Announcement

Collapse
No announcement yet.

Bolt force Equation - Why no need for Pitch

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • Bolt force Equation - Why no need for Pitch

    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.
    21" Royersford Excelsior CamelBack Drillpress Restoration
    1943 Sidney 16x54 Lathe Restoration

  • #2
    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.

    Comment


    • #3
      Originally posted by rklopp View Post
      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?
      21" Royersford Excelsior CamelBack Drillpress Restoration
      1943 Sidney 16x54 Lathe Restoration

      Comment


      • #4
        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.

        Comment


        • #5
          Originally posted by The Metal Butcher View Post
          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/mechan...sign_13982.htm

          https://www.amesweb.info/Screws/Lead...meThreads.aspx

          Comment


          • #6
            Thank you so much sir. I did some searches but wasn't as successful as you.
            21" Royersford Excelsior CamelBack Drillpress Restoration
            1943 Sidney 16x54 Lathe Restoration

            Comment


            • #7
              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
              That is your mechanical leverage
              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

              Comment


              • #8
                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.
                21" Royersford Excelsior CamelBack Drillpress Restoration
                1943 Sidney 16x54 Lathe Restoration

                Comment


                • #9
                  Originally posted by Rich Carlstedt View Post
                  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/

                  Comment


                  • #10
                    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.
                    1601

                    Keep eye on ball.
                    Hashim Khan

                    Comment


                    • #11
                      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

                      Comment


                      • #12
                        Originally posted by Rich Carlstedt View Post
                        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
                        Agree with your analysis for a square thread. Vee thread will provide even greater "locking" effect.

                        Comment


                        • #13
                          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.

                          Comment


                          • #14
                            Originally posted by strokersix View Post
                            Agree with your analysis for a square thread. Vee thread will provide even greater "locking" effect.
                            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

                            Comment


                            • #15
                              Originally posted by Rich Carlstedt View Post
                              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.
                              1601

                              Keep eye on ball.
                              Hashim Khan

                              Comment

                              Working...
                              X