 a distance from the X axis and create a rotation around that axis. My (pitch) and Mz (yaw) are, similarly, moments about the Y and Z axes, respectively. The farther a load is from the center of the cylinder’s carrier, the larger the resulting moment.
Published bending-moment capacities for rodless cylinders are usually maximums, but assume only one type of applied moment. Some applications have compound loading that combines two or more of the moments described above. Evaluate and calculate the combined effects to determine if the cylinder can handle the total moment force.
Dynamic moment loading. Even if a load is centered directly on the carrier, the cylinder will still be subject to bending moments during acceleration and deceleration. Failing to take this into account can lead to poor performance, reduced life, excessive wear, and cylinder failure. Thus, designers must also consider dynamic moment loading when determining force requirements because, unlike rod-style cylinders, many rodless cylinders support the load during acceleration and deceleration at each end of stroke. When the carrier reaches the end of stroke and stops, inertia keeps the load moving forward and creates a dynamic twisting moment (Mz) on the cylinder. The resulting dynamic moment can exceed the actuator’s rated capacity and shorten life. Shock absorbers mounted on the cylinder are normally used to help compensate for dynamic loading’s inertial effects.
Shocks and cushions
True velocity. Most rodless cylinders are equipped with internal devices to help cushion the load at the end of stroke. But is important to know the final or impact velocity to determine the cylinder’s cushioning capacity. This differs from average velocity. For instance, stroking a 24-in. actuator in 1 sec yields an average velocity of 24 in./sec. A reasonable guideline for calculating the final (impact) velocity is that it’s twice the average velocity, or 2 24 = 48 in./sec impact velocity in the example.
Deceleration forces. Given the impact velocity, engineers must 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