Notes on Power Screw

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Power Screw

Definition of Power Screw

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

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.

Main Applications of Power Screw

(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.

Power Screw Thread Types

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

• Let d = nominal or outer diameter
• d_c = core or inner diameter all in m
• d_m = 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 × d_m )

Let W is the load that 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 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, M_t = (Pd_m)/2

M_t = [{W × d_m× tan (φ + α)}/2]

Note – For a single-threaded screw, the lead is the 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)

M_t = P × (d_m/2) = [W × tan (φ – α)] × (d_m/2)

Stress in Screw

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

• Direct Compressive stress σ_c = A / B

where,  A = W and B = (π/4) × d²_c

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

• Torsional Shear Stress (τ) = [16 × Mt/πd²_c]
• Principal Shear Stress (τ_max) = sqrt [ (σ_c/2)²+T²]

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

• Transverse Shear Stress in the screw, τ_s = [W/(π × d_c × 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 the design.

Bearing area between the screw and the nut for one thread = [π/4(d² – d²_c)]

S_b = W/[π/4(d² – d²_c)]

OR

4W/[πz(d² – d²_c)]

Also Check the Below Notes

• Classification of Gears
• Gear Ratio: Definition, Formula, Advantages, Uses

For more Visit Power Screw Wikipedia