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**Lecture 9: Screws (Chapter 16)**

ME311 Machine Design Lecture 9: Screws (Chapter 16) W Dornfeld 05Nov2009 Fairfield University School of Engineering

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Thread Geometry Diameters Major Crest Pitch Root Minor Thread Height Thread Pitch Thread Angle The Pitch Diameter is midway between the Major and Minor Diameters. Hamrock Page 707

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Thread Types Lead = 1 x Pitch Lead = 3 x Pitch Single-, double-, and triple-threaded screws. Also called single-, double-, and triple-start. Acme Thread Square Thread Hamrock Page 708 Acme threads are used in C-Clamps, vices, and cartoons.

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**Details of Thread Profiles**

Thread Height Relationships 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 1.25mm Hamrock Page 708

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**Power Screws W Looking at a square thread screw, we unwind one turn: m**

rm rc Lead m Thread friction Collar friction Mean thread radius Mean collar radius Load on nut mc Looking at a square thread screw, we unwind one turn: a Lead 2p rm This shows an inclined ramp with angle The Mean Radius is midway between the Crest and Root Radii.

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**Square Thread Screw Torque**

rm rc Lead m mc The torque required to raise the load W is and to lower the load, we flip two signs: Hamrock Page 715

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**Power Screw Thread Angle**

If the thread form is not square but has an angle b, replace the thread friction m with the effective friction b The effect: Square: b = 0, b/2 = 0, 1/cos(0°) = 1.0 Acme: b = 29°, b/2 = 14.5°, 1/cos(14.5°) = 1.033 Unified: b = 60°, b/2 = 30°, 1/cos(30°) = 1.15 The thread angle effectively increases surface friction between 3 and 15% Note: Instead of b/2, Hamrock uses The difference is negligible.

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**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). a Lead 2p rm m This is the same case for a weight sliding down a ramp when the incline angle a exceeds tan-1m.

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**Ball Screws Have Low Friction**

Recirculating balls roll between ball screw and ball nut to minimize friction. These almost always overhaul.

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**Our Scissors Jack 1015 Lb 1522 Lb Tension**

Handle End with ball thrust bearing End with nut

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**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?

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**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. 16.4 But with a 60° thread angle, this is NOT an Acme. Estimate dp= (ID+OD)/2 = ( )/2 = in.

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**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 =

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**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.

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**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.

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**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

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**Failure Modes: Thread Shear**

Shear of Nut Threads The shear strength of the bolt and nut material may not be the same. Shear of Bolt Threads

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**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.

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Bolt Preload JH 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.

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Bolt Stiffness A 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

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**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 16.22/23 Lt in 16.21 Note: 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

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Joint Stiffness The 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 16.6 Hamrock Page 727

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How Bolt Preload Works Preload 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 Eqn From Norton, Chap. 14

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Bolt Strength For 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

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**Bolt Loading Generally, bolts are preloaded to: Ultimate**

Proof 0.2%Yield Ultimate Generally, bolts are preloaded to: • 75% of Proof Load for reused connections • 90% of Proof Load for permanent connections where 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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**Recommended Site: BoltScience.com**

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