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1. WOLLEGA UNIVERSITY
SCHOOL OF GRADUATE STUDIES
COLLEGE OF ENGINEERING AND TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING, MSC. IN
MANUFACTURING ENGINEERING
ADVANCED MANUFACTURING AND METROLOGY
ASSIGNMENT 04
TO: NEGASHALEMU (Professor)
BY: ALEMU MERGA (1400082)
JUNE, 2022
Nekemte, Oromia, Ethiopia

2. 1. The chordal thickness of an involute gear is being measured using a gear calliper.
Determine the chordal height to which the gear tooth calliper should be set during
measurement, if the number of teeth = 28, addendum circle diameter = 120 mm, pressure
angle = 20°, and least count of the calliper is 0.02 mm.
Solution
Given;
z=28, number of teeth
Pressure angle= 200
Addendum circle diameter=120mm,
To find the hc = Chordal height,
hc = m + gc2/4d ,
Where,
d = Pitch circle diameter
gc = Chordal thickness of gear tooth along the pitch circle
z = Number of teeth on the gear
And to find gc = Chordal thickness of gear tooth along the pitch circle,
gc = d sin (90°/z)
m = (addendum circle diameter)/ (z + 2)
m=120mm/ (28+2)
m=4
To find d = Pitch circle diameter,
d= mz
d=4(28) =112mm
Then, gc = d sin (90°/z)
gc = 112 sin (900/32)
gc =5.4956mm ,
So Theoretical value of chordal thickness is 5.4956mm
Now easily we find the chordal height of the gear as;

3. hc = m + gc2/4d ,
hc= 4+5.49562 /4(112)
hc= 4.0674mm
Thus, the gear tooth calliper should be set to a chordal height of 4.0674mm
2. Determine the effective diameter of a metric screw using the three-wire method. The following
data is available: diameter of the best size wire = 0.740 mm, distance over the wires =
25.58 mm, and pitch = 1.25 mm.
Solution
Given values;
x = 60° for metric threads.
p=1.25 mm.
d= 0.740 mm,
M=25.58 mm,
Where; M= the distance over the wires,
E= the effective diameter of the screw,
d= the diameter of best-size wires,
p= pitch
Figure principle of three wire method
Now, OC = OA cosec (x/2) =
𝑑
2
cosec(x/2)
If h is the height of the Centre of wire from the pitch line, then h = OC − BC.
h =
𝑑
2
cosec(x/2) −
𝑝
2
cot (x/2)
Distance over wires, M = E + 2h + 2r, where r is the radius of the wires.

4. Therefore, effective diameter.
E = M − d cosec (x/2) +
𝑝
2
cosec(x/2)-d
E = M − d [1 + cosec (x/2)] +
𝑝
2
cot(x/2)……………………….equation.
Now substituting given values in the formula,
E=25.58- 0.740[1+ cosec (60/2)] +
1.25
2
cot (60/2)
E=24.4425mm is effective diameter of metric screw.
3.A metric screw thread is being inspected using the two-wire method in order to measure its
effective diameter and the following data is generated: pitch = 1.5 mm, diameter of the best size
wire = 0.866 mm, distance over the wires = 26.58 mm, and thread angle = 60°. Determine the
effective diameter of the screw thread.
Solution:
Given;
p= 1.5 mm,
d=0.866 mm
M=26.58 mm,
x=60°.
Where,
p= pitch
M= distance over the wires
d= diameter of the best size wire
x= thread angle
The effective diameter,
De = T + P ………………………………………1
Where T is the dimension under the wires and P is the correction factor.
And,
T = M − 2d ………………………………………………….2
These relationships can be easily derived by referring the below figure.

5. Measurement in two wire method
Accordingly, from triangle OFD, OF =
𝑑
2
cosec (x/2)
FA=
𝑑
2
cosec (x/2) -
𝑑
2
=
𝑑[cosec(𝑥/2) − 1]
2
FG = GC cot (x/2) =
𝑝
4
cot (x/2) (because BC = pitch/2 and GC = pitch/4)
Therefore, AG = FG − FA =
𝑝
4
cot (x/2)-
𝑑[cosec(𝑥/2) − 1]
2
Since AG accounts for the correction factor only on one side of the screw, we have to multiply this
value by 2 in order to account for that on the opposite flank.
Therefore, total correction factor is as follows:
P = 2 AG=
𝑝
2
cot (x/2) − d [cosec(x/2) – 1]………………………3
So now before going to calculate for effective diameter we need to compute correction factor P,
From equation 3 above,
P =
𝑝
2
cot (x/2) − d [cosec(x/2) – 1]
P=
1.25
2
cot (60/2) −0.866 [cosec (60/2) – 1]
P= 0.2165mm
Similarly to find dimension under the wires T,

6. T= M − 2d
T=26.58-2(0.866)
T=24.848mm
Now we can compute effective diameter screw thread as,
De = T + P
De =24.848mm+0.2165mm
De= 25.064mm is effective diameter of given screw thread using two wire method.