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Kinematic Geometry of Surface Machinin Episode Episode 5

Tham khảo tài liệu 'kinematic geometry of surface machinin episode episode 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 106 Kinematic Geometry of Surface Machining Crv P of a smooth regular surface P are listed along with the corresponding sign of the mean MP and of the Gaussian GP curvatures Figure 4.6 Convex elliptic MJ 0 GP 0 in Figure 4.6a Concave elliptic MJ 0 GP 0 in Figure 4.6b Convex umbilic MP 0 GP 0 in Figure 4.6c Concave umbilic MP 0 GP 0 in Figure 4.6d Convex parabolic MP 0 GP 0 in Figure 4.6e Concave parabolic MP 0 GP 0 in Figure 4.6f Quasi-convex hyperbolic MP 0 GP 0 in Figure 4.6g Quasi-concave hyperbolic MP 0 GP 0 in Figure 4.6h Minimal hyperbolic MP 0 GP 0 in Figure 4.6i Phantom branches of the characteristic curve in Figure 4.6g through Figure 4.6i are indicated by dashed lines. For a plane local patch of a surface P the curvature indicatrix does not exist. All points of this characteristic curve are remote to infinity. 4.3.8 Introduction of the Jr k P T Characteristic Curve For the purpose of analytical description of the distribution of normal curvature in differential vicinity of a point on a smooth regular surface Bohm recommends 1 that the following characteristic curve be employed. Setting h dVP dUP at a given point of a sculptured surface P one can rewrite the equation k _ 02-P _ LP dUP 2 MP dUP dVP NP dVP P PPP EP dUP 2 FP dUP dVp GP dV2 4.46 for normal curvature in the form of kP LP 2 MP n NP n2 EP 2 FP n GP n2 4.47 In the particular case when LP MP NP EP FP GP the normal curvature kP is independent of h. Surface points with this property are known as umbilic points and flatten points. In general cases when kP changes as h changes the function kP kP n is a rational quadratic form as illustrated in Figure 4.7. The extreme values k1P and k2.p of kp kp n occur at the roots ni and n2 of n2 -n 1 EP FP GP 0 LP MP NP 4.48 2008 by Taylor Francis Group LLC 108 Kinematic Geometry of Surface Machining The discussed methods of higher-order analysis target the development of an analytical description of the rate of conformity of the generating surface T of the cutting