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robotics Designing the Mechanisms for Automated Machinery Part 4

Tham khảo tài liệu 'robotics designing the mechanisms for automated machinery part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 3.5 Pneumodrive 93 For the supercritical regime the pressure Pi in the cylinder input orifice is constant i.e. Pl PcrPr 0.528pr p. 3.113 Substituting pl from Equation 3.113 into Equation 3.111 we obtain for the supercritical flow rate Gcr r - l fc-l r ------- Gcr aFpPr- - 131141 p Lfc lJ RTr k ỉ Under standard conditions Tr 293 K we have Gcr 0.023 a Fppr. 3.115 Now let us find the time required to fill the cylinder from the initial value of the pressure Po to the final value pr 0.528PJ while the air temperature remains constant. For a cylinder volume Vc we have pVc GcRT 3.116 where Gc instantaneous value of the air weight and T the air temperature. During an infinitesimal time period dt the pressure will change over a value dp and the amount of air will change by Gcr dt. Thus p dpWc RT Gc Gcrdt . 3.117 Substituting Equation 3.116 from Equation 3.117 we obtain 3.118 RT Gcr By integration we obtain h YlP1 Po 3.119 RT Gcr By substituting Equation 3.115 into Equation 3.119 we finally reach Vc Pi-Po 3.120 0.67T aFpPr When time i has passed two outcomes are possible 1. The piston begins its movement earlier than tỵ i.e. the movement begins before pressure Pi appears in the cylinder volume . 2. The pressure in the cylinder is still not sufficient to initiate the movement of the .piston. TEAM LRN 94 Dynamic Analysis of Drives For the first case we have to integrate Equation 3.118 in the limits from Pq to some pressure p which is less than that at ip Thus in place of Equation 3.120 we obtain For the second case we have to continue our investigation for the subcritical regimes. For a subcritical regime Pỉ P PcrPr 0.528pr. Now in Equation 3.111 the value of p varies from the initial value of 0.528 to 1. In this case we must substitute in the differential Equation 3.118 G which is not constant and is defined by Equation 3.111 . Thus TZ IrTj. fc-lj vc P - dp dt V 2g fc 3.122 RT aFppr 4p2lk - p k Y lk Since p ppr dp prdp. Therefore dt O Op22 prp ỵt 1 - Ỉì k- ìỉk 1 2d 3. 3.123 To