Pneumatic Actuators PDF

163 | P a g e Pneumatic CHAPTER 9 Actuators 9.1 Pneumatic Actuator Function A pneumatic actuator was introduced in Chapter 1 as a device that converts fluid power in compressed air into linear kin...

163 | P a g e Pneumatic CHAPTER 9 Actuators 9.1 Pneumatic Actuator Function A pneumatic actuator was introduced in Chapter 1 as a device that converts fluid power in compressed air into linear kinetic power at the rod of a pneumatic cylinder, or rotational kinetic power at the shaft of a pneumatic motor, by expanding compressed air. A pneumatic cylinder is represented by the same symbol as that of a hydraulic cylinder, as given in Table 3-10. A symbol for a pneumatic motor is different from that of a hydraulic motor, and is given in Table 1-2. 9.2 Actuator Cycle Figure 9-1 shows the expansion cycle of an actuator on a pressure-volume diagram. The intake and discharge valves are manually controlled to achieve the desired performance. Johan Fourie, BCIT  164 | P a g e Figure 9-1 Pressure-volume diagram of an expansion cycle. The different processes that make up the actuator cycle are described as follows:  The intake valve is open and the air is at operating pressure.  -  The volume of air expands while the intake valve remains open and the pressure remains constant at operating pressure.  The intake valve closes to form an enclosed volume.  -  The enclosed volume expands and air undergoes polytropic expansion between operating pressure and discharge pressures.  The discharge valve opens.  -  The pressure drops promptly from the discharge pressure to atmospheric pressure. Johan Fourie, BCIT  165 | P a g e  - The volume contracts and air is discharged at atmospheric pressure. The discharge valve closes and the intake valve opens. -  The pressure rises promptly from atmospheric pressure to opeating pressure. EXAMPLE 9-1 The actuator cycle shown in Figure 9-1 operates between an operating pressure of 740 kPa abs and standard atmospheric pressure. With 𝑉 1804 cm , determine 𝑉 if the discharge pressure is 420 kPa abs and a polytropic index of 1.35 is assumed for the expansion process. Solution 𝑝3 420 kPa. 𝑝2 𝑉2 𝑝3 𝑉3 ⇒ 𝑉2 𝑉3 1804 cm3 1186 cm3 𝑝2 740 kPa 9.3 Swept Volume, Displacement Volume, and Intake Ratio The swept volume 𝑉 of an actuator is the maximum volume expansion during one actuator cycle. For the actuator cycle shown in Figure 9-1, it will be the volume at . The swept volume can typically be calculated from the geometry of the actuator. The displacement volume 𝑉 is the volume enclosed when the intake valve closes at  in Figure 9-1. The ratio of the displacement volume to the swept volume is referred to as the intake ratio 𝑘 , and is given as 𝑉 ⬚ 𝑘 ⬚ (9-1) 𝑉 ⬚ where: 𝑉 displacement volume 𝑉 swept volume When designing or specifying a pneumatic actuator, consideration must be given to the desired intake ratio. If the inlet valve is left open for the entire duration of cylinder extension (𝑘 1), then the expansion process shown between  and  in Figure 9-1 will not occur. The pressure in the cylinder remains constant at operating pressure during extension. Once the cylinder is fully extended and the discharge valve opens air at operating pressure is released to the atmosphere. Johan Fourie, BCIT  166 | P a g e If the inlet valve is closed before the cylinder reached full extension 𝑘 1 , then for the remainder of the cylinder extension, actuation continues as the air expands, as shown between  and  in Figure 9-1. The pressure in the expansion chamber should still be above the minimum pressure required to actuate the load. The minimum value for the intake ratio is determined by the minimum pressure 𝑝min required to actuate the load, and is given as: 𝑝min 𝑘min 9-2 𝑝oper where: 𝑘min inimum value for the intake ratio 𝑝min minimum absolute pressure required to actuate the load 𝑝oper absolute operating pressure 𝑛 polytropic index Whether the inlet valve is closed before the cylinder reached full extension, or not, depends on the application of the actuator:  Constant-pressure actuation 𝑘 1 exerts maximum pressure on the moving surface. However, the air consumption per cycle is also at a maximum. Thus, this option is suitable for applications where a high power output needs to be generated from a compact design, such as pneumatic hand tools, and where a high compressed air consumption rate is not a concern.  Expansion actuation 𝑘 1 is used where air supply is limited or where energy savings is of importance. For these applications the drop in the actuation pressure during air expansion can be mitigated by using multiple expansion processes that are phased in a way to balance out variations in actuation force. 9.4 Displacement Volume Flow Rate The displacement volume flow rate 𝑄 of a pneumatic motor is the product of the displacement volume and the expansion cycle rate. With one expansion cycle corresponding to one revolution of a motor, it follows that 𝑄 𝑉𝑁 𝑘𝑉 𝑁 (9-3a or, with one revolution equal to 2𝜋 radiations, 𝜔 𝜔 𝑄 𝑉 𝑘𝑉 (9-3b) 2𝜋 2𝜋 where: 𝑉 displacement volume 𝑉 swept volume volume 𝑘 intake ratio 𝜔 angular velocity in terms of radians 𝑁 cycles or angular velocity in revolutions Johan Fourie, BCIT  167 | P a g e EXAMPLE 9-2 A rotary air motor has a swept volume of 80 cm3 and operates at 1750 rpm using air regulated to an operating pressure of 650 kPa gage. The minimum actuation pressure is 380 kPa gage. Assuming a polytropic index for expansion of 1.35, compare the displacement flow rate in m3/min at inlet conditions of a motor that is designed for constant pressure actuation, to that designed for maximum expansion actuation. Solution Constant pressure actuation: 𝑘 1 3 1m rev m3 𝑄 𝑉𝑁 80 cm 1750 0.140 100 cm min min For maximum expansion: 𝑘 1 𝑝min 380 101.325 kPa. 𝑘min 0.7190 𝑝oper 650 101.325 kPa 𝑉 𝑘min 𝑉 0.7190 80 cm3 57.52 cm3 1m rev m3 𝑄 𝑉𝑁 57.52 cm3 1750 0.1007 100 cm min min Similar to the volume flow rate of pneumatic compressor, the volume flow rate of a pneumatic actuator is generally rated at standard temperature and pressure for the reasons discussed in Section 9.2. The calculation required to specify the air flow rate at standard atmospheric conditions follows from the application of the general gas law and is therefore given as 𝑄 𝑝 𝑇 (9-4) 𝑄 𝑝 𝑇 where: 𝑄 volume flow rate at STP 𝑄 intake volume flow rate 𝑝 absolute standard pressure 𝑝 absolute operating pressure 𝑇 absolute standard temperature 𝑇 absolute intake temperature Johan Fourie, BCIT  168 | P a g e 9.5 Pneumatic Motor Types and Operation Positive displacement pneumatic motors are mostly of the gear-type, piston-type, or vane- type. Both gear-type and piston-type motors come in different designs, such as gerotor gear-, axial piston- and radial piston motors. Vane-type motors are the most common motor type because of their simple and reliable design, high operating speed, and low maintenance and repair costs. Figure 9-2 shows the internal construction of a vane motor. Its principle is identical to that of a hydraulic vane motor. The unloaded speed of a pneumatic vane motor is typically around 20,000 rpm. For most applications these speeds are too high and the rotor torque is also rather small. To generate a higher torque at lower speed, a planetary gear is used. Vane motors are widely used in hand tools because of their compactness and light weight. A vane motor typically weighs only 1/4 as much as an electric motor with the same power output, and occupies only 1/6 of the space. Figure 9-3 shows different pneumatic hand tools that use vane motors. Figure 9-2 Internal construction of a vane motor. In Figure 9-4 a shows a vane motor that is designed for constant pressure actuation 𝑘 1. It resembles a hydraulic vane motor as the chambers maintain the same volume as the motor rotates clockwise. Each consecutive air chamber closes when its trailing vane is in the 12 o’clock position, but only opens when the leading vane of chamber is in the 6 o’clock position. The volume of the of the air chambers remain constant and actuation of the motor is at operating pressure. Air at operating pressure is released to the atmosphere when each air chamber opens. Figure 9-4 b shows a vane motor that allows for the air to expand in the air chambers as the rotor rotates 𝑘 1. Each consecutive air chamber closes when its trailing vane is in the 12 o’clock position, and opens when the leading vane of the chamber is in the 3 o’clock position. The expanding volume of the of the chamber allows for expansion actuation by the motor and expanded air is released to the atmosphere when each air chamber opens. Johan Fourie, BCIT  169 | P a g e Figure 9-3 Pneumatic hand tools that use vane motors. A B Figure 9-4 Constant pressure actuation vs. expansion actuation vane motor design. Johan Fourie, BCIT  170 | P a g e The derivation for the displacement volume 𝑉 of the motor rotation follows from that of a hydraulic vane motor, and is therefore given as: 𝑉 2𝜋𝑟 𝑛𝑡 𝑟 𝑟 𝐿 9-5 where: 𝑛 number of vanes 𝑡 vane thickness 𝑟 rotor ring radius 𝑟 cam ring radius 𝑟 centerline radius 𝑟 𝑟 /2 𝐿 width of the motor The cam ring radius for a constant pressure actuation motor take on a constant value. For an expansion actuation motor, the leading vane has a larger cam radius than the trailing vane. For the application of Eq. 9-5, the came radius 𝑟 takes on the mean value of that of the leading and the trailing vane 𝑟 𝑟 𝑟 9-6 2 where: 𝑟 cam ring radius of the leading vane when an air chamber closes see Figure 9-4 𝑟 cam ring radius of the trailing vane when an air chamber closes see Figure 9-4 9.6 Pneumatic Cylinders Types and Operation The construction and operation of a pneumatic cylinder is similar to that of a hydraulic cylinder and therefore share commonality with hydraulic cylinders in terms of  Terminology used for cylinder components  Cylinder sealing  Single- vs. double-action cylinder concept  Single- vs. double-rod cylinder concept  Telescopic cylinder concept  Symbols 9.7 Pneumatic Cylinder Volume Figure 9-5 shows the cross-section for a double-acting cylinder, with the cross-sectional area of the blind side shown in Figure 9-5 a and the cross-sectional area of the rod side shown in Figure 9-5 c. The blind side volume change 𝑉 is given as 𝑉 𝐴 𝑠 (9-7) where: 𝐴 piston area 𝑠 piston motion Johan Fourie, BCIT  171 | P a g e EXAMPLE 9-3 An eight-vane motor has a rotor ring radius of 115 mm and a width of 75 mm, and the thickness of the vanes is 7.5 mm. When an air chamber closes, its leading vane has a cam radius of 160 mm and its trailing vane has a cam radius of 110 mm. The motor is supplied with air at an operating pressure of 760 kPa gage and 25 C. Air is discharged from the motor at a pressure of 240 kPa gage. Determine the intake ratio and the swept volume of the motor, and the displacement volume flow rate at standard temperature and pressure that is required to maintain a speed of 1150 rpm. Assume a polytropic index of 1.35 for the expansion process. Solution 𝑝dis 240,000 101,325 Pa abs. 𝑘 0.50376 𝑝oper 760,000 101,325 Pa abs 𝑟 𝑟 160 mm 110 mm 𝑟 135 mm 2 2 𝑟 𝑟 115 mm 135 mm 𝑟 125 mm 2 2 𝑉 2𝜋𝑟 𝑛𝑡 𝑟 𝑟 𝐿 2𝜋 0.125 m 8 0.0075 0.135 m 0.115 m 0.075 m 0.0010881 m3 𝑉 𝑉 0.0010881 m3 𝑘 ⇒ 𝑉 0.002160 m3 𝑉 𝑘 0.50376 rev m3 𝑄 𝑉𝑁 0.0010881 m3 1150 1.2513 min min 𝑄 𝑝 𝑇 ⇒ 𝑄 𝑝 𝑇 𝑝 𝑇 𝑄 𝑄 𝑝 𝑇 3 m 760,000 101,325 Pa abs 15 273.15 K 1.2513 min 101,325 Pa abs 25 273.15 K m3 10.280 min Johan Fourie, BCIT  172 | P a g e A B C Figure 9-5 Cross-section for a double-acting cylinder. The rod side volume 𝑉 is given as 𝑉 𝐴 𝐴 𝑠 (9-8) where: 𝐴 piston area 𝐴 rod area 𝑠 piston motion 9.8 Residual Volume, Bypass and Volumetric Efficiency The residual air is the amount of air that remains in the air chamber after constant pressure contraction between  and in Figure 9-1, due to limitations on clearances in the chamber. Figure 9-6 shows a modified pressure-volume diagram where the residual volume 𝑉res is the volume at . As was the case for pneumatic compressors, residual volume has an adverse effect on volumetric performance of the actuator. After the discharge valve closed and the intake valve opens at in Figure 9-6, the pressure rises promptly from atmospheric pressure to operating pressure. The sudden increase in pressure compresses the residual volume. The compression of residual air is accompanied by an intake of air to operating pressure. This intake of air at operating pressure does not yield actuation, and can therefore be considered as a loss that reduces the volumetric performance of the actuator. As in the case of a compressor, limitations on the effectiveness of sealing in an actuator means that there is always a fraction of the compressed air that will leak through from the high-pressure intake to the low-pressure discharge, and will therefore not actuate the load. The amount of air lost due to leaking typically depends on the operating pressure and the operating speed; a higher operating pressure and lower operating speed typically results in more leaking per actuation cycle. Figure 9-7 shows a schematic of the volume flow rate of air at standard temperature and pressure passing through an actuator. The figure graphically shows the relationship between the actual volume flow rate 𝑄 at the intake and discharge of the actuator, the displacement volume flow rate 𝑄 in the actuator, and the bypass volume flow rate 𝑄 Johan Fourie, BCIT  173 | P a g e Figure 9-6 Modified pressure-volume diagram of an expansion cycle. resulting from the adverse affect of residual volume and leaking. In the absence of a residual volume and leaking, the actual volume flow rate and the displacement volume flow rate are the same. The volumetric efficiency 𝜂 of a pneumatic actuator is defined as the ratio of the displacement volume flow rate to the actual volume flow rate. 𝑄 𝑄 𝜂 9-9 𝑄 𝑄 𝑄 where: 𝑄 displacement volume flow rate at STP 𝑄 actual volume flow rate at STP 𝑄 bypass volume flow rate at STP Johan Fourie, BCIT  174 | P a g e Figure 9-7 Actuator with bypass flow. EXAMPLE 9-4 Determine the volumetric efficiency of an actuator if it has a swept volume of 83 cm3 and a residual volume of 7.5 cm∙ The actuator operates between an operating pressure of 720 kPa abs and standard atmospheric pressure with constant pressure actuation. Neglect bypass due to leaking and assume a polytropic index of 1.35. Solution 𝑝atm 𝑉res.. 𝑝oper 𝑉res,comp 𝑝atm. 101.325 kPa. ⇒ 𝑉res,comp 𝑉res 7.5 cm 1.7458 cm 𝑝oper 720 kPa The volume of air loss at operating pressure required to compress the residual volume is calculated as: 𝑉loss 𝑉res 𝑉res,comp 7.5 cm 1.7458 cm 5.7452 𝑉loss 𝑉res Therefore 𝑄 𝑉 𝑉 𝑉res,comp 𝜂 𝑄 𝑉 𝑉 𝑉loss 83 cm 83 cm 5.7452 cm 0.93526 93.526% Johan Fourie, BCIT  175 | P a g e EXERCISES 9-1 Determine the intake volume ratio of the actuator cycle described in Example 9-1. 9-2 A power tool uses 30 cfm of air at 110-psig and 75°F when it runs at 1800 rpm. a. Determine the air consumption rate in scfm cfm of air at standard atmospheric conditions of 14.7 psia and 59°F. b. If the tool has a intake volume ratio of 0.68 and runs at 1800 rpm, determine the swept volume of the tool and the minimum operating discharge pressure. Assume a polytropic index of 1.38 for the expansion process. 9-3 A vane motor with a swept volume of 2.5 in3 consumes 1.8 cfm of compressed air at an operating pressure of 90 psi gage. A discharge pressure of 22 psi gage is required to generate sufficient torque to drive the load. What is the expected motor speed. Assume a polytropic index of 1.38 for the expansion process. 9-4 A sprung instroked single acting pneumatic cylinder has a piston diameter of 60 mm and a stroke length of 30 mm. The cylinder operates at 700 kPa gage pressure and the intake temperature is 21 °C. The inlet valve allows the air in the cylinder to remain at a constant pressure during the first half of the extension stroke and then to expand during the second half of the stroke. Assume that the extension of the cylinder is slow enough to assume isothermal expansion during the last half of extension. Determine: a. the air consumption volume per actuator cycle at standard conditions, and; b. the minimum force available for actuation. 9-5 If testing revealed that the pneumatic cylinder in Exercise 9-4 actually has a volumetric efficiency of 85%, how much air leaks through the cylinder per stroke. Assume that the cylinder has a negligible residual volume. EXERCISE ANSWERS 9-1 0.657 9-2 247 scfm, 58.5 psig 9-3 2,705 rpm 9-4 329 m , 846.4 N 9-5 7.48 cm3 Johan Fourie, BCIT  176 | P a g e This page is intentionally blank. Johan Fourie, BCIT