Chapter 8 : Metrology

Example 8.1 Page No : 369

In [2]:
# Calculations and Results
Dd = 52.215;
print "desired value = ", Dd
Pb = 4;
print "Protected block = ", Pb
R = Dd-Pb;
print "Reminder = ", R
Tp = 1.005;
print "thousand  block = ", Tp
R = R-Tp;
print "Reminder = ", R
Hp = 1.010;
print "Hunderths block = ", Hp
R = R-Hp;
print "Reminder = ", R
Ttp = 2.20;
print "tenths block = ", Ttp
R = R-Ttp;
print "Reminder = ", R
Up = 4;
print "unit block = ", Up
R = R-Up;
print "Reminder = ", R
Tp = 40;
print "Tens block = ", Tp
R = R-Tp;
print "Reminder = ", R

desired value =  52.215
Protected block =  4
Reminder =  48.215
thousand  block =  1.005
Reminder =  47.21
Hunderths block =  1.01
Reminder =  46.2
tenths block =  2.2
Reminder =  44.0
unit block =  4
Reminder =  40.0
Tens block =  40
Reminder =  0.0

Example 8.2 Page No : 371

In [3]:
import math 

# Variables
Ps = 200.*10**3;
r = 0.6;
d2 = 0.5;
d1 = 0.5;

# Calculations and Results
a = (d2/d1**2);
x1 = (1.1-r)/(2*a);
print "x1 = ", x1
r = 0.8;
d2 = 0.5;
d1 = 0.5;
a = (d2/d1**2);
x2 = (1.1-r)/(2*a);
print "x2 = ", x2
x = x1-x2;
print "so the range is x (mm)", x
hS = math.pi*d2*10**-3;
A2 = math.pi*d2*10**-6*(x1+x2)/2;
pS = -0.4*Ps/A2;
pgS = 25*10**-3/1000;
S = hS*pS*pgS;
print "sensitivity = ", S

x1 =  0.125
x2 =  0.075
so the range is x (mm) 0.05
sensitivity =  -20000.0

Example 8.3 Page No : 373

In [4]:
# Variables
Pi = 70.*10**3;
r = 0.4;
d2 = 1.6;
d1 = 0.75;

# Calculations and Results
a = (d2/d1**2);
x1 = (1.1-r)/(2*a);
print "x1 = ", x1
r = 0.9;
x2 = (1.1-r)/(2*a);
print "x2 = ", x2
x = x1-x2;
print "so the range is x (mm)", x
d = -2*a;
Wr = 12.5/Pi;
Wx = Wr/d;
print "uncertainity in lacement (mm)",Wx

x1 =  0.123046875
x2 =  0.03515625
so the range is x (mm) 0.087890625
uncertainity in lacement (mm) -3.13895089286e-05

Example 8.4 Page No : 375

In [5]:
# Variables
N = 12.;
lem = 0.644;

# Calculations
d = N*lem/2;

# Results
print "difference between height of workpieces and pile of slip gauges (micro-meter)", d

difference between height of workpieces and pile of slip gauges (micro-meter) 3.864

Example 8.5 Page No : 377

In [6]:
# Variables
N = 5.;
lem = 546.*10**-9;

# Calculations and Results
d = ((2*N-1)*lem*10**6)/4;
print "seperation distance between two surfaces(micro-meter)", d
x = 75;
th = math.atan(d/x);
print "angle of tilt", th

seperation distance between two surfaces(micro-meter) 1.2285
angle of tilt 0.0163785352938

Example 8.6 Page No : 379

In [7]:
# Variables
x = 20./12;
L = 50-10;
lem = 0.6;

# Calculations
d = (L*lem)/(2*x);

# Results
print "difference in diameters of the rollers(micro-meter)", d

difference in diameters of the rollers(micro-meter) 7.2

Example 8.7 Page No : 381

In [8]:
# Variables
d = 4.5-2.5;

# Calculations
Tg = 2*(0.5)*0.509;

# Results
print "change in thickness along its length(micro-meter)", Tg

change in thickness along its length(micro-meter) 0.509