Optimisation of Geometric Parameters of Gears under Variable Loading Condition

2012 ◽  
Vol 445 ◽  
pp. 1005-1010 ◽  
Author(s):  
Mehmet Bozca ◽  
Ferhat Dikmen
Keyword(s):  
Contact Stress ◽  
Loading Condition ◽  
Helix Angle ◽  
Geometric Parameters ◽  
Design Parameters ◽  
Bending Stress ◽  
Variable Loading ◽  
Face Width ◽  
Matlab Program ◽  
Tooth Modification

Optimisation of geometric parameters of gears under variable loading condition is studied. Bending stress is considered as objective function and contact stress is considered as constraint function. Bending stress and contact stress are calculated depending on zero tooth modification, positive tooth modification and negative tooth modification by using developed MATLAB program respectively. Obtained results are compared and presented graphically. It is concluded that tooth modification is effective parameter for optimisation of geometric parameters of gears under variable loading condition. By optimising the geometric parameters of the gears, such as, the module, number of teeth, helix angle, and face width, it is possible to obtain a light-weight-gears structures. All optimised geometric design parameters also satisfy all constraints.

Comparative study of stress analysis of gears with different helix angle using the ISO 6336 standard and tooth contact analysis methods

2016 ◽  
Vol 230 (7-8) ◽  
pp. 1350-1358 ◽  
Author(s):  
Layue Zhao ◽  
Robert C Frazer ◽  
Brian Shaw
Keyword(s):  
Stress Analysis ◽  
Contact Stress ◽  
Helix Angle ◽  
Contact Analysis ◽  
Bending Stress ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Iso Standard ◽  
Analysis Methods

With increasing demand for high speed and high power density gear applications, the need to optimise gears for minimum stress, noise and vibration becomes increasingly important. ISO 6336 contact and bending stress analysis are used to determine the surface load capacity and tooth bending strength but dates back to 1956 and although it is constantly being updated, a review of its performance is sensible. Methods to optimise gear performance include the selection of helix angle and tooth depth to optimise overlap ratio and transverse contact ratio and thus the performance of ISO 6336 and tooth contact analysis methods requires confirmation. This paper reviews the contact and bending stress predicted with four involute gear geometries and proposes recommendations for stress calculations, including a modification to contact ratio factor Zɛ which is used to predict contact stress and revisions to form factor YF and helix angle factor Yβ which are cited to evaluate bending stress. The results suggest that there are some significant deviations in predicted bending and contact stress values between proposal methods and original ISO standard. However, before the ISO standard is changed, the paper recommends that allowable stress numbers published in ISO 6336-5 are reviewed because the mechanisms that initiate bending and contact fatigue have also changed and these require updating.

scholarly journals Effect of Helix Angle on the Gear Design Parameters in Helical Gears

2019 ◽  
Vol 8 (10) ◽  
pp. 887-890
Keyword(s):  
Helix Angle ◽  
Contact Stresses ◽  
Design Parameters ◽  
Screw Compressor ◽  
Bending Stress ◽  
Contact Ratio ◽  
Helical Gears ◽  
Gear Design ◽  
Overlap Ratio ◽  
Lower Noise

Screw compressor demands quite operation. For getting lower noise it is important to have higher contact ratio. Contact ratio can be increased by increasing the Helix angle i .e. indirectly increasing overlap ratio. The paper represents the effect of change in design parameters with respect to helix angle with the keeping same module and same centre distance. Higher helix angle leads lower bending and contact stresses. The study was conducted for screw electrical compressor. Gear was design for fixed parameters except helix angle. Also the contact stresses are analyzed (FEA) on ANSYS. The result from the calculation and FEA are compared for contact stress as well as bending stress.

Design of Equipment for Manufacturing Helically-Coiled Tubes and its Automatic Control System

2010 ◽  
Author(s):  
Chang-Nian Chen ◽  
Ji-Tian Han ◽  
Li Shao ◽  
Tien-Chien Jen ◽  
Yi-Hsin Yen
Keyword(s):  
Control System ◽  
Automatic Control ◽  
Automatic Control System ◽  
Helix Angle ◽  
Geometric Parameters ◽  
Design Parameters ◽  
Helical Axis ◽  
Loop Control ◽  
Coil Diameter ◽  
Mean Square Errors

A simple but accurate method for manufacturing helically-coiled tubes was proposed, and the manufacturing equipment and its automatic control system were designed. The main geometric parameters of helically-coiled tubes are determined exactly based on the theorem “three given points determine a circle” and the definition of the helix angle of helically-coiled tubes. The finished equipment primarily consists of the mechanical noumenon and the automatic control system. In this design, three die wheels A, B and C made of wearable steel are used to adjust the positions of the raw materials in order to determine the product geometric parameters expected in advance. Three servo motors working with precision linear sliding rheostat and PID closed-loop control functions drive the three wheels mentioned above in different directions. The parameter e determining the base circle diameter of coil diameter is obtained by adjusting the position of wheel C up and down, and the parameter e’ determining the helix angle is obtained by adjusting the relative distance between wheel B and wheel A in the helical axis direction. The whole manufacture process is automatically controlled by a piece of software compiled by Visual Basic, including the processes of baiting and cutting, installing wheels and calibration, motor controlling, bending tubes, and product inspection etc. The design parameters for manufacturing helically-coiled tubes using SUS304 stainless steel or other similar materials are tube diameters of 6–50 mm, coil diameters of 100–700 mm and helical pitches of 10–50 mm. A total of fourteen finished products were selected as random samples for inspection. The result showed that the average working velocity was about 0.6 m/min; the root mean square errors (RMSE) of coil diameter and helical pitch of finished products were 3.85 mm and 0.97 mm, respectively; and the maximum roundness error of tubes was only 0.09 mm.

scholarly journals Contact stress in helical bevel gears

2021 ◽  
Vol 49 (3) ◽  
pp. 519-533
Author(s):  
Edward Osakue ◽  
Lucky Anetor ◽  
Kendall Harris
Keyword(s):  
Contact Stress ◽  
Helix Angle ◽  
Spur Gear ◽  
Helical Gear ◽  
Design Parameters ◽  
Bevel Gears ◽  
Capacity Model ◽  
Previous Solution ◽  
The Common ◽  
Spiral Angle

Helical bevel gears have inclined or twisted teeth on a conical surface and the common types are skew, spiral, zerol, and hypoid bevel gears. However, this study does not include hypoid bevel gears. Due to the geometric complexities of bevel gears, commonly used methods in their design are based on the concept of equivalent or virtual spur gear. The approach in this paper is based on the following assumptions, a) the helix angle of helical bevel gears is equal to mean spiral angle, b) the pitch diameter at the backend is defined as that of a helical gear, and c) the Tredgold's approximation is applied to the helical gear. Upon these premises, the contact stress capacity of helical bevel gears is formulated in explicit design parameters. The new contact stress capacity model is used to estimate the contact stress in three gear systems for three application examples and compared with previous solutions. Differences between the new estimated results and the previous solutions vary from -3% and -11%, with the new estimates being consistently but marginally or slightly lower than the previous solution values. Though the differences appear to be small, they are significant because the durability of gears is strongly influenced by the contact stress. For example, a 5% reduction in contact stress may result in almost 50% increase in durability in some steel materials. The equations developed do not apply to bevel crown gears.

Design and Fatigue Analysis of an E-Drive Transmission System of Single-Speed Gear for Electric Vehicle

2020 ◽  
Vol 48 ◽  
pp. 92-107
Author(s):  
Hailemariam Nigus Hailu ◽  
Daniel Tilahun Redda
Keyword(s):  
Failure Modes ◽  
Helix Angle ◽  
Simulation Software ◽  
Design Parameters ◽  
Repeated Loading ◽  
Safety Factors ◽  
Gear Teeth ◽  
Face Width ◽  
Alloy Steels ◽  
Transmission Gear

Design an e-drive transmi ssion gear , it is very crucial, to understand the failure modes since gears should be sized correctly to withstand loads that will expect to act on the gear teeth and make sure that still be within reasonable load-carrying capacity, compact and light weight. Fatigue failure can happen on gears under repeated loading due to fatigue such as tooth root bend ing and contact stress of gear. M aterials used in this study were two candidate alloy steels of Cr-Mo and Cr-Mo-Ni and methods employed to design the e-drive transmission gear were by iteration through KISSsoft gear simulation software as well as AGMA of Matlab script, it approaches various parameters such as helix angle, face- width , and input torque . Investigations on safety factors of root bending and contact , stresses of contact and bending , weight, compactness, qui e t and smooth functioning have been done by altering the variable design parameters . To conclude that by increasing face width and helix angle both safety factors were increased uniformly regardless of the in put torque as we calculated by both approaches. Similarly , the results showed that by increasing the helix angle and face width it brings to reduce the contact and bending stress es of transmission gear . As we comparing the results , the KISSsoft values are a little higher than the analytical (AGMA) values as proven in all fatigue of safety factors versus variable gear design parameter. Based on the sa fety factor, compactness, light weight and quiet for smooth function of the designed e-drive mating gears are proven as the face width is 24.5 mm and the helix angle is 25 o .

Contact Stress Analysis of a Helical Gear

2015 ◽  
Vol 766-767 ◽  
pp. 1070-1075 ◽  
Author(s):  
R. Devaraj
Keyword(s):  
Stress Analysis ◽  
Contact Stress ◽  
Gear Tooth ◽  
Element Model ◽  
Helix Angle ◽  
Helical Gear ◽  
Bending Stress ◽  
Helical Gears ◽  
Modeling Software ◽  
Main Factors

The main factors that cause the failure of gears are the bending stress and contact stress of the gear tooth. Out of these, failure of gears due to contact stress is high compared to bending stress. Stress analysis has been a key area of research to minimize failure and optimize design. This paper gives a finite element model for introspection of the stresses in the tooth during the meshing of gears. Specifically, helix angle is important for helical gears. Using modeling software, 3-D models for different helix angles in helical gears were generated, and the simulation was performed using ANSYS 12.0 to estimate the contact stress. The Hertz equation and AGMA standard was used to calculate the contact stress. The results of the theoretical contact stress values, using Hertz and AGMA are compared with the stress values from the FEA for different helix angles and the results are tabulated and discussed.

scholarly journals Contact Stresses and Bending stresses for Worm & Helical Gear

2019 ◽  
Vol 8 (4) ◽  
pp. 11326-11328
Keyword(s):  
Contact Stress ◽  
Applied Load ◽  
Gear Tooth ◽  
Helical Gear ◽  
Contact Stresses ◽  
Bending Stress ◽  
Surface Strength ◽  
Face Width ◽  
The Face ◽  
Bending Stresses

Surface Strength of the gear tooth depends on the contact stress and the bending stress caused due to the applied load on the tip of its gear tooth. Analysis has become popular in decreasing the failures. Fatigue causes in the root bending stress and Surface indentation causes in the contact stress. Then modified Lewis beam strength is used for bending stress and the AGMA method is used for contact stresses by varying the face width. Analytical results are based on Lewis formula and the theoretical values were calculated by AGMA standard so the results were validated.

scholarly journals Maximizing Transfer Efficiency with an Adaptive Wireless Power Transfer System for Variable Load Applications

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1417
Author(s):  
Jung-Hoon Cho ◽  
Byoung-Hee Lee ◽  
Young-Joon Kim
Keyword(s):  
Loading Condition ◽  
Wireless Power Transfer ◽  
Input Voltage ◽  
Transfer Efficiency ◽  
Maximum Efficiency ◽  
Variable Load ◽  
Power Transfer ◽  
Wireless Power ◽  
Variable Loading ◽  
Power Transfer Efficiency

Electronic devices usually operate in a variable loading condition and the power transfer efficiency of the accompanying wireless power transfer (WPT) method should be optimizable to a variable load. In this paper, a reconfigurable WPT technique is introduced to maximize power transfer efficiency in a weakly coupled, variable load wireless power transfer application. A series-series two-coil wireless power network with resonators at a frequency of 150 kHz is presented and, under a variable loading condition, a shunt capacitor element is added to compensate for a maximum efficiency state. The series capacitance element of the secondary resonator is tuned to form a resonance at 150 kHz for maximum power transfer. All the capacitive elements for the secondary resonators are equipped with reconfigurability. Regardless of the load resistance, this proposed approach is able to achieve maximum efficiency with constant power delivery and the power present at the load is only dependent on the input voltage at a fixed operating frequency. A comprehensive circuit model, calculation and experiment is presented to show that optimized power transfer efficiency can be met. A 50 W WPT demonstration is established to verify the effectiveness of this proposed approach.

Improving the Characteristics of Gear Pumps: Part A — Discharge

2003 ◽  
Author(s):  
Ahmed M. M. El-Bahloul ◽  
Yasser Z. R. Ali
Keyword(s):  
Correction Factor ◽  
Helix Angle ◽  
Tooth Profile ◽  
Radius Of Curvature ◽  
Circular Arc ◽  
Pressure Angle ◽  
Face Width ◽  
Angle Change ◽  
Number Of Teeth ◽  
Gear Pumps

The main objective of this paper is to study the effect of gear geometry on the discharge of gear pumps. We have used gears of circular-arc tooth profile as gear pumps and have compared between these types of gearing and spur, helical gear pumps according to discharge. The chosen module change from 2 to 16 mm, number of teeth change from 8 to 20 teeth, pressure angle change from 10 to 30 deg, face width change from 20 to 120 mm, correction factor change from −1 to 1, helix angle change from 5 to 30 deg, and radii of curvature equal 1.4, 1.5, 2, 2.5, 2.75, and 3m are considered. The authors deduced that the tooth rack profile with radius of curvature equal 2.5, 2.75, 3m for all addendum circular arc tooth and convex-concave tooth profile, and derived equations representing the tooth profile, and calculated the points of intersections between curves of tooth profile. We drive the formulas for the volume of oil between adjacent teeth. Computer program has been prepared to calculate the discharge from the derived formulae with all variables for different types of gear pumps. Curves showing the change of discharge with module, number of teeth, pressure angle, face width, correction factor, helix angle, and radius of curvature are presented. The results show that: 1) The discharge increases with increasing module, number of teeth, positive correction factor, face width and radius of curvature of the tooth. 2) The discharge increases with increasing pressure angle to a certain value and then decreases with increasing pressure angle. 3) The discharge decreases with increasing helix angle. 4) The convex-concave circular-arc gears gives discharge higher than that of alla ddendum circular arc, spur, and helical gear pumps respectively. 5) A curve fitting of the results are done and the following formulae derived for the discharge of involute and circular arc gear pumps respectively: Q=A1bm2z0.895e0.065xe0.0033αe−0.0079βQ=A2bm2z0.91ρ10.669e−0.0047β

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