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Electrical Engineering Mechanical Systems Design Handbook Dorf CRC Press 2002819s_3

Tham khảo tài liệu 'electrical engineering mechanical systems design handbook dorf crc press 2002819s_3', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Fxj -F cosIj - jnộj Fyj Fj sin Ij - Fj cos ộj 4.18 and summing the cutting forces contributed by all teeth the total dynamic milling forces acting on the cutter are found as N-1 N-1 Fx w F Fj Ij j 0 j 0 4.19 where Ij I j p and cutter pitch angle is Ip 2n N. Substituting the chip thickness 4.16 and tooth forces 4.7 into 4.18 and rearranging the resulting expressions in matrix form yields t F F y 1 1 1 aK 2 a xx a. yx axy M ayy JlAyJ 4.20 where time-varying directional dynamic milling force coefficients are given by axx 1 - gj sin2Ij Kr 1 - cos2Ij j 0 N-1 axy -gj 1 cos2I j Kr sin 2I j j 0 ayx gj 1 - cos2I j - Kr sin2I j j 0 gj sin2Ij - Kr 1 cos2Ij j 0 Considering that the angular position of the parameters changes with time and angular velocity Equation 4.20 can be expressed in time domain in a matrix form as10 11 F t 1 aKt A t A t 4.21 2 t As the cutter rotates the directional factors vary with time which is the fundamental difference between milling and operations like turning where the direction of the force is constant. However like the milling forces A t is periodic at tooth passing frequency 0 NO. or tooth period T 2n o thus can be expanded into Fourier series. . 1 T A t Ar eirot Ar T J A t e-irotdt r -tt 0 4.22 2002 by CRC Press LLC The number of harmonics r of the tooth-passing frequency a to be considered for an accurate reconstruction of A t depends on the immersion conditions and the number of teeth in the cut. If the most simplistic approximation the average component of the Fourier series expansion is considered i.e. r 0 A0 1 í T A t dt. 4.23 T 0 Because A0 is valid only between the entry ộst and exit ộ angles of the cutter i.e. gj ộ j 1 and ộj Q t and ộp Q T it becomes equal to the average value of A t at cutter pitch angle ộp 2n N. A 0 dT í.1 A ộ dộ N a ộ p J ộ 2n Ia xx yx a xy a yy J 4.24 where the integrated functions are given as a xx a xy a yy 1 cos2ộ-2 Kộ K sin2ộ ộ ị - sin 2ộ - 2ộ Kr cos2ộ ộ 2 - sin 2ộ 2ộ Kr cos2ộ ộ 2 - cos 2ộ - 2Krộ - Kr sin 2ộ ộ