Determination of Addendum Modification Coefficients for Spur Gears Operating at Non-Standard Center Distances

2003 ◽  
Author(s):  
M. A. Sahir Arikan
Keyword(s):  
Gear Tooth ◽  
Gear Ratio ◽  
Spur Gears ◽  
Contact Ratio ◽  
Performance Variables ◽  
Practical Design ◽  
Gear Drives ◽  
Maximum Contact ◽  
Center Distance

Although it is possible to find some recommended conventional values both for the sum of the addendum modification coefficients and for the allocation of the sum of the addendum modification coefficients (e.g. ISO/TR 4467), a detailed analysis is necessary to determine the addendum modification coefficient values for the desired optimization criteria and the performance since the main objective of the above mentioned sources is to facilitate practical design of non-standard gear drives which will not have problems while operating. They give practical average values within a safe range. In this study, by considering the required gear ratio, center distance and the desired backlash, alternative gear pairs are determined and corresponding gear performance variables are calculated in order to allocate the addendum modification coefficients for the pinion and the gear by using criteria such as: not having undercut or pointed (or excessively-thinned-tip) tooth, having desired proportions for the lengths of the dedendum and addendum portions of the line of action, having maximum contact ratio, having sufficient bottom clearance, having minimum contact stresses, having balanced pinion and gear tooth root stresses, having equal pinion and gear lives, etc.

scholarly journals Design of Electrically Powered Morphing Winglet

2021 ◽  
Author(s):  
Kunj Mistry
Keyword(s):  
Material Selection ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Stepper Motor ◽  
Spur Gears ◽  
Input Shaft ◽  
Gear Drive ◽  
Electrical Actuator ◽  
Gear Drives

Cycloidal and planetary gear drives are considered for the actuation of an electrically powered morphing winglet. A torque of 6723 N*m is required at the winglet hinge. The stepper motor selected as the electrical actuator is the HT34-487 stepper motor. This motor can provide a torque of approximately 6 N*m. The cycloidal drive consists of the selected stepper motor, a bevel gearbox, and a two-stage cycloidal gearbox. The bevel gearbox is used to change the axis of rotation of the stepper motor from span-wise direction to chord-wise direction. Stage one of the cycloidal gearbox contains an input shaft, two cycloidal disks with 180 degrees offset rotation, an eccentric cam and an output shaft. The cycloidal disks in stage one have 35 lobes, providing a gear ratio of 35:1. The second stage of the cycloidal gearbox consists of only one cycloidal disk with 34 lobes, providing a gear ratio of 34:1. The total gear ratio of the cycloidal drive is 1190:1. Material selection and FEA simulations are performed on the components in the cycloidal drive to ensure the selected materials can withstand the applied loads. A differential planetary gear drive is also considered to actuate an electrically powered morphing winglet. Spur gears are selected to be used as the sun and planet gears. A ratio of 180:1 is achieved in the planetary gear drive. Using gear tooth bending calculators, it is found that designing spur gears to withstand the loads of the electrically powered morphing winglet and to fit inside the dimensions of the wingbox is not feasible.

Optimization of fillet stress to enhance the bending strength through non-standard high contact ratio spur gears

2015 ◽  
Vol 230 (7-8) ◽  
pp. 1139-1148 ◽  
Author(s):  
P Marimuthu ◽  
G Muthuveerappan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Parametric Study ◽  
Bending Strength ◽  
Spur Gear ◽  
Gear Ratio ◽  
Spur Gears ◽  
Contact Ratio ◽  
Element Analysis ◽  
Gear Drives

The present study aims to determine the improvement in the bending strength of the non-standard high contact ratio spur gears based on the balanced (optimum) fillet stress of the pinion and gear. The average number teeth in contact is more than two for high contact ratio gear drives. In the non-standard high contact ratio spur gears, the rack cutter tooth thickness factor is more than 0.5, whereas the standard rack cutter tooth thickness factor is 0.5. The maximum fillet stresses of the pinion and gear is not equal for non-standard high contact ratio spur gear drives when the gear ratio increases. In order to avoid the fatigue failure of the gear, the fillet stresses of the pinion and gear should be balanced. This balanced stress is predicted as the optimum fillet stress. Hence, the present study focuses to optimize the fillet stress with respect to the rack cutter tooth thickness factor of the pinion and gear through finite element analysis. Also, a parametric study is carried out to obtain the influence of some gear parameters, such as gear ratio, teeth number in the pinion, pressure angle, addendum height and corrected gear drives (S+, S− and So) on the optimum fillet stress with respect to the rack cutter tooth thickness factor of the pinion and gear.

scholarly journals Design of Electrically Powered Morphing Winglet

2021 ◽  
Author(s):  
Kunj Mistry
Keyword(s):  
Material Selection ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Stepper Motor ◽  
Spur Gears ◽  
Input Shaft ◽  
Gear Drive ◽  
Electrical Actuator ◽  
Gear Drives

Cycloidal and planetary gear drives are considered for the actuation of an electrically powered morphing winglet. A torque of 6723 N*m is required at the winglet hinge. The stepper motor selected as the electrical actuator is the HT34-487 stepper motor. This motor can provide a torque of approximately 6 N*m. The cycloidal drive consists of the selected stepper motor, a bevel gearbox, and a two-stage cycloidal gearbox. The bevel gearbox is used to change the axis of rotation of the stepper motor from span-wise direction to chord-wise direction. Stage one of the cycloidal gearbox contains an input shaft, two cycloidal disks with 180 degrees offset rotation, an eccentric cam and an output shaft. The cycloidal disks in stage one have 35 lobes, providing a gear ratio of 35:1. The second stage of the cycloidal gearbox consists of only one cycloidal disk with 34 lobes, providing a gear ratio of 34:1. The total gear ratio of the cycloidal drive is 1190:1. Material selection and FEA simulations are performed on the components in the cycloidal drive to ensure the selected materials can withstand the applied loads. A differential planetary gear drive is also considered to actuate an electrically powered morphing winglet. Spur gears are selected to be used as the sun and planet gears. A ratio of 180:1 is achieved in the planetary gear drive. Using gear tooth bending calculators, it is found that designing spur gears to withstand the loads of the electrically powered morphing winglet and to fit inside the dimensions of the wingbox is not feasible.

Analytical Model of the Efficiency of Spur Gears: Study of the Influence of the Design Parameters

2011 ◽  
Author(s):  
Miguel Pleguezuelos ◽  
Jose´ I. Pedrero ◽  
Miryam B. Sa´nchez
Keyword(s):  
Load Distribution ◽  
Gear Ratio ◽  
Design Parameters ◽  
Spur Gears ◽  
Transmitted Power ◽  
Power Losses ◽  
Contact Ratio ◽  
Complete Study ◽  
Uniform Model ◽  
Analytical Expressions

An analytic model to compute the efficiency of spur gears has been developed. It is based on the application of a non-uniform model of load distribution obtained from the minimum elastic potential criterion and a simplified non-uniform model of the friction coefficient along the path of contact. Both conventional and high transverse contact ratio spur gears have been considered. Analytical expressions for the power losses due to friction, for the transmitted power and for the efficiency are presented. From this model, a complete study of the influence of some design parameters (as the number of teeth, the gear ratio, the pressure angle, the addendum modification coefficient, etc.) on the efficiency is presented.

scholarly journals An experimental method to measure gear tooth stiffness throughout and beyond the path of contact

2001 ◽  
Vol 215 (7) ◽  
pp. 793-803 ◽  
Author(s):  
R. G. Munro1 ◽  
D Palmer ◽  
L Morrish
Keyword(s):  
Gear Tooth ◽  
Contact Region ◽  
Transmission Error ◽  
Spur Gears ◽  
Contact Ratio ◽  
Extended Contact ◽  
Tooth Stiffness ◽  
Simplifying Assumptions ◽  
Tooth Pair ◽  
Usual Problem

A method is presented that allows the accurate measurement of the tooth pair stiffness of a pair of spur gears. The method reveals the stiffness behaviour throughout the full length of the normal path of contact and also into the extended contact region when tooth corner contact occurs. The method makes use of the properties of transmission error plots for mean and alternating components over a range of tooth loads (Harris maps). It avoids the usual problem when measuring tooth deflections that deflections of other test rig components are difficult to eliminate. Also included are predicted Harris maps for a pair of high contact ratio spur gears, showing the effects of various simplifying assumptions, together with a measured map.

scholarly journals Optimal Tooth Numbers for Compact Standard Spur Gear Sets

1982 ◽  
Vol 104 (4) ◽  
pp. 749-757 ◽  
Author(s):  
M. Savage ◽  
J. J. Coy ◽  
D. P. Townsend
Keyword(s):  
Optimal Design ◽  
Objective Function ◽  
Design Space ◽  
Spur Gear ◽  
Gear Ratio ◽  
Contact Ratio ◽  
Bending Fatigue ◽  
Gear Mesh ◽  
Compact Design ◽  
Center Distance

The design of a standard gear mesh is treated with the objective of minimizing the gear size for a given ratio, pinion torque, and allowable tooth strength. Scoring, pitting fatigue, bending fatigue, and the kinematic limits of contact ratio and interference are considered. A design space is defined in terms of the number of teeth on the pinion and the diametral pitch. This space is then combined with the objective function of minimum center distance to obtain an optimal design region. This region defines the number of pinion teeth for the most compact design. The number is a function of the gear ratio only. A design example illustrating this procedure is also given.

scholarly journals Analytical Expressions of the Efficiency of Standard and High Contact Ratio Involute Spur Gears

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Miguel Pleguezuelos ◽  
José I. Pedrero ◽  
Miryam B. Sánchez
Keyword(s):  
Friction Coefficient ◽  
Contact Point ◽  
Load Sharing ◽  
Gear Ratio ◽  
Spur Gears ◽  
Contact Ratio ◽  
Transmission Parameters ◽  
Constant Friction ◽  
Analytical Expressions ◽  
Approximate Expressions

Simple, traditional methods for computation of the efficiency of spur gears are based on the hypotheses of constant friction coefficient and uniform load sharing along the path of contact. However, none of them is accurate. The friction coefficient is variable along the path of contact, though average values can be often considered for preliminary calculations. Nevertheless, the nonuniform load sharing produced by the changing rigidity of the pair of teeth has significant influence on the friction losses, due to the different relative sliding at any contact point. In previous works, the authors obtained a nonuniform model of load distribution based on the minimum elastic potential criterion, which was applied to compute the efficiency of standard gears. In this work, this model of load sharing is applied to study the efficiency of both standard and high contact ratio involute spur gears (with contact ratio between 1 and 2 and greater than 2, resp.). Approximate expressions for the friction power losses and for the efficiency are presented assuming the friction coefficient to be constant along the path of contact. A study of the influence of some transmission parameters (as the gear ratio, pressure angle, etc.) on the efficiency is also presented.

Computer Aided Analysis of Bending Strength of Involute Spur Gears with Asymmetric Profile

2004 ◽  
Vol 127 (3) ◽  
pp. 477-484 ◽  
Author(s):  
Kadir Cavdar ◽  
Fatih Karpat ◽  
Fatih C. Babalik
Keyword(s):  
Computer Program ◽  
Bending Strength ◽  
Spur Gears ◽  
Bending Stress ◽  
Contact Ratio ◽  
Computer Aided Analysis ◽  
Tooth Form ◽  
Stress Concentration Factors ◽  
Stress Minimization

This paper presents a method for the determination of bending stress minimization of involute spur gears. A computer program has been developed to investigate the variation of bending stress and contact ratio depending on the pressure angle on the drive side. Since asymmetric tooth is not standard, the tooth model, which was introduced by DIN 3990/Method C and ISO/TC 60, has been adjusted for asymmetric tooth by the authors. The determination of the tooth form and stress concentration factors for asymmetric tooth has been accomplished for each different parameter (pressure angles, tool radius, rack shift, etc.). The sample results, which were obtained by using a developed computer program, are illustrated with numerical examples.

The Design, Generation, and Simulation of Meshing of Worm-Gear Drive With Longitudinally Localized Contacts

2000 ◽  
Vol 122 (2) ◽  
pp. 201-206 ◽  
Author(s):  
I. H. Seol
Keyword(s):  
Computer Program ◽  
Longitudinal Direction ◽  
Worm Gear ◽  
Contact Ratio ◽  
Transmission Errors ◽  
Gear Drive ◽  
Bearing Contact ◽  
Design Generation ◽  
Gear Drives

The design and simulation of meshing of a single enveloping worm-gear drive with a localized bearing contact is considered. The bearing contact has a longitudinal direction and two branches of contact path. The purpose of localization is to reduce the sensitivity of the worm-gear drive to misalignment. The author’s approach for localization of bearing contact is based on the proper mismatch of the surfaces of the hob and drive worm. The developed computer program allows the investigation of the influence of misalignment on the shift of the bearing contact and the determination of the transmission errors and the contact ratio. The developed approach has been applied for K type of single-enveloping worm-gear drives and the developed theory is illustrated with a numerical example. [S1050-0472(00)00502-X]

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