Thermal Influence of the Tooth Geometry in Milling a Conical Gear
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mal Influence of the Tooth Geometry in Milling a Conical Gear N. V. Kanatnikova, *, A. S. Pashmentovaa, **, S. M. Bobrovskiib, ***, and A. S. Selivanovb, **** a
Turgenev Orel State University, Orel, 302026 Russia b Togliatti State University, Togliatti, 445020 Russia *e-mail: [email protected] **e-mail: [email protected] ***e-mail: [email protected] ****e-mail: [email protected]
Received January 24 , 2020; revised January 24, 2020; accepted January 24, 2020
Abstract—The thermal influence of the tooth geometry in a conical gear is considered for the case of milling by a cutting head. Formulas are derived for the maximum temperature and the temperature field in cutting as a function of the geometric parameters of the tooth. On that basis, research in a virtual environment corresponding to the actual conditions is possible at preproduction, and the thermal phenomena may be predicted as a function of the tooth geometry in the gear being milled. Keywords: gear cutting, tooth geometry, conical gears, thermal phenomena, cutting temperature DOI: 10.3103/S1068798X20110118
To meet the steadily increasing performance requirements on conical gears used in gearboxes, differentials, and similar mechanisms, specially developed tooth geometry is employed [1, 2]. The cutting tools for such gears are specially designed and produced for each new gear pair. The introduction of a new tool in established processes impairs surface quality and increases tool wear [2, 3]. At present, only scattered approaches to this problem exist [1–4]. We believe such effects are due to changes in the physical conditions of cutting, the cutter geometry, the mechanism of chip extraction, and the frictional forces at the tool surfaces. These changes increase the cutting force and impair heat extraction. Correspondingly, prediction of the physical phenomena that accompany cutting permits determination of the best cutter geometry and correction of the cutting conditions so as to ensure the required tool life and product precision. MODELING To predict the physical phenomena that accompany the machining of conical gears, we have developed a predictive modeling method [6] on the basis of a hybrid approach [5]. The input data for modeling are as follows: the geometry of the tool’s cutting edge; the machining conditions; the behavior of the material in deformation and at tool–workpiece contact; and the kinematics of cutting.
In modeling, we make the following assumptions. The workpiece is immobile, and the tool performs all the motions required for shaping. The tool is absolutely uniform and hard. The structure of the tool surface is uniform. The structure of the workpiece is geometrically and physically nonlinear. The workpiece deformation is described by the Johnson–Cook method. In Fig. 1, we show the configuration assumed in modeling. The following notation is employed in Fig. 1: a1, b1, a2, and b2 are the geometric parameters of the chip cut by the lateral cutting edge and the cutting tip; r0 is the cutter’s rounding radius; α is its profile angle; s is the s
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