1. 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

2. 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.

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

4. 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

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

6. 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

7. 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

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

9. 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)

10. 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.

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

12. 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)

13. 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)

14. 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)

15. 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.

16. 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.

17. 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)

18. 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.

19. 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.

20. 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)

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

22. 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

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