The diameter of the ram cylinder of a hydraulic press is 200mm. The stroke length of the plunger is 50mm. the effort on the plunger is 5% of the load. Calculate,
i) the volume of the liquid needed per stroke if the load has to be lifted 60mm in 30 strokes, if the slip is considered to be 0.06
ii) the diameter of the plunger
iii) the effort required on the handle to lift a load with a mass of 2 tonnes
iv) the work done by the ram if efficiency of the press is 85%
To answer these questions, we'll need to use some basic principles of fluid mechanics and hydraulic systems. Let's go step by step.
i) The volume of liquid needed per stroke can be calculated using the formula:
Volume = Area x Stroke Length
First, we need to calculate the area of the ram cylinder. The formula for the area of a circle is:
Area = π x (radius)^2
Given that the diameter of the ram cylinder is 200mm, we can calculate the radius by dividing the diameter by 2:
Radius = 200mm / 2 = 100mm = 0.1m
Using the formula for the area of a circle:
Area = π x (0.1m)^2 = 0.0314 m^2
Now, we can calculate the volume of liquid needed per stroke:
Volume = 0.0314 m^2 x 0.05 m = 0.00157 m^3
However, we need to consider the slip factor, which is 0.06. This means that 6% of the volume is lost due to slip.
Adjusted Volume = Volume / (1 - Slip)
Adjusted Volume = 0.00157 m^3 / (1 - 0.06) = 0.00166 m^3
To calculate the total volume needed to lift the load 60mm in 30 strokes, we multiply the adjusted volume by the number of strokes:
Total Volume = Adjusted Volume x Number of Strokes
Total Volume = 0.00166 m^3 x 30 = 0.0498 m^3
Therefore, the volume of liquid needed per stroke, considering slip and the specified conditions, is 0.00166 m^3.
ii) To calculate the diameter of the plunger, we need to know the relationship between the ram cylinder and the plunger. Without this information, it is not possible to determine the diameter of the plunger.
iii) The effort required on the handle to lift a load can be calculated using the formula:
Effort = Load x (Effort/Load)
Given that the load has a mass of 2 tonnes (2000 kg) and the effort is 5% of the load:
Effort = 2000 kg x (5/100) = 100 kg
Therefore, the effort required on the handle to lift a load with a mass of 2 tonnes is 100 kg.
iv) To calculate the work done by the ram, we need to know the formula for work. The formula for work is:
Work = Force x Distance
Given that the efficiency of the press is 85%, we know that the actual work done is only 85% of the calculated work.
Therefore, without knowing the applied force or the distance traveled, we cannot calculate the work done by the ram.