OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 5 No. 2 2023 The use of the obtained equations makes it possible to calculate the inclination angle of RPI side rake angle and the rotation angles of the milling cutter along the direction of the translational feed movement that will provide the best fit of the generating surface of the milling cutter and the part surface at its contact points. It is advisable to perform this calculation in the following sequence: 1) for a specified diameter of the milling cutter, using equation (7), we calculate the minimum value of the angle λ (at x = 0°) that provides the best fit of the generating surface of the milling cutter at the point of the surface with the least curvature (the largest principal radius of curvature) according to the condition: max ( , ) d R R ≈ l x , (17) where max d R is the largest radius of the profile curvature of the surface being formed; ( , ) R l x is the principal radius of the machined surface curvature by the milling cutter at a specified angle λ and the angle of the cutter rotation ξ. 2) at the specified value of angle l, we calculate the inclination angles of the milling cutter x at the remaining points of the profile of the surface being formed according to condition (17). In case when the surfaces to be machined have a large value range of the principal radius of curvature, it may not be possible to achieve strict equality (17) at all points. Then for these points it is necessary to take angle x equal to the largest possible value (x = 45°). Results and discussion The practical application of the constructed models and established regularities will be considered through the example of machining the involute surface of a spur coarse pitch gear (fig. 9, a) with pitch of 9 mm, 21 teeth and a face width equal to 50 mm and with the following equation: [ ] 0 0 ( , ) (cos sin ) (sin cos ) 1 , d r u v R u u u R u u u v Τ = + − (18) where R0 is the radius of the generating circle of the gear wheel; for our wheel R0 = 197.3 mm. The calculation of the principal radius of curvature of this surface in the across-track direction has shown that its size at u ∈ [0; 0,61] varies from 0 to 120.5 mm. Taking the diameter of the milling cutter as 30 mm, the calculation of the minimum angle value l (at x = 0°) is performed to attain the best fit of the generating surface of the milling cutter to the surface point with the least curvature (the largest principal radius of curvature) u = 0.61 according to the condition (17). By specifying the incremental step of angle l equal to 30’ and the angle x = 0°, it is found that condition (17) is fulfilled at l = 19° with R(19°) = 126.5 mm. Further, with the set the angle l = 19°, the calculation of inclination angles of the milling cutter ξ is performed for the profile points of the surface formed (fig. 10). a b Fig. 9. Spur gear: a – a geometric model; b – the result of modeling the surface of the teeth according to (17)
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