TEP 4205 INDUSTRIAL HYDRAULICS

P Chapple February 2004. Tutorial Questions February 2004. 1

TUTORIAL QUESTIONS FOR THE INDUSTRIAL HYDRAULICS COURSE TEP 4205

The book for the course is Principles of Hydraulic System Design, by Peter J Chapple. Published by Coxmoor Publishing Co., UK. Available from www.bfpa.co.uk. Tel +44 1608 647900, email enquiries@bfpa.co.uk Data:

Hydraulic Oil Density 870 kg/m3 Absolute viscosity 0.03 Ns/m2 Spool valve discharge coefficient 0.62.

Questions based on Chapters 2, 8 and 9. 1) A hydrostatic transmission has a variable displacement axial-piston pump, with a maximum displacement of 12 cm3/rev, and a fixed capacity motor of 120cm3/rev displacement. The motor speed is 138 rev/min when driving a load torque of 200Nm and when the pump is set to maximum displacement and driven at a speed of 1450 rev/min. Note This information enables the value of the total leakage and volumetric efficiency to be determined by calculating the ideal pump flow and motor speed. The total leakage is assumed to be proportional to the pressure. If the load is increased to 400 Nm and the pump control set to 50% maximum capacity, estimate: (a) the steady state speed of the motor (58.5 rev/min) (b) the input power to the pump and the overall efficiency (3.6 kW, 69%) The pump mechanical efficiency is 95% at full stroke and 90% at half stroke. The motor mechanical efficiency is 95%. 2) A hydrostatic pump and motor are used as the power transmission for a cargo winch, for which the prime mover is a 1450 rev/min induction motor. The winch drum is 0.6m diameter and the maximum load of 30 kN is lifted at speeds up to 1.8 m/s. The pump has a variable displacement so as to provide a wide range of motor speeds and has a maximum pressure rating of 200 bar. Calculate suitable sizes for the pump and motor for a motor mechanical efficiency of 94% and a pump volumetric efficiency of 92%. (130cm3/rev, 0.48 L/rev)

TEP 4205 INDUSTRIAL HYDRAULICS

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3) For hydrostatic pumps operating at constant speed sketch the graphs that relate the input and output powers and the ideal and output flows against pressure. Show the mechanical and volumetric losses. Using the Wilson method show how the mechanical and volumetric efficiencies are derived from the losses and the relationship of the efficiencies with the non-

dimensional parameter P

orP µωµω

.

A piston pump when operating at 1500 rev/min and a pressure of 100 bar has measured volumetric flow losses of 2.5%. The maximum overall pump efficiency is shown to occur in the region when the values of the slip and viscous friction loss coefficients are equal. Using this definition calculate the values of the volumetric and mechanical loss coefficients that will give maximum overall efficiency.

(1.18x10-8, 2.13x105) 4) The volumetric efficiency of a hydraulic pump is 97.5% and its mechanical efficiency is 90% when it is operating at 1450 rev/min and the delivery pressure is 100 bar. At this condition the viscous friction and coulomb friction torque losses are equal. Calculate the variation of the losses as a function of pressure and hence obtain values of overall efficiency for delivery pressures ranging from 0 to 200 bar. Determine the maximum overall efficiency. (88.1%) Question based on Chapter 8 5) The hydraulic circuit shown in Figure 1 is a simple move and press circuit with two linear actuators controlled by two directional control valves. A fixed displacement pump having a relief valve to limit the maximum system pressure supplies hydraulic fluid. The circuit is designed such that the press actuator can only be activated when the move actuator is held in the fully extended position. Figure 2 illustrates how this system could have been installed in the factory. It is required to select a suitable pipe diameter, and to estimate the resulting pressure loss between the pump and the inlet to the piston end of the ‘move’ actuator under normal operating conditions. Use the graphical data given in Figures 4 - 6. Note It is usual to aim at a mean fluid velocity of 5ms-1, which can be used to determine an initial diameter for the pipe for a first calculation.

TEP 4205 INDUSTRIAL HYDRAULICS

P Chapple February 2004. Tutorial Questions February 2004. 3

System properties: Fluid 32 Grade mineral oil (32 cSt at 400C) Temperature 50°C Pressure 100 bar Pump flow 60 L min-1

Figure 1 Move and press hydraulic circuit.

TEP 4205 INDUSTRIAL HYDRAULICS

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Figure 2 Installation diagram.

Figure 3 Resistance of Valve Ports.

TEP 4205 INDUSTRIAL HYDRAULICS

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Figure 4 Oil Viscosity Variation with Temperature

Figure 5 Pressure Loss in Pipe Bends, Connectors and Fittings (Equivalent Length as Number of Pipe Diameters)

TEP 4205 INDUSTRIAL HYDRAULICS

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Figure 6 Moody Diagram for Pipe Friction Factors

TEP 4205 INDUSTRIAL HYDRAULICS

P Chapple February 2004. Tutorial Questions February 2004. 7

Question based on Chapters 2 and 8. 6) A gear pump is used to supply flow through a long pipe to a hydraulic actuator that supports the force from a vertical load. Calculate the velocity of the actuator and the pump pressure that will be obtained when operating with the given data. Data Actuator diameter 50 mm Pump displacement 16 cm3rev Pump speed 1500 rev/min Pump delivery flow 18 L/min at 50 bar Load 104 N Pipe details 10 mm diameter, 60 m length. Oil kinematic viscosity 40 x 10-6 m2/s (i.e. 40 centistoke) Note The leakage flow loss in the pump can be calculated from the data. The pump pressure needs to be sufficient to provide the load pressure in the actuator and the pressure loss in the pipe. Assume that the pump leakage varies linearly with pressure and that the flow is laminar in the pipe to obtain an analytical solution to the problem. Check the pipe Reynolds No.

(0.13 m/s, 72.7 bar).

Flow

Pump pressure

Load pressure + Pipe loss

Pump