Conformity of Circular-Arc Gears

1965 ◽  
Vol 7 (2) ◽  
pp. 220-223 ◽  
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.

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

Improving the Characteristics of Gear Pumps: Part B — Pressure

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 oil pressure 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 pressure. 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 curvatures equal 1.4, 1.5, 2, 2.5, 2.75, and 3m are considered. The authors deduced that the tooth rack profile with radius or curvature equal 2.5, 2.75, 3m for all- addendum circular arc tooth and convex-concave tooth profile, and derived equations of pressure difference for spur, helical, and circular- are gear pumps. Computer program has been prepared to calculate the pressure from the derived formulae with all variables for different types of gear pumps. Curves showing the change of pressure with module, number of teeth, pressure angle, face width, correction factor, helix angle, and radius of curvature are presented. The results show that: 1) Pressure increases with increasing helix angle. 2) Pressure decreases with increasing face width, number of teeth, positive correction factor, module, pressure angle and radius of curvature of the tooth. 3) The all- addendum circular-arc gears generates pressure higher than helical, convex-concave and spur gear pumps. 4) A curve fitting is done for all variables with pressure and the following formulae derived for the pressure: P=A3b−0.943z−1.175m−2.1β0.175e−0.61xe−0.0048αP=A4b−1z−1.34m−2β0.119ρ1−0.393 These formulae represent simple tool for the designer to calculate the pressure of involute and circular arc gear pumps.

Conformity Factor In Wildhaber-Novikov Circular-Arc Gears

1981 ◽  
Vol 103 (1) ◽  
pp. 134-140 ◽  
Author(s):  
K. Lingaiah ◽  
K. Ramachandra
Keyword(s):  
Carrying Capacity ◽  
Maximum Load ◽  
Helix Angle ◽  
Load Carrying Capacity ◽  
Circular Arc ◽  
Face Width ◽  
Rational Index ◽  
Load Carrying ◽  
The Difference ◽  
Conformity Factor

Conformity factor, which is more rationally defined as the ratio of the area of contact to the active area of the flank of the mating teeth, is theoretically evaluated for Wildhaber-Novikov circular-arc gears, using Hertz’s theory of contact stress, without neglecting the effect of the difference in the profile radii of the pinion and wheel teeth, which is an important factor in fully-hardened gears. The variation of the conformity factor with the helix angle, pressure angle, ratio of the profile radii, module and the number of teeth follows closely the variation of load-carrying capacity per unit face-width of these gears and hence, from this study it is concluded that conformity factor is a more rational index on which the selection of the profile and material parameters should be based. This study of the conformity factor, for the particular profile geometry, indicates 7.5 to 15.0 deg as the suitable helix-angle range for achieving maximum load-carrying capacity per unit face-width.

On the influence of helix angle and face width on gear windage losses

2015 ◽  
Vol 230 (7-8) ◽  
pp. 1101-1112 ◽  
Author(s):  
Nicolas Voeltzel ◽  
Yann Marchesse ◽  
Christophe Changenet ◽  
Fabrice Ville ◽  
Philippe Velex
Keyword(s):  
Computational Fluid Dynamic ◽  
Fluid Dynamic ◽  
Helix Angle ◽  
Spur Gears ◽  
Power Losses ◽  
Flow Rates ◽  
Helical Gears ◽  
Face Width ◽  
Loss Prediction ◽  
Simulated Flow

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.

Wildhaber–Novikov circular arc gears: some properties of relevance to their design

1989 ◽  
Vol 425 (1869) ◽  
pp. 341-363 ◽  
Keyword(s):  
Contact Stress ◽  
Contact Area ◽  
Entire Range ◽  
Basic Theory ◽  
Helicopter Rotor ◽  
Basic Design ◽  
Circular Arc ◽  
Pressure Angle ◽  
Final Drive ◽  
Geometry And Kinematics

This paper follows an earlier one by Dyson et al. (Proc. R. Soc. Lond . A 403, 313 (1986)) in which a rigorous basic theory of the geometry and kinematics of Wildhaber–Novikov circular arc gears was developed. It was then applied to a pair of helicopter rotor final drive gears, operating in the conditions for which they were designed. The present paper extends this treatment by considering the effect of some variations on the same basic design, and of operating in conditions different from those for which the gears were designed. Aspects considered include the sensitivity of the pressure angle to changes in centres distance, the compromise between this sensitivity and reduction in contact stress, the relation between pressure angle and centres distance over the entire range theoretically possible, the avoidance of interference, the extent of the contact area in terms of position on the teeth, backlash and internal gears.

Analysis of Lubricating Performance for Involute Gear Based on Dynamic Loading Theory

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Shi H. Yuan ◽  
Hui L. Dong ◽  
Xue Y. Li
Keyword(s):  
Film Thickness ◽  
Dynamic Load ◽  
Elastohydrodynamic Lubrication ◽  
Helix Angle ◽  
Spur Gear ◽  
Face Width ◽  
Elastic Potential Energy ◽  
The Face ◽  
Squeeze Effect ◽  
The Impact

An integrated model for gear pair that combines the dynamic load with the mixed elastohydrodynamic lubrication (EHL) theory is proposed in this paper covering the film squeeze effect as well as the friction force generated from the rough surfaces. Comparisons between the two models of load which are, respectively, based on minimum elastic potential energy (MEPE) criterion and dynamic motion equations built up in this paper are discussed. The results show that at low speed the loads calculated by the two models are similar. However, with increasing speed, the load exhibits dynamic characteristics gradually and reaches the highest value at resonant speed. Besides, the effects of the helix angle and the lubricant viscosity are also analyzed. Increasing the ambient viscosity could intensify the film stiffness and viscous damping. Gear with larger helix angle could weaken the impact phenomenon at the shift points where one tooth-pair disengages. Moreover, it is symmetric with regard to the pressure and film thickness across the face width for spur gear. Differently, the pressure for helical gear has a higher value at the dedendum of pinion where the film becomes thinner. In addition, speeding up the pinion would generally result in higher dynamic load and film pressure but thicker film thickness.

Modeling of Error Analysis Simulation of Normal Circular Arc Bevel Gear Transmission

2013 ◽  
Vol 589-590 ◽  
pp. 606-610 ◽  
Author(s):  
Guo Jun Dong ◽  
Ming Wang
Keyword(s):  
Contact Zone ◽  
High Speed ◽  
High Strength ◽  
Helix Angle ◽  
Transmission Error ◽  
Angle Error ◽  
Circular Arc ◽  
Bevel Gears ◽  
Operation Test ◽  
Simulation Results

The normal circular arc bevel gears are used in industrial areas of high speed, high bearing and high strength widely. A mathematical simulation model is built and it can analyze transmission error and contact zone of normal circular arc bevel gears. In this model, the instantaneous engaging points of gear pair are transformed into the least-values of rotary angles of corresponding points between two gears along the final motion, so this method is very simple and effective. Under the condition of existing helix angle error, transmission error and contact zone of a pair of normal circular arc bevel gears are simulating analyzed. At last, the operation test of contact zone of gears indicates gears transmission is stable and the gears contact zones are largely in line with the simulation results.

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