Machine Design I (MCE-C 203) Mechatronics Dept., Faculty of Engineering, Fayoum University Dr. Ahmed Salah Abou Taleb Lecturer, Mechanical Engineering Dept., Faculty of Engineering, Fayoum University

Course Outlines Design of detachable joints: ( threaded joints , keys and splines). Thread Standards and Definitions. The Mechanics of Power Screws. Strength Constraints. Joints-Fasteners Stiffness. Joints-Member Stiffness. Bolt Strength. Tension Joints-The External Load. Relating Bolt Torque to Bolt Tension. Statically Loaded Tension Joint with Preload. Gasketed Joints. Fatigue Loading of Tension Joints. Shear Joints. Setscrews. Keys and Pins. Stochastic Considerations.

Introduction How can you assembled all the shown part together to get a final product? Permeate Joint Non-permeate Joint Welding Screw Bolt & Nut

Introduction Screw Uses Power Screw Thread Fastener lathe lead screw & car lifting jack which transforms rotary motion into substantial linear motion nut and bolt which joins a number of components together again by transforming rotary motion into linear motion

a) Square (b) ACME; (c) UN, ISO Thread Profile Thread profiles. a) Square (b) ACME; (c) UN, ISO

Thread Profile Lead=L=n p Terminology of screw threads. Sharp Vee Threads shown for clarity; the crests and roots are actually flattened or rounded during the forming operation

Mechanics of Power Screw 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

Mechanics of Power Screw Weight supported by three screw jacks. In each screw jack, only the shaded member rotates.

Mechanics of Square Power Screw In Figure; a square threaded power screw with single thread having a mean diameter dm, a pitch 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. ` Portion of a power screw (Square)

Mechanics of Square Power Screw Force Diagrams (a) Lifting the load; (b)lowering the load Imagine that a single thread of the screw is developed for exactly a single turn. The figure shows 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 . f is the coefficient of friction. For raising the load a force PR acts to the right and to lower the load, PL acts to the left.

Mechanics of Square Power Screw (1) For raising the load (2) For lowering the load

Mechanics of Square Power Screw By solving the previous equations one can get: (3) For raising the load For lowering the load (4) 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 (5) Torque required for lowering the load to overcome part of the thread friction in lowering the load (6)

Square Power Screw 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. (6) 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 (7)

Square Power Screw Efficiency If we let in Eq. (8-1), we obtain (8) which, is the torque required to raise the load. The efficiency is therefore (9)

Mechanics of 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. (5) are modified accordingly: Torque required to raise load F (10) 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.

Power Screw with Collar 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.

Power Screw with Collar If is the coefficient of collar friction, the torque required is: fc= collar friction coefficient dc = collar mean diameter (11) (12)

Power Screw – Coefficient of Friction Coefficients of friction f for Threaded Pairs Thrust Collar friction coefficient, fc Coefficients of friction around 0.1 to 0.2 may be expected for common materials under conditions of ordinary service and lubrication.

Power Screw Stress Analysis The following stresses should be checked on both nut and screw: Shearing stress in screw body. Axial stress in screw body Thread bearing stress (13) (14) (15) where nt is the number of engaged threads.

Power Screw Stress Analysis Thread bending stress The bending stress at the root of the thread is given by 5. Transverse shear stress at the center of the thread root and (16) (17)

Power Screw Stress Analysis The state of stress at top of root “plane” is

Power Screw Stress Analysis The engaged threads cannot share the load equally. Some experiments show that the first engaged thread carries 0.38 of the load the second engaged thread carries 0.25 of the load the third engaged thread carries 0.18 of the load the seventh engaged thread is free of load In estimating thread stresses by the equations above, substituting nt to 1 will give the largest level of stresses in the thread-nut combination

Power Screw Buckling Assuming that the column (screw) is a Johnson column where