# Mechanics of material shaft coupling

• falah alajmi
In summary: No, the bearings are not a reaction force. The second bearing is used to limit the amount of torque that can be applied to the shaft.
falah alajmi
A shaft of a total length L, connected via coupling C to the engine on the left-hand side,
transfers the power P while rotating with n revolutions per second.
A gear with pitch diameter D1 and thickness t1attached to the shaft at the distance Lg from the coupling C is in mesh with the driven gear attached to the parallel shaft. The two shaft axes are laying in a horizontal plane as well as the point in mesh.
The traction wheel with radius RT and thickness tT is fastened at the free end of the shaft and powers a driven wheel via belt. The driven wheel with radius RD is fixed on the shaft positioned at the horizontal distance x.
The shaft is supported by two bearings with the given distance of the first bearing to be LB1 from the coupling.
Assumptions:
The contact between gears is assumed to take place within a very small region (point) thus the load transfer between the gears can be simulated as a concentrated force F.
Neglect all inertia forces at this stage.
data :
P =35 KW L=1.4 m n= 124 rev/s C is a Spline shaft D1 =125mm T1=30mm Rt=73mm
tT=20mm Lg=0.98m x=0.246m RD=58mm Lb1=0.11m F=20 N
1. Design the dimensions of the shaft, and position of the second bearing so the given power can be transferred while:
a)the shear stresses developed due to torque would remain constant within the whole length of the shaft. Consider factor of safety 2.5
b)the maximum deflection of the shaft should not exceed given value a = 0.5 mm
c)the maximum angle of twist should not exceed given angle φ = 10

3. Design the brake that will be able to bring the shaft to stop and compute the stresses as they will develop in the major parts of the system.

4. Design the coupling system C specified in the data and compute stresses developed within the major elements of the coupling.

5. Calculate the maximum bending and shear stresses, and determine the position of the cross-section, where this peak stresses occurs.

6. Provide the technical detail drawing of the shaft and the coupling.
a) Full report of your material characterization – aim, methodology, and instrumentation used, measured data, computed data, analysis of the results with evaluation of the error, and final conclusion.
b) Computation of all shaft dimensions and stresses developed in the shaft, SF – BM diagram (with corresponding static equations), identification of the locations of maximum and minimum stresses, computation of favourable position of the second bearing so the shaft would be exposed to minimum wear off.
c) Evaluation of the maximum deflection with identification of the position along the shaft, and suggest changes (if any) for better design with regards to bearings position (where would you place the bearings and why).
d) Description of coupling used specifying how the power is transferred through the system, design of coupling dimensions stating all assumptions and calculation used together with reference to standards, computation of stresses in all major parts of the coupling
e) Description of the break system, how does the break work, what is the limit torque the break is able to bring to stop, and computation of stresses in all major parts of the break.

I just have this assignment but when I started doing it I don't know how to start I just draw the shaft coupling but I don't know where to place the second shaft to have the three case , so could some one give me the equations for each three cases of locate the second bear and does the bear act as a reaction force or not ?
that what I am want right now then I might ask you about some thing else ?

thanks
sincerely
falah alajmi

I found the torque to be about 44.95 N/m^2
from the equation P = 2πTƒ

I Draw the free body diagram for the shaft

is the bearing going to be a reaction force ?

Dear Falah Alajmi,

Thank you for reaching out for assistance with your assignment. I am happy to help you with the mechanics of material shaft coupling.

Data:
P = 35 KW
L = 1.4 m
n = 124 rev/s
C is a Spline shaft
D1 = 125mm
T1 = 30mm
Rt = 73mm
tT = 20mm
Lg = 0.98m
x = 0.246m
RD = 58mm
Lb1 = 0.11m
F = 20 N

Assumptions:
1. The contact between gears is assumed to take place within a very small region (point), thus the load transfer between the gears can be simulated as a concentrated force F.
2. Neglect all inertia forces at this stage.

1. Design of the shaft and position of the second bearing:
a) To ensure that the shear stresses developed due to torque remain constant within the whole length of the shaft, we need to use the following equation:

τ = (16T)/πd^3

Where,
τ = shear stress
T = torque
d = diameter of the shaft

Using the given data:
T = P/n = 35,000/124 = 282.26 Nm
d = D1 + 2t1 = 125 + 2(30) = 185 mm

Therefore, τ = (16*282.26)/(π*185^3) = 3.24 MPa

To ensure a factor of safety of 2.5, we need to design the shaft for a maximum shear stress of 3.24/2.5 = 1.3 MPa.

b) To ensure that the maximum deflection of the shaft does not exceed 0.5 mm, we need to use the following equation:

δ = (TL^3)/(3EI)

Where,
δ = maximum deflection
T = torque
L = length of the shaft
E = modulus of elasticity
I = moment of inertia

Using the given data:
T = 282.26 Nm
L = Lg + x = 0.98 + 0.246 = 1.226 m
E = 200 GPa (assuming steel material)

## 1. What is the purpose of a shaft coupling in mechanics of materials?

A shaft coupling is used to connect two shafts together in order to transmit power and torque from one shaft to the other. It also allows for misalignments between the two shafts and absorbs shock and vibration.

## 2. What are the different types of shaft couplings?

There are several types of shaft couplings, including rigid couplings, flexible couplings, universal couplings, and fluid couplings. Each type has its own unique design and application.

## 3. How do you determine the appropriate size of a shaft coupling?

The size of a shaft coupling is determined by the size and type of the shafts being connected, the amount of torque and power being transmitted, and the application and environment in which it will be used. It is important to consult with a manufacturer or engineer to ensure the proper size is selected.

## 4. What are some common failures of shaft couplings?

Common failures of shaft couplings include misalignment, overloading, fatigue, and wear and tear. It is important to regularly inspect and maintain shaft couplings to prevent failures and ensure safe and efficient operation.

## 5. How can you troubleshoot issues with a shaft coupling?

If a shaft coupling is experiencing issues, it is important to first check for any visible signs of damage or wear. Then, check for proper alignment and make sure the coupling is securely fastened to the shafts. If the issue persists, it is best to consult with a professional or replace the coupling if necessary.

• Engineering and Comp Sci Homework Help
Replies
1
Views
1K
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K
• Engineering and Comp Sci Homework Help
Replies
1
Views
3K
• General Engineering
Replies
1
Views
3K
• Mechanical Engineering
Replies
9
Views
3K
• Engineering and Comp Sci Homework Help
Replies
3
Views
13K
• Mechanical Engineering
Replies
7
Views
2K
• Engineering and Comp Sci Homework Help
Replies
20
Views
13K
• Aerospace Engineering
Replies
7
Views
2K
Replies
2
Views
1K