MACHINE DESIGN – DAY 6
I.
BRAKES
A brake is a device which is used to regulate or stop the motion of a body.
A. Simple Band Brake: Tension in the band =
where: F1 = force on tight side
F2 = force on slack side
f = coefficient of friction
q = angle of contact, rad
F1
= e fq
F2
B. Brake Torque Developed:
T = (F1 - F2)r
where: T = brake torque
r = radius of friction surface on the drum
C. Actuating Force Required:
D. Maximum Unit Pressure:
Pmax =
where: w = width of the band
D = diameter of drum = 2 r
E. Stress in Band:
S =
F1
wt
where: t = thickness of the band
F. Differential Band Brake:
F1
2 F1
=
wr wD
G. Self-Locking Differential Band Brake:
A differential band brake is self-locking when Fa is zero or negative.
H. Block Brake (Valiance p.364)
1.
Single Block:
where: F= frictional force
T = braking torque
Fr = radial force between the drum and each shoe
f = coefficient of friction
h = effective moment arm of the friction force
r = radius of the friction surface of the drum
! = angle of contact
Pmax = maximum normal pressure between block and drum
w = axial width of block
2. Double Block:
Principles of Double Block Brake:
A.
Power: " = $%&'
B.
Torque: & = ()! + )" ),
Where: r = -/2
C. FL = Frictional Force on Left Side,
0# = 1# 2# !
!
#
! "#$ "
%" &"#$ %"
"
D. FR = Frictional Force on Right Side,
0$ = 1$ 2$ !
!
#
! "#$ $
%$ &"#$ %$
"
I. Heat Dissipated in Brakes (Valiance p 374)
H = f Fr V
where: H = heat dissipated
f = coefficient of friction
Fr = radial force
V = surface velocity
J. For Brake used in lowering of a weight:
H = Wh
where: W = weight lowered
h = total distance traveled
II.
CLUTCH
A clutch is a machine member which is used to connect shafts so that the driven shaft will rotate with the
driving shaft, and to disconnect them at will.
SINGLE PLATE OF DISC CLUTCH
A. Power transmitted:
P = 2p T N
B. Clutch Starting Torque, T
Where:
T=
T = n f Fa rf
aI
g
a = angular acceleration, rad/s2
I = inertia
T = torque transmitted
n = number of pairs of mating friction surfaces = (np – 1)
f = coefficient of friction
Fa = axial load
rf = mean friction radius
np = number of plates or disc
C. Mean frictional Radius, rf
For uniform pressure disc clutch:
rf =
2 é R3 - r 3 ù 1 é D3 - d3 ù
ê
ú= ê
ú
3 êë R2 - r 2 úû 3 êë D2 - d2 úû
Pmax =
Fa
p 2 2
(D - d )
4
For uniform wear clutch worm clutch:
rf =
R+r D+d
=
2
4
D. Bearing Pressure on the jaw faces:
Pmax =
Fa
p(d / 2)(D - d)
Pb = Fb / Ab
where: Fb = bearing force = 2T/Dm
Ab = bearing area = t h nj
t = axial length
h = jaw height
nj = no. of jaws
CONE CLUTCH:
A. Power:
P = 2pTN
B. Torque:
T =
Fa f rf
sin a
T = f(Fn)rf
Where: Fa = Axial Load
C. Fn = Normal Force
Fn =
'%
"#$ (
D. Fe = Force needed to engage cone clutch
E. Pn = Normal pressure
Pn =
'&
)&
Where: An = normal area = 3-% 4
Dm = mean diameter =
b = face width =
x=
+-*
,
+-*
, "#$ .
*&+
,
III.
WIRE ROPES
A. Wire Rope Designation:
For 6 x 7 wire rope - 6 stands for the number of strands; 7
stands for the number of wires
B. Approximate wire diameters and areas:
ROPE
6x7
6x19
6x37
8x19
dw
0.106 d
0.063 d
0.045 d
0.050 d
A
0.38 d2
0.38 d2
0.38 d2
0.35 d2
where:
d = rope diameter, in
A = rope area, in2
C. Bending Stress, Sb:
Sb = Sb =
Er d w
D
where:
Sb = bending stress, psi
Er = modulus of elasticity of wire rope, psi = 12,000,000 psi (for steel)
dw = wire diameter, in
D = drum or sheave diameter, in
D. Bending Load
Fb =
A Er d w
= Sb A
D
where:
A = wire area
E. The ultimate strengths (Fu) of plow steel is approximately:
Fu = 76,000 d2, lb (for 6 x 7 and 6 x 19 ropes)
Fu = 75,000 d2, lb (for 6 x 37 ropes)
where:
d = rope diameter, in
F. The weight of wire rope is approximately:
W = 1.58 d2, lb/ft
G. Approximate wire elongation:
y=
F L
, in
A Er
FACTOR OF SAFETY, FS
FS =
Fu - Fb
Ft
where: Ft = tensile load
a
)
g
A.
If moving upward: Ft = (WL + WR )(1 +
B.
If moving downward: Ft = (WL + WR )(1 -
a
)
g
where: WL = weight attached on the rope
WR = weight of the rope
From DESIGN OF MACHINE ELEMENTS by: Faires
For 6 x 7 wire ropes
W= 1.52 Dr2, lb/ft
Dw = 0.111 Dr, in
Aw = 0.38 Dr2, in2
Er = 13x106 psi
Min. Ds = 42 Dr, in
IV.
For 6 x 19 wire ropres
W= 1.6 Dr2, lb/ft
Dw = 0.067 Dr, in
Aw = 0.40 Dr2, in2
Er = 12x106 psi
Min. Ds = 30 Dr, in
For 6 x 37 wire ropres
W= 1.55Dr2, lb/ft
Dw = 0.048 Dr, in
Aw = 0.40 Dr2, in2
Er = 13x106 psi
Min. Ds = 18 Dr, in
WELDED JOINTS
Welding a process of joining the metal by heating the metal to a state fusion permitting it to flow into a solid joint.
A. Strength of Butt weld: St = F / t L
where: F = tensile force
t = plate thickness
L = length of weld
B. Strength of Fillet weld: St = F/2A
Where: A = t L
t = throat thickness = b sin45o
So, A = (b sin 45o)
F
Therefore: St =
2( b sin 45°) L
V.
RIVETED JOINTS
Application - use for pressure vessels, building structures, tanks, bridges, etc.
Size of Rivets:
A. Before driving, rivet diameter is 1/16 inch less than the rivet hole.
B. After driving, the rivet diameter is equal to the rivet hole.
STRENGTH OF RIVETS
1. Fu = force that can be carried by unpunched plate
Fu = St (t L)
Where: St = tensile stress
t = plate thickness
L = plate length
2. Ft = force that can cause tensile stress on plate between rivets
Ft = St A
where: A = t [ L – n D ]
n = no. of rivets
D = hole diameter
3. Fs = force that cause shearing stress on rivets
Fs = Ss A
Where: Ss = Shear stress
A= n
p 2
D
4
4. Fb = force that can cause bearing stress in the rivets
Fb = Sb ( n t D)
where: Sb = bearing stress
PROBLEMS:
BRAKES
1.
A simple band brake has a 76 cm and fitted with a steel band 2/5 cm thick lined with a brake lining having a
coefficient of friction of 0.25. the arc of contact is 245 deg. The drum is attached to a 60 cm, hoisting drum that
sustain a rope load of 820 kg. The operating force has a moment arm of 1.50 m and the band is attached 12 cm
from the pivot point. Find the torque required just to support the load (clockwise).
A. 2413.26 N-m
B. 3492.31 N-m
C. 2453.29 N-m
D. 1894.82 N-m
2.
The angle of contact of a band clutch is 250 degrees. The cross-section of the band is 1/16 in x 1.5 in. The
design stress for the band material is 8000 psi. If the drum is 16 inch in diameter and rotates at 350 rpm, what is
the power capacity of the clutch if f = 0.40.
A. 20.50 hp
B. 24.50 hp
C. 27.50 hp
D. 30.50 hp
CLUTCHES
1.
A multiple disc clutch of 10 steel disc and 9 bronze disc. the effective outside and inside diameter are 20.32 cm
and 15.24 cm, respectively if the axial force of 450 Newton is applied and the shaft turns at 1200 rpm, find the
horsepower capacity, assume a coefficient of friction of 0.27.
A. 39.566 hp
B. 40.482 hp
C. 37.456 hp
D. 35. 659 hp
2.
A cone clutch has cone elements at an angle of 10o. The clutch transmits 20 hp at a speed of 100 rpm. The
mean diameter of conical friction section is 10 in and the coefficient of friction is 0.3. Find the axial force needed
to engage the clutch.
A. 1246.37 lbs
B. 2312.56 lbs.
C. 1459.23 lbs
D. 1346.76 lbs
3.
Determine the power capacity of a cone clutch under uniform pressure having 250 mm major diameter, 200 mm
minor diameter, length of contact 115 mm, 800 rpm and f = 0.30 if allowable pressure is 80 Kpa.
A. 18.39 kw
B. 20.84 kw
C. 22.41 kw
D. 24.46 kw
WELDED JOINTS
1.
A 16mm plate is lapped over and secured by fillet weld on the inside and outside to form a penstock 1.5 in
diameter. Determine the safe internal pressure, assuming an allowable stress of 140Mpa on the plate and
allowable shear stress of 90Mpa on the throat side of the 14mm fillet weld.
(Ans. 2375.76kpa)
RIVETED JOINTS
1.
Consider a section of 304.8mm of a single-riveted lap joint made with plates of 6.35mm thickness and 6 rivets,
15.87mm in diameter. Assume that rivet holes are 1.58mm larger in diameter then the rivets. In this joint, the
entire load is transmitted from one plate to the other by means of rivet. Each plate and the six rivets carry the
entire load. The design stresses are:
For shear = 589 kg/cm2
For bearing = 1406 kg/cm2
For tension = 703 kg/cm2
Calculate the following:
A) Force that can be carried by unpunched plate
B) Force that cause tensile stress on plate between rivets
C) Fore that cause shearing stress on rivets
D) Force that cause bearing stress in the rivets
E) Rivet efficiency
(Ans.13606 kg)
(Ans.8932.6kg)
(Ans.8580.90kg)
(Ans. 9347.7kg)
(Ans. 63.1%)