design of power screws

POWER OR TRANSLATIONAL SCREWS

INTRODUCTION Power or Translational screws are used to convert rotary motion into

translatory motion. Power or Translational screw is a mechanical device used for converting

rotary motion into linear motion and transmitting powerApplications of Power Screw To obtain accurate motion in machining operations -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.

To raise load - In case of screw jack, a small force applied in the horizontal plane is used to raise or lower a large load.

To clamp a work piece- Power screws are also used in vices, testing machines, presses

To load a specimen- Universal testing machine

In most of the power screws, the nut has axial motion against the resisting axial force while the screw rotates in its bearings.i.e lead screw

In some screws, the screw rotates and moves axially against the resisting force while the nut is stationary i.e. screw jack

INTRODUCTION

Advantages of Power screws Power screw has large load carrying capacity Compact in construction Manufacturing of power screw is easy – no SPM are

required Power screw has large Mechanical Advantage Power screw provides precise control and highly

accurate linear motion Provides smooth and noiseless service without any

maintenance Power screws can designed with self locking

property

INTRODUCTION

Disadvantages of Power screws Power screw has poor efficiency about 40% High friction between threads causes wear of

screw or nut

TYPES OF SCREW THREADS USED FOR TRANSLATIONAL SCREWSThree types of screw threads are mostly used for

translational screws:1. Square thread. A square thread, as shown, 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.

It is difficult to cut with taps and dies. It is usually cut on a lathe with a single point tool and it

can not be easily compensated for wear. The square threads are employed in screw jacks,

presses and clamping devices.

TYPES OF SCREW THREADS2. Acme and trapezoidal thread. An acme or trapezoidal

thread, as shown, is a modification of square thread.

The slight slope given to its sides lowers the efficiency slightly than square thread and it also introduces some bursting pressure on the nut, but increases its area in shear.

It is used where a split nut is required and where provision is made to take up wear as in the lead screw of a lathe.

Wear may be taken up by means of an adjustable split nut. An acme thread may be cut by means of dies and hence it is

more easily manufactured than square thread.

30

TYPES OF SCREW THREADS3. Buttress thread. A buttress thread, as shown is used when

large forces act along the screw axis in one direction only.

This thread combines the higher efficiency of square thread and the ease of cutting and the adaptability to a split nut of acme thread. It is stronger than other threads because of greater thickness at the base of the thread.

The buttress thread has limited use for power transmission. It is employed as the thread for light jack screws and vices

MULTIPLE THREADED SCREWS

The power screws with multiple threads such as double, triple etc. are employed when it is desired to secure a higher travelling speed. It also referred as multiple start screws

Such type of threads are usually found in high speed actuators.

MULTIPLE THREADED SCREWS

Advantages of multiple threaded screwso It provides large axial motion per revolution

of screw.o Efficiency of multiple threaded screws is

more than single threaded screws due to increase in helix angle

Disadvantages of multiple threaded screws

o The Mechanical advantage obtained with multiple threaded screws is lower than that of single threaded screw

o Self locking property is lost in multiple threaded screws

TERMINOLOGY OF POWER SCREW

(i) 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‘ .

(ii) Lead: The lead is defined as the distance, measured parallel to the axis of the screw, that 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 a double-threaded screw, the lead is twice of the pitch, and so on.


(iii) Nominal diameter: Nominal diameter is the largest diameter of the screw, It is also called major diameter. It is denoted by the letter 'd'.

(iv) Core diameter: Core diameter is smallest diameter of the screw thread. It also called minor diameter. It is denoted by letters 'dc'.


(v)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 . Helix angle is related to the lead and the mean diameter of the screw. It is also called lead angle. Helix angle is denoted by .


From fig.

dm mean dia. Can be given by

( )2 2cp pd d d P

1 1( ) ( .5 )

2 2m cd d d d d P d p

TERMINOLOGY OF POWER SCREWIf 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.This can be imagined by cutting paper in the form of the right-angle triangle with base equal to dm and height equal to l. This paper around a rod with diameter dm. The hypotenuse of the triangle become the thread around the rod. Considering this right-angle triangle, the relationship between helix angle ,mean diameter and lead can be expressed in the form,

where α is the helix angle of the thread

tan / ml d

Let p = Pitch of the screw;

dm = 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 = tanφ, where φ is the friction angle

TORQUE REQUIRED TO RAISE LOAD BY SQUARE THREADED SCREWS

Since the principle, on which a screw jack works is similar to

that of an inclined plane, therefore, the force applied on the

circumference of a screw jack may be considered to be

horizontal as shown in figure b

Since the load is being lifted, therefore the force of friction

(F = μ.RN ) will act downwards

Resolving the forces along the plane:Pcosα = Wsinα + F = Wsinα + μ.RN ...(i)

and resolving the forces perpendicular to the plane:RN = Psinα + Wcosα ...(ii)

Substituting this value of RN in equation (i), we have:

Pcosα = Wsinα + μ(Psi α + Wcos α)= Wsinα + μPsinα + μWcos αor Pcosα – μPsinα = Wsinα + μWcosαor P(cosα – μsinα) = W(sinα + μcosα)

Substituting the value of μ = tan φ in the above equation, we get:

Multiplying the numerator and denominator by cosφ, we have:

∴ Torque required to raise the load is given by

2m

t

pdM tan( )

2m

t

WdM

TORQUE REQUIRED TO LOWER LOAD BYSQUARE THREADED SCREWS When the load is being lowered, the force of friction

(F = μ.RN) will act upwards. All the forces acting on the body are shown

Resolving the forces along the plane:Pcosα = F – Wsinα= μRN – Wsinα ..(i)

and resolving the forces perpendicular to the plane:RN = Wcosα – Psinα ..(ii)

Substituting this value of RN in equation (i), we have,

Pcosα = μ(Wcosα – Psinα) – Wsinα= μWcosα – μPsinα – Wsinαor Pcosα + μPsinα = μWcosα – WsinαP(cosα + μsinα) = W(μcosα – sinα)

Substituting the value of μ = tanφ in the above equation, we have:

Multiplying the numerator and denominator by cosφ:

∴ Torque required to lower the load is given bytan( )

2m

t

WdM

Torque required to lower the load is given byOVERHAULING OF SCREW

tan( )2m

t

WdM

it can be seen that when,

the torque required to lower the load is negative. It indicates a condition that 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 'overhauling' of screw.

SELF LOCKING SCREW

When

A positive torque is required to lower the load. Under this condition, the load will not turn the screw and will not descend on its own unless effort P is applied. The screw is said to be 'self-locking' .

tan tan

/ ml d

SELF LOCKING SCREWA screw be self-locking if the coefficient of friction is equal to or greater than the tangent of the helix angle.

Self-locking of screw is not possible when the coefficient of friction is low. The coefficient of friction between the surfaces of the screw and the nut is reduced by lubrication . Excessive lubrication may cause the load to descend on its own. Self-locking property of the screw is lost when the lead is large. The lead increases with number of starts. For double-start thread, lead is twice of the pitch and for triple threaded screw, three times of pitch. Therefore, single threaded screw is better than multiple threaded screw from self locking considerations.

tan tan

/ ml d

EFFICIENCY OF SQUARE THREADED SCREW

Work output = force x distance travelled in the direction of force = W x l

Refer to force diagram for lifting the load , Suppose load W moves from the lower end to the upper end of the inclined plane. The output consists of raising the load

The input consists of rotating the screw by means of an effort P. Work input = force x distance travelled in the direction of force = P X The efficiency of the screw is given by,

m

wl

P d

md

tanW

P

tan

tan( )

EFFICIENCY OF SELF LOCKING SCREW

The efficiency of the screw is given by,

For self locking screw

Substituting the limiting value in above equation

Efficiency of self locking screw is less than 50%

tan

tan( )

TORQUE REQUIRED TO OVERCOME COLLAR FRICTION

In many applications of the power screw, there is collar friction in addition to the friction at the thread surface. The cup remains stationary under the action of load W, while the collar which is integral with the screw rotates, when the load raised or lowered.

Therefore, there is relative motion between the cup & the collar at the annular interface from diameter Di, to Do. This relative motion results in friction called collar friction. The torque required to overcome this collar friction torque (Mt)c can be determined by using uniform pressure theory or uniform wear theory.

According to the uniform pressure theory

According to the uniform wear theory,

=coefficient of friction at the collar. Do=outer diameter of the collar (mm). Di=inner diameter of the collar (mm). =collar friction torque (N-mm).

Uniform pressure theory is applicable when

the collar surface is new. Uniform wear theory is applicable to the

collar surface after the initial wear.

3 3

2 23c o i

t co i

W D DM

D D

4c

t o ic

WM D D

c

t cM

∴ Total torque required to overcome friction (i.e. to rotate the screw):

=External torque required to raise the load (N-mm). Mt = Torque required to overcome friction at the

thread surface (Mt )c = collar friction torque (N-mm).

If an effort P 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, i.e.

OVERALL EFFICIENCY OF SQUARE THREADED SCREWSEfficiency is defined as ratio of Work output to work

input

Work output= W x lWork input = x 2

ηo =

=

STRESSES IN SCREW AND NUT The body of screw subjected to

an axial force W and torsional moment (Mt)t as shown in fig.

The compressive stress is given by

The torsional shear stress is given by

The principal shear stress is given by2

2

2c

STRESSES IN SCREW AND NUT The threads of the screw which are

engaged with the nut are subjected to transverse shear stresses. The screw will tend to shear off the threads at the core diameter under the action of the load W. The shear area of one thread is given by

The transverse shear stresses in the nut are determined in a similar way. Under the action of load W, the thread of the nut will tend to shear off at the nominal diameter. The shear area of one thread is dt

STRESSES IN SCREW AND NUT The bearing pressure between the

contacting surfaces of the screw & the nut is an important consideration in design.

The bearing area between the screw & the nut for one thread is

Where z=no of threads in engagement with nut

2 2

4

b

c

WS

d d z

2 2

4 cd d

BUCKLING OF COLUMNS When a short member is subjected to axial

compressive force, it shortens according to Hooke 's law.

As the load is gradually increased, the compression of the member increases. When the compressive stress reaches the elastic limit of the material, the failure occurs in the form of bulging. However, when the length of the component is large compared with the cross-sectional dimensions, as shown in Fig. ,the component may fail under lateral buckling. The load at which the buckling starts is called critical load which is denoted by Pcr.

BUCKLING OF COLUMNS when the axial load on the column reaches

Pcr there is sudden buckling & a relatively large lateral defection occurs.

In case of buckling there is no gradual lateral deflection till the load reaches the critical load. At this point there is sudden lateral deflection which results in collapse of column. The failure due to buckling is sudden & without prior warning.

An important parameter affecting the critical load is slenderness ratio.

BUCKLING OF COLUMNS when the axial load on the column reaches

Pcr there is sudden buckling & a relatively large lateral defection occurs.

In case of buckling there is no gradual lateral deflection till the load reaches the critical load. At this point there is sudden lateral deflection which results in collapse of column. The failure due to buckling is sudden & without prior warning.

An important parameter affecting the critical load is slenderness ratio.

Slenderness ratio= Where l=length of column & k=radius of

gyration

BUCKLING OF COLUMNS

where

I=moment of inertia of c/s in mm4

A=area of c/s in mm2

When slenderness ration is less than 30 there is no effect of buckling & such components are designed on the basis of compressive stresses.

Column with slenderness ration more than 30 are designed on the basis of critical load. There are two methods for calculating critical load-Eulers equation & Jonshons equation

BUCKLING OF COLUMNSAccording to Euler

2

2cr

n EAP

lk

n=end fixity coefficient

E=Modulus of Elasticity

A=area of c/sEnd conditions n

Both ends hinged 1Both ends fixed 4One end fixed & other end hinged 2One end fixed & other end free0.25

BUCKLING OF COLUMNSAccording to Johnsons equation

=yield strength of the material

Euler's equation suitable for long columns & Jonson's equation used for short columns.The boundary between short & long column is

The ratio obtained by above equation is called critical slenderness ratio

2

214

ytcr yt

S lP S A

n E k

BUCKLING OF COLUMNS

When the actual slenderness ratio is less thancritical slenderness ratio ,screw to be treated as short column & Johnson’s equation is used

When the actual slenderness ratio is grater than critical slenderness ratio, screw to be treated as long column & Euler's equation is used

EXAMPLE A vertical two start square threaded screw of a

100mm mean diameter and 20mm pitch supports a vertical load of 18kN. The axial thrust on the screw is taken by a collar bearing of 250mm outside diameter and 100mm inside diameter. Find the force required at the end of a lever which is 400mm 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.

Given: d = 100mm; p = 20mm; W = 18kN = 18 × 103N ; D2 = 250mm or R2 = 125mm; D1 = 100mm or R1 = 50mm; l = 400mm; μ = tanφ = 0.15; μ1 = 0.20

Solution:Force required at the end of leverLet P = Force required at the end of lever

EXAMPLE

Since the screw is a two start square threaded screw, therefore lead of the screw = 2p = 2 × 20 = 40mm

1. For raising the loadWe know that tangential force required at the

circumference of the screw:

And mean radius of collar:

EXAMPLE∴ Total torque required at the end of lever:

The torque required at the end of lever (T):569150 = P1 × l = P1 × 400 or P1 = 569150/400 =

1423N2. For lowering the loadThe tangential force required at the circumference

of the screw:

EXAMPLE

Torque required at the end of the lever:

The torque required at the end of lever (T):335315 = P1 × l = P1 × 400 or

P1 = 335315/400 = 838.3N

design of power screws

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