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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 1

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints 8-1 Thread Standards and Definitions 8-2The Mechanics of Power Screws 8-3Strength Constraints 8-4Joints-Fasteners Stiffness 8-5Joints-Member Stiffness 8-6Bolt Strength 8-7Tension Joints-The External Load 8-8Relating Bolt Torque to Bolt Tension 8-9Statically Loaded Tension Joint with Preload 8-10Gasketed Joints 8-11Fatigue Loading of Tension Joints 8-12Shear Joints 8-13Setscrews 8-14Keys and Pins 8-15Stochastic Considerations 8-1 Thread Standards and Definitions 8-2The Mechanics of Power Screws 8-3Strength Constraints 8-4Joints-Fasteners Stiffness 8-5Joints-Member Stiffness 8-6Bolt Strength 8-7Tension Joints-The External Load 8-8Relating Bolt Torque to Bolt Tension 8-9Statically Loaded Tension Joint with Preload 8-10Gasketed Joints 8-11Fatigue Loading of Tension Joints 8-12Shear Joints 8-13Setscrews 8-14Keys and Pins 8-15Stochastic Considerations CH-8 LEC 34 Slide 2

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Announcements HW #5 Ch. 18, on WebCT Due Date for HW #5 is Mon. DEC. 31, 2007 Quiz on Ch. 18, Mon. DEC. 31, 2007 ????? CH-8 LEC 34 Slide 3

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints 8-2The Mechanics of Power Screws CH-8 LEC 34 Slide 4

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 5 A power screw is 23 mm in diameter and has a thread pitch of 7 mm. (a) Find the thread depth, the thread width, the mean and root diameters, and the lead, provided square threads are used. (b) Repeat part (a) for Acme threads. Example-1 Given: Diameter of the power screw, d = 23 mm Thread pitch, p = 7 mm

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 6

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 7

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints The Mechanics of Power Screws A power screw is a device used in machinery to change the angular motion into linear motion, and usually, to transmit power. Applications: Lead screws of lathes Screws for vises, presses and jacks Figure 8-4 The Joyce worm-gear screw jack. CH-8 LEC 34 Slide 8

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints The Mechanics of Power Screws In Figure 8-5 a square threaded power screw with single thread having a mean diameter d m, a pitch angle p, and a lead angle λ, and a helix angle ψ is loaded by the axial compressive force F. We wish to find an expression for the torque required to raise this load, and another expression for the torque required to lower the load. Figure 8-5Portion of a power screw (Square) CH-8 LEC 34 Slide 9

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Imagine that a single thread of the screw is enrolled or developed (Fig. 8-6) for exactly a single turn. Then on edge of the thread will form the hypotenuse of a right triangle whose base is the circumference of the mean-thread- circle and whose height is the lead. The angle λ is the lead angle of the thread. For raising the load a force P R acts to the right and to lower the load, P L acts to the left. CH-8 LEC 34 Slide 10 Figure 8-6Force Diagrams (a) Lifting the load; (b)lowering the load

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints For raising the load (a) For lowering the load (b) CH-8 LEC 34 Slide 11

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints For raising the load (c) For lowering the load (d) CH-8 LEC 34 Slide 12 Eliminating N from the previous equations and solving for P gives

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints For raising the load (e) For lowering the load (f) CH-8 LEC 34 Slide 13 Next, divide the numerator and the denominator of these equations by cos λ and use the relation

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints (8-1) (8-2) CH-8 LEC 34 Slide 14 The torque is the product of the force P and the mean radius Torque required for raising the load to overcome thread friction and to raise the load Torque required for lowering the load to overcome part of the thread friction in lowering the load

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 15 Self Locking Condition If the lead is large or the friction is low, the load will lower itself by causing the screw to spin without any external effort. In such cases the torque from Eq. (8-2) will be negative or zero. When a positive torque is obtained from this equation, the screw is said to be self locking Condition for Self Locking: Dividing both sides of the above inequality by and recognizing that, we get (8-3)

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 16 The critical coefficient of friction for the lead concerned, If f = f cr the nut is on the point of moving down the thread without any torque applied. If f > f cr then the thread is self-locking in that the nut cannot undo by itself, it needs to be unscrewed by a definite negative torque; Clearly self-locking behavior is essential for threaded fasteners. Car lifting jacks would not be of much use if the load fell as soon as the operating handle was released. Self Locking Condition

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Some applications of power screws require overhauling behavior. 1.The Archimedean drill 2.Pump action screwdrivers (Yankee screw drivers) These devices incorporate very large lead angles Power Screw-Overhauling If f < f cr then the thread is overhauling in that the nut will unscrew by itself under the action of the load unless prevented by a positive tightening torque. Increasing lead (angle) overhauling CH-8 LEC 34 Slide 17

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints decreasing thread friction overhauling Sensitive linear actuators may incorporate recirculating ball screws such as that illustrated here to reduce thread friction to levels which go hand-in-hand with overhauling. CH-8 LEC 34 Slide 18 Power Screw-Overhauling

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints decreasing thread friction overhauling Sensitive linear actuators may incorporate recirculating ball screws such as that illustrated here to reduce thread friction to levels which go hand-in-hand with overhauling. CH-8 LEC 34 Slide 19 Power Screw-Overhauling

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 20 Efficiency If we let in Eq. (8-1), we obtain which, is the torque required to raise the load. (8-4) (g) The efficiency is therefore

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints f CH-8 LEC 34 Slide 21 Efficiency

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 22 Power Screw- ACME Thread F is parallel to screw axis i.e. makes angle α = 14.5° with thread surface ignoring the small effect of l, the resultant normal force N is F/cos α. The frictional force = f N is increased and thus friction terms in Eq. (8.1) are modified accordingly: Torque required to raise load F (8-5) ACME thread is not as efficient as square thread because of additional friction due to wedging action but it is often preferred because it is easier to machine.

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints In most of power screw applications (load lifting) a collar is to be designed. The presence of collar increases the friction torque. A thrust collar bearing must be employed between the rotating and stationary members in order to carry the axial component CH-8 LEC 34 Slide 23 Power Screw with Collar

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 24 Power Screw with Collar

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints f c = collar friction coefficient d c = collar mean diameter CH-8 LEC 34 Slide 25 Power Screw with Collar If is the coefficient of collar friction, the torque required is (8-6)

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Power Screws-friction coefficients Friction wears thread surface for safe applications Max thread bearing pressure is given in Table 8-4. CH-8 LEC 34 Slide 26

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Power Screws-friction coefficients CH-8 LEC 34 Slide 27 Table 8-5 Coefficients of friction f for Threaded Pairs

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Power Screws-friction coefficients CH-8 LEC 34 Slide 28 Table 8-6 Thrust Collar friction coefficient, f c Coefficients of friction around 0.1 to 0.2 may be expected for common materials under conditions of ordinary service and lubrication.

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Example-2 Problem # 8.8 Problem # 8.8 (modified) Given: 5/8”-6ACME? i.e. d=5/8” and N=6 f=f c = 0.15 d c =7/16 in P = 6 lb L arm =2 3/4 in Required: F, efficiency, Self-Lock? P L arm F CH-8 LEC 34 Slide 29

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Lever torque Clamping force R l =1/N p/2 =1/2N d CH-8 LEC 34 Slide 30 Example-2 (Cont.’d)

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ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Efficiency Self-lock which is clear that it is self lock CH-8 LEC 34 Slide 31 Example-2 (Cont.’d)

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