Available online at ScienceDirect. Procedia Engineering 150 (2016 )

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1 Available online at.sciencedirect.com ScienceDirect Procedia Engineering 15 (16 ) International Conference on Industrial Engineering, ICIE 16 Finishing of the Helical-Bevel Gear Teeth Flanks B.A. Lopatin*, S.V. Plotnikova Zlatoust branch of the South Ural State University (National Research University), Turgeneva 16, Zlatoust,4569, Russia Abstract This paper describes methods of teeth shaving and gridding at helical-bevel gears of involute-bevel gearings. Furthermore, the opportunity of doing these operations on machines for teeth processing in common bevel gears is shon. The possibility of these operations performance on the equipment that is used for common helical gears teeth processing is shoed. 16 The Authors. Published by Elsevier by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-revie under responsibility of the organizing committee of ICIE 16. Peer-revie under responsibility of the organizing committee of ICIE 16 Keyords: involute-conical gear; teeth shaving; teeth grinding 1. Gear teeth shaving This paper describes involute helical-bevel gearing (HBG). The involute helical-bevel gearing commonly includes a cylindrical and a involute-bevel gear [1, ]. This gearings can be designed for any position of the shaft axes [3-5]. Due to a number of advantages (arrangement, exploitative, technological) involute HBG is using in many directions of mechanical engineering (motor car construction, shipbuilding, space equipment) [6-1]. It is knon that in helical-bevel gearing line contact of gears is possible ith certain combination of parameters for one direction of rotating beteen ske axes (fig. 1). Condition of gears line contact shon in [1]. tg sin tg cos 1 (1) * Corresponding author. Tel.: address: lopatinba@susu.ac.ru The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-revie under responsibility of the organizing committee of ICIE 16 doi:1.116/j.proeng

2 89 B.A. Lopatin and S.V. Plotnikova / Procedia Engineering 15 ( 16 ) Fig. 1. Location of gears in the gearing This condition is obtained on the basis of equality to zero beteen linear generatrices of involute helicoids of gears. These linear generatrices are lines of contact beteen tooth of the gear and counterpart rack hile cutting. If cylindrical cog-heel in the gearing ill be replaced by shaver, that is identical in geometry to it, then cutting edges of shaver ill machine all collateral border of tooth of the conical gear at once during rotation ith enough idth. The processing is did ithout changing relative position of the shaver and gear by single-flank gearing scheme ith blank rotation slo doning. Shavers must have different in algebraic sign incline angles of teeth for processing left and right side of cog. For example condition of the line contact of the machining gear cogs and the shaver for the spur involute-conical gear shon in: tg tg tg (), here: gearing angle beteen the shaver and the cog-heel; gear pitch angle; incline angle of the tooth trace at basic shaver cylinder. Values are seted in the shaver designing and parameters computation of its installation: m nominal engagement module; basic rack pressure angle; z, z number of teeth of shaver and gear; xt, xt basic front sections displacement coefficients of gear and shaver; reference plane incline angle of the tool at cutting helical-bevel gear. Engagement angle and helix angle are being determined on the pitch cylinder of the shaver, values of and should conform ith line contact condition (1) and theoretically gapless engagement condition of the shaver and the gear, hich include in implicit form.

B.A. Lopatin and S.V. Plotnikova / Procedia Engineering 15 ( 16 ) 889 893 891 xt zinvt inv t z invt inv t tg xt cos cos (3) Fig.

3 B.A. Lopatin and S.V. Plotnikova / Procedia Engineering 15 ( 16 ) xt zinvt inv t z invt inv t tg xt cos cos (3) Fig.. Single-sided shaver from the involute-bevel gear Task is reduced to solving equalizations (1) and (), hich can be done only by numerical method. Rough value can be obtained from the approximate equation, hich is obtained on the assumption, that gear and shaver axes are parallel: tgt xt xt invt inv, (4) z+z here tgt tgcos. Further calculation is made according to the formulas: cos t cos cos (5) cos t sin sin sin (6) sin tg tg (7) tg cos sin sin (8) cos tg tgt (9) cos

4 89 B.A. Lopatin and S.V. Plotnikova / Procedia Engineering 15 ( 16 ) cos coscos cos (1) cos cos t t Values of t, t, t, t are substituted in equation (3). Value is refined, if difference from zero of left part is significant. Shaver installation parameters concerning gear can be calculated, after determination of and values: shaft angle, center distance, displacements l and l of basic planes from center distance (fig. 1) cos cos cos (11) a mcos z z sin cos cos cos cos sin (1) mcos zcos z sin ; (13) cos cos cos sin mcos z z sin cos (14) cos cos cos sin Line contact condition of teeth in gearing are observed only ith one side of tooth contact, using this shaving method for bevel gear teeth. Point contact take place for orking of teeth other side. This localization loer loadcarrying capacity of reversal gear drive. One is effective methods of increasing load-carrying capacity in this case is using gearing implementation ith modified tooth profile. Longitudinal modification allos to get theoretically line contact of orking flanks and to align load-carrying capacity of the gearing in the contact ith both flanks of the tooth. This modification can be did by shaving helical gears ith involute-bevel shaver ith parameters, hich is identically to bevel gear parameters in the gearing. on flanks The modified profile of gear tooth orking flanks implement point ise in the result of shaving by this shaver, hich provide theoretically line contact ith involutebevel gear teeth by the second Olivier method. The cutting edges ill process all side flanks at once ith enough length of the involute-bevel shaver. Involute-bevel shaver for processing helical spiral gear in gearing ith crossing axes is shon on fig., here = 1, m = 5, number of bevel gear teeth is z =1, number of helical gear teeth is z =4. Relative position of involute-bevel shaver and shaving gear are being calculated on formulas (1-13) using this shaving method. Processing is did using the single-flank gear scheme like as the first time. Cutting speed is teeth longitudinal sliding speed ith previously mentioned methods of shaving. If gear hone ill be used instead of the shaver, then helical-bevel gearing heel teeth honing could be did.. Helical-bevel gearing heel teeth grinding Equipment, hich is used for helical gears teeth grinding in helical-bevel gearings, is similar to equipment for common gears. It is necessary to incline blank axis on angle concerning to feed longitudinal direction of grinding heel in teeth grinding, ith angular equal-velocity joint arbors (fig. 3, a) or to provide grinding heel motion using this angle to blank axis, like it is did in circular cutter (fig. 3, b). Machine adjustment to require angle can be did by installing appropriate edges under of grinding heel head guide of machine in serial processing involute-bevel gears. Such adjustment as done at "Nails" machine for grinding involute-bevel gears of marine reducers [1].

5 B.A. Lopatin and S.V. Plotnikova / Procedia Engineering 15 ( 16 ) Fig. 3. Gridding of involute-bevel gear in helical-bevel gearing 3. Conclusion Methods of helical-bevel gearing finishing processing, hich are shon in article, sho, that same devices are might be used for this as in processing of helical gears. This allos to receive high precision of HBG, hich is similar to bevel gearings. References [1] B.A. Lopatin, O.N. Tsukanov, Helical-bevel gears, Monograph, SUSU, Chelyabinsk, 5. [] B.A. Lopatin, O.N. Tsukanov, Helical-bevel gearing, Mezhdunarodnij Jurnal eksperimentalnogo obrazovaniya. 11 (1) [3] B.A. Lopatin, S.V. Plotnikova, S.A. Khaustov, Involute helical-bevel gearing, Procedia Engineering. 19 (15) [4] V.V. Bruzhas, B.A. Lopatin, Development of solid-state models for the gears of different geometry, Procedia Engineering. 19 (15) [5] B.A. Lopatin, S.V. Plotnikova, Cilingrical gear formed by helical-bevel gearing, Nauka I obrazovanie v zhizni sovremennogo obshestva. 8 (15) 111. [6] B.A. Lopatin, O.N. Tsukanov, S.V. Plotnikova, Helical-bevel gears in transmissions, Vestnik mashinostroeniya. 8 (3) 7 9. [7] F.I. Plekhanov, B.A. Lopatin, RU Patent (15). [8] B.A. Lopatin, S.V. Plotnikova, About advantages of involute helical-bevel gearings, in: Proceeding of 11 th International Scientific and Practical Conference Prospective studies are science and techniques 15. (15) 813. [9] B.A. Lopatin, Gearings ith involute-bevel gears, in: Proceeding of 66th Scientific Conference, Nauka YuUrGU. (14) [1] B.A. Lopatin, R.I. Zaynetdinov, E.A. Poluektov, B.E. Buhvalov, V.G. Sapryikin, RU Patent (6).

Available online at ScienceDirect. Procedia Engineering 129 (2015 ) International Conference on Industrial Engineering

Available online at ScienceDirect. Procedia Engineering 129 (2015 ) International Conference on Industrial Engineering Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 129 (2015 ) 563 570 International Conference on Industrial Engineering Improved design of machine for cold cutting of oil pipes