AGMA-05FTM10-2005.pdf
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1、05FTM10 Finite Element Study of the Ikona Gear Tooth Profile by: J.R. Colbourne, University of Alberga, S. Liu, Ikona Gear International TECHNICAL PAPER American Gear Manufacturers Association Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Empl
2、oyees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 12:08:51 MDTNo reproduction or networking permitted without license from IHS -,-,- Finite Element Study of the Ikona Gear Tooth Profile John R. Colbourne, University of Alberta and Shubin Liu, Ikona Gear International The statements and
3、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 The Ikona gear tooth profile is a patented non-involute tooth profile for internal gear pairs. Gears with this profile have the foll
4、owing properties: the teeth are conjugate; the contact ratio is very high; there is no tip interference, even when only a one-tooth difference between the pinion and internal gear; there is minimal backlash; and the gears can be cut on conventional gear-cutting machines. Large reduction ratios can b
5、e achievedbyasinglegearpairandahighcontactratioresultsinlowertoothstressesthanforasimilarinvolute gear. Plus, minimal backlash makes the Ikona profile ideal for many applications, such as servo-drives, medical prostheses, and robots. Stress analysis of these gears assumes that the contact force is e
6、qual at each contacting tooth pair. Finite element results demonstrate how the number of tooth pairs in contact may increase under load. Finally, an estimate will be presented, showing the variation of tooth force between the contacting teeth. Copyright 2005 American Gear Manufacturers Association 5
7、00 Montgomery Street, Suite 350 Alexandria, Virginia, 22314 October, 2005 ISBN: 1-55589-858-0 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 12:08:51 MDTNo reproduction or netwo
8、rking permitted without license from IHS -,-,- Finite Element Study of the Ikona Gear Tooth Profile John R. Colbourne, Professor Emeritus, University of Alberta, Canada Shubin Liu, Senior Mechanical Engineer, Ikona Gear International, Coquitlam, BC, Canada Tip Interference The Ikona tooth profile wa
9、s originally developed to eliminate tip interference. For involute internal gear pairs, there is generally tip interference if the difference in the tooth numbers is less than six. The purpose of the Ikona design was to create tooth profiles in which there would be no tip interference, even when the
10、 tooth number difference was as low as one. Consider a gear pair in which the internal gear has one tooth more than the pinion. The internal gear is fixed, while the pinion is mounted on an eccentric. In a conventional design, either involute or non-involute, the eccentricity (ie the center distance
11、) would be about 0.5 modules. During one revolution of the eccentric, the axis of the pinion would move up and down about 1.0 modules. A tooth of the pinion, initially in contact with a tooth of the internal gear, would be required to move from one tooth space of the internal gear, around one of the
12、 teeth, and into the adjacent tooth space. However, in a conventional design the working depth of the teeth would be at least 1.6 modules. Thus the pinion tooth would inevitably collide with the internal gear tooth, and tip interference would occur. In the Ikona gear pair with a one-tooth difference
13、, the center distance is increased to about 1.0 modules, so that the pinion tooth moves from one tooth space to the next without hitting the internal gear tooth. The pitch circle radii Rp1 and Rp2 of the pinion and the internal gear are given by Rp1 = N1C / (N2 N1) (1) Rp2 = N2C / (N2 N1) (2) where
14、N1 and N2 are the tooth numbers and C is the center distance. With a one-tooth difference, and a center distance of 1.0 modules, the pitch circle radii are equal to N1m and N2m, where m is the module. For a conventional pinion, the radius of the tip circle is approximately (0.5N1+1)m, so the pitch c
15、ircle now lies entirely outside the pinion. It is advantageous to redefine the module, as applied to the Ikona tooth profile. The module is generally defined for involute gears as the reference circle diameter of either gear, divided by the number of teeth. For non-involute gears, where only one pit
16、ch circle exists, the module would be the diameter of the pitch circle divided by the number of teeth. In either case, the module is then used as a measure of the tooth size. In the case of the Ikona profile, the pitch circle diameter is now much larger than the tip circle diameter. If the conventio
17、nal definition of the module is used, the module would be unrelated to the tooth size. For this reason, the module is now defined in terms of the pinion tip circle diameter Dtip1: m = Dtip1 / (N1 + 2) (3) This definition means that an Ikona gear of a given module will have teeth of approximately the
18、 same pitch as an involute gear of the same module. Path of Contact and Tooth Profiles Figure 1 shows the tip circles of an Ikona gear pair, with the line of centers vertical, and the gear centers at fixed points C1 and C2. Any contact between the teeth must take place in the crescent-shaped area wh
19、ere the tip circles overlap. The pitch point lies on the line of centers, but well outside the tip circles. The Law of Gearing states that at any contact point, the common normal to the gear teeth must pass through the pitch point. This implies that the path of contact crosses the line of centers at
20、 the pitch point. Since the path of contact must lie within the crescent-shaped area, and the pitch point lies outside it, it follows that the path of contact does not intersect the line of centers, but lies entirely on one side. Copyright American Gear Manufacturers Association Provided by IHS unde
21、r license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 12:08:51 MDTNo reproduction or networking permitted without license from IHS -,-,- Figure 1 Crescent-shaped area formed by the pinion and gear tip circles, and the path of contact. The path of contact
22、 will start at a point on the internal gear tip circle, and will end at a point on the pinion tip circle. At any point on the path of contact, the common normal to the tooth profiles must pass through the pitch point. Therefore, we know the direction of the common tangent, and hence we can calculate
23、 the pressure angles of the tooth profiles at that point. For the Ikona gear, the initial point of the path of contact is generally chosen as the point on the internal gear tip circle giving a pressure angle of 8 degrees. The final point is generally chosen as the point on the pinion tip circle givi
24、ng a pressure angle of 35 degrees. For the path of contact between these two points, we can choose any curve whose radius of curvature is approximately equal to the tip circle radius of the pinion, so that the curve remains within the crescent-shaped area. The curve chosen for the Ikona gear is an A
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