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/m 3 Absolute viscosity 0.03 Ns/m 2 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 cm 3 /rev, and a fixed capacity motor of 120cm 3 /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%. (0.48 L/rev, 130cm 3 /rev) P Chapple February 2005. Tutorial Questions 1
3) 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 4) 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. The D Arcy equation for the pressure drop is: 2 L ρ U p = 4f where L is the equivalent length of the pipe including the allowance d 2 for pipe fittings and bends. 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. System properties: Fluid 32 Grade mineral oil (32 cst at 40 0 C) Temperature 50 C Pressure 100 bar Pump flow 60 L min -1 P Chapple February 2005. Tutorial Questions 2
Figure 1 Move and press hydraulic circuit. Figure 2 Installation diagram. P Chapple February 2005. Tutorial Questions 3
Figure 3 Resistance of Valve Ports. Figure 4 Oil Viscosity Variation with Temperature P Chapple February 2005. Tutorial Questions 4
Figure 5 Pressure Loss in Pipe Bends, Connectors and Fittings (Equivalent Length as Number of Pipe Diameters) P Chapple February 2005. Tutorial Questions 5
Figure 6 Moody Diagram for Pipe Friction Factors P Chapple February 2005. Tutorial Questions 6
5) a) For the circuit shown in Figure 1, it is required to determine the size of the restrictor ( as a rated flow) that is to be used during extension of the actuator. For the data given calculate the rated flow of the restrictor valve (L/min) at a rated pressure drop of 10bar that will provide the specified actuator velocity. (19L/min) P P Q P P S A B P S Q S P T P smax Data Figure 1 Actuator Circuit Opposing force on the actuator rod = 20 kn Actuator velocity = 0.5 ms -1 Actuator piston diameter = 50 mm Actuator rod diameter = 25 mm Relief valve set pressure (P smax ) = 200 bar Pump flow = 80 L/min The pressure in the return line from the actuator can be assumed to be zero. b) Show how the circuit can be modified in order that the extending actuator velocity will be controlled when the force is negative (pulling). c) In order to prevent the actuator velocity changing with changes in the load force a pressure compensated flow control valve can be used in place of the restrictor valve. Draw a sketch of this type of valve and briefly describe its method of operation. P Chapple February 2005. Tutorial Questions 7
Question based on Chapter 7, 5.4 6) A1 A 2 Velocity U E Force F Q 1 Q 2 P 1 P 2 Rod for equal area actuator A B α = A 1 /A 2 P T P S i) A four-way spool valve is used to position a hydraulic actuator with a supply pressure of 250 bar. The valve spool is a fully annular design of 6 mm diameter, with a maximum movement of 0.5 mm and C q = 0.62. For a double ended actuator (equal area) having areas of 12.5 cm 2 calculate the maximum power which can be transmitted to the actuator and its speed and thrust at this condition. (20.8 x 10 3 N, 0.46m/s, 9.6 kw) ii) For an unequal area actuator with zero force conditions show that the ratio of extension velocity (u E ) to retraction velocity (u R ) is given by: u u E R A = 1 A 2 iii) For an unequal area actuator having areas of 12.5 and 25 cm 2 respectively, and using the valve and supply pressure in i) calculate the thrust and actuator pressures when extending at 0.49 ms -1. (58bar, 48bar, 8.5kN) 7) Questions based on Chapters 3 and 7 It is required to select an actuator, which is pin jointed at both ends and mounted horizontally, to move a load as described in the data. Using the data sheet in Table 1 for a range of available actuators having different mounting methods, select an actuator that will provide the necessary stroke length and required stall force for the extension of the actuator. P Chapple February 2005. Tutorial Questions 8
Calculate the actuator pressures and flows for the given load duty condition and determine the rated flow for a valve rated total pressure drop of 70 bar (35 bar across each valve metering edge, or land). (case 3 & 4 at 100bar 860mm, case 3, 82bar, 4.3bar, 131L/min) Table 1 Actuator Data P Chapple February 2005. Tutorial Questions 9
Load Data Maximum stall force Actuator stroke 31000 N 800 mm Load operating condition Force = 25000 N at 0.5 m/s velocity. 8) A four-way spool valve is used to control a hydraulic motor operating against a steady load with a supply pressure of 140 bar. The valve has fully annular ports with a spool of 12.5mm diameter, which is opened by 1.25 mm. The motor has a displacement of 64 cm 3 /rev, with a mechanical efficiency 90% and a volumetric efficiency of 95%. For a load torque of 32 Nm. calculate the motor speed and the overall efficiency of the system. (2980 rev/min, 21.4%) 9) Question based on Chapters 5 and 7 and worked example No. 10 Figure 1 shows a weight-loaded actuator that is operated by a central bypass type of open centre valve. The actuator ports are connected together so that the piston and annulus pressures are always equal and the rod area determines the actuator velocity (i.e. the inlet flow from the valve = the piston flow the annulus flow) a) For the given data tabulate, or plot graphically, the relationship between the actuator velocity and pump pressure with the valve position for zero actuator load force. (max velocity = 1.72 m/s, at x = 6mm and zero at x = 2mm) b) For a valve opening of 5mm determine the stalled actuator load and the maximum possible actuator velocity. (136.2kN and 1.29m/s from a)) c) For the valve opening in b) estimate the actuator force when the flow from the outlet port A of the valve is 100 and 200 L/min respectively. (76kN, 30kN) Describe the purpose of the check valve shown in Figure 1. (to prevent load reversal) P Chapple February 2005. Tutorial Questions 10
A Figure 1 Valve control of a weight loaded actuator Data Pump flow Valve spool diameter (d) Central bypass opening for valve in central position (L) Valve overlap at port A (x 0 ) Actuator rod diameter Actuator piston diameter = 400 L/min = 12 mm = 6 mm = 2 mm = 70 mm = 100 mm 10) Question based on Chapter 6 a) Show that the volume that can be discharged from a gas type accumulator is given by the following equation: P2 P 0 V0 = V 1 P2 γ 1 P 1 p 0 is the precharge pressure V 0 is the stored volume at the precharge pressure P 1 is the minimum pressure required for operation of the system P 2 is the maximum required pressure Assume that the gas is compressed isothermally from P 0 to P 2 and expands adiabatically from P 2 to P 1 with the adiabatic index γ. b) A hydraulic actuator is required to perform 60 cycles per hour, each cycle requiring 0.9 litres of oil to operate the actuator in a time of 8s. A fixed displacement pump supplies 1 litre/min to the system the outlet pressure of which is controlled by a relief valve at a pressure of 100 bar. P Chapple February 2005. Tutorial Questions 11
Determine the volumetric capacity of the accumulator that is required to operate the system at a minimum pressure of 75 bar. The precharge pressure is set at 90% of the minimum pressure and the adiabatic index to be used is 1.6. (5.6L) Question based on Chapters 2, 7, 8, and 9. 11) A closed loop hydrostatic transmission system is to be used to drive the tracks of an excavator for which there are two motors, each one being used to drive a track as shown in the Figure 1. Figure 1 Excavator track drive a) Using the given data calculate the motor torque required to start moving the excavator up an incline of 20 0 and the motor speed required to drive the excavator on level ground at maximum speed. Use these values to select a suitable motor type from the table that will provide the required performance. (288rev/min, B) b) Calculate: i. The maximum flow from each pump that is required to drive the selected motors. (25L/min) ii. The maximum displacement of each pump. (14.6 cm 3 /rev) iii. The pump pressure and the total input power to the pump that are required to drive the excavator at the maximum speed on level ground. (144bar, 6.65kW) c) Calculate the maximum speed when using a hydraulic fluid having a viscosity of 20 cst. (268rev/min) d) Sketch a circuit for the hydrostatic system, which includes: Relief valves for limiting the maximum circuit pressure Brake control valves The method for supplying boost flow into the circuit. P Chapple February 2005. Tutorial Questions 12
e) It is intended to use variable displacement motors for the excavator track drive system. Calculate the minimum value of motor displacement that can be used to drive the excavator on level ground at the maximum motor flow from b) i) at the maximum pressure of 210bar. (67.8cm 3 /rev) Data Total weight 5400N Maximum speed (U max ) 6m/s Static friction force to start moving the excavator 450N Friction force at speeds > 0 250 + 250U (U = velocity m/s) N Track drive wheel diameter 0.4m Motor mechanical efficiency 85% for starting at zero speed ( η MS ) 92% for motor speeds greater than zero ( η MD ). Pump and motor volumetric efficiencies 95% (with a hydraulic fluid viscosity of 32 centistoke cst) ( ηpv, η MV ) Pump mechanical efficiency Pump speed Maximum pressure 95% ( η PM ) 1800 rev/min (N) 210 bar ( P max ) Motor Data Motor type Theoretical displacement (cm 3 /rev) A 102 250 B 83 300 C 67 350 Maximum speed (rev/min) 12) Question from Chapter 6 A Figure 1 Pump and motor system P Chapple February 2005. Tutorial Questions 13
Data Torque required at maximum motor speed 175Nm Motor displacement 82cm 3 /rev (D M ) Motor mechanical efficiency 92% for motor speeds greater than zero ( η MM ). Motor volumetric efficiency 93% ( η MV ) Pump mechanical efficiency 95% ( η PM ) Pump volumetric efficiency 96% ( η PV ) Pump speed 1800rev/min (N P ) Pump displacement 15cm 3 /rev (D P ) Fluid specific heat 2100J/kg/ 0 C (C P ) Heat dissipated in the cooler for a water inlet temperature of 20 0 TOW C 3 kw 40 ( TOW is the difference between the cooler oil inlet and water inlet temperatures). Pump external drain leakage flow = 50% of the total pump leakage a) For operating the motor against the stated torque that is required at the maximum motor speed calculate: 1) The pressure required at the motor inlet. 2) The pump outlet flow. 3) The motor speed at this operating condition. 4) The flow at the cooler inlet (point A in Figure 2). b) Assuming that all of the volumetric and mechanical losses are dissipated into the hydraulic system fluid and that there is no heat transfer from the fluid to the environment through the pipes calculate: 1) The total heat generated by the losses. 2) The temperature increase in the hydraulic fluid between the pump inlet and the cooler inlet assuming that there is perfect mixing of the flows at point A. 3) The temperature of the hydraulic fluid at the cooler inlet (point A) that is required to dissipate the heat that is generated in 1). (Note that the heat extracted from the fluid in the cooler is dependent on the difference Tow between the temperatures of the hydraulic fluid at the cooler inlet and the cooling water inlet). 4) The reduction in the fluid temperature through the cooler and the temperature in the reservoir. P Chapple February 2005. Tutorial Questions 14