Instrumentation and Measurements

ESS3270 LectureSpring 2012

Part B

Experimental Methods for Engineers by J. P. Holman Displacement and Area Chap. 5 Pressure Chap. 6 Flow Chap. 7 Temperature Chap. 8 Strain Chap. 10

Grading: Final Exam (35%), HW (7%)Quiz and Class Attendance (8%)

Chapter 5: Displacement and Area Measurement

ESS3270 LectureSpring 2012

5.1 Introduction

Dimensional Measurement Determination of the size of an object

Displacement Measurement Determination of the movement of a point from one

position to another Static or Dynamic

Area Measurement Combination of appropriate dimensional

measurement through a correct analytical relationship Determination of areas of irregular geometric shapes

involves a mechanical, graphical, or numerical integration

Displacement Measurement

Dimensional Measurement (in/cm)

Tapes and scales 0.01 Primary errors: thermal expansion/contraction of the scale (fixed

errors which may be corrected if the temperature is known) Readability errors

Improved readability Vernier calipers 0.001

Vernier scale arrangement for fractional part of primary scale division (http://www.physics.smu.edu/~scalise/apparatus/caliper/tutorial/)

Micrometer calipers 0.0001 Calibrated screw thread and circumferential scale division

Dial indicators 0.001 Mechanical amplification of the displacement of a pointer or

follower Gear rack connected to a displacement sensing shaft Pinion for gear-train amplification of the movement

Gage blocks 0.0001

Example 5.1

0.035%

Screws:maintain conditions

3+0.50+0.25(19/25)

Improve readability

Signal amplification

5.3 Gage Blocks Industrial dimension standards Small steel blocks about 3/8 x 13/8 inch Highly polished parallel surfaces A set of 81 blocks

Any dimension between 0.10 and 8.000 inch can be obtained in increments of 0.0001 inch

Thoroughly clean surfaces Blocks are stacked through a wringing (,) process Gage blocks are frequently used for calibration of other

dimensional measurement devices Tolerances for blocks less than 1 inch thick

Tolerances, -inch Grade2 AA4 A8 B

5.4 Optical Method Interferometer

Application of the interference principle Calibration of gage blocks and other dimensional standards

Essence of the interference principle Two light waves from a single source travel along paths of different

lengths The difference in the distance = integral multiple of wavelength

=> reinforcement of the wave 2d = even multiple of /2 Reflected beam will augment beam B

The difference in the distance=odd multiple of the half-wavelengths => cancellation

2d = /2, 3 /2, .. Cancellation at P => detect no reflected light on S

Optical Method I

Parallel plates One plate is a transparent, strain-free glass,

accurately polished flat within a few micro-inches (optical flat)

Other plate has a reflecting metal surface The separation distance between the plates is

d (quite small) Additional travel distance of 2d for Beam A

Problems 5.3:The spacing distance d can be represented by d=(2n-1)/4

For no reflected light 2d = /2, 3/2, 5/2, 2d = n-/2

where n =1, 2, is the number of fringe (dark) lines d = n/2-/4 = (2n-1)/4

S

Haidinger fringes

Optical Method II

Same two plates + tilted slightly The distance between the plates is a variable Alternate light and dark regions on the screen

indicating the variation in the plate spacing => fringes (dark lines)=> the change in the separation distance between

two consecutive fringes Convenient means for measuring small surface defects Schematic of interferometer (Fig.5.6)

Calibration of gage blocks Extremely precise absolute dimensional measurement

a

b

Example 5.2

3.0

=> fringe pattern => alignment of workpiece

Pneumatic Displacement Gage

d1 = 0.03 in

d2 = 0.062 in

x = 0.0145 ~ 0.0509 in

5.5 Pneumatic Displacement Gage

Air is supplied at a constant P1 Assumption: incompressible

Q = volumetric flow rate = uA= L3/s= CA(P)

C = discharge coefficient A = flow area of the orifice P = pressure differential across the orifice

Two Orifices Obvious one Flow restriction between the outlet and the workpiece

Pneumatic Displacement Gage

Pneumatic Displacement Gage

x

r

Example 5.3

= )x,...,x,x(RR n212

12n

n

22

2

21

1R ])wx

R(...)wxR()w

xR[(w

px wpxw

212

1

/2)/(1.1

ddpppx a

Example 5.3

Electrical Displacement Gage

Fixed reference: the base does not move Small static and dynamic displacement

in to small fractions of an inch Variable Resistance Sensors Variable Capacitance Sensors

Large magnitudes displacement From fractions of an inch to several inches

Differential Transformers Greater range displacement

Small fractions of an inch to several feet Resistance Potentiometers Photosensing Transducers

Resistance Potentiometer

Measurements of linear and angular motions Slide-wire resistance potentiometer

Slide-Wire Resistance Potentiometer

Simplest type of potentiometer Vo=(x/)Vi or x=(Vo/Vi) Disadvantage of straight wire resistors

Short length of wire=> low resistance=> excessive power requirement

Wind the high resistance wire around an insulating core

The resistance ranges from 10 to 106

Resistance increases in a stepwise manner as the wiper moves from one turn to the adjacent turn

Step change in resistance limits the resolution of the potentiometer to L/n (n: # of turns, L: coil length)

Resolution ranging from 0.05 to 1% are common lower limits many turns of small diameter wire

The range of the potentiometer is controlled by the active length L of the coil (linear potentiometer up to 1 m)

Potentiometer sensor with a resistance Rp A recording instrument with a resistance RM A power supply supplying voltage Vs A capacitor C smooth the output signal as wiper moves

from wire to wire along the helical resistance coil Output voltage Vo

Analysis

The effect of load imposed on the output signal by the voltage-measuring instrument

Output voltage VoVo = iMRM = (i - iM)R = Vs- i(Rp-R)= Vs/[(Rp-R)/RM+(Rp-R)/R+1] = Vs/[Rp/RM+RP/R-R/RM]

introducing a nonlinear factor

= f (R/Rp, Rm/Rp)

Summary of Potentiometer

Only for static or quasi-static measurement where a high-frequency response is not required

Electronic noise Occurs as the electrical contact on the wiper moves from

one wire turn to the next Minimized by ensuring that the coil is (a) clean (b) free of

oxide films (c) lubricated with thin film of light oil Advantages

Inexpensive yet accurate Simplicity of operation

Disadvantages Limited frequency response => not for dynamic

5.6 Area Measurements

Graphical determinations of the area of the survey plots from maps

The integration of a function to determine the area under a curve

Analyses of experimental data plots

5.7 The Planimeter

A mechanical device for the measurement of plane areas

Polar planimeter Planimeter and area are placed on a flat,

relatively smooth surface => wheel w only slide when BT undergoes an axial translational movement

5.8 Graphical and Numerical Methods

Simple method Count the number of squares on coordinate paper ()

Numerical integration Determine the area under an irregular curve

Calculating A = ydx using equal increments x along x-axisjoining the ordinates of curve with straight line

(1) trapezoidal rule

(2) simpsons rule (no. of increments is even)