Calculating Maximum Permissible Torque in Ship Propulsion System

In this video, we tackle an engineering problem involving the calculation of the maximum permissIn this video, we tackle an engineering problem involving the calculation of the maximum permissible torque transmitted between two flanged shafts in a ship propulsion system using bolts. We'll go through the detailed steps to determine the torque, considering the given shear stress and bolt specifications.

Topics Covered:

Understanding torque transmission in flanged shafts
Calculating shear stress in bolts
Determining the maximum permissible torque
Example problem solving
Tags:
#Engineering #ShipPropulsion #TorqueCalculation #MechanicalEngineering #ShearStress #BoltedConnection #EngineeringProblems #STEM #Educational #ExamPrep

Solution Outline
To find the maximum permissible torque, we need to calculate the total shear force that the bolts can withstand and then relate it to the torque. Here are the steps:

Determine the shear force per bolt:

Given:

Allowable shear stress (
𝜏
𝑎
𝑙
𝑙
𝑜
𝑤
τ
allow
​
) = 85 MPa
Diameter of bolts (
𝑑
𝑏
𝑜
𝑙
𝑡
d
bolt
​
) = 20 mm
Shear force per bolt (
𝐹
𝑏
𝑜
𝑙
𝑡
F
bolt
​
) can be calculated using the formula:

𝐹
𝑏
𝑜
𝑙
𝑡
=
𝜏
𝑎
𝑙
𝑙
𝑜
𝑤
×
𝐴
𝑏
𝑜
𝑙
𝑡
F
bolt
​
=τ
allow
​
×A
bolt
​

where
𝐴
𝑏
𝑜
𝑙
𝑡
A
bolt
​
is the cross-sectional area of the bolt.

𝐴
𝑏
𝑜
𝑙
𝑡
=
𝜋
4
𝑑
𝑏
𝑜
𝑙
𝑡
2
A
bolt
​
=
4
π
​
d
bolt
2
​

Substituting the values:

𝐴
𝑏
𝑜
𝑙
𝑡
=
𝜋
4
(
20
 mm
)
2
=
𝜋
4
(
0.02
 m
)
2
=
3.14
×
1
0
−
4
 m
2
A
bolt
​
=
4
π
​
(20 mm)
2
=
4
π
​
(0.02 m)
2
=3.14×10
−4
 m
2


𝐹
𝑏
𝑜
𝑙
𝑡
=
85
×
1
0
6
 Pa
×
3.14
×
1
0
−
4
 m
2
=
26.69
 kN
F
bolt
​
=85×10
6
 Pa×3.14×10
−4
 m
2
=26.69 kN
Calculate the total shear force for all bolts:

There are 10 bolts, so the total shear force (
𝐹
𝑡
𝑜
𝑡
𝑎
𝑙
F
total
​
) is:

𝐹
𝑡
𝑜
𝑡
𝑎
𝑙
=
10
×
𝐹
𝑏
𝑜
𝑙
𝑡
=
10
×
26.69
 kN
=
266.9
 kN
F
total
​
=10×F
bolt
​
=10×26.69 kN=266.9 kN
Relate the shear force to torque:

The torque (
𝑇
0
T
0
​
) is related to the shear force and the radius of the bolt circle. The radius
𝑟
r is half of the diameter of the bolt circle:

𝑟
=
𝑑
2
=
250
 mm
2
=
125
 mm
=
0.125
 m
r=
2
d
​
=
2
250 mm
​
=125 mm=0.125 m
The torque
𝑇
0
T
0
​
is given by:

𝑇
0
=
𝐹
𝑡
𝑜
𝑡
𝑎
𝑙
×
𝑟
T
0
​
=F
total
​
×r
Substituting the values:

𝑇
0
=
266.9
×
1
0
3
 N
×
0.125
 m
=
33.36
 kNm
T
0
​
=266.9×10
3
 N×0.125 m=33.36 kNm
Therefore, the maximum permissible torque is 33.36 kNm.ible torque transmitted between two flanged shafts in a ship propulsion system using bolts. We'll go through the detailed steps to determine the torque, considering the given shear stress and bolt specifications.

Topics Covered:

Understanding torque transmission in flanged shafts
Calculating shear stress in bolts
Determining the maximum permissible torque
Example problem solving
Tags:
#Engineering #ShipPropulsion #TorqueCalculation #MechanicalEngineering #ShearStress #BoltedConnection #EngineeringProblems #STEM #Educational #ExamPrep

Solution Outline
To find the maximum permissible torque, we need to calculate the total shear force that the bolts can withstand and then relate it to the torque. Here are the steps:

Determine the shear force per bolt:

Given:

Allowable shear stress (
𝜏
𝑎
𝑙
𝑙
𝑜
𝑤
τ
allow
​
) = 85 MPa
Diameter of bolts (
𝑑
𝑏
𝑜
𝑙
𝑡
d
bolt
​
) = 20 mm
Shear force per bolt (
𝐹
𝑏
𝑜
𝑙
𝑡
F
bolt
​
) can be calculated using the formula:

𝐹
𝑏
𝑜
𝑙
𝑡
=
𝜏
𝑎
𝑙
𝑙
𝑜
𝑤
×
𝐴
𝑏
𝑜
𝑙
𝑡
F
bolt
​
=τ
allow
​
×A
bolt
​

where
𝐴
𝑏
𝑜
𝑙
𝑡
A
bolt
​
is the cross-sectional area of the bolt.

𝐴
𝑏
𝑜
𝑙
𝑡
=
𝜋
4
𝑑
𝑏
𝑜
𝑙
𝑡
2
A
bolt
​
=
4
π
​
d
bolt
2
​

Substituting the values:

𝐴
𝑏
𝑜
𝑙
𝑡
=
𝜋
4
(
20
 mm
)
2
=
𝜋
4
(
0.02
 m
)
2
=
3.14
×
1
0
−
4
 m
2
A
bolt
​
=
4
π
​
(20 mm)
2
=
4
π
​
(0.02 m)
2
=3.14×10
−4
 m
2


𝐹
𝑏
𝑜
𝑙
𝑡
=
85
×
1
0
6
 Pa
×
3.14
×
1
0
−
4
 m
2
=
26.69
 kN
F
bolt
​
=85×10
6
 Pa×3.14×10
−4
 m
2
=26.69 kN
Calculate the total shear force for all bolts:

There are 10 bolts, so the total shear force (
𝐹
𝑡
𝑜
𝑡
𝑎
𝑙
F
total
​
) is:

𝐹
𝑡
𝑜
𝑡
𝑎
𝑙
=
10
×
𝐹
𝑏
𝑜
𝑙
𝑡
=
10
×
26.69
 kN
=
266.9
 kN
F
total
​
=10×F
bolt
​
=10×26.69 kN=266.9 kN
Relate the shear force to torque:

The torque (
𝑇
0
T
0
​
) is related to the shear force and the radius of the bolt circle. The radius
𝑟
r is half of the diameter of the bolt circle:

𝑟
=
𝑑
2
=
250
 mm
2
=
125
 mm
=
0.125
 m
r=
2
d
​
=
2
250 mm
​
=125 mm=0.125 m
The torque
𝑇
0
T
0
​
is given by:

𝑇
0
=
𝐹
𝑡
𝑜
𝑡
𝑎
𝑙
×
𝑟
T
0
​
=F
total
​
×r
Substituting the values:

𝑇
0
=
266.9
×
1
0
3
 N
×
0.125
 m
=
33.36
 kNm
T
0
​
=266.9×10
3
 N×0.125 m=33.36 kNm
Therefore, the maximum permissible torque is 33.36 kNm.

A torque T0 is transmitted between two flanged shafts of a ship propulsion
system by means of ten 20-mm bolts (see Figure Q5). The diameter of the bolt
circle is d = 250 mm. If the allowable shear stress in the bolts is 85 MPa, what
is the maximum permissible torque? (Disregard friction between the flanges.)