6.1 Linear actuators

The basic linear actuator is the cylinder, or ram, shown in sche­matic form in Figure 6-1. Practical constructional details are dis­cussed later. The cylinder in Figure 6-1 consists of a piston, radius R, moving in a bore. The piston is connected to a rod of radius r which drives the load. Obviously if pressure is applied to port X (with port Y venting) the piston extends. Similarly, if pressure is applied to port Y (with port Z venting), the piston retracts.

The force applied by a piston depends on both the area and the applied pressure. For the extend stroke, area A is given πR². For a pressure P applied to port X, the extend force available is:

. (6.1)

The units of expression 6.1 depend on the system being used. If SI units are used, the force is in newtons. Expression 6.1 gives the maximum achievable force obtained with the cylinder in a stalled condition. One example of this occurs where an object is to be gripped or shaped. In Figure 6-2 an object of mass M is lifted at constant speed. Because the object is not accelerating, the upward force is equal to Mg newtons (in SI units) which from expression 6.1 gives the pres­sure in the cylinder.

Figure 6-1. A Simple cylinder

This is lower than the maximum system pres­sure; the pressure drop occurring across flow control valves and system piping. Dynamics of systems similar to this are discussed later.

Figure 6-2. A mass supported by a cylinder

When pressure is applied to port Y, the piston retracts. Total piston area here is reduced because of the rod, giving an annulus of area A_a where:

and r is the radius of the rod. The Maximum retract force is thus:

. (6.2)

This is lower than the maximum extend force. In Figure 6-3 identi­cal pressure is applied to both sides of a piston. This produces an extend force F_c given by expression 6.1, and a retract force F_r given by expression 6.2. Because F_c is greater than F_r, the cylinder extends.

Normally the ratio A/A_a is about 6/5. In the cylinder shown in Figure 6-4, the ratio A/A_a of 2:1 is given by a large diameter rod. This can be used to give an equal extend and retract force when connected as shown.

Cylinders shown so far are known as double-acting, because fluid pressure is used to extend and retract the piston. In some applications a high extend force is required (to clamp or form an object) but the retract force is minimal. In these cases a single-acting cylinder (Figure 6-5) can be used, which is extended by fluid but retracted by a spring. If a cylinder is used to lift a load, the load itself can retract the piston.

Figure 6-3. Pressure applied to both sides of piston

Single-acting cylinders are simple to drive (particularly for pneumatic cylinders with quick exhaust valves but the extend force is reduced and, for spring-return cylinders, the Figure length of the cylinder is increased for a given stroke to accom­modate the spring.

Figure 6-4. Cylinder with equal extend/retract force

A double rod cylinder is shown in Figure 6-6a. This has equal fluid areas on both sides of the piston, and hence can give equal forces in both directions. If connected as shown in Figure 6-3 the piston does not move (but it can be shifted by an outside force). Double rod cylinders are commonly used in applications similar to Figure 6-6b where a dog is moved by a double rod cylinder acting via a chain.

Figure 6-5. Single-acting cylinder

The speed of a cylinder is determined by volume of fluid deliv­ered to it. In the cylinder in Figure 4.7 the piston, of area A, has moved a distance d. This has required a volume V of fluid where:

If the piston moves at speed v, it moves distance in time t where:

Flow rate, V_f to achieve speed v is thus:

, (4.4)

The flow rate units of expression 4.4 depend on the units being used. If d is in metres, v in metres min^-1 and A in metres², flow rate is in metres³ min^-1.

Figure 6-6. Double rod cylinder (with equal extend /retract force)

In pneumatic systems, it should be remembered, it is normal to express flow rates in STP. Expression 6.4 gives the fluid volumetric flow rate to achieve a required speed at working pressure. This must be normalised to atmospheric pressure by using Boyle's law.

Figure 6-7. Derivation of cylinder speed

The air consumption for a pneumatic cylinder must also be nor­malised to STP. For a cylinder of stroke S and piston area A, nor­malised air consumption is:

, (6.5)

where P_a is atmospheric pressure and P_w the working pressure. The repetition rate (e.g. 5 strokes min^-1) must be specified to allow mean air consumption rate to be calculated.

It should be noted that fluid pressure has no effect on piston speed (although it does influence acceleration). Speed is deter­mined by piston area and flow rate. Maximum force available is unrelated to flow rate, instead being determined by line pressure and piston area. Doubling the piston area while keeping flow rate and line pressure constant, for example, gives half speed but doubles the maximum force. Ways in which flow rate can be con­trolled are discussed later.