Skru KuasaSkru Kuasa A power screw is a device used in A power screw is a device used in

machinery to change angular machinery to change angular motion into linear motionmotion into linear motion

Usually it is used to transmit Usually it is used to transmit powerpower

E.g.. Lead screw of lathes, vises, E.g.. Lead screw of lathes, vises, presses and jack.presses and jack.

Forces acting on the screw threadForces acting on the screw thread When using a power screw to When using a power screw to

exert a force either raising or exert a force either raising or lowering a load, we must know lowering a load, we must know how much torque must be applied how much torque must be applied to the nut of the screw to move the to the nut of the screw to move the load.load.

Hence; the parameter involved in Hence; the parameter involved in raising or lowering a load are:raising or lowering a load are: F the load) to be movedF the load) to be moved Size of the screw indicated by Size of the screw indicated by

pitch diameter dpitch diameter dmm

ll the lead of the screw which is the lead of the screw which is defined as the axial distance that defined as the axial distance that the screw would move in one the screw would move in one complete revolution.complete revolution.

f f the coefficient of frictionthe coefficient of friction

Figure on the left show a square Figure on the left show a square thread power screw with single thread thread power screw with single thread having a mean diameter dhaving a mean diameter dmm, a pitch , a pitch pp, , a lead anglea lead angle and a helix angle and a helix angle is is loaded by axial compressive force F.loaded by axial compressive force F.

Hence the forces acting on the screw Hence the forces acting on the screw thread are as follow:-thread are as follow:-

(a) For raising the load, the torque required to overcome thread friction and to raise the load is given by

Tu = ( F dm/ 2 ) [ ( f dm + l ) / ( dm – f l ) ]

Where dm = d – p/2 and l = np

and f = coefficient of friction of thread.

(b) For lowering the load, the torque required to overcome a part of the friction .

Td = ( F dm/ 2 ) [ f dm – l ) / ( dm – f l ) ]

For well-lubricated steel screw f = 0.15

From the forces diagram, the lead angle is given as tan = l / dm

Hence for both the square thread and acme thread (as well as others) the equations can be rewritten as:-

Self-locking the lead angle should be small enough and the friction force is large enough to oppose the load and keep it from sliding down the plane. Hence condition for self-locking, f dm > l or f > tan

(a) For raising the load, the torque required to overcome thread friction and to raise the load is given by

Tu = ( F dm/ 2 ) [ (cos tan + f ) / (cos – f tan ) ]

= ( F dm/ 2 ) [ ( l + f dm sec ) / (dm – f l sec ) ]

(b) For lowering the load, the torque required to overcome a part of the friction .

Td = ( F dm/ 2 ) [ (f - cos tan ) / (cos + f tan ) ]

For axially loaded power screw, a thrust or collar bearing must be employed between the rotating and stationary members in order to carry the axial component. Hence; if the coefficient of collar friction is fc , then the torque required to overcome this friction is Tc = F fc dc / 2 must be added to get the total torque.

The efficiency is e = T0 / T where T0 = F l / 2

Efficiency of Power ScrewEfficiency of Power Screw

In general efficiency is the ratio of work output to work input. Hence, efficiency for the transmission of a force by a power screw can be defined as the ratio of the torque required to move the load without friction to that with friction.

Letting f = 0, hence torque required without friction T’ is

T0 = ( F dm/ 2 ) [ l / dm] = F l / 2

The power to drive a power screw is given by the equation

P = T n / 63000 ; P in horsepower hp , n in rpm

P = 2 n T ; P in kW , n in rpm

Stresses On Power Screw

Stresses occurred in power screw can be analyze for stresses on body and on thread

•Stresses on body

•Nominal body stresses in power screws can related to thread parameters as follows:-

•Nominal shear stress in torsion of the screw body is

•Axial stress in the body of screw is

•Where dr = d - p

3

16

rd

T

2

4

rd

F

Nominal thread stresses in power screws can related to thread parameters as follows:-

Bearing stress on thread B is

Bending stress on root of thread b is

Transverse shear stress at the centre of the root of thread is

Where nt is the number of engaged threads.

pnd

F

pnd

F

tmtmB

2

2/

pnd

F

pndc

Iand

FpwhereMcI

M

trc

trc

6244/

2

pnd

F

pnd

F

A

V

trtr 3

2/2

3

2

3