Effects of Carburized Part, Helix Angle and Face Width on Residual Stresses of Case-Hardened Helical Gears

This paper investigates the windage power losses generated by helical gears rotating in pure air based on experimental results and a computational fluid dynamic code. It is found that the simulated flow patterns are totally different from those calculated for spur gears and that both tooth face width and helix angle are influential. The windage losses derived from Dawson’s and Townsend’s formulae are critically assessed using computational fluid dynamic results thus highlighting the limits of a unique formulation for accurate windage loss prediction. Finally, an analytical approach is suggested which gives good results providing that the flow rates at the boundaries of the inter-tooth domains can be estimated.

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Analysis of time-varying friction excitations in helical gears with refined general formulation

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406215583886 ◽

2015 ◽

Vol 229 (13) ◽

pp. 2467-2483 ◽

Cited By ~ 2

Author(s):

Hanjun Jiang

Keyword(s):

Friction Force ◽

Contact Line ◽

Sliding Friction ◽

Helix Angle ◽

Universal Method ◽

Time Varying ◽

Contact Ratio ◽

Friction Forces ◽

Helical Gears ◽

Face Width

Time-varying sliding friction force and friction torque are regarded as non-negligible excitation sources of vibration and noise in gears. The sliding friction force primarily excites the motion along the off-line-of-action direction, which transmits vibration to the housing through shafts and bearings and then radiates noise. Since the contact line intersects with the pitch line, and the directions of the friction forces are opposite on both sides of the pitch line, the calculation of the friction excitations in helical gears becomes more difficult, especially in the high contact ratio helical gears. However, there is no universal method for calculating the friction excitations in helical gears with different range of contact ratio. The changes of friction excitations in helical gears are highly dependent on the geometric parameters such as helix angle and face width among others. Yet, there exist very limited studies on these topics. In this study, a refined general formulation for the calculation of time-varying contact line and friction excitations is proposed by assuming uniform load distribution along the contact lines with time-varying normal force and friction coefficient. Key gear parameters such as modification coefficient, helix angle, and face width are analyzed to illustrate their effects on the time-varying contact line and friction excitations. The results demonstrate that the refined general formulation is effective for the calculation of the friction excitations in helical gears with different range of contact ratio, and the parametric analysis could supply some guidance for choosing gear parameters in the design of helical gears to reduce the friction excitations.

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Influence of Profile Modification and Lubricant Viscosity on Scoring of Helical Gears

Journal of Engineering for Industry ◽

10.1115/1.3438332 ◽

1974 ◽

Vol 96 (1) ◽

pp. 71-77

Author(s):

T. Matsunaga

Keyword(s):

Testing Machine ◽

Normal Pressure ◽

Helix Angle ◽

Power Circuit ◽

Helical Gears ◽

Profile Modification ◽

Face Width ◽

Carburized Steel ◽

Load Carrying ◽

Lubricant Viscosity

Scoring limit of helical gears made of carburized steel is investigated experimentally. Gear testing machine used for the tests is a closed power circuit type and designed for operation up to 23,000 rpm. All tests are made with pairs of 14 and 141-tooth gears of 3-module, 20-deg normal pressure angle, 29.066-deg helix angle, and 30-mm face width. The effect of profile modification on the scoring limit is investigated, and the effects of lubricant viscosity and location of oil supply nozzle are investigated in connection with the effect of profile modification. Three kinds of lubricants of various viscosity ordinarily used in a gear system are tested (lubricant viscosity: 32, 53, 70 cSt at 40 C). Load carrying capacity of the lubricant of the highest viscosity is higher by 25 percent than that of the lowest one. But the effect of modification is much larger than that of lubricant viscosity.

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Design Method of Vibrationally Optimum Tooth Flank Form for Involute Helical Gears with Scattering in Pressure Angle and Helix Angle Deviation.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C ◽

10.1299/kikaic.66.1959 ◽

2000 ◽

Vol 66 (646) ◽

pp. 1959-1966 ◽

Cited By ~ 5

Author(s):

Masaharu KOMORI ◽

Aizoh KUBO ◽

Yoshiki KAWASAKI

Keyword(s):

Design Method ◽

Helix Angle ◽

Helical Gears ◽

Pressure Angle ◽

Angle Deviation ◽

Tooth Flank

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Improving the Characteristics of Gear Pumps: Part A — Discharge

Volume 4: 9th International Power Transmission and Gearing Conference, Parts A and B ◽

10.1115/detc2003/ptg-48119 ◽

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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Enhanced application limits for crossed helical gearboxes using new geometries for smaller sliding paths or smaller contact pressures

MATEC Web of Conferences ◽

10.1051/matecconf/201928701010 ◽

2019 ◽

Vol 287 ◽

pp. 01010

Author(s):

Christoph Boehme ◽

Dietmar Vill ◽

Peter Tenberge

Keyword(s):

Calculation Method ◽

Helix Angle ◽

Helical Gear ◽

Design Parameters ◽

Helical Gears ◽

Positive Effects ◽

Tooth Stiffness ◽

Lubrication Condition ◽

Overlap Ratio ◽

Helical Gear Pair

Crossed-axis helical gear units are used as actuators and auxiliary drives in large quantities in automotive applications such as window regulators, windscreen wipers and seat adjusters. Commonly gear geometry of crossed helical gears is described with one pitch point. This article deals with an extended calculation method for worm gear units. The extended calculation method increases the range of solutions available for helical gears. In general, for a valid crossed helical gear pair, the rolling cylinders do not have to touch each other. In mass production of many similar gears, individual gears can be reused because they can be paired with other centre distances and ratios. This also allows the use of spur gears in combination with a worm, making manufacturing easier and more efficient. By selecting design parameters, for example the axis crossing angle or the helix angle of a gear, positive effects can be achieved on the tooth contact pressure, the overlap ratio, the sliding paths, the lubrication condition, the tooth stiffness and, to a limited extent, on the efficiency of the gearing. It can be shown that for involute helical gears, in addition to the known insensitivity of the transmission behaviour to centre distance deviations, there is also insensitivity to deviations of the axis crossing angle. This means that installation tolerances for crossed helical gearboxes can be determined more cost-effectively.

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Effect of Gear-Side Case-Hardening on Residual Stresses of Case-Hardened Gears

Volume 6: 8th International Power Transmission and Gearing Conference ◽

10.1115/detc2000/ptg-14385 ◽

2000 ◽

Author(s):

Kouitsu Miyachika ◽

Satoshi Oda ◽

Hiroshige Fujio

Keyword(s):

Residual Stresses ◽

Three Dimensional ◽

Case Depth ◽

Case Hardening ◽

3D Fem ◽

Face Width ◽

Dimensional Finite Element ◽

The Face ◽

Standard Pressure ◽

Three Dimensional Finite Element

Abstract This paper presents a study on effects of the case depth, the case-hardened part, the face width, the rim thickness and the standard pressure angle on residual stresses of case-hardened gears. A heat conduction analysis and an elastic-plastic stress analysis for the case-hardening process of spur gears were carried out by the three-dimensional finite-element method (3D-FEM), and then residual stresses were obtained. It was found that the compressive residual stress σ*θ = 30° at Hofer’s critical section of the end of the face width is smaller in magnitude than that of the middle of the face width, and that the absolute value of σ*θ = 30° of the middle of the face width decreases owing to case-hardening the gear-side and the decreasing rate increases with an increasing case depth and a decreasing face width.

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Conformity of Circular-Arc Gears

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1965_007_030_02 ◽

1965 ◽

Vol 7 (2) ◽

pp. 220-223 ◽

Cited By ~ 15

Author(s):

M. J. French

Keyword(s):

Contact Area ◽

Helix Angle ◽

Circular Arc ◽

Face Width ◽

Torque Capacity

The conformity of circular-arc profile gears of the Wildhaber-Novikov sort is examined. It is indicated that the contact area may be a banana shape rather than the ellipse hitherto assumed. Two consequences of this are that too small a difference between the profile radii may reduce the useful conformity, and that it is not possible to increase the torque capacity per unit face width indefinitely by reducing the helix angle.

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