Topics: Screws, Force, Acme thread form Pages: 18 (3289 words) Published: September 26, 2012
Introduction
• Design of machine elements needs geometry and joints; single integral parts will not do • Parts are joined by fasteners and they are conveniently classified as permanent, semi-permanent and nonpermanent joints • Permanent :Welded joints, adhesive bonding Semi-permanent : Riveted joints Non-permanent fasteners: Threaded/ non threaded joints Non threaded joints- keys, pins etc. Threaded joints- screws, bolts and nuts, studs etc. BITS Pilani, Pilani Campus

BITS Pilani, Pilani Campus

• Lead is the distance moved by nut parallel to the screw axis when the nut is given one turn. l = p * multiplicity of threading • Single threaded, l=p • Double threaded, l=2p • Triple-threaded, l=3p

BITS Pilani, Pilani Campus

nominal major diameter of 12 mm

M12×1.75 mm ×
metric designation pitch of 1.75 mm

d = major diameter dr = minor diameter = d - 1.226 869p dp = pitch diameter = d - 0.649 519p p = pitch

basic ISO 68 profile with 60◦ symmetric threads

H =

3 p 2
BITS Pilani, Pilani Campus

BITS Pilani, Pilani Campus

Power screw or Screw jack mechanism
A device used in machinery to change angular motion into linear motion, and, usually, to transmit power Find use in machines such as universal tensile testing machines, lead screws of lathes and other machine tools, automotive jacks, vises, linear actuators, adjustable floor posts and micrometers etc

BITS Pilani, Pilani Campus

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 BITS Pilani, Pilani Campus

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

tanλ=(l / πdm)

Raising:

Lowering:

∑F ∑F

H

= PR − N sin λ − fN cos λ = 0

V

= F + fN sin λ − N cos λ = 0

∑F ∑ FV

H

= − PL − N sin λ + fN cos λ = 0

= F − fN sin λ − N cos λ = 0
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Torque, (a) raising and (b) lowering
Raising : = F (sin λ + P
R

f cos λ ) cos λ − f sin λ

   F  l  πd  + f  m    PR =   1 −  f .l  πd m   

TR

Fd m = 2

Lowering:
PL = F ( f cos λ − sin λ ) cos λ + f sin λ

 l + π fd m   π d − fl m 

   

  Ff − l  πd  m   PL =   1 +  f .l  πd m   

Fd m TL = 2

 π fd m − l   π d + fl  m

   
BITS Pilani, Pilani Campus

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 BITS Pilani, Pilani Campus

Self-locking of power screws The condition for self-locking is TL ≥ 0 ⇒ πfd m > l Divide both sides by πdm. Since l/ πdm =tanλ

f > tan λ

The screw is self locking whenever the coefficient of friction is greater than the tangent of the lead angle.

BITS Pilani, Pilani Campus

Accounting for 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,...