tailieunhanh - 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 | Pneumodrive 93 For the supercritical regime the pressure Pi in the cylinder input orifice is constant . Pl PcrPr p. Substituting pl from Equation into Equation 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 a Fppr. Now let us find the time required to fill the cylinder from the initial value of the pressure Po to the final value pr while the air temperature remains constant. For a cylinder volume Vc we have pVc GcRT 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 . Substituting Equation from Equation we obtain RT Gcr By integration we obtain h YlP1 Po RT Gcr By substituting Equation into Equation we finally reach Vc Pi-Po aFpPr When time i has passed two outcomes are possible 1. The piston begins its movement earlier than tỵ . 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 in the limits from Pq to some pressure p which is less than that at ip Thus in place of Equation we obtain For the second case we have to continue our investigation for the subcritical regimes. For a subcritical regime Pỉ P PcrPr . Now in Equation the value of p varies from the initial value of to 1. In this case we must substitute in the differential Equation G which is not constant and is defined by Equation . Thus TZ IrTj. fc-lj vc P - dp dt V 2g fc 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. To