is solved by numerical method. And the continuous model is built when the belt is treated as elastic body then it is solved by mathematical method. This paper puts forward the establishment of continuous model, the model is solved by FDM and the simulation results are given.

A study of the contact stress analysis of cylindrical gears using the hybrid finite element method

2012 ◽  
Vol 227 (1) ◽  
pp. 3-18 ◽  
Author(s):  
Zheng-Xiang Zhang ◽  
Zhang-Hua Fong ◽  
Yu-Huo Li ◽  
Hong-Sheng Fang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Stress ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Compliance Matrix ◽  
Tooth Contact ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Element Method

In this study, the hybrid finite element method combined with the tooth contact analysis was applied to solve the static contact stress problem of meshing a cylindrical gear set. The hybrid finite element method has two special features. First, the dimension of the stiffness matrix was reduced to a small condensed compliance matrix with degrees of freedom in the possible contact region. The contact force was iteratively solved based on the condensed compliance matrix by the normal gap distance at the contact point. Second, the contact force at the meshing positions was solved using the same condensed compliance matrix with a different normal gap distance calculated by the tooth contact analysis. Using the examples in this study, the contact stress of the meshing gears was calculated and compared to the data obtained by ANSYS in order to validate the proposed hybrid finite element method. The hybrid finite element method with tooth contact analysis proposed in this study can be used to determine the amount of tooth surface modification.

Parametric finite element modeling and tooth contact analysis of spur and helical gears including profile and lead modifications

2017 ◽  
Vol 34 (8) ◽  
pp. 2877-2898 ◽  
Author(s):  
Yanzhong Wang ◽  
Yang Liu ◽  
Wen Tang ◽  
Peng Liu
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Element Analysis ◽  
Tooth Contact ◽  
Content Type ◽  
Helical Gears ◽  
Element Modeling ◽  
Finite Element Software

Purpose The finite element method has been increasingly applied in stress, thermal and dynamic analysis of gear transmissions. Preparing the models with different design and modification parameters for the finite element analysis is a time-consuming and highly skilled burden. Design/methodology/approach To simplify the preprocessing work of the analysis, a parametric finite element modeling method for spur and helical gears including profile and lead modification is developed. The information about the nodes and elements is obtained and exported into the finite element software to generate the finite element model of the gear automatically. Findings By using the three-dimensional finite element tooth contact analysis method, the effects of tooth modifications on the transmission error and contact stress of spur and helical gears are presented. Originality/value The results demonstrate that the proposed method is useful for verifying the modification parameters of spur and helical gears in the case of deformations and misalignments.

scholarly journals A Mathematical Model of a Piezo-Resistive Eight-Beam Three-Axis Accelerometer with Simulation and Experimental Validation

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3641 ◽  
Author(s):  
Jinlong Song ◽  
Changde He ◽  
Renxin Wang ◽  
Chenyang Xue ◽  
Wendong Zhang
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Optimal Design ◽  
Experimental Validation ◽  
Fem Simulation ◽  
Normal Direction ◽  
Fem Model ◽  
Working Principle ◽  
The Mathematical Model

A mathematical model of a sensor is vital to deeply comprehend its working principle and implement its optimal design. However, mathematical models of piezo-resistive eight-beam three-axis accelerometers have rarely been reported. Furthermore, those works are largely focused on the analysis of sensing acceleration in the normal direction, rather than in three directions. Therefore, a complete mathematical model of a piezo-resistive eight-beam three-axis accelerometer is developed in this paper. The validity of the mathematical model is proved by a Finite Element Method (FEM) simulation. Furthermore, the accelerometer is fabricated and tested. The prime sensitivities of X, Y and Z axes are 0.209 mV/g, 0.212 mV/g and 1.247 mV/g at 160 Hz, respectively, which is in accord with the values obtained by the model. The reason why the prime sensitivity SZZ is bigger than SXX and SYY is explained. Besides, it is also demonstrated why the cross-sensitivities SXZ and SYZ exceed SZX and SZY. Compared with the FEM model, the developed model could be helpful in evaluating the performance of three-axis accelerometers in an accurate and rapid way.

Optimizing the design of straight bevel gear with reduced scoring effect

2020 ◽  
Vol 37 (7) ◽  
pp. 2391-2409
Author(s):  
Paridhi Rai ◽  
Asim Gopal Barman
Keyword(s):  
Mathematical Model ◽  
Bevel Gear ◽  
Computational Time ◽  
Contact Ratio ◽  
Design Constraints ◽  
Content Type ◽  
Gear Design ◽  
Gear Drive ◽  
Straight Bevel Gear ◽  
The Mathematical Model

Purpose The purpose of this paper is to minimize the volume of straight bevel gear and to develop resistance towards scoring failure in the straight bevel gear. Two evolutionary and more advance optimization techniques were used for performing optimization of straight bevel gears, which will also save computational time and will be less computationally expensive compared to a previously used optimization for design optimization of straight bevel gear. Design/methodology/approach The following two different cases are considered for the study: the first mathematical model similar to that used earlier and without any modification to show efficiency of the optimization algorithm for straight bevel gear design optimization and the second mathematical model consist of constraints on scoring and contact ratio along with other generally used design constraints. Real coded genetic algorithm (RCGA) and accelerated particle swarm optimization (APSO) are used to optimize the straight bevel gear design. The effectiveness of the algorithms used has been validated by comparing the obtained results with previously published results. Findings It has been found that APSO and RCGA outperform other algorithms for straight bevel gear design. Optimized design values have reduced the scoring effect significantly. The values of the contact ratio obtained further enhances the meshing operation of the bevel gear drive by making it smoother and quieter. Originality/value Low volume is one of the essential requirements of gearing applications. Scoring is a critical gear failure aspect that leads to the broken tooth in both high speed and low-speed applications of gears. The occurrence of scoring is hard to detect early and analyse. Scoring failure and contact ratio have been introduced as design constraints in the mathematical model. So, the mathematical model demonstrated in this paper minimizes the volume of the straight bevel gear drive, which has been very less attempted in previous studies, with scoring and contact ratio as some of the important design constraints, which the objective function has been subjected to. Also, two advanced and evolutionary optimization algorithms have been used to implement the mathematical model to reduce the computational time required to attain the optimal solution.

Research on the Influencing Factors of Dynamic Characteristics of Electronic Injector

2010 ◽  
Vol 44-47 ◽  
pp. 260-264
Author(s):  
Hui Qiang Liu ◽  
Si Fang Zhao ◽  
Jing Jing Wang
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Electromagnetic Field ◽  
Dynamic Measurement ◽  
Fuel Injector ◽  
The Finite Element Method ◽  
Core Diameter ◽  
Working Principle ◽  
The Mathematical Model

Base on the structure and working principle of electronic fuel injector, according to the related theories of electromagnetic field and flow field, the mathematical model of the electromagnetic force and fuel pressure have been deduced. Then using the finite element method to make a detailed analysis of magnetic permeability, core diameter, the working air gap, winding radius influence on the dynamic characteristic of the injector. According to this analysis, optimize those parameters for a new electronic injector, using the dynamic measurement system for a test, the results show the optimized injector has a better dynamic response than the unoptimized one.

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