Excitation modes: the simple step function, the simple harmonic, complex periodic inputs. 4. First-Order Systems (1)Step response
P P (1 e
t

) PAe
4. Sampling of continuous–time signals y(k)=yc(kt) <k< The sampling period; the sampling frequency; sampling theorem; the Nyquist frequency; frequency resolution 5. Fourier series for discrete-time periodic signals
The process or the act of measurement consists of obtaining a quantitative comparison between a predefined standard and a measurand.
2. What are the fundamental methods of measurement?
F (t ) A0 Cn cos(nt n ) 2 n 1
The transient term+ The steady-state term
SouthwestJiaotongUniversity
Mechanical Measurement Review
Xuemei Wang 2017Spring
Chapter 2
1. Error Classification and Characteristics.
Systematic error and Precision or random errors
2. Propagation of Uncertainty y= f (x1,x2,…xn)
u y (u x1 f 2 f 2 f 2 ) (u x 2 ) (u xn ) (P=68.2%, Gaussian distribution) x1 x 2 x n f 2 f 2 f 2 ) (u x 2 ) (u xn ) x1 x 2 x n
c. Over-damping (过阻尼)
>1
2 1 )nt
2 1 ( P 1 e Ps 2 2 1

2 1
2 2 1
e (
2 1 )n t
Figure 5.15 Response of step-excited second-order system (2) The harmonic response The transient term+ The steady-state term The steady-state term:
(1)Step response a. Under-damping (欠阻尼
<1
P 1 1 e nt cos(nd t ) Ps 1 2
tan 1[

1 2
]
=1
b. Critical-damping (临界阻尼)
P 1 - e nt (1 nt ) Ps
Figure 5.17 The phase response to harmonic excitation of the second-order system Ideally the system is expected to have linear phase shift for all frequency range. Actually the damping ratios of the order of 65%~75% of critical provide an approximately linear shift for the frequency ratio range of 0%~ 40%. (3) General Periodic Forcing
SouthwestJiaotongUniversity
Mechanical Measurement Review
Xuemei Wang 2017Spring
The unitless damping ratio:
; c
2 Damped natural frequency: nd n 1
t

=/k , time constant
(2) The harmonic response The transient term+ The steady-state term The steady-state term:
P Ps 1 () 2 cos(t )
The amplification ratio:
y (k )
2 N
A N2 2nk 2nk [ An cos( ) Bn sin( )] 2 n1 N N
A
y (k )
k 1
N
An
2 N 2 y (k ) cos( nkt )t Nt k 1 Nt 2nk y (k ) cos( ) N k 1
SouthwestJiaotongUniversity
Mechanical Measurement Review
Xuemei Wang 2017Spring
Mass; Spring Force; Viscous damping Example: the scale beam (The importance of damping; What might be an optimum value?)
Direct Comparison； Indirect comparison through the use of a calibrated system.
3. What is the generalized measuring system? 4. How may the input quantities be classified? Static; Dynamic 5. What is the analog signal? And what is the digital signal?
SouthwestJiaotongUniversity
Mechanical Measurement Review
Xuemei Wang 2017Spring
Chapter 3
1. Simple harmonic motion: s s0 sin t 2. Special Waveforms: The square wave, the sawtooth wave, the triangle wave. 3. Fourier series for continuous-time periodic signals
Xuemei Wang 2017Spring
Phase lag:
2 / n 1 t an [ ] 1 ( / n ) 2
Figure 5.16 The frequency response to harmonic excitation of the second-order system Ideally the system is expected to be insensitive to changes in the frequency of input F(t), that is the amplitude ratio is constant for all frequency range. Actually it is reasonably constant for only a limited frequency range and then only for certain damping ratios. Practically, if the damping ratio in the neighborhood of 65%~75% is used, then the amplitude ratio will approximate unity over a range of frequency ratios of about 0%~40%.
x x kSx
7. The Student’s t – distribution (t-test)-- small sample 8. Terms: Confidence limits; Confidence interval; Level of significance; Confidence level 9. Examples and Exercises.
SouthwestJiaotongUniversity
Mechanical Measurement Review
Xuemei Wang 2017Spring
Mechanical Measurement Review Chapter 1
1. What is the process of measurement?
N
2 N
Bn 2 N
n=0, 1, … ,
y(k ) sin(
k 1
N
2nk ) N
5. Examples fidelity（保真度）:
Good frequency response and Phase Response
2. Mechanical Elements:
The steady-state term:
P Ps
n 1

Pns cos(nt n Ψ n ) n [1 ( ) 2 ]2 (2n ) 2