TAILIEUCHUNG - Gear Geometry and Applied Theory Episode 3 Part 7

Tham khảo tài liệu 'gear geometry and applied theory episode 3 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Generation of a Surface with Optimal Approximation 763 Figure Determination of maximal deviations along line Lgk. MINIMIZATION OF DEVIATIONS 6p j. Consider that deviations i j i 1 . n j 1 . m of sg with respect to sp have been determined at the n m grid points. The minimization of deviations can be obtained by corrections of previously obtained function p 1 ớp . The correction of angle p is equivalent to the correction of the angle that is formed by the principal directions on surfaces st and sg. The correction of angle p can be achieved by turning of the tool about the common normal to surfaces st and sp at their instantaneous point of tangency Mk. The minimization of deviations 5i j is based on the following procedure Step 1 Consider the characteristic Lgk the line of contact between surfaces st and sg that passes through current point Mk of mean line Lm on surface sp Fig. . Determine the deviations 5k between st and s p along line Lgk and find out the maximal deviations designated as 5kmax and 5kmax- Points of Lgk where the deviations are maximal are designated as Nfr1 and N 2 . These points are determined in regions I and II of surface sg with line Lm as the border. The simultaneous consideration of maximal deviations in both regions enables us to minimize the deviations for the whole surface sg. Note. The deviations of st from s p along Lgk are simultaneously the deviations of sg from sp along Lgk because Lgk is the line of tangency of st and sg. Step 2 The minimization of deviations is accomplished by correction of angle Pk that is determined at point Mk Fig. . The minimization of deviations is performed locally for a piece k of surface sg with the characteristic Lgk. The process of minimization is a computerized iterative process based on the following considerations i The objective function is represented as Fk min ax 42rLx with the constraint 5i j 0. ii The variable of the objective function is APk. Then considering the .

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