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The hob overrun must not be less than the hob idle distance U. In cases where the actual hob idle distance is shorter than or equal to U.the actual longitudinal profile AD of the gear tooth deviates from its desirable l.ongitudinaJprofile AC (Fig. 11). Maximal deviation occurs at the point D. at which deviation is equal toS. It is required that the maximal deviation 0, does not exceed tolerance [0] on the gear tooth accuracy. The length AU depends on the relative location of the work and on the involute hob in axial direction of the work. Incorporating a tolerance on gear tooth longitudinal profile yields a, significant reduction of the length of the required gear hob idle distance. Analysis of Figure 1i yields a formula for computation of the allowed shortening of the hob idle distance that is shown in Equation 6. For engineering computation, a simplified approximate formula is valid and presented in Equation 7. In that equation, Rp;;;;; R l.h is the first principle radius of curvature of the machining surface of the involute hob. ]t is already proven (Refs. 9, 10) that the value of the first principle radius of the machining surface of the involute hob can be computed, The computation method i explained in Equation 8. Base helix angle 'V'b.h call be calculated from the formula laid out in Equation 9. For example, for the left-hand involute gear hob of modulus m =. 3 rnm with pitch diameter d = 70 mm, normal profile angle ,an;;;;; 14,30°,. number of starts Z" = 5, and hob-setting angle /;,,,= 12.4 0 , one can compute the hob base diameter by using the formula in Equation 10. The hob base helix angle is equal to two formulas listed in Equation 11, The hob helix angle (Ref. 6) can be found in Equation 12. The above results yield a final calculation shown in Equation 13. That result yields U = 28.47l rnm, Inthe case, with the tolerance equal to 0= OJ mm, one can compute that t!.U ::: 4.561 mm •.and therefore the actual hob idle distance required for perfect involute gear tooth profile generating is equal to U" ::: 28.47]-3.949;::: 23.910 mm. Hob idle distance U* = 23.910 mm is 19.1 % shorter than Lhe hob idle distance U = 28.471 mm, This reduces the length of the hob idle distance that leads to corresponding reduction of the size and weight of a cluster gear and of the gear train hen ing as well. Conclusions Methods of analytical mechanics of gears are applied to determine the exact minimal axial length of 3. cluster gear 1'OIr conventional and climb hobbing of spur and helical gears. The results reponed in the paper allow users to cut bobbing time and to reduce the size and weight of a gear train and its housing. The approach is especially important for applying the multi-start hob of small diameter. A similar approach can be utilized for bobbing of a non-involute profile, for instance, while machining splines, sprocket. ratchets, etc. The results presented might be incorporated as a part into software for CNC hobbing machines. 0 Referen.ces 1. ANSIIAGMA 1012-F90. American National Standard; Gear Nomenclature. Definitions of Terms with Symbols. AGMA Standard, February 1990,56 p. 2. Buckingham. E. Analytica] Mechanics of Gears. Dover Publications, Inc., 1963, 546 p. 3. Dudley, D.W. Handbook of Practical Gear Design. Tecbnomic Publishing Co., Inc., Lancaster, Basel, 1994. 4. FETIE. Gear Cutting Tools: Hobbing, Gear r Ml'lling. Leitz Metalworking Technology Group, 1196p. 5. Gear Design: Manufacturing and Inspection Manual. Society of Automotive Engineers. Inc., 1990,.643 p, 6. Modern Methods of Gear Manufacture. National Broach & Machine Division. Lear Siegler. Inc., 1972, 159 p. 7. Radzevich, S.P. "About Hob Idle Distance in Gear Hobbing Operation," ASME J. of Mechanical Design, Vol. 124, December 2002, pp.772-786, 8. Radzevich, S.P. "Conditions of Proper Sculptured Surface Machining." Compu,ter-Aided Design, Vol. 34, No. 10. September 2002, pp. 727-740. 9. Radzevich, S,P. Fundamentals of Part Susface Generating ..Monograph, Kiev, Rastan, 2001, 592 p. (In Russian]. W. Radzevich, S.P., E.D. Goodman and V.A. Palaguta, "Tooth Surface Fundamental. Forms in Gear Technology," University of Nis, The Scientific Journal Facta Universitatis, Series: Mechanical Engineering, Vol. 1, No.. 5, 1998, PI'. 515-525. n. Townsend. D.P: Dudley's Gear Handbook. The Desjr' .A!anufacture, G,!,d Application of Gears. 2 Edition, McGraw HIll, Inc., NY, 1992. Tell Us What You nink ... Visit www.,ean.dllJology.com to • Rate this article • Request more information • Contact the author • Make a suggestion Or can (841) 431-&604 to talk to one of our eclitofsl 50 JULY/AUGUST 2003 • GEAR TECHN10LOGiY- www,geart,eclmology.,com • www.pow,ert.ransmiss.io.n.com
- ----------------- Accuspirals AGMA AlI,n .AlII!!!!i SI!IJHlI SIlVicK Inc. American Arrow' Gear Co. A/W Systems Co, B & IRMachine BllrillmBmalional Metal Trealing Co. lOll Gear Corp,. Corp. BDl!JI!& IKocl! M.Il:hil1lTo!!/ Chamlermalic In~, Dr, Kai.Br (S.L MUlllonl Dm,S.r TIle ,G"~f 'ndust", e.. , Motions line. GI0108 GillSon Corp, .Ho.me,f'lIg.' ICutting Tools Corp. Th. Gleeson 'Works Co, Greg Allen CoJl!!!lt" T,~hoologie:l lne, Insco Corp. Inl8rslale Tool Corp. nw Helll'lIIlItJl JAM InI.emalionalln~, Koro Sbarpening Servin U,hhlu M!!1]l'oSJ ICOJ1!'_ Midwest Midwest Gal! Tlc'bno'iogy Co. Gear 110ToullK, Cu, Corp, Mosay IMan!!l!!CI!!fing Co. Inc, Nlc'hi Machining Tec'holl'logy Co. Niagara Gear Co'p. Plulo Plodu~ Co. h"" tBcb.nolGfl Corp. p~>WJtTlfn_is;s.iIm.I:D!IJ Pr~ision Pras;iile Tbel'lIldy Gagl Co. IIIG, Corp·. CO~P" "-yc .. Gear" Madine Co, Russelll Holbrook. &, H ndarsao Inc. Star·SU Inc, fS:lV!fransmeclnicl' (Gregl A11.el!Co.1 ADVIERTISER INDEX USE RAPIID READER RESPONS!Eto, contact any ,advertiser in this iissue www.g.earlechn%gy.com/m:htm Rapid Reader Response: It's FAST! Ifs EASY! Its ONLY ONLINE! Pig" !!;t. Pbone (925I285-3921l 1,15 (J1I3J 684-0211 54 (1:121' 2!i9-2937' 55, (2161Q1~ 4,22 (6JOI 969-1:640' 2D,22 (2481544-3852 16 (BOO) .238-06511 4.24 (M1j.m-8121 54 (8151 '965-4013 2J (815) 636-5082 14 (lI0II1365-1185 22,4a (1001115-1390 5.23 1!,53 (847) 437'-li604 .a (847)437-6604 54 (315) 481-0100 55 [211611621·3333 1Ft. 54 (SIS) 47J..l000 1,54,55 (815J 817-11901]1 54 (585) 473·1000 25, (44011195-4621 21 (603111i6-2652 43 (9'18) 44I-S6II, 55 (216) S11·1on 43 (320) 762-8182 lUI (815) ,282-9330 55 (763)42S-S2U 3 (1341 42!1-1m 1i,211 31 (5116) 754-8923 55 (33G142S-4419 55 17fi5) II83-alO 11,24, !;t (5116) 2IiJ..01 00 54 C2 1St (IIQiJPAUl04U (1&l1138·25Z5 13 (1471,437-6604 31 (630J 655-2n1 10,23 (2161 441
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