Formula Sheet: Threaded Joints and Power Screws | Design of Machine Elements - Mechanical Engineering PDF Download

 Page 1


Threaded Joints & Power Screws Formula
Sheet
1. Thread Terminology
• d: Major (nominal) diameter
• d
c
: Core (minor) diameter
• p: Pitch (distance between adjacent threads)
• n: Number of starts
• l: Lead = n· p
• ? : Thread angle
2. Threaded Joint Design (Bolts)
(a) Tensile Stress Area (Approx)
A
t
˜ p 4

d+d
c
2

2
(b) Load-Stress Relations
P =s t
· A
t
(Tensile)
t =
T
J
· r (Torsion)
(c) Initial Bolt Tension (Preload)
F
i
=s proof
· A
t
(d) Torque Required to Tighten a Bolt
T =K· F
i
· d
K˜ 0.2 (depends on friction, thread type)
3. Power Screws
Used for lifting or applying large axial forces (e.g., screw jack).
1
Page 2


Threaded Joints & Power Screws Formula
Sheet
1. Thread Terminology
• d: Major (nominal) diameter
• d
c
: Core (minor) diameter
• p: Pitch (distance between adjacent threads)
• n: Number of starts
• l: Lead = n· p
• ? : Thread angle
2. Threaded Joint Design (Bolts)
(a) Tensile Stress Area (Approx)
A
t
˜ p 4

d+d
c
2

2
(b) Load-Stress Relations
P =s t
· A
t
(Tensile)
t =
T
J
· r (Torsion)
(c) Initial Bolt Tension (Preload)
F
i
=s proof
· A
t
(d) Torque Required to Tighten a Bolt
T =K· F
i
· d
K˜ 0.2 (depends on friction, thread type)
3. Power Screws
Used for lifting or applying large axial forces (e.g., screw jack).
1
Threaded Joints & Power Screws
(a) Lead and Lead Angle
l =n· p ; tan? =
l
pd
m
where d
m
= mean diameter = (d+d
c
)/2
(b) Torque to Raise Load (Square Thread)
T =
W· d
m
2
· tan? +µ 1- µ tan? (c) Torque to Lower Load
T =
W· d
m
2
· tan? - µ 1+µ tan? (d) Efficiency of Screw
? =
tan? tan(? +? )
where tan? =µ (e) Self-Locking Condition
µ> tan? ? Self-locking
(f) Power Transmitted
P = 2pNT ; (Watt if T in Nm, N in rev/s)
(g) Stresses in Screw
s axial
=
W
A
c
; t =
16T
pd
3
c
2