Further Evaluation of Spur Gear Tooth Profile Designs Used in Heavily Loaded Transmissions

2011 ◽  
Author(s):  
Nihat Yıldırım ◽  
Hakan I˙s¸c¸i ◽  
Abdullah Akpolat
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Profile ◽  
Design Parameters ◽  
Preference Order ◽  
Spur Gears ◽  
Tooth Root ◽  
Contact Ratio ◽  
Practical Applications

Aerospace applications require special procedures for component design and manufacturing. Spur gears of different designs, because of their simpler geometries, are used in vital units-transmissions of helicopters and alike aerospace vehicles. In this study, performances of various profile designs of previously researched low and high contact ratio spur gears with some realistic design parameters are studied. Effects of the realistic parameters of variable tooth pair stiffness, relief shape, and adjacent pitch error on Transmission Error (TE), tooth loads and root stresses are presented; composition of these parameters determines the efficiency of the gearbox assembly. Detail of minimization of tooth root stress through optimized/proper design of relief is described. More comprehensive comparison of the gear tooth profile design cases is done to be able to guide aerospace transmission designers for practical applications with realistic parameters for each of the design cases. A preference order is done among the design cases, depending on effect of some design parameters on the results such as tooth loads, tooth root stresses, TE curves and peak-to-peak TE values.

scholarly journals Selection of Pressure Angle based on Dynamic Effects in Asymmetric Spur Gear with Fixed Normal Contact Ratio

2019 ◽  
Vol 69 (3) ◽  
pp. 303-310
Author(s):  
Benny Thomas ◽  
K. Sankaranarayansamy ◽  
S. Ramachandra ◽  
Suresh Kumar S.P.
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Dynamic Factor ◽  
Spur Gears ◽  
Contact Ratio ◽  
Normal Contact ◽  
Pressure Angle ◽  
Side Pressure ◽  
Static Transmission Error

Asymmetric spur gears are finding application in many fields including aerospace propulsion and automobile which demand unidirectional or relatively higher load on one side of the gear flank. Design intend to maximise the load carrying capacity of the drive side of asymmetric gear by increasing the pressure angle is achieved at the expense of coast side capacity. Multiple solution for coast to drive side pressure angle exist for a given contact ratio and each of these have relative merits and demerits. In the present work asymmetric spur gears of theoretically equal contact ratio as that of corresponding symmetric gears are selected to investigate the change in gear tooth static transmission error and dynamic behaviour with coast and drive side pressure angle. Study shows that dynamic factor of normal contact ratio asymmetric spur gears below resonance speed are relatively lower than corresponding symmetric gears of same module, contact ratio, number of teeth, coast side pressure angle and fillet radii. Results also show that, coast and drive side pressure angle can be suitably selected for a given contact ratio to reduce the single tooth and double tooth contact static transmission error and dynamic factor of asymmetric spur gears.

Explicit Parametric Method for Optimal Spur Gear Tooth Profile Definition

2013 ◽  
Vol 633 ◽  
pp. 87-102 ◽  
Author(s):  
Ivana Atanasovska ◽  
Radivoje Mitrovic ◽  
Dejan Momcilovic
Keyword(s):  
Gear Tooth ◽  
Load Capacity ◽  
Parametric Method ◽  
Spur Gear ◽  
Tooth Profile ◽  
Spur Gears ◽  
Element Analysis ◽  
Engineering Research ◽  
Profile Optimization ◽  
Current Engineering

The gear tooth profile has an immense effect on the main operating parameters of gear pairs (load capacity, working life, efficiency, vibrations, etc). In current engineering research and practice, there is a strong need to develop methods for tooth profile optimization. In this paper a new method for selecting the optimal tooth profile parameters of spur gears is described. This method has been named the Explicit Parametric Method (EPM). The addendum modification coefficient, radius of root curvature, and pressure angle of the basic rack for cylindrical gears, have been identified as the main tooth profile parameters of spur gears. Therefore, the EPM selects the optimal values for these three tooth profile parameters. Special attention has been paid to develop a method of adjustment for the particular working conditions and explicit optimization requirements. The EPM for optimal tooth profile parameters of gears uses contact nonlinear Finite Element Analysis (FEA) for calculation of deformations and stresses of gear pairs, in addition to explicit comparative diagrams for optimal tooth profile parameter selection.

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.

An Analytical Study of the Effect of the Contact Ratio on the Spur Gear Dynamic Response

1999 ◽  
Vol 122 (4) ◽  
pp. 508-514 ◽  
Author(s):  
Anette Andersson
Keyword(s):  
Dynamic Response ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Contact Ratio ◽  
Constant Stiffness ◽  
Gear Mesh ◽  
Critical Rotational Speed ◽  
Stiffness Variation ◽  
Gear Mesh Stiffness

A model was used, where the total gear mesh stiffness was approximated by two constant stiffness levels, in order to analyze the influence of the contact ratio on the dynamic response of spur gears. Due to the stiffness variation there is parametric excitation of the transmission error, which generally causes tooth separation at certain critical rotational speeds. The present paper discloses a method to analytically calculate which contact ratio to use in order to avoid tooth separation near a specific critical rotational speed. [S1050-0472(00)02604-0]

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.

Performance Rating and Optimization of Spur Gear Drives With Small Number of Teeth

2000 ◽  
Author(s):  
M. A. Sahir Arikan
Keyword(s):  
Gear Tooth ◽  
Spur Gear ◽  
Maximum Length ◽  
Performance Rating ◽  
Tooth Root ◽  
Contact Ratio ◽  
Geometry Factor ◽  
Factor I ◽  
Number Of Teeth ◽  
Gear Drives

Abstract Performance rating of spur gear drives with small number of teeth is made and variations of contact ratio, circular tooth thicknesses at pinion and gear tooth tips, lengths of the pinion addendum and dedendum portions of the line of action, AGMA geometry factor J for the pinion and the gear and their ratio, and AGMA geometry factor I with addendum modification coefficient are determined. Thus, it is made possible to design gear drives with properties such as, maximum possible contact ratio, maximum length of the pinion addendum portion of the line of action, maximum length of the pinion dedendum portion of the line of action, equal AGMA geometry factors J for the pinion and the gear (i.e. equal pinion and gear tooth root stresses), and maximum AGMA geometry factor I (i.e. minimum tooth contact stress). Rack cutter tip fillet radius and rack cutter geometry are considered in the analysis, which are the basic factors that determine the gear tooth fillet profile.

A Further Study on High Contact Ratio Spur Gears in Mesh With Double Scope Tooth Profile Modification

2007 ◽  
Author(s):  
Jiande Wang ◽  
Ian Howard
Keyword(s):  
Weight Ratio ◽  
Transmission Error ◽  
Tooth Profile ◽  
Spur Gears ◽  
Contact Ratio ◽  
Profile Modification ◽  
Tooth Profile Modification ◽  
Major Interest ◽  
Higher Power ◽  
Lower Transmission

Compared to the commonly used Low Contact Ratio Spur Gears (LCRG), High Contact Ratio Spur Gears (HCRG) can provide higher power to weight ratio, and can also achieve smoother running with lower Transmission Error (TE) variations. To achieve the benefits of High Contact Ratio Spur Gears (HCRG), its tolerance to manufacturing errors and elastic deformation has to be increased. After various attempts by previous researchers, double scope tooth profile modifications have been seen as being of major interest showing great potential for improvements in most applications. Research presented in this paper concentrated on providing further proofs and verifications on the topic by using modern numerical methods and comprehensive analysis. Additionally, a general Bulk Tooth Rotation (BTR) type tooth profile modification is introduced and applied to the High Contact Ratio Spur Gears (HCRG) in order to improve the tooth profile design and some common higher order analysis is shown allowing further comments to be made.

scholarly journals Dynamic Tooth Loads and Stressing for High Contact Ratio Spur Gears

1978 ◽  
Vol 100 (1) ◽  
pp. 69-76 ◽  
Author(s):  
R. W. Cornell ◽  
W. W. Westervelt
Keyword(s):  
Dynamic Model ◽  
Gear Tooth ◽  
Closed Form Solution ◽  
Time History ◽  
Spur Gear ◽  
Form Solution ◽  
Tooth Profile ◽  
Contact Ratio ◽  
Modification System ◽  
Work Done

A time history, closed form solution is presented for a dynamic model of spur gear systems for all practical contact ratios. The analysis determines the dynamic response of the gear system and the associated tooth loads and stressing. The dynamic model is based on work done by Richardson and Howland [2, 3], and assumes the two gears act as a rigid inertia and the teeth act as a variable spring of a dynamic system excited by the meshing action of the teeth. Included in the analysis are the effects of the non-linearity of the tooth pair stiffness during mesh, the tooth errors, and the tooth profile modifications. Besides reviewing the features, solution, and program of this analysis, preliminary results from applying the analysis are presented, which show that tooth profile modification, system inertia and damping, and system critical speeds can affect the dynamic gear tooth loads and stressing significantly.

The Influence of Gear Design Parameters on Gear Tooth Damage Detection Sensitivity

2002 ◽  
Vol 124 (4) ◽  
pp. 794-804 ◽  
Author(s):  
Lin Liu ◽  
Darryll J. Pines
Keyword(s):  
Damage Detection ◽  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Detection Sensitivity ◽  
Design Parameters ◽  
Gear Design ◽  
Gear Mesh ◽  
Pressure Angle ◽  
Number Of Teeth

This paper develops an analytical model to simulate the gear mesh contact for a spur gear pair with and without tooth damage. Three common gear tooth faults are simulated including pitting, wear and root cracks. The effect of tooth face width on detection sensitivity for pitting and the effect of crack width on detection sensitivity for crack are investigated. Using static performance measures, such as transmission error, results suggest that basic gear design parameters, such as diametral pitch, pressure angle and number of teeth, may have a significant effect on damage detection sensitivity. It appears that a decrease in diametral pitch will enhance damage detection sensitivity for all the three types of damage. An increase in pressure angle or number of teeth will enhance detection sensitivity for pitting damage, but tends to decrease the sensitivity to crack or wear damage.

Dynamic Load Analysis of Spur Gears Using a New Tooth Profile

1996 ◽  
Vol 118 (1) ◽  
pp. 1-6 ◽  
Author(s):  
K. Y. Yoon ◽  
S. S. Rao
Keyword(s):  
Dynamic Load ◽  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Profile ◽  
Spur Gears ◽  
Gear Drive ◽  
Novel Method ◽  
Static Transmission Error ◽  
Load Analysis ◽  
Gear Profile

A novel method was presented by the authors to minimize the static transmission error using cubic splines (C.S.) for gear tooth profile. A reduction in the transmission error is expected to reduce the gear vibration and noise by lowering the dynamic tooth load in a meshing cycle. To establish this fact, a dynamic analysis of the gear drive with involute tooth and modified tooth profiles (using C.S.) is performed. For this, first the tooth deformation is found and then the tooth dynamic load is determined for all reasonable speeds. A parametric study is conducted to establish the superiority of the C.S. based gear profile over the involute profile as well as the other profiles based on the use of linear and parabolic tip reliefs.

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