Power Screw Threads

Square thread

Acme thread

Lead screws of lathes and other machine tools, automotive jacks,

vises, linear actuators, adjustable floor posts and micrometers etc

ButtressThreads

Multi-start

Screw Jack

Lead Screw

Lathe

DVD drive

Ball Screw

The Mechanics of Power Screws

Square-threaded power screw

single thread

Mean diameter ‘dm’

pitch ‘p’

lead angle ‘λ’

helix angle ‘ψ’

loaded by the axial compressive force ‘F’

Helix angle: Angle that thread makes with plane perpendicular to thread axis

Lead angle : Angle between the helix and a plane of rotation

FBD of one thread, (a) raising and (b) lowering

0cossin fNNPF RH

0cossin NfNFFV

0cossin fNNPF LH

0cossin NfNFFV

Raising load: Lowering Load:

A single thread of the screw is unrolled or developed for exactly a single turn. Then one edge

of the thread will form the hypotenuse of a right triangle whose base is the circumference of

the mean-thread-diameter circle and whose height is the lead

tan=(l / dm)

sincos

cossin

f

fFPR

sincos

sincos

f

fFPL

m

m

R

dlf

fd

lF

P

.1

m

m

L

dlf

dlfF

P

.1

fld

fdlFdT

m

mmR

2

fld

lfdFdT

m

mmL

2

Raising:

Lowering:

Torque, (a) raising and (b) lowering

Self locking of power screws

• TL gives the torque required to overcome the

friction in order to lower the load

• In certain instances, the load may itself lower by

causing the screw to spin

• In such cases, TL is either zero or negative.

• Whenever, the load does NOT lower by itself

unless a positive TL is applied, the screw is said to

be self-locking

fld

lfdFdT

m

mmL

2

lfdT mL 0 tanf

Self-locking of Screw jack

A screw is self locking whenever the coefficient

of friction is greater than the tangent of the lead

angle.

tanf

Collar friction

• Normally a collar is employed to enable the power screw system to have sufficient bearing area hold the component being raised

• Since the collar slides against the component being raised, additional torque needs to be applied to raise the load, this is called as collar friction torque Tc

• To estimate the Tc, whenever the collar is not too big, it is enough to use a mean diameter, dc, at which the collar friction force is concentrated

2

ccc

dFfT

Total torque required to rise the load; TR’ = TR + Tc

Total torque required to rise the load; TL’= TL + Tc

Power screw’s raising efficiency

• It is the ratio of raising torque without friction to the raising torque with friction

• Can be defined both with and without collar friction

2

FlTo

RR

o

T

Fl

T

T

2

fld

fdlFdT

m

mmR

2

Coefficient of friction (f)

Use Tables 8-5 and 8-6 for values of coefficient of f and fc.

Table 8–5 Coefficients of Friction ‘f’ for Threaded Pairs

Table 8–6 Thrust-Collar Friction Coefficients

Raising torque for ACME screws

• A simple approximate equation is

The effect of the thread angle in ACME thread is to increase the

friction force between the screw and the nut due to the wedging

action of the thread.

For power screw application, though the ACME thread is not

suitable due to higher frictional force resulting from wedging action,

is commonly used because it is easier to manufacture than the

square threads.

sec

sec

2 fld

fdlFdT

m

mmR

fld

fdlFdT

m

mmR

2

Critical element at which the

von-Mises stress is evaluated

Bearing

pressure

T

F

Body stresses in power screws

0

4

6

2

z

r

y

tr

x

d

F

pnd

F

n=Number of engaged threads

Body stresses in power screws

• Bending stress, x

• Torsional shear stress, xy

• Axial compressive stress, y

• Transverse shear (no contribution to von-Mises stress because it is maximum where bending stress is zero and is zero where bending stress is maximum; hence needs to be only independently checked for)

• Bearing pressure (no contribution to von-Mises stress because it is distributed over the thread and is maximum at the middle of thread and is zero at the root of the thread)

resultant is von-mises

stress at top of the root

plane

Body stresses in the screw threads: von-

Mises stress at the critical element

3

16

r

Rxy

d

T

3

16

r

Lxy

d

T

or 2

4

r

yd

F

A

F

pd

F

pnd

F

cI

M

rtr

x

28.26

Power screws are operated normally at low speeds and

hence static design is enough.

42)(

12

1;

4

3p

candp

ndIp

FM tr

The engaged threads cannot share the load equally. Some experiments show that the first

engaged thread carries a maximum of 38% of the load. In estimating thread stresses by

the equations above, substituting 0.38F for F and setting nt to 1 will give the largest level of

stresses in the thread-nut combination.

21

2222226

2

1' zxyzxyxzzyyx

Resultant von-Mises stress

Body stresses in the screw threads:

von-Mises stress at the critical element

21

22226

2

1' xyxyyx

Body stresses: Transverse shear and bearing

pnd

F

pnd

F

tmtm

B

2

2

pd

F

pnd

F

pnd

F

A

V

rtrtr

14.13

22

3

2

3

Must be less than the safe bearing pressure

given in Table 8-4. Causes too much wear

and sometimes crushing.

It is at the centre of the root

area. Must be less than the shear

yield strength of material.

substituting 0.38F for F and setting nt to 1

will give the largest level of stresses in the

thread-nut combination.

pd

F

pnd

F

mtm

B

76.02

Table 8–4

Screw Bearing Pressure

need to be independently checked (no need to consider in von-Mises stress)

Problem

A power screw has triple thread of major diameter 25 mm,

minor diameter 21.5 mm and pitch of 3 mm. A vertical load

on the screw reaches a maximum of 6 kN. The coefficient

of friction is 0.06 for threads and 0.03 for collar. The

friction diameter of the collar is 30 mm. Find the following:

(a) total torque required to raise the load, (b) total torque

required to lower the load, (c) efficiency, (d) bending stress,

axial normal stress, torsional shear stress and the resultant

von-Mises at the root for one thread (by assuming the first

engaged thread carries a maximum of 0.38 of the load). (e)

bearing and transverse shear stress