1. DEPARTMENT OF MECHANICAL ENGINEERING
v-semester
Design of machine elements
CHAPTER NO.4
design of power screw
brakes and clutches

2. CHAPTER 3:- SYLLABUS . 1 Design of power screw
Thread forms, multiple threaded screws, Terminology of power screw, design of screw jack. 2 3
Design of brakes and clutches 4
Design of clutches and brakes: Single and multiple plate clutch, 5
Constant wear and constant pressure theory for plate clutches, 6
Internal and external shoe brakes.
DTEL 2

3. CHAPTER-1 SPECIFIC Objective / course outcome
The student will be able to:
Design of power screw, screw jack with its function, uses and its terminology also understand the design of clutches and brakes and its types. 1
DTEL 3

4. LECTURE 1 : - Design of Power Screw Introduction DTEL
The power screws (also known as translation screws) are used to convert rotary motion into translatory motion. For example, in the case of the lead screw of lathe, the rotary motion is available but the tool has to be advanced in the direction of the cut against the cutting resistance of the material. In case of screw jack, a small force applied in the horizontal plane is used to raise or lower a large load. Power screws are also used in vices, testing machines, presses, etc.
In most of the power screws, the nut has axial motion against the resisting axial force while the screw rotates in its bearings. In some screws, the screw rotates and moves axially against the resisting force while the nut is stationary and in others the nut rotates while the screw moves axially with no rotation.
DTEL 4

5. Types of Screw Threads used for Power Screws
LECTURE 1 : -
Design of Power Screw
Types of Screw Threads used for Power Screws
Following are the three types of screw threads mostly used for power screws :
2. Acme or trapezoidal thread: - An acme or trapezoidal thread, as shown in Fig. (b), is a modification of square thread. The slight slope given to its sides lowers the efficiency slightly than square thread and it also introduce some bursting pressure on the nut, but increases its area in shear.An acme thread may be cut by means of dies and hence it is more easily manufactured than square thread.
1. Square thread: - A square thread, as shown in Fig. (a), is adapted for the transmission of power in either direction. This thread results in maximum efficiency and minimum radial or bursting pressure on the nut. The square threads are employed in screw jacks, presses and clamping devices.
DTEL 5

6. LECTURE 1 : - Design of Power Screw
3. Buttress thread: - A buttress thread, as shown in Fig. (c), is used when large forces act along the screw axis in one direction only. This thread combines the higher efficiency of square thread. The buttress thread has limited use for power transmission. It is employed as the thread for light jack screws and vices.
DTEL 6

7. LECTURE 1 : - Design of Power Screw
Torque Required to Raise Load by Square Threaded Screws: - The torque required to raise a load by means of square threaded screw may be determined by considering a screw jack as shown in Fig. (a). The load to be raised or lowered is placed on the head of the square threaded rod which is rotated by the application of an effort at the end of lever for lifting or lowering the load.
DTEL 7

8. LECTURE 1 : - Design of Power Screw DTEL
A little consideration will show that if one complete turn of a screw thread be imagined to be unwound, from the body of the screw and developed, it will form an inclined plane as shown in Fig.
Let p = Pitch of the screw,
d = Mean diameter of the screw,
α = Helix angle,
P = Effort applied at the circumference
of the screw to lift the load,
W = Load to be lifted, and
μ = Coefficient of friction, between the screw and nut
= tan φ, where φ is the friction angle.
we find that, tan α = p / π d
DTEL 8

9. LECTURE 1 : - Design of Power Screw DTEL
Since the principle, on which a screw jack works is similar to that of an inclined plane,
∴ Torque required to overcome friction between the screw and nut,
When the axial load is taken up by a thrust collar as shown in Fig. (b), so that the load does not rotate with the screw, then the torque required to overcome friction at the collar,
... (Assuming uniform pressure conditions)
...(Assuming uniform wear conditions)
where R1 and R2 = Outside and inside radii of collar,
R = Mean radius of collar = R1+ R2 / 2, and
μ1 = Coefficient of friction for the collar.
DTEL 9

10. Torque Required to Lower Load by Square Threaded Screws
LECTURE 1 : -
Design of Power Screw
∴ Total torque required to overcome friction (i.e. to rotate the screw),
T = T1 + T2
If an effort P1 is applied at the end of a lever of arm length l, then the total torque required to overcome friction must be equal to the torque applied at the end of lever,
Torque Required to Lower Load by Square Threaded Screws
∴ Torque required to overcome friction between the screw and nut,
Note : When α > φ, then P = W tan (α – φ).
Efficiency of Square Threaded Screws
The efficiency of square threaded screws may be defined as the ratio between the ideal effort (i.e. the effort required to move the load, neglecting friction) to the actual effort (i.e. the effort required to move the load taking friction into account)
DTEL 10

11. Efficiency of Self Locking Screws
LECTURE 1 : -
Design of Power Screw
Over Hauling and Self Locking Screws
We know that the effort required at the circumference of the screw to lower the
load is P = W tan (φ – α) and the torque required to lower the load,
In the above expression, if φ < α, then torque required to lower the load will be negative.
In other words, the load will start moving downward without the application of any torque. Such a condition is known as over hauling of screws. If however, φ > α, the torque required to lower the load will be positive, indicating that an effort is applied to lower the load. Such a screw is known as self locking screw. In other words, a screw will be self locking if the friction angle is greater than helix angle or coefficient of friction is greater than tangent of helix angle
i.e. μ or tan φ > tan α.
Efficiency of Self Locking Screws
We know that the efficiency of screw,
DTEL 11

12. Stresses in Power Screws
LECTURE 1 : -
Design of Power Screw
Stresses in Power Screws
Direct tensile or compressive stress due to an axial load
∴ Direct stress (tensile or compressive) = W / Ac
2. Torsional shear stress
We know that torque transmitted by the screw,
3. Shear stress due to axial load.
Shear stress for screw,
and shear stress for nut,
DTEL 12

13. LECTURE 1 : - Design of Power Screw DTEL
4. Bearing pressure: - The bearing pressure on the threads is given by
where d = Mean diameter of screw,
t = Thickness or width of screw = p / 2, and
n = Number of threads in contact with the nut
= Height of the nut = h / p
Pitch of threads
DTEL 13

14. LECTURE 1 : - Design of Power Screw DTEL
Example 1: - A vertical screw with single start square threads of 50 mm mean diameter and 12.5 mm pitch is raised against a load of 10 kN by means of a hand wheel, the boss of which is threaded to act as a nut. The axial load is taken up by a thrust collar which supports the wheel boss and has a mean diameter of 60 mm. The coefficient of friction is 0.15 for the screw and 0.18 for the collar. If the tangential force applied by each hand to the wheel is 100 N, find suitable diameter of the hand wheel.
Example 2: - An electric motor driven power screw moves a nut in a horizontal plane against a force of 75 kN at a speed of 300 mm / min. The screw has a single square thread of 6 mm pitch on a major diameter of 40 mm. The coefficient of friction at screw threads is 0.1. Estimate power of the motor.
Example 3: - The cutter of a broaching machine is pulled by square threaded screw of 55 mm external diameter and 10 mm pitch. The operating nut takes the axial load of 400 N on a flat surface of 60 mm and 90 mm internal and external diameters respectively. If the coefficient of friction is 0.15 for all contact surfaces on the nut, determine the power required to rotate the operating nut when the cutting speed is 6 m/min. Also find the efficiency of the screw.
DTEL 14

15. LECTURE 1 : - Design of Power Screw DTEL
Example 4: - A vertical two start square threaded screw of a 100 mm mean diameter and 20 mm pitch supports a vertical load of 18 kN. The axial thrust on the screw is taken by a collar bearing of 250 mm outside diameter and 100 mm inside diameter. Find the force required at the end of a lever which is 400 mm long in order to lift and lower the load. The coefficient of friction for the vertical screw and nut is 0.15 and that for collar bearing is 0.20.
Example 5: - The mean diameter of the square threaded screw having pitch of 10 mm is 50 mm. A load of 20 kN is lifted through a distance of 170 mm. Find the work done in lifting the load and the efficiency of the screw, when 1. The load rotates with the screw, and 2. The load rests on the loose head which does not rotate with the screw. The external and internal diameter of the bearing surface of the loose head are 60 mm and 10 mm respectively. The coefficient of friction for the screw and the bearing surface may be taken as 0.08.
DTEL 15

16. LECTURE 1 : - Design of Brakes Introduction DTEL
A brake is a device by means of which artificial frictional resistance is applied to a moving machine member, in order to retard or stop the motion of a machine. In the process of performing this function, the brake absorbs either kinetic energy of the moving member or potential energy given up by objects being lowered by hoists, elevators etc. The energy absorbed by brakes is dissipated in the form of heat. This heat is dissipated in the surrounding air (or water which is circulated through the passages in the brake drum) so that excessive heating of the brake lining does not take place. The design or capacity of a brake depends upon the following factors :
1. The unit pressure between the braking surfaces,
2. The coefficient of friction between the braking surfaces,
3. The peripheral velocity of the brake drum,
The projected area of the friction surfaces, and
5. The ability of the brake to dissipate heat equivalent to the energy being absorbed.
The major functional difference between a clutch and a brake is that a clutch is used to keep the driving and driven member moving together, whereas brakes are used to stop a moving member or to control its speed.
DTEL 16

17. Materials for Brake Lining
LECTURE 1 : -
Design of Brakes
Materials for Brake Lining
The material used for the brake lining should have the following characteristics :
1. It should have high coefficient of friction with minimum fading. In other words, the coefficient of friction should remain constant over the entire surface with change in temperature.
2. It should have low wear rate It should have low coefficient of thermal expansion It should have adequate mechanical strength It should have high heat resistance.
6. It should have high heat dissipation capacity.
7. It should not be affected by moisture and oil.
Properties of materials for brake lining.
DTEL 17

18. LECTURE 1 : - Design of Brakes Types of Brakes DTEL
The brakes, according to the means used for transforming the energy by the braking element, are classified as :
1. Hydraulic brakes e.g. pumps or hydrodynamic brake and fluid agitator,
2. Electric brakes e.g. generators and eddy current brakes, and
3. Mechanical brakes.
The hydraulic and electric brakes cannot bring the member to rest and are mostly used where large amounts of energy are to be transformed while the brake is retarding the load such as in laboratory dynamometers, high way trucks and electric locomotives. These brakes are also used for retarding or controlling the speed of a vehicle for down-hill travel. The mechanical brakes, according to the direction of acting force, may be divided into the following two groups :
Radial brakes: - In these brakes, the force acting on the brake drum is in radial direction. The radial brakes may be sub-divided into external brakes and internal brakes. According to the shape of the friction element, these brakes may be block or shoe brakes and band brakes.
Axial brakes: - In these brakes, the force acting on the brake drum is in axial direction. The axial brakes may be disc brakes and cone brakes. The analysis of these brakes is similar to clutches.
DTEL 18

19. LECTURE 1 : - Design of Brakes Single Block or Shoe Brake: - DTEL
It consists of a block or shoe which is pressed against the rim of a revolving brake wheel drum. The block is made of a softer material than the rim of the wheel. This type of a brake is commonly used on railway trains and tram cars. The friction between the block and the wheel causes a tangential braking force to act on the wheel, which retard the rotation of the wheel. The block is pressed against the wheel by a force applied to one end of a lever to which the block is rigidly fixed as shown in Fig. The other end of the lever is pivoted on a fixed fulcrum O.
Figure : - Single block brake. Line of action of tangential force passes through the fulcrum of the lever.
DTEL 19

20. LECTURE 1 : - Design of Brakes DTEL
Let P = Force applied at the end of the lever,
RN = Normal force pressing the brake block on the wheel,
r = Radius of the wheel,
2θ = Angle of contact surface of the block,
μ = Coefficient of friction, and
Ft = Tangential braking force or the frictional force acting at the contact surface of the block and the wheel.
If the angle of contact is less than 60°, then it may be assumed that the normal pressure between the block and the wheel is uniform. In such cases, tangential braking force on the wheel, Ft = μ.RN (i)
and the braking torque,
TB = Ft. r = μ RN . r
DTEL 20

21. LECTURE 1 : - Design of Brakes DTEL
Let us now consider the following three cases :
Case 1 : - When the line of action of tangential braking force (Ft) passes through the fulcrum O of the lever, and the brake wheel rotates clockwise as shown in Figure then for equilibrium, taking moments about the fulcrum O, we have,
RN × x = P × l or
∴ Braking torque,
Figure 1: - line of action of tangential braking force (Ft) passes through the fulcrum
DTEL 21

22. LECTURE 1 : - Design of Brakes DTEL
Case 2: - When the line of action of the tangential braking force (Ft) passes through a distance ‘a’ below the fulcrum O, and the brake wheel rotates clockwise as shown in Figure then for equilibrium, taking moments about the fulcrum O,
RN × x + Ft × a = P.l
RN × x + μ RN × a = P.l or
and braking torque,
RN × x = P.l + Ft × a = P.l + μ.RN × a
RN (x – μ.a) = P.l or
and braking torque,
Figure 2: - Line of action of Ft passes below the fulcrum.
DTEL 22

23. LECTURE 1 : - Design of Brakes DTEL
Case 3 : - When the line of action of the tangential braking force passes through a distance ‘a’ above the fulcrum, and the brake wheel rotates clockwise as shown in figure then for equilibrium, taking moments about the fulcrum O, we have
RN.x = P.l + Ft.a = P.l + μ.RN.a
RN (x – μ.a) = P.l or
and braking torque,
RN × x + Ft × a = P.l
RN × x + μ.RN × a = P.l or
and braking torque,
Figure 3: - line of action of the Ft passes through a distance ‘a’ above the fulcrum
DTEL 23

24. LECTURE 1 : - Design of Brakes DTEL
Notes 1: - From above we see that when the brake wheel rotates anticlockwise in case 2 [Fig. 2 (b)] and when it rotates clockwise in case 3 [Fig.3 (a)], the equations (i) and (ii) are same, i.e RN × x = P.l + μ.RN.a
From this we see that the moment of frictional force (μ. RN.a) adds to the moment of force (P.l). In other words, the frictional force helps to apply the brake. Such type of brakes are said to be self energizing brakes. When the frictional force is great enough to apply the brake with no external force, then the brake is said to be self locking brake.
From the above expression, we see that if x ≤ μ.a, then P will be negative or equal to zero. This means no external force is needed to apply the brake and hence the brake is self locking. Therefore the condition for the brake to be self locking is x ≤ μ.a.
The self-locking brake is used only in back-stop applications.
2. The brake should be self-energizing and not the self-locking.
3. In order to avoid self-locking and to prevent the brake from grabbing, x is kept greater than μ.a.
4. If Ab is the projected bearing area of the block or shoe, then the bearing pressure on the shoe, pb = RN / Ab We know that Ab = Width of shoe × Projected length of shoe = w (2r sin θ)
5. When a single block or shoe brake is applied to a rolling wheel, an additional load is thrown on the shaft bearings due to heavy normal force (RN) and produces bending of the shaft.
DTEL 24

25. LECTURE 1 : - Design of Brakes Pivoted Block or Shoe Brake
when the angle of contact is less than 60°, then it may be assumed that the normal pressure between the block and the wheel is uniform. But when the angle of contact is greater than 60°, then the unit pressure normal to the surface of contact is less at the ends than at the centre. In such cases, the block or shoe is pivoted to the lever as shown in Figure instead of being rigidly attached to the lever. This gives uniform wear of the brake lining in the direction of the applied force. The braking torque for a pivoted block or shoe brake (i.e. when 2θ > 60°) is given by
TB = Ft × r = μ'.RN. R
where μ' = Equivalent coefficient of friction = and
μ = Actual coefficient of friction.
Figure: - Pivoted block or shoe brake.
These brakes have more life and may provide a higher braking torque.
DTEL 25

26. LECTURE 1 : - Design of Brakes DTEL
Example 1: - A single block brake is shown in figure no.1 The diameter of the drum is 250 mm and the angle of contact is 90°. If the operating force of 700 N is applied at the end of a lever and the coefficient of friction between the drum and the lining is 0.35, determine the torque that may be transmitted by the block brake.
Figure No: 1
Figure No: 2
Example 2: - Figure 2 shows a brake shoe applied to a drum by a lever AB which is pivoted at a fixed point A and rigidly fixed to the shoe. The radius of the drum is 160 mm. The coefficient of friction of the brake lining is 0.3. If the drum rotates clockwise, find the braking torque due to the horizontal force of 600 N applied at B.
DTEL 26

27. UNIT 1 : - Introduction to M. E. D.
References Books:
[1] P.S.G Design Data book, Coimbatore.
[2] A text book of Machine Design by Malive Hartman, USA.
[3] A text book of Machine Design by V.B. Bhandari, Tata Mc-Graw Hill Publications, India
[4] A text book of Machine Design by B. D. Shiwalkar, India
[5] A textbook of Production Technology and Manufacturing Processes by P.C. Sharma, S. Chand publication, 2009, p.p. (90-125).
[6] A text book of Electrical Technology, Volume – II, S. Chand Publisher, 2008, p.p. ( ).
[7] A text book of Machine Design by - R. S. Khurmi, India.
[8] Cubberly, W. H.; Ramon, Bakerjian, Tool and Manufacturing Engineers handbook, Society of Manufacturing Engineering SME (1989), p.p
[9] Edward J. Thornton and J. Kirk Armintor, “The fundamentals of ac electric induction motor design and application”, Proceedings of the twentieth International Pump users symposium, Texas p.p
DTEL 27

28. UNIT 1 : - Introduction to M. E. D.
THANK YOU
DTEL 28