# Chapter 5 Force Torque and Shaft power Measurement¶

## Example 5_1 pgno:294¶

In :
#CHAPTER 5_ Force,Torque and Shaft Power Measurement
# Example 1# Page 294
from math import sqrt

Sg=2.;   # Strain gage factor
Rg=120.;    # Gage resistance
v=0.3    # poissons ratio
E=210*10**9;    # for steel
Pd=1.   #('enter the power dissipation capacity=:')
# Looking for a suitable voltage measuring system
sig_f=700*10**6   #('enter the fatigue strength=:')
# For a load cell of square cross-section d,
d=sqrt(P_max/sig_f);
Ei=sqrt(4*Rg*Pd)   #input excitation to the bridge circuit
x=(Sg*sig_f*(1+v))/(2*E);
dEo_max=x*Ei*10**3;
print ("x=(Sg*sig_f*(1+v))/(2*E)")
print ('a voltmeter with a maximum range of  mV is suitable for measurement',round(dEo_max))
print ("Round it off to get the suitable range voltmeter")

x=(Sg*sig_f*(1+v))/(2*E)
('a voltmeter with a maximum range of  mV is suitable for measurement', 95.0)
Round it off to get the suitable range voltmeter


## Example 5_2 pgno:295¶

In :
#CHAPTER 5_ Force,Torque and Shaft Power Measurement
# Example 2# Page 295

b=.2   #('enter the width of load cell=:')
h=.05   #('enter the thickness of load cell=:')
Sg=2.;
Rg=120.;
sig_f=150*10**6   #('enter the fatigue strength=:')
E=70.;      #(in GPa) for aluminium
v=0.33;           #poissons ratio
# Let dE/V_max be represented by W
W=Sg*sig_f/E;
print('(dE/V)_max= d\n ',W)
P_max=100000.   #('enter the value of maximum load=:')
l=sig_f*b*h**2/(6*P_max);

S=(6*Sg*l)/(E*b*h**2);
print'Sensitivity of this load cell is  nV/N/per unit excitation',round(S,2)

('(dE/V)_max= d\n ', 4285714.285714285)
Sensitivity of this load cell is  nV/N/per unit excitation 42.86


## Example 5_3 pgno:296¶

In :
#CHAPTER 5_ Force,Torque and Shaft Power Measurement
# Example 3# Page 296
from math import sqrt
Sg=2;
v=0.3;    #poissons ratio
Ei=10.   #('enter the excitation voltage=:')
A=5*10**-4  #('enter the area of load cell=:')
E=200.;   #(in Gpa) Youngs modulus
# Let sensitivity Eo/P be represented by Se
Se=Sg*(1+v)*Ei/(2*A*E)*.001;
print'Sensitivity of this load cell is  micro V/N\n',Se
Rg=120.   #given
Pd=1. #('enter the power dissipated in each gage=:')
Ei_max=sqrt(4*Rg*Pd)
Se_max=Sg*(1+v)*Ei_max/(2*A*E)*.001
print'The maximum density that can be achieved without endangering the strain gage sensors is micro V/N\n',Se_max
# Let (Eo/Ei)_max be represented by Em
sig_f=600*10**6  #('enter the fatigue strength=:')
Em=Sg*sig_f*(1+v)/(2*E)*10**-6
print'The voltage ratio is mV/V',Em

Sensitivity of this load cell is  micro V/N
0.13
The maximum density that can be achieved without endangering the strain gage sensors is micro V/N
0.284815729903
The voltage ratio is mV/V 3.9


## Example 5_4 pgno:302¶

In :
#CHAPTER 5_ Force,Torque and Shaft Power Measurement
#Caption : Piezoelectric Transducers
# Example 4# Page 302
from math import sqrt,pi
mc=0.04   #('enter the connector mass=:')
m=0.01   #('enter the seismic mass=:')
k=10**9   #('enter the stiffness of the sensing element=:')
Sf=.005   #('enter the sensitivity of the transducer=:')
Xi=100*10**-6 #  ('enter the displacement amplitude of the shaker vibration=:')
Eo=.1   #('enter the reading of voltage recorder connected to the transducer=:')
wnc=sqrt(k/(m+mc));
R=20;    #20N (rms)
Z=(1/(m+mc))*(1/wnc**2)*R;
print('Relative displacement is d',Z)
print("wnc**2 is approx. 10**9. So,")
print("Z is approx. 20nm(rms)")
f=100.;   # given

F=R-((2*pi*f)**2*(m+mc)*Xi);
print'Actual force transmitted to the plate is d N',round(F,2)

('Relative displacement is d', 1.9999999999999997e-08)
wnc**2 is approx. 10**9. So,
Z is approx. 20nm(rms)
Actual force transmitted to the plate is d N 18.03


## Example 5_5 pgno:308¶

In :
#CHAPTER 5_ Force,Torque and Shaft Power Measurement
#Caption : Torque measurement on rotating shaft
# Example 5# Page 308
Sg=2.;
Rg=120.;
G=80*10**9   #('enter the sheer modulus of elasticity=:')
D=0.05   #('enter the shaft diameter=:')
dR=0.1   # given
# we have to find the load torque
from math import pi

y=2*dR/(Rg*Sg);
tou_xy=y*G;
j=pi*D**4;
T=tou_xy*2*j/(D*32);
print'The load torque is d N-m',round(T)

The load torque is d N-m 1636.0


## Example 5_6 pgno:310¶

In :
#CHAPTER 5_ Force,Torque and Shaft Power Measurement
#Caption : Piezoelectric Transducers
# Example 6# Page 310
from math import sqrt,pi
mc=0.02   #('enter the connector mass=:')
m=0.06  #('enter the seismic mass=:')
k=10**9   #('enter the stiffness of the sensing element=:')
Sf=.008   #('enter the sensitivity of the transducer=:')
Xi=100*10**-6 #  ('enter the displacement amplitude of the shaker vibration=:')
Eo=.1   #('enter the reading of voltage recorder connected to the transducer=:')
wnc=sqrt(k/(m+mc));
R=20;    #20N (rms)
Z=(1/(m+mc))*(1/wnc**2)*R;
print('Relative displacement is d',Z)
print("wnc**2 is approx. 10**9. So,")
print("Z is approx. 20nm(rms)")
f=100.;   # given

F=R-((2*pi*f)**2*(m+mc)*Xi);
print'Actual force transmitted to the plate is d N',round(F,2)

('Relative displacement is d', 2e-08)
wnc**2 is approx. 10**9. So,
Z is approx. 20nm(rms)
Actual force transmitted to the plate is d N 16.84


## Example 5_7 pgno:311¶

In :
#CHAPTER 5_ Force,Torque and Shaft Power Measurement
# Example 7# Page 311
from math import sqrt
Sg=5;
v=0.3;    #poissons ratio
Ei=50.   #('enter the excitation voltage=:')
A=3*10**-4  #('enter the area of load cell=:')
E=500.;   #(in Gpa) Youngs modulus
# Let sensitivity Eo/P be represented by Se
Se=Sg*(1+v)*Ei/(2*A*E)*.001;
print'Sensitivity of this load cell is  micro V/N\n',Se
Rg=120.   #given
Pd=1. #('enter the power dissipated in each gage=:')
Ei_max=sqrt(4*Rg*Pd)
Se_max=Sg*(1+v)*Ei_max/(2*A*E)*.001
print'The maximum density that can be achieved without endangering the strain gage sensors is micro V/N\n',Se_max
# Let (Eo/Ei)_max be represented by Em
sig_f=600*10**6  #('enter the fatigue strength=:')
Em=Sg*sig_f*(1+v)/(2*E)*10**-6
print'The voltage ratio is mV/V',Em

Sensitivity of this load cell is  micro V/N
1.08333333333
The maximum density that can be achieved without endangering the strain gage sensors is micro V/N
0.474692883171
The voltage ratio is mV/V 3.9