# Thread: Bolt force Equation - Why no need for Pitch

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A Dissertation on Locking screws

Any taper less than Seven (7) Degrees is considered a locking taper.
So the thread of a screw is a taper if you laid out the Pitch Diameter as a leg length on a 2 D drawing and the thread " Pitch" as the height of a triangle . 7 degrees (Tangent is .1228) has a taper height of roughly 1/8 the length of the leg of the laid out triangle
length of Leg equals 1 and height equals .1228 = Tangent of 7 degrees !
Since we want the to know what pitch will lock, we know that the long leg of the triangle was D x Pi, all we have to do is multiply the height by Pi to find the ratio of a locking screw . Therefore, .1228 times Pi = .385
So when the Thread "Pitch" is less than 38 % of the Thread Pitch "Diameter", the screw is locking.
As an Example on a 1" diameter screw, a 2 1/2 TPI would not lock, while a 3 TPI would. ( 2 1/2= .4% while 3 = .33%)

None of this applies to a milling machine leadscrew , nor is it intended to.
Vibration from cutting is like a hammer being taken to the part. Even Press fits can be moved with a hammer.

Rich

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Originally Posted by Rich Carlstedt
A Dissertation on Locking screws

Any taper less than Seven (7) Degrees is considered a locking taper.
So the thread of a screw is a taper if you laid out the Pitch Diameter as a leg length on a 2 D drawing and the thread " Pitch" as the height of a triangle . 7 degrees (Tangent is .1228) has a taper height of roughly 1/8 the length of the leg of the laid out triangle
length of Leg equals 1 and height equals .1228 = Tangent of 7 degrees !
Since we want the to know what pitch will lock, we know that the long leg of the triangle was D x Pi, all we have to do is multiply the height by Pi to find the ratio of a locking screw . Therefore, .1228 times Pi = .385
So when the Thread "Pitch" is less than 38 % of the Thread Pitch "Diameter", the screw is locking.
As an Example on a 1" diameter screw, a 2 1/2 TPI would not lock, while a 3 TPI would. ( 2 1/2= .4% while 3 = .33%)

None of this applies to a milling machine leadscrew , nor is it intended to.
Vibration from cutting is like a hammer being taken to the part. Even Press fits can be moved with a hammer.

Rich

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Also, the thrust is taken somewhere resulting in additional friction. Under head for a bolt, thrust bearings for a lead screw. This friction must be added.

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Originally Posted by strokersix
Respectfully disagree, a normal V thread is 60 degrees or 30 degrees depending on how you look at it.
In either case, that is much higher than 7 Degrees and therefore not a locking angle.
Rich

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Originally Posted by Rich Carlstedt
Respectfully disagree, a normal V thread is 60 degrees or 30 degrees depending on how you look at it.
In either case, that is much higher than 7 Degrees and therefore not a locking angle.
Rich
Locking screw threads would not be popular.....!

But you missed the point, which I think was that there may be added force normal to the surface from the wedging action of the 60 deg angle.

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Originally Posted by J Tiers
Locking screw threads would not be popular.....!

But you missed the point, which I think was that there may be added force normal to the surface from the wedging action of the 60 deg angle.
Wedging Action ?
Never heard of it Jerry
Under tension, screws stretch and therefore "space" occupied by the screw's volume is stretched over a longer length which means the diameter shrinks ..Wedging ...I think not !

Rich

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Originally Posted by Rich Carlstedt
Wedging Action ?
Never heard of it Jerry
Under tension, screws stretch and therefore "space" occupied by the screw's volume is stretched over a longer length which means the diameter shrinks ..Wedging ...I think not !

Rich
Well, that's as may be....

But, the threads form a conical surface and an axial force on the screw will, with anything other than a square thread, develop a force inward radially on the screw due to the slope of the thread flanks. (and outward against the female threads as well)

Now you have heard of it.

As for its significance, I have not bothered to look into that. I am inclined to think that it may affect friction, but whether if is a net increase or decrease I have not investigated.

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Originally Posted by J Tiers
Well, that's as may be....

But, the threads form a conical surface and an axial force on the screw will, with anything other than a square thread, develop a force inward radially on the screw due to the slope of the thread flanks. (and outward against the female threads as well)

Now you have heard of it.

.....................
To "wedge" something you need to fill a space completely. Your thesis lacks clarity and is plumb wrong.
As I said, the Screw gets longer under load and that actually makes it smaller in diameter and that vacates space on the screw OD. Not much, but that is a physical reality
Suggest you look at a spring . When a spring is under tension , the coil diameter shrinks
Rich

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Originally Posted by Rich Carlstedt
To "wedge" something you need to fill a space completely. Your thesis lacks clarity and is plumb wrong.
As I said, the Screw gets longer under load and that actually makes it smaller in diameter and that vacates space on the screw OD. Not much, but that is a physical reality
Suggest you look at a spring . When a spring is under tension , the coil diameter shrinks
Rich
!) It's not MY "thesis"...... you replied to strokersix commenting on it, and I suggested you had the wrong idea of what HE said... which seems to be along the lines I explained. I make no claims about its degree of effect, I only state that it exists, and that Strokersix was probably talking about it.

2) You are being ultra-literal.... so that you avoid the presented thought on a technicality.... It is a FACT that the v-thread has a non-90 degree angle to the screw axis.... so an axial force has a side vector component that appears due to the sloped surface. That is inward on the screw, from all points around it on the helix.

If you prefer to call the "wedge" an "inclined plane", which topologically it is, and if that will allow you to pass by the word "wedge" and see what is meant, then go for it. "Inclined plane" is perhaps a better term. but, note that it is NOT the "inclined plane" of the thread helix, but the "inclined plane at right angles to the helix, the one formed by the "60 degree" threadform, and NOT the pitch.
Last edited by J Tiers; 07-13-2019 at 12:04 AM.

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Rich, as a thought experiment, lets make a screw with vee thread of 166 degrees (180-7-7, chosen for illustration) included angle instead of the typical 60 degrees. There is no way you will be able to get any tension on this screw at all by turning it. It will immediately lock in place and twist off without developing tension. Increased thread friction comes with increased included angle. Same effect occurs at 60 degrees just not as much.

This is one reason we use acme threads for lead screws. Included angle is small for reduced thread friction. Vee threads, acme screws, ball screws, nuts and bolts all operate with the same principles. Geometry is different, results are different, principles are the same.

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