Mechanics of material shaft coupling

[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
Task:
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.
Your report must include:
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

 

[falah alajmi]

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

 

[falah alajmi]

I Draw the free body diagram for the shaft

 

[falah alajmi]

is the bearing going to be a reaction force ?

 

[DeeNos]

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.

First, let's start with the given data and assumptions:

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.

Task:

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)