Mechanical engineering systems Question Answer 2022

Mechanical engineering systems
[Document subtitle]
OCTOBER 9, 2019

Question1.
I. Internal torque diagram
C-d section.
Most sensitive stretch segment of the shaft
II. By torsion equation
FEDCBA
Internal
torque
diagram
A F
EDCB
300
Nmm
480Nm
m
240Nm
m
420Nm
m
420Nm
m 300Nm
m
A F
EDCB
240Nm
m
480Nm
m

τ
r = T
Ip = Gɵ
l
Where τ =shear stress due to torque at radius ‘r’ from centroidal axis
ɵ = angle of twist
l = length of each segment
Ip = polar moment of inertia
G = shear modulas or modulas of rigidity
Gɵ
l = T
Ip
ɵ= Tl
GIp
III. let DB , C, D, E = dia of shaft B, C, D, E
∑Max = 3.5° = π
180 x 3.5 = 0.061
ɵB= ( TBlB) / (GIpB)
Ip = (π/32) (DB)4
ɵB= (32 TBlB) / (GπDB4)
ɵB = (32x420 x 500)/(9000 x π x 0.061 x 10) = 389.62522
DB = 4.4428 mm
DC =4
√ 32 X 240 X 500
90000 X π X 0.061 = 3.8628 mm
DC = 4
√ 32 X 480 X 500
90000 X π X 0.061 = 4.5937 mm
DC =4
√ 32 X 300 X 500
90000 X π X 0.061 = 4.0844 mm
IV. τ= (Tr)/Ip
RB = 2.2214 mm, TB = 420 Nmm (CW)
Rc = 1.9314 mm, Tc = 240 Nmm (CCW)
RD = 2.2968 mm, TD = 480 Nmm (CCW)
RE = 2.0422 mm, TE = 300 Nmm (CW)
IPB = (π/32) X (Dp)4 = (π/32) X (4.4428)4 = 38.25 mm4