1. POWER SCREWS

2. Power Screws:
A power screw is a mechanical device used for converting rotary motion into linear motion and transmitting power. Its also called as translation screw.
Power screw has three essential parts screw ,nut and part to hold either the screw or the nut in its place. Depending upon the holding arrangement power screw operate in two different ways. In first case the screw rotates in its bearing, while the nut has axial motion eg. Lead screw. In second case the nut is kept stationary and the screw moves in axial direction eg. Screw jack, machine vice.

3. Advantages of power screws:
It has large load carrying capacity.
Overall dimensions are small hence compact construction.
It is simple to design.
The manufacturing of power screw is easy.
It provides large mechanical advantage.
It gives smooth and noiseless service without any maintenance.
It has few parts hence reduces cost and increases reliability.
A power screw can be designed with self locking property.

4. Disadvantages of power screws:
It has very poor effciency as low as 40%.
High friction in threads causes rapid wear of the screw or the nut.
Applications of power screws:
To raise the load eg. Screw jack
To obtain accurate motion in machining operations eg. Lead screw of lathe.
To clamp a work piece eg. Vice.
To load a specimen eg. Universal testing machine.

5. Forms of threads: 𝟏.Square thread
There are two popular types of threads used for power screw.
Square thread.
ISO metric trapezoidal thread.
𝟏.Square thread

6. Advantages of square threads:
Square threads has high effciency.
There is no radial pressure or side thrust on the nut.
Disadvantages of square threads:
Square threads are difficult to manufacture.
Square threads have less thickness at the core diameter hence this reduces the load carrying capacity.
If thread surface is weared it is not possible compensate for wear in square threads, therefore when worn out, the nut or the screw requires replacement.
Square threads are used for screw jack, presses and clamping devices.

7. Advantages of trapezoidal threads:
Trapezoidal threads are economical to manufacturing.
It has more thickness at the core diameter hence it has large load carrying capacity.
The axial wear on the surface of trapezoidal threads can be compensated by means of a spilt-type of nut.

8. Disadvantage of trapezoidal threads:
It has less efficiency.
There is radial pressure or side thrust on the nut.
There is special type of trapezoidal thread called acme thread. Trapezoidal and acme threads are identical in all respects expect the thread angle. In acme thread the thread angle is instead of

9. Trapezoidal and acme threads are used for lead-screw and other power transmission devices in machine tools.
Buttress thread:
It combines the advantages of square and trapezoidal threads. Buttress threads are used where a heavy axial force acts along the screw axis in one direction only.

10. Advantages of buttress thread:
It has higher efficiency as compared with trapezoidal threads.
It can be economically manufactured.
The axial wear at the thread surface can be compensated by means of a spilt type nut.
A screw with buttress thread is stronger the an equivalent screw with either square or trapezoidal threads.
Buttress threads have one disadvantage it can transmit power and motion only in one direction.
Buttress threads are used in vices, where force is applied in one direction only.

11. Terminology of Power Screw
Pitch:
The pitch is defined as the distance measured parallel to the axis of the screw from a point on one thread to the corresponding point on the adjacent thread.
It is denoted by the letter p.
Lead:
It is defined as the distance measured parallel to the axis of the screw which the nut will advance in one revolution of the screw.
It is denoted by the letter l.
For a single-threaded screw, the lead is same as the pitch. For double-threaded screw, the lead is twice of the pitch, and so on.

12. Nominal Diameter:
Nominal diameter is the largest diameter of the screw. It is also called major diameter.
It is denoted by the letter d.
Core Diameter:
The core diameter is the smallest diameter of the screw thread. It is also called minor diameter.
It is denoted by the letter dc.
Helix Angle:
The helix angle is defined as the angle made by the helix of the thread with a plane perpendicular to the axis of the screw. It is also called lead angle.
It is denoted by α.

13. And , dm is the mean diameter of the screw.
Helix Angle continued...
From fig.
And , dm is the mean diameter of the screw.
It is given by,

14. Considering the right angle triangle, the relationship between the helix angle, mean diameter and lead can be expressed in the following form:

15. l Force analysis of square thread: 𝟏.Lifting load:
The screw is considered as an inclined plane with inclination α as shown in fig.
Forces act at a point on inclined plane
Load W
Normal reaction N
Frictional force µN
Effort P N P l µN W α
π 𝑑 𝑚
𝐹𝑜𝑟𝑐𝑒 𝑑𝑖𝑎𝑔𝑟𝑎𝑚 𝑓𝑜𝑟 𝑙𝑖𝑓𝑡𝑖𝑛𝑔 𝑙𝑜𝑎𝑑
- Prepared by Sangram Nikam (FY M Tech CAD-CAM ) 15

16. P = 𝑊(𝜇 cos 𝛼 + sin 𝛼 ) ( cos 𝛼 − 𝜇 sin 𝛼 )
Dividing right hand side by cos α
P = 𝑊( µ + tan α ) (1 − µ tan α ) (c)
The coefficient of friction
µ= tan ϕ ϕ = friction angle

17. 𝑃= 𝑊( tan ϕ + tan α ) ( 1 − tan ϕ tan α ) or 𝑃=𝑊 tan (ϕ+α)
Substituting µ= tan ϕ in eq. (c)
𝑃= 𝑊( tan ϕ + tan α ) ( 1 − tan ϕ tan α ) or
𝑃=𝑊 tan (ϕ+α)
The torque required to raise the load is given by
𝑀 𝑡 = 𝑃 𝑑 𝑚 2
𝑀 𝑡 = 𝑊 𝑑 𝑚 2 tan (ϕ+α)

18. 𝟐.Lowering load:
The forces acting at a point on the inclined plane as shown in fig. N P µN l W α
π 𝑑 𝑚
𝐹𝑜𝑟𝑐𝑒 𝑑𝑖𝑎𝑔𝑟𝑎𝑚 𝑓𝑜𝑟 𝑙𝑜𝑤𝑒𝑟𝑖𝑛𝑔 𝑙𝑜𝑎𝑑
Considering the equilibrium of horizontal & vertical forces
𝑃= µ𝑁 cos α −𝑁 sin α (a)
𝑊=𝑁 cos α+ µ𝑁 sin α (b)

19. 𝑃= 𝑊(𝜇 cos 𝛼 − sin 𝛼 ) ( cos 𝛼 + 𝜇 sin 𝛼 )
Dividing (a) by (b)
𝑃= 𝑊(𝜇 cos 𝛼 − sin 𝛼 ) ( cos 𝛼 + 𝜇 sin 𝛼 )
Dividing right hand side by cos α
𝑃= 𝑊( µ − tan α ) (1+ µ tan α ) (c)
Substituting µ= tan ϕ in eq. (c)
𝑃= 𝑊( tan ϕ − tan α ) ( 1 + tan ϕ tan α )
𝑃=𝑊 tan (ϕ−α) 𝑀 𝑡 = 𝑊 𝑑 𝑚 2 tan (ϕ−α)

20. Force analysis of trapezoidal thread:
For trapezoidal thrread2Ѳ= 30 0
For acme thread 2Ѳ= 29 0
W is the axial force on the screw (load) 𝑊 cos Ѳ or (𝑊 sec Ѳ ) is the normal force on the thread surface.
The frictional force depends upon the normal force therefore the effect of thread angle is to increase the frictional force by a term sec Ѳ.
To account for this effect the coefficient of friction is taken as µ 𝑠𝑒𝑐Ѳ
𝑊 cos Ѳ W Ѳ 2Ѳ

21. 𝑃= 𝑊( µ sec Ѳ + tan α ) (1 − µ sec Ѳ tan α )
Case 1. Lifting load
Modifying eq. (c) in case of square thread lifting load.
𝑃= 𝑊( µ sec Ѳ + tan α ) (1 − µ sec Ѳ tan α )
𝑀 𝑡 =𝑃 𝑑 𝑚 2 = 𝑊 𝑑 𝑚 2 ( µ sec Ѳ + 𝑡𝑎𝑛 α ) ( 1 − µ sec Ѳ tan α )
Case 2. Lowering load
Modifying eq. (c) in case of square thread lowering load
𝑃= 𝑊( µ sec Ѳ − tan α ) (1+ µ sec Ѳ tan α )

22. Self-locking Screw:
The torque required to lower the load 𝑀 𝑡 = 𝑊 𝑑 𝑚 2 tan (ϕ−α)
Case 𝟏.
when ϕ<αthe torque required to lower the load is negative. It indicates no force is required to lower the load. The load itself will begin to turn the screw and descend down, unless a restraining torque is applied. This condition is called as overhauling of screw or back driving of screw. This property not used in screw jack application. It is used in Yankee screwdriver.
Case 𝟐.
when ϕ≥α positive torque is required to lower the load. In this condition the load will not return the screw and will not descend on its own unless an effort P is applied. In this case the screw is said to be self-locking. A self-locking screw will hold the load in place without a brake. This property is used in screw jack application.

23. A screw will be self-locking if the coefficient of friction is equal to or greater than the tangent of the helix angle.
For a self-locking screw,
ϕ>α
tan ϕ > tan α
µ> 1 π 𝑑 𝑚
Self-locking of screw is not possible when the coefficient of friction is low.
Self-locking property of the screw is lost when the lead is large.

24. Collar friction:
In many applications of the power screw there is collar friction in addition to the friction at the thread surface. The principle of collar friction explained with help of fig.
The cup remains stationary under the action of load W, while the collar that is integral with the screw rotates when the load is being raised or lowered. Therefore, there is relative motion between the cup and the collar at the annular interface from diameter 𝐷 𝑖 to 𝐷 𝑜 . This relative motion results in friction called collar friction. The torque required to overcome this friction is collar friction torque. Collar friction torque can be determined by using uniform pressure theory or uniform wear theory.

25. Overall Efficiency (Mt)t = Mt + (Mt)c
The total external torque required to raise the load consists of two factors- the torque required to overcome friction at the thread surface and the collar friction torque.
Therefore,
(Mt)t = Mt + (Mt)c
Where,
(Mt)t= external torque required to raise the load (N-mm);
Mt = torque required to overcome friction at the thread surface (N-mm); and
(Mt)c = collar friction torque (N-mm)
Work output = fore * distance travelled in the direction of force = (Wl)
The input consists of torque applied to the screw (Mt)t,
Work input = torque * angle turned through = [(Mt)t * (2π)]
The overall efficiency ηo of the power screw is given by,

26. Stresses in screw: σ 𝑐 = 𝑊 ( π 4 𝑑 𝑐 2 ) τ 𝑚𝑎𝑥 = ( σ 𝑐 2 ) 2 + τ 2
The body of the screw is subjected to an axial force W and torsional moment 𝑀 𝑡 as shown in fig.
The direct compressive stress σ 𝑐
σ 𝑐 = 𝑊 ( π 4 𝑑 𝑐 2 )
The torsional shear stres
τ= 16 ( 𝑀 𝑡 ) 𝑡 π 𝑑 𝑐 3
The principal shear stress
τ 𝑚𝑎𝑥 = ( σ 𝑐 2 ) 2 + τ 2

27. τ 𝑠 = transverse shear stress at the root of the screw ( 𝑁 𝑚𝑚 2 )
The threads of the screw is subjected to transverse shear stress
τ 𝑠 = 𝑊 π 𝑑 𝑐 𝑡 𝑧
τ 𝑠 = transverse shear stress at the root of the screw ( 𝑁 𝑚𝑚 2 )
𝑡= thread thickness at the core diameter (mm)
z = number of threads in engagement with the nut.
π 𝑑 𝑐 𝑡= shear area of one thread
The threads of the nut is subjected to transverse shear stress
τ 𝑛 = 𝑊 π 𝑑 𝑡 𝑧
τ 𝑛 = transverse shear stress at the root of the nut ( 𝑁 𝑚𝑚 2 )
π 𝑑 𝑡= shear area of one thread
The bearing pressure between the contacting surfaces of the screw and the nut.

28. 𝑆 𝑏 = unit bearing pressure (N/ 𝑚𝑚 2 )
𝑆 𝑏 = 𝑊 [ π 𝑑 2 − 𝑑 𝑐 2 𝑧]
𝑆 𝑏 = 4𝑊 [𝑧 𝑑 2 − 𝑑 𝑐 2
𝑆 𝑏 = unit bearing pressure (N/ 𝑚𝑚 2 ) ,

29. Differential & Compound Screws:
Differential Screw:
A differential screw is defined as a mechanical device consist of two screws in series, which are arranged in such way that the resultant motion is the difference of individual motions of the two screws.
The composite screw consist of larger part 𝑆 1 (pitch=4𝑚𝑚) & smaller part 𝑆 2 (pitch=3𝑚𝑚). The hand of helix for both the screw is right-handed. The 𝑆 1 moves through frame F. There is square nut N on 𝑆 2 .
The rotation of nut is prevented is shown in fig (c) it can only slide in axial direction w.r.t. frame.

30. The handle turned through one revolution in clockwise direction when viewed from right hand side. The direction of movement of the nut is opposite to that of the screw. The 𝑆 1 will move through 4𝑚𝑚 to the left w.r.t. frame & nut 3𝑚𝑚 to the right w.r.t. frame. The resultant motion of the nut w.r.t. frame will be 4−3 𝑚𝑚 to the left. In general if 𝑝 1 & 𝑝 2 are the pitches of the screws the resultant motion is equal to ( 𝑝 𝑝 2 )or the difference of the individual motion of the two screws.
Compound Screws:
A compound screw isdefined as a mechanical device consist of two screws in series, which are arranged in such way that the resultant motion is the sum of individual motions of the two screws. The arrangement is same as differential screw, except hand of helix for two screws are different.

31. The threads on 𝑆 1 are right handed while those on 𝑆 2 left handed
The threads on 𝑆 1 are right handed while those on 𝑆 2 left handed. The resultant motion of the nut w.r.t. frame will be 4+3 𝑚𝑚 to the left.
In general if 𝑝 1 & 𝑝 2 are the pitches of the screws the resultant motion is equal to ( 𝑝 1 + 𝑝 2 ) or the sum of the individual motion of the two screws.

32. Recirculating Ball Screw:
It consist of screw & nut, the surfaces of which separated by a series of balls. The screw & nut have semi-circular thread profiles. As the screw rotated, the balls advance in the grooves in nut & screw. They are collected at the end of the nut & returned back. It is also called as ball bearing screw or ball screw.
Such screws are preloaded and give accurate motion due elimination of backlash. There is no heat generation due to negligible friction. These screw can be used for high speed even upto10 𝑚 𝑚𝑖𝑛 . The balls, nut, screw are subjected to contact stresses.

33. Advantages: Disadvantages: Applications:
Due to rolling friction efficiency is high as 90%.
It is wear-free due to presence of lubricating film between contacting surfaces & protection from contamination by dirt particles.
It has large load carrying capacity.
Operation of RBS is smooth.
Disadvantages:
RBSis more costly.
They are usually overhauling due to low friction.
In RBS buckling of screw & critical speed are serious problem.
RBS requires a high degree of cleanliness.
Applications:
Automobile steering gear, power actuators, X-Y recorders of CNC machines, aircraft landing gear retractors, hospital bed adjustors, machine tool control.