Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 129 (2015) 369 – 373
International Conference on Industrial Engineering
Development of solid-state models for the gears of different geometry Bruzhas V.V.*, Lopatin B.A. South Ural State University, 76, Lenin Avenue, Chelyabinsk, 454080, Russian Federation
Abstract This article describes the preparation methods for solid models of gears of different geometries using emulation cutting tooth profile generating circuit rack and further processing in Autodesk Inventor. The parameters of the rack contour can be set at a designer’s request. © 2015 The Authors. Published by Elsevier Ltd. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE(http://creativecommons.org/licenses/by-nc-nd/4.0/). 2015). Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE-2015) Keywords: solid model, spur gear, helical gear, conical involute gear, bevel wheel non-involute tooth profile.
1. Intorduction In assessing the stress-strain state of gears it is necessary to obtain solid models that accurately reflect the geometry of the tooth profiles, depending on the parameters of the tool and the trajectory of its movement. The analysis of existing software products has shown that at present there are no universal developments, allowing the generation of gears produces complex shapes of working surfaces of teeth. These software products represent only a graphical representation of the gear, and the libraries of CAD systems are a simplified representation, usually a standard profile. The aim of the study was to develop solid models that accurately reflect the shape of the surfaces of the teeth obtained when profiling tool rack with different parameters of the original circuit. 2. Production models of gears The basis of the working surfaces of the teeth getting laid emulation software package cutting gear rack * Corresponding author. Tel.: +7-919-324-19-86. E-mail address:
[email protected]
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the International Conference on Industrial Engineering (ICIE-2015)
doi:10.1016/j.proeng.2015.12.125
370
V.V. Bruzhas and B.A. Lopatin / Procedia Engineering 129 (2015) 369 – 373
generating circuit [1]. The developed program allows for the processing of cylindrical gears with different parameters of the original contour (Į, ha *, hf *, c *, ȡ *) and different coefficients of x bias generating circuit rack (Fig. 1). For the further construction of three-dimensional model using a program Autodesk Inventor, with which obtained on the basis of the profile, you can create models of various gears.
Fig. 1. The scheme forming the tooth profile in the face section wheels.
3. Spur and helical gear To create the model spur gear (Fig. 2) is sufficient to use the extrusion operation. In contrast to the spur gear created by standard means of Autodesk Inventor (via the Design Wizard gears) profile tooth surfaces completely fit the profile, really get at run-rack instrument to the settings of the original path. In the case of a helical gear (Fig. 3) extrusion is not a straight line, and the spiral. You can use the application spring. In this application, given shape in the form of a sketch prepared tooth profile and its position relative to the axis of the wheel. The angle of the tooth wheel E is given through a step helix and the length of the pitch circle.
Fig. 2. Spur gear.
Fig. 3. Helical gear.
V.V. Bruzhas and B.A. Lopatin / Procedia Engineering 129 (2015) 369 – 373
371
4. Involute-bevel gear Solid models of gears with more complex geometry surfaces of the teeth, you can create a combination of the two above-described software systems. For example, involute bevel wheel (Fig. 4). Involute-bevel gear (IBG) - the wheel, sliced tool rack type (Gear comb, hob, grinding wheel) with variable displacement along the axis of the wheel tool [2]. A feature of such wheels is that in each face section profile is obtained with a certain offset coefficient which is changed in each section by the amount (1)
'x = s tgG / m, where s – move; ¨x – increment of bias; G – taper angle IBG; m – module. Coefficient of radial clearance: ct*
c*
cos E . cos G
(2)
The coefficient of the tooth head height tool:
hat*
ha*
cos E , cos G
(3)
Socket module:
mt
m . cos E
(4)
Fig. 4. Involute-bevel gear
With the help of emulation tooth profile rack-type tool to create a number of profiles with a certain step s along the axis of the wheel. In Autodesk Inventor, create work planes at a distance from each other at a pitch s, and copy to the appropriate profiles. IBG get a solid model using the Loft applications. 5. Bevel gears with teeth profile non-involute These wheels are formed on the basis of the wheel and producing involute gear is used for special purposes [3]. To construct a model using the software package: "The calculation and analysis of the geometry of the links cylinder-conical gears", created at the Department of technical mechanics, a branch of South Ural State University. [4]
372
V.V. Bruzhas and B.A. Lopatin / Procedia Engineering 129 (2015) 369 – 373
The complex consists of several modules: a) a module for calculating the coordinates of points of the lateral surface of the conical wheels non-involute tooth profile, is an executable file exe MS-DOS (KOORD.exe); b) a module for calculating the coefficients of the displacement of various sections non-involute bevel gear, is an executable file exe MS-DOS (KOSM.exe); c) a module for preparing data for profile modification non-involute bevel gear, which is a file-aided calculation and data storage applications Microsoft Excel (MOD.xls); d) a module for calculating the trajectory of the cutters, is an executable file exe MS-DOS (FREZ.exe); e) detailed operating instructions of «calculation and analysis of the geometry of the links cylinder-conical gears", including a step by step description of the actions of the operator workstation (a solid copy and electronic version in format PDF). The procedure for constructing a solid model of the conical wheels non-involute tooth profile with the parameters (z = 38, m = 2 mm., E = 0o, b = 5 mm.), As follows: 1. With the help of the module software package [4] calculated the parameters of face sections of the wheels through a step along the axis of the wheel (Table 1); 2. Using a complex emulation gear cutting rack generating circuit formed end section of the tooth. The parameters of initial contour are selected from the table for each value of w. Table 1. The parameters of the mechanical section of the conical wheels The average Coefficient Applicate Thickness radius of the bias section tooth s tooth r1 xt w 0.0 2.584 42.517 2.815 0.5 2.556 42.447 2.853 1.0 2.525 42.377 2.886 1.5 2.491 42.307 2.912 2.0 2.453 42.236 2.934 2.5 2.414 42.166 2.951 3.0 2.371 42.096 2.964 3.5 2.325 42.026 2.972 4.0 2.278 41.955 2.977 4.5 2.229 41.885 2.978 5.0 2.178 41.815 2.976
Įt
h*ta
h*te
ɫ*t
19,887 19,865 19,841 19,815 19,788 19,759 19,728 19,695 19,660 19,624 19,586
1,006 1,007 1,009 1,010 1,012 1,013 1,015 1,017 1,019 1,021 1,023
2,012 2,015 2,017 2,020 2,023 2,027 2,030 2,034 2,038 2,042 2,046
0,252 0,252 0,252 0,253 0,253 0,253 0,254 0,254 0,255 0,255 0,256
Before the formation of the toothed wheel in the program Autodesk Inventor, you must in each profile format AutoCAD allocate segments with one tooth as in the construction of helical wheel. In Autodesk Inventor, create sketches of the mechanical section of teeth at a certain distance from each other along the axis of the wheel and insert in each of its segments. With the application "Loft" form a solid-tooth, which were formed by applying an array of bevel gear (Fig. 5).
Fig. 5. The conical wheel non-involute tooth profile.
V.V. Bruzhas and B.A. Lopatin / Procedia Engineering 129 (2015) 369 – 373
373
6. Summary Thus, using the software "Simulation cutting involute spur gear generating rack contour" software "Calculation and analysis of the geometry of gearing helical bevel gears" and of Autodesk Inventor, you can get a solid model of involute bevel and bevel gears with non-involute profile teeth, which further allows to produce a study of stressstrain state of the transmission data composed of gears. References [1] B.A. Lopatin, S.A. Khaustov, RU patent ʋ6853. (2006). [2] B.A. Lopatin, O.N. Tsukanov, Helical-bevel gears: monograph, SUSU, Chelyabinsk, 2005. [3] B.A. Lopatin, O.N. Tsukanov, E.A. Poluektov, Angular adjustment electromechanical drive in aerospace industry, Vestnik mashinostroeniya. 2 (2009) 14–16. [4] B.A. Lopatin, S.A. Khaustov, E.A. Polouektov, RU certificate of state registration of the computer software package 200961002, ʋ 2009614819. (2009).
