ACTUATORS
Chapter 3
Linear actuators
Mounting methods
For working against pushing load forces the actuator acts as a strut for which the Euler failure criteria are applied according to the method of mounting the strut. The Euler buckling load, FE, is given by:
where:
Thus it is seen that for a given strength factor the buckling load varies proportionally with the fourth power of diameter and inversely with the length squared.
The values for the strength factor, SF, that apply to the mounting styles in Figure 4 are:
i)Fixed actuator mounting with unconstrained rod end (as a))SF = 0.25
ii)Actuator and rod attached by free pivots but with constrained rod end (as c))SF = 1
iii)Fixed actuator mounting with constrained rod end (as d))SF = 2
Actuator manufacturers usually give the maximum capability of actuators with the mounting style in terms of maximum extension at a given actuator piston pressure.
A typical example is given in Table 1 for an actuator of 50mm diameter at 100 bar pressure.
Table 1 Maximum Actuator Extension (refers to Figure 4)
Maximum Piston Extension (mm)d (mm) / Case a) / Case b) / Case c) / Case d)
28 / 390 / 610 / 500 / 1260
36 / 690 / 1120 / 730 / 1690
Cushioning
To retard inertial loads and increase the fatigue life of actuators, some form of internal cushioning is often used. An example of actuator cushioning can be seen in Figure 5.
When the actuator outlet flow is directed through the restrictor, the pressure drop generated will create a backpressure on the actuator, thus causing it to be retarded. The restrictor must be sized such that the maximum pressure, which occurs when the plunger first blocks the normal outlet port, does not exceed the safe value for the actuator.
1
Figure 5 Actuator cushioning.
For simple inertial loads, with no other forces acting, the actuator velocity decays exponentially, as does the actuator outlet pressure. This can be shown by simple analysis assuming an incompressible fluid and neglecting friction. Thus from Newton's Law we have:
Inertial force
(1)
where X is the movement of the actuator from the commencement of cushioning.
Flow
Restrictor
(2)
Actuator:(3)
Now: so we get from equations (1), (2) and (3): (4)
And:(5)
Solution
Figure 6 Velocity and pressure variation
The solution of equation (5) gives:
The velocity and pressure variations with the distance, X, which the actuator has moved after cushioning has commenced are shown in Figure 6. At the start of the cushioning the pressure rises to a maximum value, PCm, when the flow is a maximum. For a given mass and initial velocity, the maximum cushion pressure is determined by the size of the adjustable restrictor. This also determines the distance that is required for the actuator velocity to reduce to an acceptable value.
It is normal that PC max should not exceed 350bar which is a normal fatigue pressure rating for 106 actuator cycles. The change in the pressure, and velocity, will be slightly modified by the effect of the fluid compressibility but in most systems this effect will be small and the cushion performance can be calculated using the equations.
Rotary actuators
Figure 7 Typical rack and Pinion Rotary Actuator
Figure 8 Screw Type Rotary Actuator (Danfoss)
Table 2 Summary of rotary actuator performance
Type / Angle range / Torque NmRack and pinion / > 3600 / 42000
Vane / < 2800 / 22000
Helical / < 4200 / 26000
Figure 9 Vane Rotary Actuator
Applications
Rotary actuators are used for the following applications:
Steering systemsGate valvesBoom slew of backhoe
Manipulator driveTunnelling machineContainer handling