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The Metal Butcher
07-11-2019, 06:23 PM
Hi all,

I was trying to calculate the clamping load from a vise based on the leadscrew TPI. All of the calculators I can find online use the equation P = (KxD)/T where:

• T Target tighten torque (the result of this formula is in inch pounds, dividing by 12 yields foot pounds)
• K Coefficient of friction (nut factor), always an estimation in this formula
• D Bolts nominal diameter in inches
• P Bolt's desired tensile load in pounds

-Techshop

So, why doesn't the pitch of the screw come into play? Surely a 3/4"-5TPI Acme thread takes way more torque than a 3/4"-20 screw. Yet the formula does not account for this, and so I do not really trust it. Advice? Thanks.

rklopp
07-11-2019, 06:58 PM
The pitch (lead, to be more precise) is buried in the variable K. Shigley's Mechanical Engineering Design, 1989, p. 346, says, "The interesting fact...is that K~0.20 for µ=µC=0.15 [the "typical" coefficient of friction] no matter what size bolts are employed and no matter whether the threads are coarse or fine." The main reason is that the wedging action caused by the 60° thread flank included angle dominates over the effect of the lead angle. Thus, the formula would not work for square-threaded screws.

At the end of the day, the formula is only an approximation, so you should only trust it as an approximation. The torque-tension relationship is fairly loosey-goosey. A better-but-still-imperfect method of bolt tightening is to tighten to some given torque less than "handbook" full torque and then tighten another 60°, i.e., turn one by more point on the hex head.

The Metal Butcher
07-11-2019, 07:00 PM
The pitch (lead, to be more precise) is buried in the variable K. Shigley's Mechanical Engineering Design, 1989, p. 346, says, "The interesting fact...is that K~0.20 for µ=µC=0.15 [the "typical" coefficient of friction] no matter what size bolts are employed and no matter whether the threads are coarse or fine." The main reason is that the wedging action caused by the 60° thread flank included angle dominates over the effect of the lead angle. Thus, the formula would not work for square-threaded screws.

At the end of the day, the formula is only an approximation, so you should only trust it as an approximation. The torque-tension relationship is fairly loosey-goosey. A better-but-still-imperfect method of bolt tightening is to tighten to some given torque less than "handbook" full torque and then tighten another 60°, i.e., turn one by more point on the hex head.

I see. Thanks. So are there any good formulas for power transmission/square thread?

CCWKen
07-11-2019, 07:02 PM
Because of this disclaimer:

"This relationship is based on the assumption that regular series nuts and bolts with rolled threads are used, acting on surfaces with industry standard thread pitch and flank angle."

Also that K is variable. Ops, I see that's been covered.

Lee Cordochorea
07-11-2019, 07:46 PM
I see. Thanks. So are there any good formulas for power transmission/square thread?

To quote the wascally wabbit... "mhhyeehh, could be."

https://www.engineersedge.com/mechanics_machines/power_screws_design_13982.htm

The Metal Butcher
07-11-2019, 08:46 PM
Thank you so much sir. I did some searches but wasn't as successful as you.

Rich Carlstedt
07-11-2019, 09:14 PM
I think You are asking for what the force is between the jaws when you turn the handle ?
That is a simple leverage calculation and is a function of Pitch,PD, and lever arm (handle length) and thread can be Buttress, square,Acme , of V Thread. Friction occurs is all but for a lubricated thread, I would assume a 15 % loss.
You want the Circumference of the Pitch Diameter versus the Pitch for the leverage
Say the screw is .950 in diameter at Pitch Center and the OD is 1 " ( Just for grins here) and the pitch is 8 TPI or .125"
So the Circumference is .95 times Pi ( 3.14 ) which is 3"
Divide the C by the Pitch ( 3 /.125 ) and you get 24
So if your Handle is one foot in length and you put one pound of force on the end of the handle ( one FP) , the thread exerts 24 pounds of force (minus friction of 15 % approx)
So (PD x Pi) /P x FP = F x .85

Rich

The Metal Butcher
07-11-2019, 10:19 PM
Interesting forumula Rich.

Using a 1 1/2-4 thread (1.375? Pitch) and the amesweb calculator above, 400 ft-lbs gives a 24000lbs pull. Using your calculations, I get a 8000lbs force, which seems more reasonable. These are quite different though but from what I've seen from Royce (the guy that built the big 1400lb vise) yours seems much more accurate. I guess I should take some time to make sense of the formulas on the amesweb site.

strokersix
07-12-2019, 07:28 AM
I would assume a 15 % loss.

Maybe for a very well lubricated system, ball nut, ball thrust, etc. I bet the real friction loss is greater for a typical machine vise. If it was really only 15% the vise might not even stay tight. Might unwind as soon as you let go of the handle. Think about it. This is one of the objections to using ball lead screws on manual machines. Cutting forces can backdrive the screws.

Friction loss for bolted joints is more like 80%. This is why thread pitch does not appear in the formula. The difference between coarse and fine thread is a very small percentage, like 1 or 2%. Lost in the noise.

http://www.boltscience.com/

J Tiers
07-12-2019, 10:56 AM
As an approximation, presumably it is only useful over a small range covering typical bolts (what it's for). A pitch of 100mm on a 25mm dia round object would not be within that range.

Rich Carlstedt
07-12-2019, 11:01 AM
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

strokersix
07-12-2019, 12:13 PM
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

strokersix
07-12-2019, 12:16 PM
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.

Rich Carlstedt
07-12-2019, 05:21 PM

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

J Tiers
07-12-2019, 06:14 PM
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.

Rich Carlstedt
07-12-2019, 07:27 PM
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

J Tiers
07-12-2019, 10:11 PM
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.

Rich Carlstedt
07-12-2019, 11:04 PM
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

J Tiers
07-13-2019, 12:01 AM
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.

strokersix
07-13-2019, 08:38 AM
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.

Rich Carlstedt
07-13-2019, 09:25 AM
Jerry and Stroker. I think you both are so far out in the woods that you have left practicality !

First Jerry, YOU called it a "Wedge", I did not !
Second Stroker, I think you better study a Buttess thread, or a square thread. It is less than seven degrees to the axis of the Screw, but the pitch of the screw presents a different angle AND fellows we are talking "Machine Screws".
This is entirely different than Wood screws which do "wedge " into the hole.

The purpose of this website I believe is to expand the knowledge of those interested in machining.
Doing so requires clear and accurate information.
My post to the Op explained the physics AND math required or involved in the question
Your responses confuse these fellows and lack real world experience IMHO
I built Dies at one shop for 10 years upto 52,000 pounds in Weight and had to maintain hydraulic pressures
( at joints) of upto 15,000 PSI at 500 degrees. We did destructive testing of screws upto 35 mm ( 1-3/8"~).
Those screws took 3,000 foot pounds of torque by the way. We tested screws and fasteners across the board.
Did you know that some machine screws come with lot numbers ? That should explain to you that the manufacturer realized how important his product was to the customer working in critical conditions (Our Product). It also meant if we in the shop ignored the above by substituting a different fastener, we were fired -really !

Please stay focused on the task at hand . and bring real world experience to the table, not gossip or opinion-unless it is stated so. No Smoke please !

Rich

PS
By the way, anyone who thinks pitch has nothing to do with force is an idiot !
Park your car on a grade and then release the brake and tell me the slope has nothing to do with force !

J Tiers
07-13-2019, 11:44 AM
Still focused on that "wedge", despite all efforts to dislodge you....

And bringing in odd facts like 2000 years experience and lot numbered screws.

You and stroker can argue about it, I only tried to point you at what he said, instead of what you wanted to talk about..... I am making NO claims other than what I said happens does happen, that there is an innward force due to the thread "60 degree" angle.

You guys fight it out.....

BTW,,,, the "wedge" can be seen between the underside of the head, and the 60 deg angled thread surface...... but don't let that stop you from discussing 52000 lb dies.

strokersix
07-13-2019, 11:47 AM
Not going to fight. I tried to put into plain language and simple concepts to no avail.

rklopp
07-13-2019, 12:24 PM
Just get Shigley's book and read it. It explains the math behind the development of the forces in screws. We all know an extreme case of the wedging action - the Morse taper. Even though it's not a screw, it is a tapered flank wedging in a tapered seat. The sides of threads so the same thing, except, because the angle is nowhere as steep as a Morse taper, the wedging effect is nowhere near as big, but it still exists.

07-14-2019, 10:04 AM
When I was working in a Yuasa plant we had some machinery that was made by Yuasa and shipped to us. One of them had some quick-change tooling that was secured by a coarse-threaded cone basically. You lifted the tooling up into the machine and locked it with a very small twist. I didn't examine it carefully but it seemed to wedge into position rather than have a positive latch. May or may not be relevant to this thread, depending on how it worked. I've never seen anything like it since. The thread angle was very steep... could easily have been five or more threads.

johansen
07-14-2019, 03:26 PM
in this calculator you can change the thread angle, from 0 to 45 degrees (the half angle of the thread, so 30 for normal screws)
and you can see its effect on the friction.

https://www.roton.com/resources/formula-calculators/efficiency-power-screws-forward-drive/
https://www.roton.com/resources/formula-calculators/efficiency-power-screws-backdrive/

Paul Alciatore
07-14-2019, 03:52 PM
I fear that many engineering "equations" are actually approximations that can only be properly applied under limited circumstances. It appears that this is one of them. In the engineering world, you can not just find an equation that seems to have the terms that you want and blindly apply it.

I am not familiar with this equation, but it seems that it may be applicable to standard, 60 degree screws. A vise will surely have an Acme thread or perhaps a square one so it is doubtful that this equation will be very helpful. In any case, one should know a lot more about the assumptions in and limitations of that formula before any attempt to employ it. I would suspect that there is another formula that is more applicable in this case (vise with an Acme screw). I think you are correct to not trust it in this instance.

When a screw, Vee, Acme, or square, is tightened, the torque will be divided into two primary factors: the force produced along the axis of the screw and the force needed to overcome the friction of the threads. It is this division that you are seeking to nail down: how much goes to friction and how much to the desired axial force. In a vise, that frictional force along the threads is absolutely needed to prevent the vise from self loosening. The thread MUST lock in the tightened position.

Unfortunately, there are many factors that will effect that friction. These include but may not be limited to the materials used, the amount and quality of the lubricant used (if any), the surface finish of the thread's mating surfaces, the effects of the angle of the thread's faces, and probably the ambient temperature. All of these factors and probably others will make a prediction of the actual amount of clamping force that will be generated at the vise's jaws vs. the amount of tightening torque a very difficult and error prone task. This is why engineers have developed equations and tables that are APPROXIMATE. Even if you get an engineering text that addresses this problem you are going to find that it will have many assumptions in all of the methods that it recommends.

The pitch of the screw does have an effect. That effect is not directly due to the pitch (tpi) itself, but due to the helix angle of the ramp formed by that pitch. And, as others have said, that factor is probably assumed to be a nominal value for the screws that are most likely to be in use in the country/area where that equation was developed (UNC, UNF, metric, etc.) Please notice that a vise thread is not likely to follow any of these conventions for threads used in fasteners (screws, bolts, etc.) I know that the pitch of the screw DOES have an effect on the torque developed due to some practical work that I did with chassis punches. I wanted to obtain longer draw bolts for existing punches and quickly found that grade 3 or even grade 5 bolts were totally inadequate: they quickly failed being simply pulled apart. In my work, these are lubricated threads and I had to calculate the amount of axial force that they were developing. I DID have to take the helix angle or TPI of the thread into account.

The engineering sites that I visited did not give a lot of explanation as to how this equation was developed or what it's actual limitations may be. This does not strengthen my faith in the bridges and skyscrapers. I hate to say it, but I suspect that a lot of mechanical engineering is being done "seat of the pants".

I would suggest a trip to the library at a local engineering college. I doubt that they will allow you to check out any books, but you should be able to explore the text books on this subject while you are there. Pack your lunch .... and dinner.

Hi all,

I was trying to calculate the clamping load from a vise based on the leadscrew TPI. All of the calculators I can find online use the equation P = (KxD)/T where:

-Techshop

So, why doesn't the pitch of the screw come into play? Surely a 3/4"-5TPI Acme thread takes way more torque than a 3/4"-20 screw. Yet the formula does not account for this, and so I do not really trust it. Advice? Thanks.

strokersix
07-15-2019, 07:04 AM
To the OP. This thread got derailed and lost in the details.

Direct answer to your question: For typical threaded fasteners the torque/tension relationship is roughly: 40% of the torque goes to underhead friction, 40% goes to thread friction and only 20% actually goes into fastener tension. Thread pitch coarse versus fine only applies to the 20%.

So, 20% of the applied torque to a fine thread fastener goes to tension. Less for a coarse thread, let's say it's 15%. So, you are only talking about a 5% difference in fastener tension for a given applied torque.

Using torque to tension fasteners is notoriously variable, largely due to friction effects, both in the threads and underhead. By variable, I mean +/- 50% is common. +/- 20% with careful and consistent conditions. Any closer than that requires other methods such as measuring fastener stretch.

So, the point is, the 5% effect from thread pitch difference is insignificant compared to friction effects. This is why thread pitch does not appear in the equation.

The above example is for typical bolted joints. Other cases the principles are the same but the proportions are different.

PStechPaul
07-15-2019, 05:42 PM
I found a pretty good discussion of bolt clamping force and torque, which mostly confirms the assertions claimed above:

https://www.fastenal.com/content/feds/pdf/Article%20-%20Bolted%20Joint%20Design.pdf

There are some more accurate methods of assuring a particular clamping force, such as spring washers and hydraulic pretensioners. For something like a vise, it would be interesting to put a strain gauge (or maybe a spring scale) between the jaws, and note the torque versus pressure. Other means might be a spring with known displacement versus force, or a hydraulic cylinder and fluid pressure gauge. And perhaps it would be possible to drill a hole through the bolt and insert a rod through the head and secured at a certain point within the length subject to elongation. Then it should be possible to observe or measure how far it is pulled into the head, and use the rated amount of elongation along with the bolt's elastic properties to determine compression force on the joint.