Design and Geometry of Face-Gear Drives,

The authors have developed the analytical geometry of face-gear drives, proposed the method for localization of bearing contact, developed computerized simulation of meshing and bearing contact, investigated the influence of gear misalignment on the shift of bearing contact and transmission errors. Application for design is discussed. The obtained results are illustrated with numerical examples. Introduction This paper is based on the research that was performed at the University of Illinois at Chicago (UIC), Lucas Western Inc. (LW), and McDonnell Douglas Helicopter Co. (MDH). The research was initiated and supported financially by MDH. Face-gear manufacturing equipment is a product of the Fellows Corporation. Face-gears have had widespread use in low power applications but have not had much development of design and manufacturing practice for high power use. The theory of face-gear drives has not been developed sufficiently for the needs of the designers and manufacturers. The contents of this paper cover the main problems of design and manufacturing of face-gear drives with intersected axes where the drive pinion is a spur gear. The research performed is based on methods that have been developed by F. L. Litvin The paper covers the following topics: (1) localization of bearing contact; (2) meshing of shaper with the face-gear being generated; (3) limitation of length of face-gear teeth caused by pointing and undercutting; (4) computerized simulation of meshing and contact of pinion-face-gear tooth surfaces (TCATooth Contact Analysis); and (5) results of TCA. Generation of Face-Gear Drives with Localized Bearing Contact The generation of the face-gear by a shaper is shown in Transactions of the ASME Copyright © 1992 by ASME contacting surfaces and results in the undesirable contact at the edge. To avoid this, it is necessary to use a shaper with a larger number of teeth. The difference is denoted as AN = N s -Ni = 1 -3 (iVi is the number of the pinion teeth). The geometric aspects of localization of bearing contact are illustrated with drawings of The contact of the pinion and the face-gear surfaces under the load is a contact over an elliptical area; the center of such an ellipse is the theoretical contact point of E 2 and E^ The input design data for an example of a face-gear drive are given in Meshing of the Shaper and the Face-Gear The shaper tooth surface Z s and the face-gear tooth surface E 2 contact each other at every instant at a spatial line L s2 . Contact lines on E s and E 2 are shown in (/) Contact lines on the shaper surface ( Limitations of Face-Gear Tooth Surface The length of the tooth surface of a face-gear is limited, due to the possibility of undercutting by the shaper in the dedendum area and the pointing of the teeth in the addendum area The investigation of conditions of nonundercutting of the face-gear is based on the theorem that has been proposed by Litvin [5]. There is a limiting line L on the generating surface (shaper surface L s ) that generates singular points on face-gear surface E 2 . The limiting line on E s can be determined with the equation V, (s) + V (i2) = 0 (5) Here: Vr S) is the velocity of contact point in its motion over E s ; v (s2) is the sliding velocity of the shaper with respect to the face-gear. The reflection line of the conjugate meshing part and the fillet on the face-gear tooth surface is designated by L sp as shown in Computer programs for determination of limitations of the length of the face-gears have been developed at the University of Illinois at Chicago. A quick review of results obtained are represented in the following charts. Computerized Simulation of Meshing and Contact of Pinion and Face-Gear The bearing contact of pinion and face-gear tooth surfaces Ei and E 2 is localized using the technique described in section 1. Ei and E 2 are in point contact at every instant. The computerized simulation of meshing and contact of E, and E 2 (Tooth Contact Analysis) can provide information on trans-644/Vol. 114, DECEMBER 1992 Transactions of the ASME Our investigation shows that the gear misalignment (change of the shaft angle, crossing of axes instead of intersection, axial displacement of face-gear) does not cause transmission errors. This is a great advantage of face-gear drives in comparison with spiral bevel gear drive. However, gear misalignment does result in the shift of the contact path on the gear surfaces. The patterns of the bearing contact can be determined considering the motion of the instantaneous contact ellipse over the pinion-gear tooth surfaces in the process of meshing. The dimensions and orientation of the instantaneous contact ellipse can be found if the principal directions and curvatures of the contacting surfaces are determined at the current point of surface contact Theoretical and Real Contact Ratio The contact ratio m c is determined with the equation Here: </>\' and <j>\' represent the angles of rotation of the pinion that correspond to the beginning and the end of meshing for one pair of teeth; N t is the number of pinion teeth. Angles 0i 2) and <j>\ l) can be determined from drawings of The localization of bearing contact is accompanied with the reduction of contact ratio, since the number of potential contact ellipses is reduced Conclusion The authors have developed (7) Equations of tooth surfaces of the pinion and facegear. (2) Determined limitations of tooth length to avoid tooth pointing and undercutting. Charts for fast review of such limitations have been developed. (3) A method for localization of bearing contact has been proposed. (4) A method and computer programs for simulation of meshing and bearing contact has been developed. (5) The influence of misalignment on the shift of bearing contact and transmission errors has been investigated. (6) The obtained results with numerical examples have been illustrated

Feasibility study of a rotorcraft health and usage monitoring system (HUMS) : usage and structural life monitoring evaluation /

"February 1996"--Cover."U.S. Army Research Laboratory"--Cover."U.S. Department of Transportation, Federal Aviation Administration"--Cover.Bibliography: p. 59.Final contractor report.Mode of access: Internet