__Machine
Design II - Lab (ME 308)__

__Project
# 1 – Design of Shaft and Selection of Bearings__

__Summary
of Class # 3__

** **

**Step # 1: Calculation of Deflections under
the gear # 3 and gear # 4**

Moment Equation :** **

Slope Equation :

Deflection Equation :

Deflection equations for our Shaft in the **y-
axis**:

__ __

__BOUNDARY
CONDITIONS__

Equations 1 through 6 above involve 6
unknowns (C_{1}, C_{2} , C_{3} , C_{4} , C_{5}
, C_{6} ) and hence, 6 boundary conditions are needed to solve for the
6 unknowns. The 6 boundary conditions are as follows:

1. The deflection under the 1^{st} bearing is
equal to 0

2. The deflection under the 2^{nd} bearing is
equal to 0

3. The continuity equations, where the slope of the shaft
is equal (Under the gear # 3)

4. The continuity equations, where the deflection under
the gear # 3 must be equal.

5. The continuity equation at the location of the 2^{nd}
bearing is

Using the above boundary conditions the 6
equations are solved for the 6 constants.

The deflections under the gear # 3 and gear #
4 in the y –axis are calculated by substituting these values in equations Eqn #
2 or Eqn # 4 ( for gear # 3) and Eqn # 6 ( for gear # 4). In these equations

----- is the youngs modulus for carbon steel.

NOTE: The above analysis has been done only
for the y-axis, a similar analysis has to be done in the z-axis too and the
deflections under the gear # 3 and gear # 4 must be calculated for the z-axis
too.

Once the deflections under the gear # 3 ( and ) and under the gear # 4 (and ) are calculated the resultant
deflections are to be calculated as follows:

Step # 2 : Calculation of the first critical
speed

By using the Rayleigh method the first
critical speed is calculated by using the equation which is given below.

where

is the resultant force acting at the position 3 under
the gear # 3

is the resultant force acting at the position under
the gear # 4

Check whether the first critical speed is
greater then 1000 rpm.

If it is not greater than 1000 rpm then you
have to increase the diameter of the shaft and repeat the calculations.

If it is less than 1000 rpm then, select a
design speed for the shaft, which should be equal to

to

**Bearing
Selection**

For the bearing selection we have to go to
Eqn (11-9) which is as follows:

where

is the rated
load

is the
design load ( in our case R_{A }and R_{B} )

= 10^{6} rev

is the
design life = 8000 hrs to 14000 hrs

is the
design speed = (0.6 to 0.8)

is the
reliability = 90 %

for deep
groove ball bearings = 3

Once you calculate the rated load for each
bearing, the load ratings have to be calculated by

(Application
Factor)

Taking this value of appropriate bearings have to be selected
from the Table (11-3).

NOTE: Do convert the units of to KN before you go to the Table
(11-3).

After the bearing selection, do finalize the
diameters of the shaft.

**KEY
DESIGN**

**Step # 1**: A material for the key has to be assumed from the list of materials
given to you in the text book. One can choose any CD material or any HR
material, except that it should satisfy only one condition.

**Step # 2: **From the table (8-15), a square key has to be chosen
depending upon the range of the diameters of the shaft. Interpolate the data
for shaft sizes greater than . Select the width and the height which are equal in a square
key. Lets assume that it is "a".

**Step # 3**: Calculate the length for the key by solving Shear and Beraing stress
equations for the key.

Bearing Stress: (Solve for l)

Shear Stress: (Solve for l)

The final value of the length (l) of the key
will be the larger of the two values calculated for each location. Generally,
key sizes must fall within the following range by length.

**The
End**

**All the best and have a nice vacation. But
do not forget to submit me the report on your analysis, in the class immediately
after the vacation.**

** **

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