AGMA-97FTM6-1997.pdf
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1、97FTM6 On the Location of the Tooth Critical Section for the Determination of the AGMA J-Factor by: Jos I. Pedrero, UNED, Carlos Garca-Masi, and Alfonso Fuentes, Universidad de Murcia TECHNICAL PAPER * Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee
2、=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 10:49:54 MDTNo reproduction or networking permitted without license from IHS -,-,- On the Location of the Tooth Critical Section for the Determination of the AGMAJ-Factor Jos I. Pedrero, UNED, Carlos Garca-Masi and Alfonso Fuent
3、es, Universidad de Murcia 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 The bending strength geometry factor J depends on the location of the critical section
4、and the tooth thickness at this section. The critical section is that in which the uncorrected bending stress, given by Naviersequation, is maximum and consequently it is defined by the point of tangency of the Lewis Parabola and the tooth profile. This point of tangency is usually placed over the r
5、oot fillet, but in some casts the tangency may occur at the involute. For these cases the methods descriied in literature for determining the AGMA J-factor are not suitable. This paper presents the condition for tangency at the involute and a method to determine the J factor under this condition. Co
6、pyright O 1997 American Gear Manufacturers Association 1500 King Street, Suite 201 Alexandria, Virginia, 22314 November, 1997 ISBN: 1-55589-700-2 Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Res
7、ale, 04/18/2007 10:49:54 MDTNo reproduction or networking permitted without license from IHS -,-,- S T D - A L M A 77FTMb-ENGL 1777 Ob87575 0005107 Li58 D ON THE LOCATION OF THE TOOTH CRITICAL SECTION FOR THE DETERMINATION OF THE AGMA J-FACTOR Jos I. Pedrero, Professor (*i Carlos Garca-Masi, Associa
8、te Professor (+*I Alfonso Fuentes, Assistant Professor (“1 (“1 (*+) UNED, Departamento de Mecnica, Apdo. 601 49, 28080 Madrid, Spain Universidad de Murcia, Departamento de Ingeniera Mecnica y Energtica, Po Alfonso XII1 44, 30203 Cartagena, Murcia, Spain Introduction Location of the critical section
9、To evaluate the maximum bending stress arising at any point of the tooth during the entire meshing interval, AGMA introduces the bending strength geometry factor, also known as AGMA J-factor 1 I. According to Naviers equation, the point of maxi- mum bending stress is located at the point of tangency
10、 of the tooth profile and the inscribed equal-stress parabola, or Lewis parabola 21, whose vertex is placed on the intersection of the line of action, at any contact point, and the tooth centerl- ine. The most severe conditions correspond with the tooth loaded at the tip, for conventional helical ge
11、ars, and at the highest point of single tooth contact, for spurs and low axial contact ratio helical gears. Consequently, the critical section of the tooth is defined by the point of tangency of the tooth profile and the Lewis parabola for load acting at the above points, and J factor can be express
12、ed as a function of the height of the Lewis parabola (distance from the critical section to the vertex of the parabola) and the tooth thickness at the critical section. Since the point of tangency is usually placed over the root fillet, existing methods to compute the AGMA J-factor 3,41 involve iter
13、ative procedures to find the point of tangency of the parabola and the root trochoid. However, tangency may occur at the involute, as seen in Fig. 1. Under these conditions, results provided by the above methods could be inappropriate. In this paper the tangency condition at the involute profile is
14、established. Also a method for computing the AGMA J-factor under this condi- tion is presented. . . AGMA defines the bending strength geometry factor J as 31 I cos (ur cos cy where C , is the helical overlap factor, Kf the stress correction factor 51, mN the load sharing ratio, cy, the operating hel
15、ix angle, cy the standard helix angle, qnL the load angle, nr the operating normal pressure angle, h, the height of the Lewis parabola, s , the tooth thickness at the critical section and C, the helical factor 161. Figure 1 shows an example of tangency occur- ring at the involute. Involute profile a
16、nd root trochoid are tangent at point E. This means there is neither undercutting nor tool protuberance (or grinding after generation by shaper cutter with Protuberance), although for small undercutting and/or tool protuberance, it is possible that the tangency point still remains at the involute, a
17、s shown in Fig. 2. However, under this condition of tangency at the involute, the point of tangency shouldnt be considered neither for locating the critical section nor for determining the J factor. Though Naviers stress is maximum at this point, the stress concentration is very small at the invo- l
18、ute, and corrected bending stress is greater at any- point of the root fillet. Therefore, the J factor should be computed considering the section of the root in which Naviers stress is maximum, which -1 - Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licen
19、see=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 10:49:54 MDTNo reproduction or networking permitted without license from IHS -,-,- STD-AGHA 77FTMb-ENGL 1777 = b87575 0005108 394 D will be defined by the point of intersection of the root trochoid and the thinnest parabola c
20、ontaining a point of the trochoid. Obviously, the parabola tangent to the trochoid, if it exists, coincides with the above thinnest parabola, hence the mentioned existing methods are suitable for this case. This occurs for tangency of the Lewis.paraboia at the root and also for tangency at the invol
21、ute if under- cutting (or tool protuberance) exists. - -._ -. c /“i “ ., Figure 1 : Tangency at the involute profile Figure 2: Tangency at the involute profile for small undercutting and/or tool protuberance Nevertheless, for the case of tangency at the involute with no undercutting, no tool protube
22、r- ance, tangency of the tangent parabola and the trochoid occurs at an improper point of tangency Pi, beyond the end of the root trochoid, as shown in Fig. 1, and improper values for the height of the Lewis parabola, h , and for the tooth thickness, s , , would be obtained if the above mentioned me
23、thods were employed. In this case, the thinnest parabola containing a point of the trochoid is that containing the point of tangency of the root trochoid and the involute (point E in Fig. 11, and this point defines the critical section, which should be considered for computing the J factor. Conditio
24、n for tangency at the involute For the case of no undercutting and no tool protu- berance it is necessary to know if tangency of the parabola and the profile occurs at the involute or at the trochoid. This condition will be established in two ways. First, in terms of the results of the iterative pro
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