I need help in determining the angle at which slippage will not occur at between two tapered wedges that make up an adjustable chock that will sit under a machine. Each chock is 400 x 250mm. The height need to be 62.5+/-5mm. Each chock will be carrying 48T(metric). Anyone info would be much appreciated as I can not calculate this by myself.
We'll need to know what material the chocks are made from. Are they steel on steel?
Don Kansas City
The wedges run the long dimension (400 mm) of the choke or the short dimension?
Unless the blocks are lubed somehow, a low number for the coef. of friction should be 0.1. That's for steel on steel.
It does not matter which direction the wedge runs, nor do the linear dimensions matter at all. Friction is independent of surface area and only depends on the coefficient of friction between the two surfaces and the normal force applied.
In fact, in this case only the angle matters, independent of the weight. If you do a free body diagram, the normal force on the wedge is
N = w * cos A
where A is the wedge angle and w is the weight applied. The force along the slope is
F = w * sin A
The resisting friction force f is
f = u * N = u * w * cos A
where u is the static coefficient of friction. The point at which the wedge breaks free is when F > f, so
w * sin A > u * w * cos A
The weight w cancels out and we're left with
u < tan A
So the tangent of the wedge angle must be less than the coefficient of friction to prevent sliding.
For clean steel on steel, u = 0.8 approximately and the critical angle is
A = arctan (0.8) = 38.7 deg.
But this is the critical point where the wedge comes loose. To be safe we must have a smaller angle. Really, to be sure that the chock doesn't slide even if it suffers a shock and breaks the static friction, we should use the coefficient of kinetic friction, so that it still can't slide.
So, u = .4 and A = 21.8 deg maximum.
If the wedge is in an oily environment, then u = .03 (kinetic) and
A = 1.72 deg. max., even if oiled.
Don Kansas City
Yes it does! You need to know which length to use to go with the height to determine the angle (or determine the height from the angle).
He asked for the angle. You don't need any size dimensions to determine the slip angle. When he machines the wedges he will set the angle on his mill in degrees. The angle can go in either direction...or even at a rotated gradient. The length and height of the block are immaterial.
Don Kansas City
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That's all fine. But the design envelop was given. The choke's max angle is 8.88-14 deg depending on which length dimension is used.
I liked Don's response, though it must be said he cast his net wide.
I have been chided in the past for offering an angle of 15 degrees as providing non-loosening grip, from such things as taper pins. People have mentioned more conservative values, less than 3 degrees if I recall - but it stuck with me that someone offered the cautionary note that no taper at all can be considered proof against vibration - which can move the adjacent surfaces.
Brian Whatcott Altus OK
The wedges run along the 400mm length
Jeff F>
rule of thumb for brakes and gears is self-engagement (no slip) at less than
3 degrees.Mark's Handbook has details on it - brakes section.
>
That's based on 2 triangular wedges. Tapered pentagonal wedges will yield a wider range of angles.
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