lab2 flatness composite lab 2 ahmedawad
DESCRIPTION
MetrologyTRANSCRIPT
Flatness
Using Dial Indicator
Flatness error is the departure of the surface from a true flat plane
Objectives:
To determine the maximum out of flatness of a steel sheet using dial
indicator
Materials:
Three block gauges (Provide a rest to workpiece on three points on the bottom surface.
This will stop the movement along z-axis, rotation with respect to x-axis and y-axis)), dial
indicator, dial indicator holder and the measured sheet
Apparatus:
Experimental work:
A network is marked on the tested surface.
Determine the z coordinate of the measured point
Use round contact tip
m n o p
i j k l
e f g h
a b c d
Reading:
position a b c d e f g h i j k l m n o p
Reading 8.54 8.53 8.52 8.61 8.51 8.52 8.52 8.58 8.54 8.50 8.55 8.57 8.50 8.48 8.45 8.54
Profile:
0
30
60
908.3
8.4
8.5
8.6
8.7
0
30
60
90
Chart Title
8.6-8.7
8.5-8.6
8.4-8.5
8.3-8.4
Calculation:
x y z x'=x-xbar y' z' x'^2 y'^2 x'y' y'z' x'z' z'' delta
0 0 8.54 -45 -45 0.011875 2025 2025 2025 -0.53437 -0.53437 0.000675 0.0112
0 30 8.51 -45 -15 -0.01812 2025 225 675 0.271875 0.815625 -0.01553 -0.0026
0 60 8.54 -45 15 0.011875 2025 225 -675 0.178125 -0.53437 -0.03173 0.0436
0 90 8.5 -45 45 -0.02812 2025 2025 -2025 -1.26562 1.265625 -0.04793 0.0198
30 0 8.53 -15 -45 0.001875 225 2025 675 -0.08438 -0.02813 0.016425 -0.01455
30 30 8.52 -15 -15 -0.00812 225 225 225 0.121875 0.121875 0.000225 -0.00835
30 60 8.5 -15 15 -0.02812 225 225 -225 -0.42187 0.421875 -0.01598 -0.01215
30 90 8.48 -15 45 -0.04812 225 2025 -675 -2.16562 0.721875 -0.03218 -0.01595
60 0 8.52 15 -45 -0.00812 225 2025 -675 0.365625 -0.12187 0.032175 -0.0403
60 30 8.51 15 -15 -0.01812 225 225 -225 0.271875 -0.27187 0.015975 -0.0341
60 60 8.55 15 15 0.021875 225 225 225 0.328125 0.328125 -0.00023 0.0221
60 90 8.45 15 45 -0.07813 225 2025 675 -3.51563 -1.17188 -0.01643 -0.0617
90 0 8.61 45 -45 0.081875 2025 2025 -2025 -3.68438 3.684375 0.047925 0.03395
90 30 8.58 45 -15 0.051875 2025 225 -675 -0.77813 2.334375 0.031725 0.02015
90 60 8.57 45 15 0.041875 2025 225 675 0.628125 1.884375 0.015525 0.02635
90 90 8.54 45 45 0.011875 2025 2025 2025 0.534375 0.534375 -0.00067 0.01255
sum 720 720 136.45 0 0 7.11E-15 18000 18000 0 -9.75 9.45
aver 45 45 8.528125
Errors including in this method are:
- block error
- Tilting error
�̅� =720
16= 45
𝑦 =720
16= 45
𝑧̅ =136.45
16= 8.528125
𝑎 =∑ 𝑦′2 ∑ 𝑥′𝑧′ − ∑ 𝑥′𝑦′ ∑ 𝑦′𝑧′
∑ 𝑥′2 ∑ 𝑦′2 − (∑ 𝑥′𝑦′)2
𝑎 =18000 × 9.45 − 0 × −9.75
18000 × 18000 − 02 = −0.4854
𝑏 =∑ 𝑥′2 ∑ 𝑦′𝑧′ − ∑ 𝑥′𝑦′ ∑ 𝑥′𝑧′
∑ 𝑥′2 ∑ 𝑦′2 − (∑ 𝑥′𝑦′)2
𝑏 =444000 × −9.75 − 76208 × 9.45
18000 × 18000 − 02= −0.34669
𝑧𝑖′′ = 𝑎𝑥𝑖
′ + 𝑏𝑦𝑖′ = 0.000525𝑥′ − 0.00054𝑦′
𝛿𝑖 = 𝑧𝑖′ − 𝑧𝑖
′′
Maximum out of flatness = |0.0436| + |−0.0403| = 0.0839𝑚𝑚 = 83.9 𝑚𝑖𝑐𝑟𝑜𝑛𝑠
0.08
Flatness
Using Sensitive Level
Objectives:
To determine the maximum out of flatness of a drilling machine worktable
using sensitive level
Materials:
Two identical gauge blocks, Optical clinometer
Micrometer clinometers: clinometers used to measure small angle of inclination
with reference to the horizontal plane by placing on the surface and raising the spirit
level by micrometer until the level is accurately horizontal
Apparatus:
Experimental work:
A network is marked on the tested surface.
Determine the angle of each line
Turn the turret and turn the adjustment screw until the air bubble is
centered
Take the reading
Network:
Readings:
Level of each point relative to the preceding one
Position ba cb dc fe gf hg ji kj
Reading (angle in minute) forward
-12 -17 -15 -18 -17 -15 -18 -10
Reading (angle in minute) backward
+1 -2 -3 +1 -1 -3 -1 -2
Position lk nm on po ea ie mi
Reading (angle in minute) forward
-23 -18 -17 -16 -3 -4 -3
Reading (angle in minute) backward
+2 -1 -2 -3 -15 -13 -13
Distance between the two measured point = 100 mm
Calculations:
forward forward mm backward backward mm average
ba -12 -0.34907 1 0.029089 -0.18908
cb -17 -0.49451 -2 -0.58178 0.043631
dc -15 -0.43634 -3 -0.02873 -0.2038
ea -3 -0.08727 -15 -0.43634 0.174534
fe -18 -0.5236 1 0.029089 -0.27635
gf -17 -0.49451 -1 -0.02909 -0.23271
hg -15 -0.43634 -3 -0.02873 -0.2038
ie -4 -0.11636 -13 -0.37816 0.130901
ji -18 -0.5236 -1 -0.02909 -0.24726
kj -10 -0.29089 -2 -0.58178 0.145444
Lk -23 -0.66905 2 0.581776 -0.62541
Mi -3 -0.02873 -13 -0.37816 0.174715
Nm -18 -0.5236 -1 -0.02909 -0.24726
On -17 -0.49451 -2 -0.58178 0.043631
Po -16 -0.46542 -3 -0.02873 -0.21835
m n o p
i j k l
e f g h
a b c d
0.481 0.234 0.278 0.06
0.306 0.059 0.204 -0.421
0.175 -0.101 -0.334 -0.538
0 -0.189 -0.145 -0.349
accumulative
0.481 0.234 0.278 .06
0.306 0.059 0.204 -0.421
0.175 -0.101 -0.334 -0.538
0 -0.189 -0.145 -0.349
Make the right down corner = 0
0.481 0.350 0.510 0.409
0.306 0.175 0.46 -0.072
0.175 0.015 -0.102 -0.189
0 -0.073 0.087 0
Make the left upper corner = 0
0 -0.131 0.029 -0.072
-0.015 -0.146 0.115 -0.393
0.015 -0.145 -0.262 -0.349
0 -0.073 0.087 0
Rotate about the diagonal
0 -0.119 0.053 -0.036
-0.039 -0.146 0.127 -0.369
0.003 -0.157 -0.262 -0.325
-0.036 -0.085 -0.063 0
Maximum out of flatness = |0.127| + |−0.325| = 0.452𝑚𝑚 = 452 𝑚𝑖𝑐𝑟𝑜𝑛𝑠
0.45
0
100
200
300
0
30
60
90
Chart Title
0-0.2
-0.2-0
-0.4--0.2
Flatness
Using Rochdale Arm
Objectives:
To determine the maximum out of flatness of a planner machine waorktable
using Rochdale Arm
Materials:
Rochdale Arm, dial indicator
Apparatus:
Experimental work:
A network is marked on the tested surface (use the rochdale arm)
The arm is placed on a reference plate and takes the
dial reading.
The arm is made to rest on the tested surface on its feet
such that the feet are on two successive marked
points and the dial plunger is on contact with the
next point.
The reading of the dial is observed and recorded
The arm is then moved to another position till the
entire area is scanned.
The readings are then analyzed to determine the
surface profile, (X, Y, Z coordinates of every
point).
Network:
Readings:
Line abc aho bhn cio bcd bip djp cjq cde
Readings(mm) 1.98 1.96 1.89 1.91 1.93 2.06 1.96 1.99 2.02
R corrected 0.05 0.03 -0.04 -0.02 0 0.13 0.03 0.06 0.09
Line ekq qkr qrs els rlf rst cfg smg tmf
Readings(mm) 2.11 1.96 2.01 2.21 1.97 1.88 1.99 1.91 2.07
R corrected 0.18 0.03 0.08 0.28 0.04 -0.05 0.06 -0.02 0.14
The height readings relative to the plane aco
𝑅 = 2𝑞 − 𝑝 + 𝑦
Where:
R: level of the point under the dial indicator plunger
q: level of the point under the middle leg
p: level of the point under the end leg
y: dial indicator reading
Line Rule Point Level Line Rule Point Level
abc c = 2b -a + R abe b 0.025 ekq q = 2kk -e + R ekq k -0.025
aho o = 2h - a + R aho h 0.015 qkr r = 2k - q + R qkr r -0.11
bhn n = 2h - b + R bhn n -0.035 qrs s = 2r - q + Rqrs s -0.23
cio o = 2i - c + R cio i -0.01 els s = 2l - e + R els l -0.235
bcd d = 2c - b + R bcd d -0.025 rlf f = 2l - r + R rlf f -0.32
bip p = 2i - b + R bip p 0.085 rst t = 2s - r + R rst t -0.4
djp p = 2j - d + R djp j 0.015 cfg g = 2f - c + R cfg g -0.58
cjq q = 2j - c + R cjq q 0.09 smg g = 2m - s + R smg m -0.395
cde e = 2d - c + R cde e 0.04 tmf f = 2m - t + R tmf f -0.25
𝐸𝑟𝑟𝑜𝑟 𝑖𝑛 𝑟𝑒𝑎𝑑𝑖𝑛𝑔𝑠 =−0.32 − −0.25
−0.32= 0.21875
Error within ±0.21875 from the reading
�̅� =1060
20= 70.66667
𝑦 =229.4967
20= 15.29978
𝑧̅ =−1.53
20= −0.102
𝑎 =∑ 𝑦′2 ∑ 𝑥′𝑧′ − ∑ 𝑥′𝑦′ ∑ 𝑦′𝑧′
∑ 𝑥′2 ∑ 𝑦′2 − (∑ 𝑥′𝑦′)2
𝑎 = −0.00289
𝑏 =∑ 𝑥′2 ∑ 𝑦′𝑧′ − ∑ 𝑥′𝑦′ ∑ 𝑥′𝑧′
∑ 𝑥′2 ∑ 𝑦′2 − (∑ 𝑥′𝑦′)2
𝑏 = −0.00116
𝑧𝑖′′ = 𝑎𝑥𝑖
′ + 𝑏𝑦𝑖′ = −0.00289𝑥′ − 0.00116𝑦′
𝛿𝑖 = 𝑧𝑖′ − 𝑧𝑖
′′
Maximum out of flatness = |0.253024| + |−0.24046| = 0.493484𝑚𝑚
0.49348
0
-0.6
-0.4
-0.2
0
0.2
0
13.2
5
26.5
39.7
5
53
66.
25
79.
5
92.7
5
106
119
.25
13
2.5
145.
75
159
0-0.2
-0.2-0
-0.4--0.2
-0.6--0.4
Calculation:
x y z x'=x-xbar y' z' x'^2 y'^2 x'y' y'z' x'z' z'' delta
a 0 0 0 -70.6667 -15.2998 0.102 4993.778 234.0833 1081.184 -1.56058 -7.208 0.221974 -0.11997
b 26.5 0 0.025 -44.1667 -15.2998 0.127 1950.694 234.0833 675.7403 -1.94307 -5.60917 0.145389 -0.01839
c 53 0 0 -17.6667 -15.2998 0.102 312.1111 234.0833 270.2961 -1.56058 -1.802 0.068804 0.033196
d 79.5 0 -0.025 8.833333 -15.2998 0.077 78.02778 234.0833 -135.148 -1.17808 0.680167 -0.00778 0.084781
e 106 0 0.04 35.33333 -15.2998 0.142 1248.444 234.0833 -540.592 -2.17257 5.017333 -0.08437 0.226366
f 132.5 0 -0.32 61.83333 -15.2998 -0.218 3823.361 234.0833 -946.036 3.335352 -13.4797 -0.16095 -0.05705
g 159 0 -0.58 88.33333 -15.2998 -0.478 7802.778 234.0833 -1351.48 7.313295 -42.2233 -0.23754 -0.24046
h 13.25 22.94967 0.015 -57.4167 7.649893 0.117 3296.674 58.52087 -439.231 0.895038 -6.71775 0.15706 -0.04006
i 39.75 22.94967 -0.01 -30.9167 7.649893 0.092 955.8403 58.52087 -236.509 0.70379 -2.84433 0.080475 0.011525
j 66.25 22.94967 0.015 -4.41667 7.649893 0.117 19.50694 58.52087 -33.787 0.895038 -0.51675 0.00389 0.11311
k 92.75 22.94967 -0.025 22.08333 7.649893 0.077 487.6736 58.52087 168.9351 0.589042 1.700417 -0.07269 0.149695
l 119.25 22.94967 -0.235 48.58333 7.649893 -0.133 2360.34 58.52087 371.6573 -1.01744 -6.46158 -0.14928 0.01628
m 145.75 22.94967 -0.395 75.08333 7.649893 -0.293 5637.507 58.52087 574.3795 -2.24142 -21.9994 -0.22586 -0.06714
n 0 45.89935 -0.035 -70.6667 30.59957 0.067 4993.778 936.3335 -2162.37 2.050171 -4.73467 0.168731 -0.10173
o 26.5 45.89935 0 -44.1667 30.59957 0.102 1950.694 936.3335 -1351.48 3.121156 -4.505 0.092146 0.009854
p 53 45.89935 0.085 -17.6667 30.59957 0.187 312.1111 936.3335 -540.592 5.722119 -3.30367 0.015561 0.171439
q 79.5 45.89935 0.09 8.833333 30.59957 0.192 78.02778 936.3335 270.2962 5.875117 1.696 -0.06102 0.253024
r 106 45.89935 -0.11 35.33333 30.59957 -0.008 1248.444 936.3335 1081.185 -0.2448 -0.28267 -0.13761 0.129609
s 132.5 45.89935 -0.23 61.83333 30.59957 -0.128 3823.361 936.3335 1892.073 -3.91674 -7.91467 -0.21419 0.086194
t 159 45.89935 -0.4 88.33333 30.59957 -0.298 7802.778 936.3335 2702.962 -9.11867 -26.3233 -0.29078 -0.00722
Sum 1060 229.4967 -1.53 -5E-08 0 -2.2E-16 39911.21 3862.375 -4054.44 7.229147 -110.704
Average 70.66667 15.29978 -0.102