The clamping angle is the angle of engagement of the sprag against the shaft and housing relative to the line going from the engagement point to the centerline of the shaft. It is represented with an α in the below image.
This angle is important because of its relation to the coefficient of static friction. For an object to engage and not slip, the friction force (FS) must be larger than the force trying to make the object slip (FR). The friction force is dependent on the normal force (FN) and the coefficient of static friction (μ0) such that:
FS = μ0FN
That means that the object doesn’t move if:
μ0FN > FR
Now here’s where the clamping angle comes into play.
For an object on an incline plane (similar to how the engagement between a sprag and the shaft and housing can be modeled), both the normal force and the force trying to make the object slip can be calculated from the force of the sprag pushing against the shaft and housing (FE) because that force acts along that line going from the engagement point to the centerline of the shaft. The force equations then become:
FN = FEcos α
FR = FEsin α
Then, by adding these equations in to the one above, for the sprags to stay in contact with the shaft and housing:
μ0FEcos α > FEsin α
From this equation, we can see that the sprag force (FE) doesn’t matter in keeping the sprag from slipping since it’s on both sides of the equation. Also, since the clamping angle is on both sides, the equation can be rearranged to:
μ0 > sin α/cos α → μ0 > tan α
What this shows then is that keeping the sprags engaged and not slipping is a factor of only the coefficient of static friction and the clamping angle. GMN clutches require the sprags to operate against hardened and ground steel. So, the coefficient of static friction value of 0.11 can be used. That means that:
0.11 > tan α → α < 5.8°
As long as the clamping angle is less than 5.8°, the sprag should stay engaged and not slip. However, this is not as easy as it seems because that clamping angle is the result of:
- The torque applied,
- The radius of curvature of the engagement curve, and
- The shaft and housing diameter.
As a result, for many sprag clutch manufacturers, the clamping angle is never constant.
This is where GMN sprag clutches are unmatched. GMN has developed a unique, complex sprag curvature radius that ensures that the clamping angle remains below 5.8° throughout the engagement zone, regardless of shaft and housing diameters. If the torque is within the limits and the sprag engagement remains within the operating zone, the clamping angle will stay below 5.8°.
No Catastrophic Failures
GMN sprag clutches have an additional unique feature that relates to the clamping curve. Typically, when a sprag experiences excessive torque the engagement point will move past the operating zone of the sprag and it will roll over. This will result in catastrophic failure of the clutch and will likely damage other components.
However, GMN designed the sprag curvature radius so that when the engagement point begins to move past the operating zone, the clamping angle starts to exceed the 5.8° value. That means when the torque gets too high, the GMN sprags will tend to slip instead of roll over protecting the clutch from catastrophic damage*.
*Even though this is a feature of GMN sprags, this performance cannot be relied upon, and care must be taken to ensure the maximum torque for the application isn’t exceeded.
Have questions about the clamping angle in your sprag clutch application? Contact our engineers for more information!
Interested in GMN Sprag Clutches?
Check out our Sprag Clutch Guide resources below for more information.