Problem

(A) A double-acting hydraulic cylinder has an inside diameter of 80 mm. The piston rod has a diameter of 15 mm. The hydraulic power source can generate up to 4.0 MPa of pressure at a flow rate of 125,000 mm3/sec to drive the piston. (a) What are the maximum possible velocity of the piston and the maximum force that can be applied in the forward stroke? (b) What are the maximum possible velocity of the piston and the maximum force that can be applied in the reverse stroke?

Step-by-step solution

1. Step 1 of 7

   Calculate the forward stroke area.

   

   Here,  is the inside diameter of the cylinder.

   Substitute 80mm for .

   

   Calculate the reverse stroke area.

   

   Here,  is the diameter of the piston rod.

   Substitute  for , and 15mm for .

   

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2. Step 2 of 7

   a)

   Calculate the maximum possible velocity of the piston.

   

   Here,  is the flow rate, A is the area of cylinder, and d is the diameter of the cylinder.

   Substitute  for Q and  for .

   

   Hence, the maximum possible velocity of the piston is .

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3. Step 3 of 7

   Calculate the maximum force that can be applied in the forward stroke.

   

   Here, p is the hydraulic power source.

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4. Step 4 of 7

   Substitute  for p, and  for .

   

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5. Step 5 of 7

   Hence, the maximum force that can be applied in the forward stroke is .

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6. Step 6 of 7

   b)

   Calculate the maximum possible velocity of the piston.

   

   Substitute  for Q and  for .

   

   Hence, the maximum possible velocity of the piston is .

   Comment

7. Step 7 of 7

   Calculate the maximum force that can be applied in the reverse stroke.

   

   Substitute  for p, and  for .

   

   Hence, the maximum force that can be applied in the reverse stroke is .

   Comment