1、14FTM10 AGMA Technical Paper Involute Spiral Face Couplings and Gears: Design Approach and Manufacturing Technique By Dr. A.L. Kapelevich, AKGears, LLC, and S.D. Korosec, Koro Industries, Inc. 2 14FTM10 Involute Spiral Face Couplings and Gears: Design Approach and Manufacturing Technique Dr. Alexand
2、er L. Kapelevich, AKGears, LLC and Stephen D. Korosec, Koro Industries, Inc. The statements and opinions contained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association. Abstract Face gears typically have a straight
3、 or skewed tooth line and varying tooth profile in normal cross section at different radii from major to minor diameter. These face gears are engaged with spur or helical involute pinions at intersecting or crossed axes. This paper presents spiral face gears with an involute tooth line and an identi
4、cal tooth profile in the normal section at any radius. There are two main applications for such face gears. One of them is an alternative solution with certain advantages in performance and fabrication technology to the straight tooth, Hirth, or Curvic flange couplings. Another application is when a
5、 face gear is engaged with an involute helical pinion or worm at intersecting or crossed axes. Potential advantages of spiral face couplings and gears include high power transmission density and highly productive machining of face spiral gears. The paper describes gear geometry analysis, and design
6、technique of spiral face involute gears with symmetric and asymmetric tooth profiles. It also explains a hobbing method of these gears and tool design specifics, and then illustrates gear and tool design with numerical examples. Copyright 2014 American Gear Manufacturers Association 1001 N. Fairfax
7、Street, Suite 500 Alexandria, Virginia 22314 October 2014 ISBN: 978-1-61481-102-2 3 14FTM10 Involute Spiral Face Couplings and Gears: Design Approach and Manufacturing Technique Dr. Alexander L. Kapelevich, AKGears, LLC and Stephen D. Korosec, Koro Industries, Inc. Introduction Face gears typically
8、have a straight or skewed tooth line and varying tooth profile in normal cross section at different radii from major to minor diameter. These face gears are engaged with spur or helical involute pinions at intersecting or crossed axes. This paper presents spiral face gears with an involute tooth lin
9、e and an identical tooth profile in the normal section at any radius. There are two main applications for such face gears. One of them is an alternative solution with certain advantages in performance and fabrication technology to the straight tooth, Hirth, or Curvic flange couplings. Another applic
10、ation is when a face gear is engaged with an involute helical pinion or worm at intersecting or crossed axes. Potential advantages of spiral face couplings and gears include high power transmission density and highly productive machining of face spiral gears. The paper describes gear geometry analys
11、is, and design technique of spiral face involute gears with symmetric and asymmetric tooth profiles. It also explains a hobbing method of these gears and tool design specifics, and then illustrates gear and tool design with numerical examples. Geometry of involute spiral face gears Spiral angle at s
12、ome reference diameter d db is: arccosbdc(1) Unlike conventional spur or helical gears that have involute tooth flank profiles and straight or helical tooth lines, these spiral face gears have straight tooth flank profiles in the normal section and the involute tooth line. Any tangent to the base cy
13、linder diameter dbis normal to the involute tooth line section of the spiral face gear presenting a straight flank gear rack (see Figure 1, Section A-A). The spiral face gear tooth parameters and its root fillet profile can be optimized using Direct Gear Design optimization technique 1 to amplify lo
14、ad capacity by increasing tooth surface durability and minimizing bending stress concentration. Involute spiral face machining Since any normal to the involute tooth line section of the spiral face gear presents a straight flank gear rack, a gear hob can be used in manufacturing. Thus a spiral face
15、gear per this design can be hobbed with the same accuracy as spur and helical gears utilizing conventional hobbing equipment. Schematics of spiral face gear hobbing are shown in Figures 2 and 3. Hobbing center distance “a” is: cos2cosbda (2) Where the “+” sign if the spiral gear and hob have opposit
16、e hands left-right (Figure 2) or right-left, the “ ” sign if the spiral gear and hob have the same hands right -right (Figure 3) or left-left. The normal section of the spiral gear tooth profile is an impression of the hob tooth profile in normal section (Figure 2, Section A-A). 4 14FTM10 Figure 1.
17、Face involute spiral gear; db, di, d, and doare base, minor, reference and major diameters, is spiral angle at reference diameter, m module, profile (pressure) angle, s tooth thickness at reference (pitch) line, ha tooth addendum, w whole depth; 1 tooth flank, 2 - root fillet Figure 2. Schematics of
18、 left hand spiral face gear (black) hobbing with right hand hob (blue); hob lead angle, L hob length, dc hob major diameter; section A-A is tangent to base circle dband normal to the gear tooth line; section B-B is parallel to the hob axis, 1 concave gear tooth flank, 2 convex flank 5 14FTM10 Figure
19、 3. Schematics of right hand spiral face gear (black) hobbing with right hand hob (blue) In order to avoid interference and undercut of the concave tooth flank the minimal gear flank curvature radius rgmust be greater than the maximum hob helical surface radius rcmeasured parallel to the hob axis (s
20、ee Figure 2, Section B-B) from base diameter dbto the hob centerline offset by distance “a” or: g min c maxrr (3) The minimal gear flank curvature radius rg minand minor diameter diis: tan arccos2big miniddrd (4)A profile of the hob helical surface section parallel to its axis presents a complex cur
21、ve and exact definition of its maximum radius rc maxat a contact point with the concave gear flank is a difficult task. However, this maximum radius rc maxcould be defined with sufficient accuracy for a practical solution by equation 5. 2tancc maxdr (5) A higher profile (pressure) angle and a smalle
22、r hob major diameter dc, results in a smaller spiral face gear minor diameter, achieved without concave flank undercut. Spiral face couplings A pair of spiral face gears can be used as a flange coupling (also known as Endicon coupling 2). Application of this type of coupling is similar to the Hirth
23、and Curvic couplings. The Hirth coupling flange (Figure 5) has tapered, symmetrical teeth. Both mating flanges of the Hirth coupling have identical tooth geometry. The Curvic coupling flanges (Figure 6) have teeth with a circular tooth line, though the tooth flank profiles are straight. One flange o
24、f a coupling has concave tooth lines and the mating one has convex tooth lines. 6 14FTM10 Figure 4. Hirth couplings Figure 5. Curvic couplings A distinct difference of the involute spiral face coupling (Figure 6) is that the normal to the tooth line section tooth geometry and the normal load are the
25、 same at any radius. This results in even stress distribution and potentially greater load transmission capacity. Both mating flanges of the involute spiral face coupling have the same tooth geometry, but tooth spiral line directions have opposite clockwise and counterclockwise directions. Spiral fa
26、ce gear parameter selection could be limited by a choice for manufacturing technology. For example, the minor diameter and pressure angle for a hobbed gear are limited by a condition per equation 3. Figure 7 presents a sample of involute spiral face coupling assembly. Experimental involute spiral fa
27、ce coupling gear parameters are presented in Table 1. Figure 6. Experimental involute spiral face coupling mating flanges and hob (the same hob was used to machine both right and left hand spiral face gears) 7 14FTM10 Figure 7. Sample of involute spiral face coupling assembly Table 1. Experimental i
28、nvolute spiral face coupling gear parameter Number of teeth 16 Normal module, mm 6.0 Tooth addendum, mm 3.7 Whole depth, mm 8.0 Normal pressure angle 45 Reference diameter, mm 150.0 Spiral angle at reference diameter, mm 50.2 Minor diameter, mm 120.0 Spiral angle at minor diameter 36.9 Major diamete
29、r, mm 180.0 Spiral angle at major diameter 57.8 Spiral face gears A spiral face gear can be engaged with an involute helical pinion or worm at intersecting or crossed axes. Such engagement is used in the Helicontype gears 3. In order to avoid interference of the helical pinion tooth (worm thread) ti
30、p with the spiral face gear tooth tip at its concave flank, the pinion and spiral gear geometry must satisfy to the condition (3). This condition requires a high pressure angle in in mesh with the spiral face gear tooth concave flank and the mating helical pinion flank. At the same time the effectiv
31、e tooth height in the gear mesh must provide a contact ratio greater than 1.0. In most cases both these conditions cannot be satisfied with symmetric tooth profile in the normal section that is used for spiral face couplings. Application of an asymmetric gear tooth profiles with high pressure angle
32、for the concave flank and low pressure angle for the convex flank of the spiral face gear allows a contact ratio greater than 1.0 in both flank gear meshes. A sample of the spiral face gear pair and its data are shown in Figure 8 and Table 2 accordingly. Asymmetric tooth hobs for the helical pinion
33、and spiral face gear are shown in Figure 9. Potential applications Spiral face couplings have greater load capacity and utilize cost effective hobbing fabrication methods in comparison to the Hirth and Curvic type flange couplings. They may find many application areas including aerospace, automotive
34、, agriculture, robotics, etc. For example, this type of coupling could be used to connect an airplane propeller to an engine shaft. 8 14FTM10 Figure 8. Sample of spiral face gear pair Figure 9. Asymmetric tooth hobs - a) helical pinion, b) spiral gear Table 2. Spiral face gear data Gear Pinion Spira
35、l face gear Number of teeth 5 26 Normal module, mm 0.85 0.85 Normal drive flank pressure angle45 45 (concave flank) Normal coast flank pressure angle 10 10 (convex flank) Helix/spiral angle 57.9 32.0 Helix /spiral hand Left Right Pitch diameter (pd), mm 9.600 29.068 Base diameter, mm 4.504/9.1111)24
36、.650Major diameter, mm 11.00 36.00 Minor diameter, mm 7.74 28.00 Addendum, mm 0.70 0.70 Whole depth, mm 2.00 2.00 Normal tooth thickness at pd, mm 1.270 1.270 Face width, mm 10.00 4.00 Center distance, mm 6.3500.025 Contact ratio 1.05/2.601)NOTE: 1) Drive/coast flank Spiral face gears that utilize c
37、onvex-concave tooth contact at high pressure angle on drive tooth flanks have potentially greater load capacity in comparison to conventional face gears. This makes it suitable for different power drives and actuators, and also in positioning systems for many industries and applications. Summary - G
38、eometry of involute spiral face gears and their tooth machining technology are described. - Spiral face couplings and spiral face gears are described. - Potential applications of spiral face couplings and spiral face gears are suggested. 9 14FTM10 References 1. Kapelevich, A.L., Direct Gear Design, CRC Press, 2013. 2. http:/ . 3. Paul, D., SpiroidAnd HeliconGearing, http:/
