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Tham khảo tài liệu 'theory and design of cnc systems part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 4.2 Acc Dec Control After Interpolation 125 Wx t Ae a Bcoswt sinwt 4.47 where A wK -wK awK w2 a2 w2 a2 w2 a2 Wt t in Eq. 4.47 denotes the speed of the X-axis and by integrating Wx t we obtain the path radius after Exponential-type Acc Dec control has been applied. Equation 4.48a shows the result of the integration of Wx t . From Eq. 4.48a we know that after Acc Dec time the radius of the path from Exponential-type Acc Dec control R is given by Eq. 4.48b. r Ae at B2 C sin wt - 9 a w w2 4.48a where 9 cos B2 73 w2 R B2 C2 B 1 ầ w2 w2 wK w2 a2 a2 w2 4.48b ỉ a . 1 _L W2 ị I 1 2 V1 a2 V1 a2 As the machining error is the difference between the radius of the commanded path and the distorted path due to Exponential-type Acc Dec control the error is simplified as Eq. 4.49. 1 AR C1 2 a2 R R R 1 AR R 1 - 1 -1 n2- w 4.J 2 a 8 a so AR R wV 1 TF2 2 a 2 R 1 z . . z _ where x_ y -m n R 1 z m yy 11 1 m7 m m 1 72 m m 1 m 2 73 1 - mz --2 z----------3 -----z from a binomial series. 4.49 126 4 Acceleration and Deceleration 4.2.3.4 Machining Error Summary The machining error due to the Acc Dec control depends on the type of Acc Dec control filter. The machining errors are summarized in Table 4.5 with respect to each type of Acc Dec control filter. According to Table 4.5 the machining error is proportional to the square of the feedrate and the Acc Dec time. It is also in inverse proportion to the radius of the circular path. Therefore from this we know that the higher the feedrate the longer the Acc Dec time the shorter the radius of the circular path and the larger the machining error. We also know that the accuracy of the S-shape-type Acc Dec control is better than that of the alternatives. Table 4.5 Machining error due to Acc Dec filter Control type Machining Error Remarks Linear AR _ F2T2 AR 24R F Feedrate Exponential AR f 2 AR 2R t Time constant S-shape AR Fr AR 48R R Radius of circle 4.2.4 Block Overlap in ADCAI As mentioned in Chapter 2 the G-code system provides various .
