**For Objective Type Questions (Machine Design)- Click Here**

**Note –** If you come across any error, please write to us or comment below.

**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

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.*

**For Objective Type Questions (Machine Design)- Click Here**

**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})]**

**Read More⇒ Classification of Gears**

**Read More⇒ Gear Ratio: Definition, Formula, Advantages, Uses**