scholarly journals A Multiobjective Optimization Analysis of Spur Gear Pair: The Profile Shift Factor Effect on Structure Design and Efficiency

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Samya Belarhzal ◽  
Kaoutar Daoudi ◽  
El Mostapha Boudi ◽  
Aziz Bachir ◽  
Samira Elmoumen
Keyword(s):  
Multiobjective Optimization ◽  
Power Transmission ◽  
Spur Gear ◽  
Shift Factor ◽  
Structure Design ◽  
Operating Conditions ◽  
Gear Pair ◽  
Contact Ratio ◽  
Face Width ◽  
Volume Equation

Spur gears are an indispensable element of power transmission, most of the time used in small environments with severe operating conditions such as high temperature, vibrations, and humidity. For this reason, manufacturers and transmission designers are required to look for better gear designs and higher efficiency. In this paper, a multiobjective optimization was conducted, using genetic algorithms (GAs) for corrected spur gear pair with an objective to reduce the structure volume and transmission power loss and reveal the influence of the profile shift factor on the optimal structure fitness. The optimization variables included are the pinion and wheel profile shift factors in addition to the module, face width, and the number of pinion teeth mostly used in standard gear optimization. The profile shift factor influences the shape of the gear teeth, the contact ratio, and the load sharing. It affects then the optimal results meaningfully. The gear pair volume, center distance, and efficiency presented the objective functions while contact stress, bending stress, face with coefficient, and tooth tip interferences served as constraints. Furthermore, a volume equation was developed, in which a bottom clearance formula is included for more accurate results. "Multiobjective optimization" is conducted at medium and high speeds, and the results show that the structure design is compact compared to standard gears with reasonable efficiency for medium contact ratio.

Oil Churning Power Losses of a Gear Pair: Experiments and Model Validation

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
S. Seetharaman ◽  
A. Kahraman ◽  
M. D. Moorhead ◽  
T. T. Petry-Johnson
Keyword(s):  
Power Loss ◽  
Spur Gear ◽  
Companion Paper ◽  
Design Parameters ◽  
Measured Parameter ◽  
Gear Pair ◽  
Power Losses ◽  
Gear Design ◽  
Face Width ◽  
Wide Range

This paper presents the results of an experimental study on load-independent (spin) power losses of spur gear pairs operating under dip-lubricated conditions. The experiments were performed over a wide range of operating speed, temperature, oil levels, and key gear design parameters to quantify their influence on spin power losses. The measurements indicate that the static oil level, rotational speed, and face width of gears have a significant impact on spin power losses compared with other parameters such as oil temperature, gear module, and the direction of gear rotation. A physics-based gear pair spin power loss formulation that was proposed in a companion paper (Seetharaman and Kahraman, 2009, “Load-Independent Spin Power Losses of a Spur Gear Pair: Model Formulation,” ASME J. Tribol., 131, p. 022201) was used to simulate these experiments. Direct comparisons between the model predictions and measurements are provided at the end to demonstrate that the model is capable of predicting the measured spin power loss values as well as the measured parameter sensitivities reasonably well.

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

Simulation of the Rotational Vibration Response of a Spur Gear Pair With One Cracked Tooth

2000 ◽  
Author(s):  
Sidi M. Berri ◽  
J. M. Klosner
Keyword(s):  
Differential Equations ◽  
Power Transmission ◽  
Equations Of Motion ◽  
Spur Gear ◽  
Crack Size ◽  
Vibration Response ◽  
Time Varying ◽  
Gear Pair ◽  
Rotational Vibration ◽  
Tooth Pair

The present study introduces a developed simulator on rotational vibrations of a power transmission spur gear set with one cracked pinion tooth. The simulator computes the expected vibration response of the meshing gears by solving the differential equations of motion. In additions to accounting for the time-varying stiffness of the meshing tooth pair, the simulator also includes gear errors and damping. Dynamic tooth loads as a function of crack size are also computed. The simulated outputs depict precisely the experimental behaviors. Results for rotational vibrations of the power transmission system are presented as a function of crack size.

Effect of Face Width on Bending Stress of Spur Gear Using AGMA and FEA

2014 ◽  
Vol 945-949 ◽  
pp. 840-844
Author(s):  
Abdurrahman Ahmad Umar ◽  
Abdulrahaman Shuaibu Ahmad ◽  
Auwalu Gidado Yusuf ◽  
Zulfiqar Ibrahim Bibi Farouk
Keyword(s):  
Power Transmission ◽  
Spur Gear ◽  
Spur Gears ◽  
Bending Stress ◽  
Ansys Software ◽  
Modeling And Analysis ◽  
Face Width ◽  
Complex Design ◽  
Software Skills ◽  
Heavy Loads

Spur gears are widely used in industry where the power transmission is required at heavy loads with smoother and noiseless operation. The study in this paper shows that the complex design problem of spur gear requires superior software skills for modeling and analysis. The problem been has solved using Pro/E and ANSYS software which provides equivalent results to that of AGMA. In this paper, spur gear was modeled using Pro/Engineer wildfire 4.0 and stress analysis was carried out using ANSYS 11.0. The results obtained from both AGMA and FEM were compared and found to be approximately similar.

Strength Evaluation and Fatigue Prediction of a Spur Gear Pair by Computer Simulation

2006 ◽  
Author(s):  
Zhong Hu ◽  
Fereidoon Delfanian
Keyword(s):  
Computer Simulation ◽  
Mechanical Design ◽  
Gear Tooth ◽  
Three Dimensional ◽  
Spur Gear ◽  
Operating Conditions ◽  
Gear Pair ◽  
Working Cycle ◽  
Fatigue Design ◽  
Time Histories

Fatigue prediction of a three-dimensional mechanical component under dynamic load is critical for mechanical design. In this paper, computer simulation of three-dimensional dynamic stress followed by fatigue calculation was performed on a spur-gear pair using finite element modeling. Starting from gear pair geometry and operating conditions, the time histories of the dynamic loads and multi-axial stresses for a complete working cycle of a gear tooth were computed, and then post processed to produce fatigue strength information. Along with certain material properties obtained from experiments, this computer simulated fatigue design provides a useful tool for predicting fatigue failure of mechanical components.

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 Synthesis of Tooth Profile Shapes and Spur Gears of High Load Capacity

1970 ◽  
Vol 92 (3) ◽  
pp. 543-551 ◽  
Author(s):  
A. O. Lebeck ◽  
E. I. Radzimovsky
Keyword(s):  
Bending Strength ◽  
Load Capacity ◽  
High Capacity ◽  
High Hardness ◽  
Spur Gear ◽  
Speed Ratio ◽  
Spur Gears ◽  
Gear Pair ◽  
Contact Ratio ◽  
High Load Capacity

In this work a method is presented for the synthesis of high capacity noninvolute spur gears and tooth profiles. Two gear capacity criteria are used in the synthesis: (1) the capacity based on maximum allowable Hertz stress and (2) the capacity based on the bending strength of the tooth. These capacity criteria are related to a generalized noninvolute gear geometry which includes the factors number of teeth and contact ratio. It was found that there are certain optimal relationships which exist among the noninvolute parameters which lead to a solution, for a maximum capacity noninvolute gear pair. For a speed ratio of one to five it was found that a significant capacity advantage exists for the synthesized noninvolute gear pair (compared to a 20-deg involute spur gear pair) for moderate as well as high hardness values. For a speed ratio of one to one a capacity advantage was found for moderate hardness but the advantage decreased significantly for high hardness.

Evaluation of Spur Gear Pair on Tooth Root Bending Stress in Yawing Misalignment Contact Condition

2014 ◽  
Vol 980 ◽  
pp. 97-101 ◽  
Author(s):  
Mohd Rizal Lias ◽  
Mokhtar Awang ◽  
T.V.V.L.N. Rao ◽  
M. Fadhil
Keyword(s):  
Influence Factor ◽  
Spur Gear ◽  
Dynamics Simulation ◽  
Gear Pair ◽  
Tooth Root ◽  
Bending Stress ◽  
Time Dynamics ◽  
Gear Design ◽  
Face Width ◽  
Assembly Error

This paper evaluates the effects of yawing misalignment contact on the tooth root bending stress values of spur gear pair during the gear meshing cycle. A model basedon involute 3DparametricCAD geometry, of spur gear design ISO 6336:2006 is analyzed with worst loading position when yawing misalignment (Y) exist due to assembly error (AE) between 0.20 to 0.40 in degree scale values. Finite-element method (FEM) with dynamics module from ANSYS is used in order to calculate the tooth root bending stress (TRBS) at the critical region with respect to face width of pinion and gear section. A comparison is made between standard high point single tooth contactmodels (HPSTC) to this model as verification. Further analysis showeda good agreement that these methodologies are adequate in order to conduct a real time dynamics simulation to define the value of TRBS in Y condition due to AE. Yawingmisalignment influence factor (YMIF) was introduced as an indication of TRBS values in consideration of Y due to AEshows a higher result for pinion, give a good justification that the pinion is weaker compared to the gear in Y condition.

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.

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