2 Thread GeometryDiametersMajorCrestPitchRootMinorThread HeightThread PitchThread AngleThe Pitch Diameter is midway between the Major and Minor Diameters.Hamrock Page 707
3 Thread TypesLead = 1 x PitchLead = 3 x PitchSingle-, double-, and triple-threaded screws. Also called single-, double-, and triple-start.Acme ThreadSquare ThreadHamrock Page 708Acme threads are used in C-Clamps, vices, and cartoons.
4 Details of Thread Profiles Thread HeightRelationships for M (metric) and UN (unified = US) screw threads.Example:UN: ¼-20, means 0.25in. Major diameter & 20 threads/inch.M: M8x1.25, means 8mm Major diameter & pitch of 1.25mmHamrock Page 708
5 Power Screws W Looking at a square thread screw, we unwind one turn: m rmrcLeadmThread frictionCollar frictionMean thread radiusMean collar radiusLoad on nutmcLooking at a square thread screw, we unwind one turn:aLead2p rmThis shows an inclined ramp with angleThe Mean Radius is midway between the Crest and Root Radii.
6 Square Thread Screw Torque rmrcLeadmmcThe torque required to raise the load W isand to lower the load, we flip two signs:Hamrock Page 715
7 Power Screw Thread Angle If the thread form is not square but has an angle b, replace the thread friction m with the effective frictionbThe effect:Square: b = 0, b/2 = 0, 1/cos(0°) = 1.0Acme: b = 29°, b/2 = 14.5°, 1/cos(14.5°) = 1.033Unified: b = 60°, b/2 = 30°, 1/cos(30°) = 1.15The thread angle effectively increases surface friction between 3 and 15%Note: Instead of b/2, Hamrock uses The difference is negligible.
8 Power Screws - Overhauling If the collar friction is small (e.g., it may have a ball thrust bearing), too small a thread friction may let the weight screw down on its own.This can happen when (the numerator goes negative).aLead2p rmmThis is the same case for a weight sliding down a ramp when the incline angle a exceeds tan-1m.
9 Ball Screws Have Low Friction Recirculating balls roll between ball screw and ball nut to minimize friction.These almost always overhaul.
10 Our Scissors Jack 1015 Lb 1522 Lb Tension Handle End with ball thrust bearingEnd with nut
11 Scissors Jack Analysis Thread ID = in. Thread OD = in. Estimate dp= ( )/ = in. Handle length = 135/25.4 = 5.31 in.Lead = 0.10 in. Thread angle b = 29°Guess m = mc = 0 due to bearing W = 1522 Lb.What torque is required to raise the jack? What force is required on the handle?
12 C-Clamp Analysis What torque is required to cause the 500 Lb. squeeze? Thread ID = in. Thread OD = in. Handle length = 3 in. N = 8 Threads/Inch Thread angle b = 60°Guess m = mc = 0 to simplify things W = 500 Lb.What torque is required to cause the 500 Lb. squeeze?Note: If Acme, could use Eqn. 16.4But with a 60° thread angle, this is NOT an Acme.Estimate dp= (ID+OD)/2 = ( )/2 = in.
13 Using Dornfeld Lecture Equations dp= in. N = 8 Threads/Inch Lead = 1/N = in.Thread angle b = 60°m = W = 500 Lb.Because this is not a square thread, must use effective coefficient of friction = m/cos(b/2) = 0.15/cos(30°) = 0.15/0.866 =
14 Using Hamrock Equations dp= in. N = 8 Threads/Inch Lead = 1/N = in.Thread angle b = 60°m = W = 500 Lb.How close is this to b/2 = 30°?[Eqn ]The equations are equivalent. Pick whichever one suits you best.
15 Overhauling Revisited • Power screws can lower all by themselves if the friction becomes less than the tangent of the lead angle, a.• This corresponds to the numerator in the Tlower equation going negative, with the transition being where the numerator is Zero.• You can use either Dornfeld or Hamrock equation, but remember that the Dornfeld equation is Effective friction, and you must multiply by cos(b/2) to get the actual friction.Transition when:Hamrock:Dornfeld:The equations are equivalent. Pick whichever one suits you best.
16 Failure Modes: Tensile Overload When the tensile stress on a bolt exceeds the material’s Proof Strength, the bolt will permanently stretch.Where At is the Tensile Stress Area for the bolt – the equivalent area of a section cut through the bolt.For UN threads,dc = Crest Dia (in.) n = threads/in.For M threads,dc = Crest Dia (mm) p = pitch (mm)Hamrock Page 731
17 Failure Modes: Thread Shear Shear of Nut ThreadsThe shear strength of the bolt and nut material may not be the same.Shear of Bolt Threads
18 Failure Modes: Shank Shear Bolts are not really intended to be used this way unless they are Shoulder Bolts:Typically the preload from tightening the bolt clamps the joint, and the friction between the members holds the joint.
19 Bolt PreloadJH Bickford explains : 'When we tighten a bolt, ( a) we apply torque to the nut, ( b) the nut turns, ( c) the bolt stretches, ( d) creating preload.'So the bolt is really a spring that stretches and creates preload on the joint.We use the Power Screw equations to determine how torque results in preload. This can be approximated simply by:Where T is torque, Dcrest is the bolt crest diameter, P is the preload, and K is a dimensionless constant. K = 0.20 for clean, dry threads and K = 0.15 for lubricated threads.
20 Bolt StiffnessA bolt looks like two springs in series: one rod with the Crest diameter and one with the Root diameter.Their lengths are increased to reflect the head and nut.Hamrock Page 725
21 Bolt Stiffness Exercise Calculate the stiffness of a 3/8-16 screw that is 4 in. long and clamps 3.5” of material. Use Eqn to determine shank length.Lt in 16.22/23Lt in 16.21Note: Hamrock uses Lt in Eqns and 16.22/23, BUT THEY ARE DIFFERENT THINGS! In it is the Clamped thread length; in 16.22/23 it is Total thread length.Hamrock Page 726
22 Joint StiffnessThe material clamped by the bolt also acts like a spring – in compression.Effectively, only the material in the red double conical area matters.There are many methods to calculate this stiffness.Compare these calculator stiffness results from tribology-abc.com with Hamrock’s Example 16.6Hamrock Page 727
23 How Bolt Preload WorksPreload isolates the bolt from most of any external loads.The joint stiffness factor, Cj, determines what fraction of external loads the bolt actually sees.Hamrock EqnFrom Norton, Chap. 14
24 Bolt StrengthFor Metric grades, the first number x 100 = Sut in MPa. The fraction x Sut = Sy. Ex: grade 12.9 has Sut ≈1200 MPa and Sy ≈ 0.9x1200 = 1080 MPa.Hamrock Page 731
25 Bolt Loading Generally, bolts are preloaded to: Ultimate Proof0.2%YieldUltimateGenerally, bolts are preloaded to:• 75% of Proof Load for reused connections • 90% of Proof Load for permanent connectionswhere Proof Load = Proof Strength x At.The Proof Strength is approximately at the elastic limit for the material.Hamrock Page 733
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