GATE Machine Design Theory of Machines

Notes on Power Screw

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Power Screw

Definition

A power screw is a mechanical device used for converting rotary motion into linear motion and for transmitting power.

Main Applications-

(i) To raise the load
(ii) To obtain accurate motion in machining operations
(iii)To clamp a work-piece
(iv) To load a specimen

The main advantage of power screws is theoretically large load carrying capacity with small overall dimensions.

There are four types of threads used for power screws. These are Squares, Acme, ISO metric trapezoidal and Buttress.

Guidelines for the selection of a proper thread profile for the power screw.

(i) The efficiency of square threads is more than that of other types of threads.
(ii) Square threads are difficult to manufacture.
(iii) The strength of a screw depends upon the thread thickness as the core diameter.
(iv) The wear of the thread surface becomes a serious problem in applications like the lead-screw of the lathe.
(v) Buttress threads can transmit power and motion only in one direction.

Force Analysis- Square Threads

Pitch (p)

It is defined as the distance measured parallel to the axis from a point on one thread to the corresponding point on the adjacent thread.

Lead (l)

It is defined as the distance measured parallel to the axis that the nut will advance in one revolution of the screw.

Let d = nominal or outer diameter

dc = core or inner diameter all in m

dm = mean diameter

Note- All dimensions in mm

When the square thread is used for the screw, the helix angle ‘α’ of the thread is given by –

tan α = 1/(Π × dm )

Let W is the load which is raised or lowered by rotating ‘a’ screw by means of an imaginary force P acting at the mean radius.

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Case 1: Lifting Load

For an equilibrium of horizontal forces,

P = μN cos α + N sin α   ………(i)

For vertical forces, W =N cos α – μN sin α   ………(ii)

Dividing (i) by (ii), we get

P = W tan (φ + α)

The torque required to raise the Load, Mt = (Pdm)/2

Mt = [{W × dm× tan (φ + α)}/2]

Note – For single-threaded screw, the lead is same as the pitch, and for the double threaded screw, the lead is twice the pitch and so on. 

Case 2: Lowering Load

Considering the equilibrium of Horizontal and Vertical forces,

P = μN cos α – N sin α   ………(i)

For vertical forces, W = N cos α + μN sin α   ………(ii)

Dividing (i) by (ii), we get

μ = tan φ

P = W × tan (φ – α)

Mt = P × (dm/2) = [W × tan (φ – α)] × (dm/2)

Stress in Screw

  • The body of a screw is subjected to an axial force ‘W’ and torsional moment ‘Mt’. 

Direct Compressive stress σc = A / B

where,  A = W

and, B = (π/4) × dc2

  • For the long and slender screws, buckling is considered instead of compression.

Torsional Shear Stress (τ) = [16 × Mt/πdc3]

Principal Shear Stress (τmax) = [ (σc/2)2 + τ2 ]1/2

  • The threads of the screw which are engaged with the nut are subjected to transverse shear stresses.

Transverse Shear Stress in the screw, τs = [W/(π × dc × t × z)]

z = no. of threads in engagement

Transverse shear stress in the nut, τ = [W/ (π × d × t × z)]

  • The bearing pressure between the contacting surfaces of the screw and the nut is an important consideration in design.

Bearing area between the screw and the nut for one thread = [π/4(d2 – dc2)]

Sb = W/[π/4(d2 – dc2)]

OR

4W/[πz(d2 – dc2)]

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