 then review load position and the resulting moments on the cylinder to determine if shock absorbers or external load-stopping devices are needed. Consider the following example. A cylinder carries a 10-lb load offset 12 in. from the carrier, and travels at a final velocity of 80 in./sec when it hits shock absorbers at the ends of the cylinder stroke. The load must stop within the shock absorber stroke of 0.50 in. The Mz and equivalent force applied to the cylinder’s load carrier need to be within the cylinder’s rated capacity.
To determine this, first calculate the deceleration rate:
a = vf2/(2s)
= (80 in./sec)2/(2 0.50 in.)
= 6400 in./sec2
a is the deceleration rate, in./sec2,
s is shock stroke, in., and
vf is final velocity, in./sec.
Then calculate deceleration force, Fd, from:
Fd = (a P)/g
= (6400 in./sec2 10 lb)/(386.4 in./ sec2)
= 165.6 lb
Fd is the deceleration force, lbf,
g is the gravitational constant, 386.4 in./sec2, and
P is the load.
Finally, the moment load created during stopping is:
Mz = Fd L = 165.6 lb 12 in. = 1987.2 lb-in.
Mz is moment about Z axis, and
L is distance of load from the cylinder’s load carrying device.
|Designers must know the difference between average and final or impact velocity to determine the cylinder’s cushioning capacities and correctly size rodless cylinders. |
Compare this value to the actuator’s rated load capacity to ensure proper sizing. If the moments created during deceleration are more than the actuator’s load capacity, you have two choices: Select a cylinder with a larger moment rating; or put shock absorbers at the load’s center of gravity. The latter theoretically eliminates all moments on the carrier during deceleration. If final velocity cannot be accurately determined, consider using limit switches with valve deceleration circuits, in addition to shock absorbers.
Motion lag. It is important to understand how other forces and losses affect the total force needed to generate the desired motion. The total force is the sum of acceleration force, frictional forces, and the breakaway force. Here’s a closer look at each.
Breakaway force. It always takes a certain amount of force to move a rodless cylinder even with no load attached. This force is referred to as breakaway force. When reviewing performance data for a cylinder, be sure to account for breakaway force in the calculations. In pneumatic applications, it is best to have excess force available to ensure reasonable acceleration.
Acceleration force. The force needed to accelerate a load is typically larger than the force needed to keep it in motion. When selecting an actuator, the cylinder’s breakaway force and the load’s frictional drag must be added to acceleration force requirements.
Friction forces. Two materials sliding across each other generate frictional force in the opposite direction of the motion. The amount is defined by a numeric value called the coefficient of friction, μ, which varies by material and the type of friction (sliding or rolling). Engineering reference tables list coefficient values for a variety of materials.
For horizontal applications, the force required to overcome the friction is:
Ff = μ W
Ff is the frictional force, lbf, and
W = weight of the load, lb.
Mounting orientation. Vertically mounting the cylinder brings additional force, load, and air considerations. Vertical cylinders need to overcome the force of gravity before they can accelerate loads upward, which means they must produce more force than horizontal cylinders. In vertical applications, it is best to select cylinders with twice the force needed for adequate acceleration.
In addition, some types of pneumatic rodless actuators may leak air. If the actuator needs to hold a load vertically for any length of time, the air leak can affect how well that position is maintained. In certain circumstances, holding devices such as a brakes or external guidance systems may be required to safely control the load. Keep in mind that vertical applications with externally guided loads still see moment loads due to gravity. For example, a 50-