MECH 3050 Lab Manual

7/31/2019 MECH 3050 Lab Manual

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Measurement & InstrumentationLaboratory Manual

Edited by

John F. Maddox

&Jordan C. Roberts

MECH 3050

Fall 2012



Contents

1 Dimensional Analysis of Granular Flow 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.1 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.3 Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Sound and Signal Processing 82.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Simple Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.2 Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Flow Rate Sensor Calibration 133.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 Rotameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1.2 Vortex Shedding Meter . . . . . . . . . . . . . . . . . . . . . . . . . 143.1.3 Turbine Flow Meter . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.2 Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Passive Circuits 194.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.2.1 Breadboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.2.2 Voltage Divider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2.3 Circuit Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.4 Input Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2.5 Thermistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

i



CONTENTS ii

5 Active Circuits 275.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.2.1 Reference Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.2.2 Thermistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.2.3 Initial Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.2.4 Active Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.2.5 Final Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.2.6 Final Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6 Digital to Analog Conversion 346.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

6.2.1 Binary Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356.2.2 Boolean (Logical) Operators . . . . . . . . . . . . . . . . . . . . . . 35

6.2.3 DAC Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

7 Pressure Sensor Calibration 387.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

7.1.1 Dead Weight Tester . . . . . . . . . . . . . . . . . . . . . . . . . . . 387.1.2 Bourdon Tube Dial Pressure Gauge . . . . . . . . . . . . . . . . . . 397.1.3 Membrane Pressure Transducer . . . . . . . . . . . . . . . . . . . . 417.1.4 Mercury Barometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

7.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447.2.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447.2.2 Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

8 PID Controls 478.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

8.2.1 Open Loop System . . . . . . . . . . . . . . . . . . . . . . . . . . . 498.2.2 Closed Loop System with Proportional Feedback Only . . . . . . . 508.2.3 Closed Loop System with Proportional and Integral Feedback . . . 51

9 Temperature Sensor Calibration 539.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

9.1.1 Liquid Bulb Thermometer . . . . . . . . . . . . . . . . . . . . . . . 53

9.1.2 Bimetallic Strip Thermometer . . . . . . . . . . . . . . . . . . . . . 549.1.3 Thermistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559.1.4 Platinum RTD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569.1.5 Thermocouple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

9.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579.2.1 Constant Temperature Water Bath Operation . . . . . . . . . . . . 579.2.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58



CONTENTS iii

9.2.3 Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

10 Load Cell Use and Instrumentation 6010.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

10.1.1 Theory of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 60

10.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6110.2.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Bibliography 69

A Sensor Calibration 70

B Additional Resources 74B.1 741 Operational Amplifier Pinout Diagram . . . . . . . . . . . . . . . . . . 74B.2 Resistor Color Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75B.3 RL10 Thermistor Specification Sheet . . . . . . . . . . . . . . . . . . . . . 76

B.4 Probability Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77B.5 Thermistor Conversion Table . . . . . . . . . . . . . . . . . . . . . . . . . 80



List of Figures

3.1 Operational diagram of a rotameter. . . . . . . . . . . . . . . . . . . . . . 143.2 Operational diagram of a vortex shedding meter. . . . . . . . . . . . . . . . 153.3 Operation diagram of a turbine flow meter. . . . . . . . . . . . . . . . . . . 17

4.1 Layout of a typical breadboard . . . . . . . . . . . . . . . . . . . . . . . . 204.2 Voltage divider circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3 Voltage divider circuit with two resistors in parallel. . . . . . . . . . . . . . 224.4 A resistor in series with a digital multimeter. . . . . . . . . . . . . . . . . . 244.5 Thermistor voltage divider circuit. . . . . . . . . . . . . . . . . . . . . . . . 25

5.1 Circuit used to amplify a thermistor reading and filter out noise. . . . . . . 285.2 Voltage divider section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.3 Thermistor section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.4 Initial gain section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.5 Butterworth filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.6 Final gain section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6.1 Digital to analog conversion circuit . . . . . . . . . . . . . . . . . . . . . . 36

7.1 Operational diagram for a dead weight tester. . . . . . . . . . . . . . . . . 397.2 Operational diagram of a bourdon tube pressure gauge. . . . . . . . . . . . 407.3 Operational diagram of a pressure membrane transducer. . . . . . . . . . . 417.4 Operational diagram for a mercury barometer . . . . . . . . . . . . . . . . 44

8.1 Example of an open loop control system. . . . . . . . . . . . . . . . . . . . 478.2 Example of a closed loop control system. . . . . . . . . . . . . . . . . . . . 48

9.1 Bonded metals with different coefficients of thermal expansion . . . . . . . 54

9.2 Operational diagram of a thermocouple. . . . . . . . . . . . . . . . . . . . 57

10.1 Wheatstone Bridge Configuration . . . . . . . . . . . . . . . . . . . . . . . 61

A.1 Sensor calibration example . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

B.1 Pinout diagram for a generic 741 opamp. . . . . . . . . . . . . . . . . . . . 74B.2 Resistor color code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

iv



List of Tables

1.1 Particle and tube properties. . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Bulk density measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Experimental results for constant starting height. . . . . . . . . . . . . . . 71.4 Experimental results for constant orifice size. . . . . . . . . . . . . . . . . . 7

3.1 Interpolation data for turbine flow meter. . . . . . . . . . . . . . . . . . . . 173.2 Measured values for flow sensor calibration. . . . . . . . . . . . . . . . . . 18

4.1 Experimental values for voltage divider circuit. . . . . . . . . . . . . . . . . 224.2 Experimental values for loaded circuit. . . . . . . . . . . . . . . . . . . . . 234.3 Experimental values for voltage drop across a DMM. . . . . . . . . . . . . 244.4 Experimental values for voltage drop across a DMM. . . . . . . . . . . . . 26

5.1 Experimental values for thermistor amplification and filtering. . . . . . . . 32

6.1 Logic gate truth table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356.2 Experimental digital to analog conversion values. . . . . . . . . . . . . . . 37

7.1 Sensitivity values for membrane transducer . . . . . . . . . . . . . . . . . . 427.2 Measured values for pressure sensor calibration. . . . . . . . . . . . . . . . 45

9.1 Measured values for temperature sensor calibration. . . . . . . . . . . . . . 59

A.1 Sensor calibration example . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

B.1 Properties for RL10 thermistors. . . . . . . . . . . . . . . . . . . . . . . . . 76B.2 Areas under the Standard Normal Curve . . . . . . . . . . . . . . . . . . . 78B.3 Student’s t-Distribution (Values of tα,ν ) . . . . . . . . . . . . . . . . . . . . 79B.4 Conversion table for thermistor. . . . . . . . . . . . . . . . . . . . . . . . . 80

v



Lab 1

Dimensional Analysis of GranularFlow

1.1 IntroductionThe flow of a granular material through an orifice constitutes a problem extremely impor-tant to the design of grain storage elevators, production and packaging of pharmaceuticals,nuclear charge testing, etc. The multi-phase system of interest in this problem involves amixture of solid particles and the gas phase (air) existing between the particles. Becauseof the multi-phase medium, the flow of such a system will differ markedly from that of asingle phase system. In a solid-gas multi-phase medium, it is noted that the particulatesneither act as a solid nor a fluid. For example, the free surface of the particulates tends tobe inclined downward in a conical shape rather than remaining horizontal as for the caseof a fluid. Due to the complex behavior of granular flows, empirical relations are necessaryto predict flow characteristics. Developing such an empirical relation among the variousparameters and determining the significance of each variable is the objective of this experi-ment. Detailed knowledge of the particular multi-phase flow system is of great importancein the following industries:

Pharmaceuticals The flow of particulate solids is a crucial factor in the productionof pharmaceuticals. In such processes, high-speed filling machines are used to deliver aspecified quantity of a powder or granulation into its package. It is vital that the materialflows consistently to ensure the desired fill. Solid dosage forms such as tablets, capsules,and divided powders require a measured filling for the production of each unit. In this

particular application, a relationship between flow rate, particle size, and orifice diameterof the filling machine for the granular material to be used must be determined for designpurposes.

Agriculture A similar situation occurs in grain elevators, hoppers, and bins with thedistinction being that the operation is on a much larger scale and some accuracy canbe sacrificed. The material is also much larger and usually coarse in nature. However,

1



LAB 1. DIMENSIONAL ANALYSIS OF GRANULAR FLOW 2

the relationship between the flow rate, the particle size, and the orifice diameter must bedetermined in order to accurately model the system.

Nuclear Charge Testing Underground nuclear charge testing poses a situation similar

to the previous examples. When underground nuclear tests are conducted, a large area of ground above the charge collapses and the surface sinks downward in a conical shape. Theknowledge of how the ground surface will be affected by the blast is of prime importanceto scientists to ensure proper burial of the nuclear charge. In this experiment, the granularflow through orifices with various geometric shapes under the action of gravity will beanalyzed. It is expected that the mass flow rate will be influenced by various physicalquantities, e.g. diameter of the cylindrical vessel, the hydraulic diameter of the orifices,the spherical diameter of particles, density of particles, head of packing, etc. To examinethe effects of all these parameters one by one seems impossible because it requires a greatamount of work. Fortunately, dimensional analysis can be utilized to reduce the numberof variables and save a lot of time.

1.2 Theoretical Analysis

The primary objective of this experiment is to find the relationship among the overall massflow rate, m (kg/s), of granular materials and the relevant control variables. Consider theprocess of a granular material flowing inside a cylindrical vessel through an orifice. It isexpected that the following variables will affect the mass flow rate:

D = diameter of the cylindrical vessel, m

Dh = hydraulic diameter of the orifice, m

h = head of packing above the orifice, m

ds = spherical diameter of the particles, m

ρ = true density of the particles, kg/m2

ρB = bulk density of the particles, kg/m2

g = gravitational acceleration, m/s2

S = shape factor.

Since the materials being used are not elastic, it will be assumed that the bulk density isindependent of height and thus remains constant. In addition, the mass flow rate measured

through the cylinder is considered to be an average flow rate and not the instantaneousflow rate. A study performed by Fowler and Glastonbury [1] suggested that the coefficientof friction was a function of roughness, shape, and diameter. However, the coefficient of friction is omitted in our study in favor of the more fundamental variables listed above.Variables such as humidity, wall roughness, and the electrical charge between the particleswithin the flow are other variables that could affect the mass flow rate. Since humidity isdifficult to experimentally control and wall roughness and electrical charge between particlesare difficult to accurately measure, these variables will be neglected in this investigation.




In summary, a general relationship between the overall mass flow rate and other controlphysical quantities can be expressed as:

m = f (D, Dh, h , ds, ρ , ρB, g , S ). (1.1)

Due to the large number of variables involved, it is advantageous to utilize dimensionalanalysis to reduce the number of parameters. We will apply the Buckingham Π Theoremto determine the dimensionless numbers or groups. Following the procedure outlined ina number of undergraduate fluid mechanics textbooks (see Fox and McDonald [2]) thedimensionless numbers affecting this phenomenon are derived as follows:

Step 1) List all parameters involved

m,D,Dh,h,d,ρ,ρB, g , S

n = 9 parameters

Step 2) Select a set of fundamental (primary) dimensions.

For this case, the primary dimensions are mass, length, and time.

M, L, and t

Step 3) List the dimensions of all the parameters in terms of the primary dimensions.

m D Dh h ds ρ ρB g S M/T L L L L M/L3 M/L3 L/T 2 −

m = r = 3 primary dimensions

Step 4) Select the repeating parameters.

When choosing the repeating parameters, it is necessary that each of the primarydimensions be represented. It is also preferable to choose those parameters whichwill be easy to either measure or estimate and will either remain constant or beeasy to control. For this case the repeating parameters are chosen to be the bulkdensity, the spherical diameter of the particles, and gravity.

ρB, ds, g

Step 5) Set up equations for n − m = 6 dimensionless groups.The first dimensionless group, Π1, will contain the mass flow rate, m, and therepeating parameters:

Π1 = ρaB dbs gc m =

M L3

a

(L)b

LT 2

c

M L

= M 0L0T 0 (1.2)

Equating the exponents of M , L, and T results in

M : 0 = a + 1 a = −1

L : 0 = −3a + b + c b = −5/2

T : 0 = −2c − 1 c = −1/2




Therefore,

Π1 =m

ρB d5/2s g1/2

(1.3)

The five remaining dimensionless groups can be formed using the same procedure.

Π2 =h

ds(1.4)

Π3 =Dh

ds(1.5)

Π4 =D

ds(1.6)

Π5 =ρ

ρB(1.7)

Π6 = shape factor (1.8)

Step 6) Model the system as a function of the dimensionless groups.If all the parameters involved have been accounted for, then the system can bedescribed as a function of the dimensionless groups.

0 = f (Π1, Π2, Π3, Π4, Π5, Π6) (1.9)

which can be rewritten as

Π1 = f (Π2, Π3, Π4, Π5, Π6) (1.10)

or

mρB d

5/2s g1/2

= f

hds

, Dhds

, Dds

, ρρB

, S

(1.11)

This states that the dimensionless mass flow rate is a function of the other fivedimensionless groups.

Due to time constraints, the diameter of the cylinder will be held constant, there-fore Π4 will remain constant. Π5 is assumed to be constant because of the difficultyin controlling the bulk density and because the ratio ρ/ρb varies little.1 Π6 remainsconstant because the experiment will only include one type of particle. Since Π4,Π5, and Π6 will remain constant, their effects can be absorbed into a constant, C .Therefore, the relationship is reduced to:

Π1 = f (Π2, Π3, C ) (1.12)

orm

ρB d5/2s g1/2

= f

h

ds,

Dh

ds, C

(1.13)

1Fowler and Glastonbury [1] reported that for most cases of randomly packed beds, the bed porositylies between 30% and 50% and the ratio of ρ/ρB lies between 1.30 and 1.50.




A decision must then be made regarding the form of the equation to be used. Someknowledge of the system, or similar systems, can aid in choosing an appropriateform, i.e. linear, quadratic, logarithmic, power series, etc. For this lab a powerseries form was chosen because it has been shown to do a good job of modelingfluid flow and it is convenient to work with. Therefore, it is assumed that thesystem can be described by a function of the form

Π1 = C Πn22 Πn3

3 (1.14)

1.3 Experiment

1.3.1 Experimental Apparatus

An experimental apparatus consisting of three 48 inch long vertically mounted Plexiglascylinders with inside diameters of 3.0, 4.0, and 5.5 inches will be used to observe mass

flow rates through changeable orifice plates. The removable orifice plates will have threedifferent opening geometries (circular, square, and triangular) with varying opening sizes(hydraulic diameters).

A number of granular materials such as sand, salt, sugar, seed, rice, wheat, polymerbeads, and metal beads may be used. The bulk densities of the materials, ρB, will bemeasured by filling a graduated cylinder of known volume and weight with each materialand weighing the graduated cylinder. By determining the mass of the material with a knownvolume, the bulk density of the material can be calculated. A sample of five independentreadings will be taken and averaged for the granular material used by each group.

A series of experiments to cover a range of combinations of orifice size and head will beexecuted to determine the constant C and the exponents n2 and n3 in Eq. (1.14). A graphof Π1 as a function of the varying dimensionless number can be plotted. The appropriateexponent can then be determined using a power fit. First, the Plexiglas cylinder is filledwith the granular material to a certain head. The head is measured from the orifice plateto the top of the bed. The flow rate, m, is then determined by collecting the material overa measured duration of time, and weighing the quantity collected. A series of experimentswill be conducted to find the exponent n2 by varying the dimensionless group Π2, whileholding the others constant. Another series of experiments will be conducted to find theexponent n3 by varying the dimensionless group Π3, while holding the others constant. Theexperimental conditions and results of your runs should be summarized in Tables 1.1-1.4.

1.3.2 ProcedureThe experimental procedure for this lab will be as follows:

1) Once your group has been assigned a material, perform 10 spherical diameter measure-ments using a Vernier caliper. Take the average and record your results in Table 1.1.

2) Perform five bulk density measurements using a 500 ml flask and the scale. Record yourresults in Table 1.2.




3) Your group will also be assigned to one of the three cylinders so all your measurementswill be for a given grain size, ds, in a given cylinder diameter, D.

4) Using the orifice plates given, measure the mass flow rate for six different plate-openingdiameters, Dh. All six measurements should be taken with the starting height held

constant. Record your results in Table 1.3. This data will be used to determine thevalue of n2.

5) Repeat step 4 at three additional starting heights using a single orifice plate. Recordyour results in Table 1.4. This data will be used to determine the value of n1.

Table 1.1: Particle and tube properties.

Material

Orifice shape

Spherical diameter

Tube diameter

Table 1.2: Bulk density measurements.

No. Volume (m3) Mass (kg) Bulk Density (kg/m3)

1

2

34

5

Average (ρB)

1.3.3 Report

1) Plot Π1 vs. Π2 using the data collected in Table 1.4. Apply a power fit to determine

the value of n2. Your result should be of the form

Π1 = A · Πn22 (1.15)

whereA = C 1 · Πn3

3 . (1.16)




Table 1.3: Experimental results for constant starting height.

hΠ2

Dh Π3

Time Mass mΠ1(cm) (cm) (s) (kg) (kg/s)

Table 1.4: Experimental results for constant orifice size.

hΠ2

Dh Π3

Time Mass mΠ1

(cm) (cm) (s) (kg) (kg/s)

2) Plot Π1 vs. Π3 using the data collected in Table 1.3. Apply a power fit to determinethe value of n3. Your result should be of the form

Π1 = B · Πn33 (1.17)

whereB = C 2 · Πn2

2 . (1.18)

3) Plug the value for n2 from Eq. (1.15) into Eq. (1.18) to get a value for C 2. Then plugthe value for n3 from Eq. (1.17) into Eq. (1.16) to get a value for C 1. Take the averageof the two C values for use in the final correlation.

4) Combine your results from steps 1–3 and report the final correlation for the flow rate.It should be of the form

Π1 = C · Π

n2

2 · Π

n3

3 . (1.19)



Lab 2

Sound and Signal Processing

2.1 Introduction

In many types of signals such as sound and vibration, frequency and amplitude content aremore important than the variation of the signal with respect to time. Information is oftenencoded in the sinusoids that make up a waveform such as radio waves, telephone electricalsignals, and even human speech. In order to extract this information, the frequency andamplitude characteristics of the waveform must be examined. While the measurement of a signal is always made with respect to time, this type of analysis is nearly always easierto perform in the frequency domain. The time domain and frequency domain are justalternative ways of looking at the same data.

The Fourier transform is most commonly used to move between the time domainand the frequency domain. When analyzing discretely sampled data, one of the manyalgorithms, collectively known as a Fast Fourier Transform (FFT), is used to transformthe sampled data between the time domain and the frequency domain. By computing theFFT of a sampled signal, the frequency and amplitude characteristics can be more easilydetermined.

The FFT is not without its limitations however. One basic assumption of the Fouriertransform is that the signal to be transformed is periodic, extending from −∞ to +∞.This is clearly not possible with a sampled data set. Even periodicity is not guaranteedsince you may only capture an incomplete cycle during your sampling period. This resultsin something known as spectral leakage where information content is spread across a rangeof frequencies instead. In addition, if you do not sample at least twice as fast as the highestfrequency component that is present, aliasing effects will be introduced which results in

false peaks and/or incorrect interpretation of the signal. Various methods of digital signalprocessing are used to limit or reduce the effect of these errors. Windows and filters aretwo of the most common methods used.

In this lab, you will be using LabVIEW to compute and display the power spectrumof various waveforms. The power spectrum is computed from the FFT of the incomingwaveform and will show the frequency content of the signal of interest as well as the powercontent at specific frequencies. You will begin by generating some relatively simple periodicwaveforms and analyzing these. Then you will analyze waveforms that are captured by the

8



LAB 2. SOUND AND SIGNAL PROCESSING 9

soundcard in the computer through a microphone. Remember that the range of frequenciesover which the human ear can perceive is 20 Hz to 20,000 Hz. Expect that the frequencyrange of your speech and musical sounds that you can make are less than a few thousandHertz.

2.2 Exercises

2.2.1 Simple Signals

Some relatively simple signals will be generated and analyzed with regard to their frequencycontent. Use the VI DS Arbitrary Waveform Generator to create a waveform signal andDS Benchtop Spectrum Analyzer to analyze the waveform. Run both VIs.

Single frequency sine wave

On the DS Arbitrary Waveform Generator front panel, clear any waveforms on the graphdisplay by choosing both channels in the Select Channel to Edit and press Clear Channel.

We want to create a sine wave on channel 0. Choose channel 0 for the Choose Channel

to Edit. Press Create From Library to form the signal. A separate window will appearthat will allow you to create the waveform. Choose a sine wave from the Signal Type

combo box. Enter a number less than 10 in the Waveforms per Buffer box. Now pressDone. The edit waveform window will disappear and the waveform should be displayed inthe graph of the waveform generator.

Using the default setting of 10,000 points per sec, what will be the frequency of the waveform? Note that there are 1000 points per buffer.

Move the Continuous/Single Shot switch to the Continuous position and pressStart. Now switch to the DS Benchtop Spectrum Analyzer . Select None for the Window

combo box and press the Acquire On/Off switch.

Do you see a single peak or multiple peaks in the power spectrum (lower graph)? 1

1Ensure that the scale for the graph is set to linear, not decibel.




What is the frequency of the dominant peak?

Change the window type to Hann, then Hamming. How does the spectrum change?

Complicated Sine Wave

Now we will combine a second frequency component with the original sine wave from above.

Press Stop on the front panel of the DS Arbitrary Waveform Generator . Choose channel1 for the Choose Channel to Edit. Press Create From Library to form the signal. Aseparate window will appear that will allow you to create the waveform. Choose a sinewave from the Signal Type combo box. Enter a different number, less than 10, in theWaveforms per Buffer box. Enter a smaller number in the Amplitude box, and pressDone.

On the front panel of the DS Arbitrary Waveform Generator , press 0+1->0 to combinethe two waveforms. Press Start to begin output of the waveform.

Calculate and report the frequencies that are present in the combined waveform.

Switch to the DS Benchtop Spectrum Analyzer . You should see two major peaks.

Square Wave I

A square wave can be generated by combining multiple sine waves with specific frequencyand amplitude content. Specifically, a square wave is generated by adding the odd har-monics of the fundamental frequency together as shown in the equation below.

f (x) = Aff

sin x + 13 sin3x + 15 sin5x + . . .

where Aff is the amplitude of the fundamental frequency.Starting with a fundamental frequency of 2 cycles per buffer and Aff = 3 V, create a

square wave on channel 0 by combining sine waves up to the 9 th harmonic. Note that thiswaveform will not be a true square wave but it should begin to resemble one. Press Start

to begin output of the waveform on the DS Arbitrary Waveform Generator . Analyze thesignal using the DS Benchtop Spectrum Analyzer .




How does the frequency content of the generated square wave compare to what you expected?

Do you see a peak for each harmonic that is part of the combined waveform that you generated?

Square Wave II

Consider the frequency content of a true square wave that is generated by the waveformgenerator. Clear all waveforms from the DS Arbitrary Waveform Generator . Create asquare wave on channel 0 by pressing Create from Library and selecting a square wavefrom the Signal Type combo box. Analyze the signal using the DS Benchtop Spectrum Analyzer .

How many harmonics do you see now?

How many harmonics would it take to generate a true square wave by combining sine waves?

2.2.2 Sound

Speech and music are much more complicated waveforms with many frequencies presentat different power levels. In this part of the lab you will record some speech using themicrophone and sound card and will analyze these signals just as you did previously todetermine the frequency and power content.

Open the VI Sound Spectrum Analyzer . Buttons to start and stop recording are inthe top left corner. When recording, keep the duration short, under a few seconds, tokeep the processing time reasonable. Filtering, windowing and performing an FFT arecomputationally intensive.




Select None for the Window type and None for the Filter Model. Record a shortduration of yourself whistling. Start whistling before pressing record and hold the noteuntil after you have stopped recording. Try to hold the same note, don’t whistle a tune.Press the Record button then press the Stop button a couple of seconds later. The powerspectrum of your whistled note will be calculated and displayed in the lower graph. Oncedisplayed, you can change Window and Filter settings to attempt to enhance the spectrumanalysis. The Hann and Hamming windows work best for frequency resolution. Try a highpass filter type with the low cutoff frequency of 20 Hz.

What is the dominant frequency of your whistled note?

How did the power spectrum change as a result of different window and filter settings?

Record an impulse event by either gently tapping the microphone on the desktop orclapping your hands.

How did the spectrum change?

Was there a dominant frequency?

Play the audio file provided by your instructor and record a segment with the Sound Spectrum Analyzer .

Use what you have learned to identify and report the five dominant frequencies between 550 Hz and 2500 Hz present in the complex waveform.



Lab 3

Flow Rate Sensor Calibration

3.1 Introduction

The purpose of this lab is to produce calibration functions for a rotameter and a vortexshedding meter using a turbine flow meter as the calibration standard.

3.1.1 Rotameter

Principle of Operation

As illustrated in Figure 3.1, a rotameter operates on the principle of force equilibriumbetween the weight of an object pulling it down and a fluid dynamic drag pushing it up.The object is contained in a vertical tube of expanding diameter (small at the bottom,large at the top). When the object is on the bottom of the tube, it closes off the tube

entirely. When the object is at the top of the tube, there is a large clearance betweenthe object and the tube walls. Fluid flowing vertically through the tube pushes the object(called a slider) off of its seat, and pushes the slider up in the tube until the weight of the slider matches the drag on the slider (proportional to velocity squared). If the sliderwent higher, the clearance area would be greater, the velocity would be lower, the dragforce would be lower, and the weight force would pull the slider down. If the slider wentlower, the clearance would be lower, the velocity accelerated higher, leading to a drag forcegreater than the weight, and the slider would rise.

Operation

The tube is vertical, with an upward flow, so that the weight and drag will be oppositelyoriented. The tube is tapered in such a way (linear variation of diameter) that the heightof the slider is proportional to the flow rate through the meter. The tube is clear so thatthe slider position can be seen, and the tube is marked so that the slider position can bemeasured.

13



LAB 3. FLOW RATE SENSOR CALIBRATION 14

Flow

Flow

Figure 3.1: Operational diagram of a rotameter.

Data Reduction

The rotameter tube is marked in percentage of the maximum volumetric flow rate thatcan go through it. The maximum flow rate is marked on the manufacturer’s name plateattached to the device.

Uncertainty

The rotameter is rated by its manufacturer to have an uncertainty of 2% of its full scaleoutput.

3.1.2 Vortex Shedding Meter


The operation of a vortex shedding meter is illustrated in Figure 3.2. As fluid moves acrossa bluff body inserted in the flow stream, vortices are formed alternately from one side tothe other. The movement of the vortices across a sensing tube situated downstream fromthe bluff body causes it to vibrate at a given frequency. Inside the tube is a piezoelectricelement that creates a small voltage output when flexed. The frequency is proportional to




the velocity of the flow. This output is amplified and converted to a current signal rangingfrom 4-20 mA.

Operation

The signal output (in milliamps) is displayed through the multimeter.

Data Reduction

The current can be converted to a flow rate with

V =

V rangeI range

(I measured − I o) (3.1)

where,

˙V range = (25 − 2.1) gpm = 22.9 gpm (3.2)I range = (20 − 4) mA = 16 mA (3.3)

I measured = Measured Current (3.4)

I o = Offset Current (3.5)

Uncertainty

The accuracy of the vortex shedding meter is 1% of its designated full scale, while itrepeatability is 0.25% of the actual flow.

Small Vortex Strut Shed Vortices Receiving Transducer

Transmitting Transducer

Flow

Figure 3.2: Operational diagram of a vortex shedding meter.




3.1.3 Turbine Flow Meter


A turbine flow meter consists of a tube with a turbine wheel mounted inside. The turbinewheel is like a propeller with short, wide blades, which are just long enough to fill the tube.The turbine wheel rotates about the centerline of the tube. The turbine wheel spins onlow friction bearings, so that there is essentially no torque resisting its rotation. Torqueapplied to the blades is caused by an angle of attack between the flow direction relativeto the blades (a function of the blade rotational speed) and the orientation of the bladeitself. If there is a nonzero angle of attack, lift will result. This lift (causing an appliedtorque) will spin the wheel faster. Faster spin will decrease the angle of attack relativeto the moving blades. The turbine wheel will spin as fast as it must in order to keep theangle of attack at zero, since there is no resisting torque. The turbine wheel rotationalspeed is proportional to the velocity (and hence volumetric flow rate) of the fluid flowingthrough the tube. Therefore, if the rotational frequency of the wheel is measured by placing

a small magnet in one of the blades, whose passing frequency can be picked up with anelectronic frequency counter, then this frequency can be calibrated to the volumetric flowrate through the meter.

Operation

As illustrated in Figure 3.3, a magnetic pickup is mounted on the side of the turbine meter(similar in appearance to an electrical connector). The pickup converts magnetic pulses toelectrical pulses, which are transmitted down a cable and measured by a frequency counter.Some units have an industrial interpretation package mounted to them, which counts thefrequency and creates a voltage proportional to frequency for transmission to some remote

receiving station. In this case, conversion from voltage to frequency is an additional datareduction step.

Data Reduction

The frequency output by the turbine flow meter can be converted to a flow rate throughinterpolation of the values in Table 3.1.

Uncertainty

The turbine flow meter rated by its manufacturer to have an uncertainty of ±0.31% of the

actual value over the flow range of 1.25 to 9.00 gpm. in Figure 4.3

3.2 Experiment

3.2.1 Procedure

The flow loop consists of an accumulation tank of water, which feeds a centrifugal pump(driven by an electric motor), which feeds a line with three different flow meters installed




Rotor BearingsSupporting web

Pulse pick-up

Output to pulse counter

Flow

Figure 3.3: Operation diagram of a turbine flow meter.

Table 3.1: Interpolation data for turbine flow meter.

Frequency Flow Rate(Hz) (gpm)

28.09 0.30644.20 0.45062.61 0.62394.50 0.931

130.81 1.290199.43 1.963250.23 2.467442.92 4.360631.71 6.233909.61 9.009




in series. The flow passes through a rotameter, a turbine flow meter, and a vortex sheddingmeter.

Run the pump and open the upstream valve so that the rotameter reads about 80% of its maximum flow rate. Using the valve to adjust the flow rate, record the readings fromeach of the flow meters in Table 3.2.

Table 3.2: Measured values for flow sensor calibration.

Rotameter Turbine Flow Meter Vortex Shedding Meter(% of Max. Flow Rate) (Hz) (mA)

80

70

60

50

4030

40

50

60

70

80

Rotameter maximum flow rate (gpm)Vortex shedding meter offset current (mA)

3.2.2 Report

Using the turbine flow meter as the standard, follow the procedure in Appendix A to createa calibration curve for the rotameter and the vortex shedding meter. Plot each calibrationcurve as a deviation. Fit a linear regression line to each calibration curve. Comment on theappropriateness of the linear regression form. Report the calibration curve along with its

uncertainty. Compare the calibrated uncertainty to the manufacturer’s stated uncertainty,as completely as it is known or can be determined.1 Comment on any hysteresis present inthe readings.

1It may be necessary to propagate the uncertainties given by the manufacturer into the data reductionprocedure.



Lab 4

Passive Circuits

4.1 Introduction

In this lab, you will be building passive circuits and characterizing their behavior. Thebasic circuit will be a voltage divider. The different exercises are variations on this theme.The most important thing to gain is an understanding of how the choices for particular cir-cuit elements affect the voltage output, current draw, and power dissipation of the circuit.In the final exercise, you will build a common temperature measurement circuit based onlyon passive circuit elements.

Before coming to lab, be sure to complete and bring all the Pre-lab exer-cises.

Some equations that you will find useful in this lab are given below.

Ohm’s Law V = IR

Power P = IV = I 2R =V 2

RResistors in Series Req = R1 + R2 + . . . + Rn

Resistors in Parallel1

Req=

1

R1

+1

R2

+ . . . +1

Rn

or

Req =R1 × R2 × . . . × Rn

R1 + R2 + . . . + Rn

The thermistor used in this lab can be characterized by the following equation.

RT = R0 exp

β (T 0 − T )

T · T 0

(4.1)

19



LAB 4. PASSIVE CIRCUITS 20

where

RT = thermistor resistance (Ω)

R0 = specified resistance at temperature T 0, (Ω)

T 0 = reference temperature, (K )T = temperature, (K )

β = thermistor constant, slope of ln RT vs 1/T

4.2 Experiment

4.2.1 Breadboard

A breadboard is an organized arrangement of sockets which facilitates the construction of

prototype circuits. The layout of the breadboard is shown in Figure 4.1. This exercise is tofamiliarize you with the breadboard layout by making use of the most common applicationof using a digital multimeter (DMM) measuring resistance.

Figure 4.1: Layout of a typical breadboard

Set the multimeter to the 200 kΩ range setting (your meter may not have this specificsetting, use something of the same order, e.g. 100 kΩ). Actually any setting will work,however the results displayed can be misleading. Small range settings, 200 Ω for instance,aggravate the possibility of mistaking an out-of-range reading as an open circuit. Out-of-range readings appear as an open circuit on a DMM. Beware of open circuit readings whenusing a small range setting. Large range settings, 20 MΩ for instance, may actually displaya valid number however this too can be deceiving. Your body’s resistance may actuallymeasure a few mega ohms. In addition, it takes longer for the meter to settle on a finalreading at large range settings.

Insert probe tips into two adjacent holes on the breadboard (don’t force the probe tipif it is too large, insert a short piece of solid wire in the hole instead and measure through




it). Conductive paths are indicated by a short circuit (0.00 Ω). Nonconductive paths areindicated by an open circuit. These should be the only two readings present on an emptybreadboard.

Check the resistance across various points on the breadboard. You should begin to getan idea of how the conductive paths on the breadboard are arranged.

4.2.2 Voltage Divider

Pre-Lab Exercise

Using Ohms Law, predict the values of the output voltage, V o, and the current,I , for the circuit shown in Figure 4.2, when R 1 = 10 kΩ, R 2 = 10 kΩ, andV i = 10 Vdc. What will be the total power dissipated by the circuit. How muchpower do you expect to be dissipated by each resistor.

V o =

I =

P tot =

P R1=

P R2=

R1

R2 V o

V i

I

Figure 4.2: Voltage divider circuit.

In-Lab Exercise

Resistors are typically labeled based on their nominal resistance. However actual resistancevalues of a resistor will vary depending on the tolerance of the resistor. Measure tworesistors labeled as 10 kΩ.




How will the difference between the actual resistance and the nominal values affect the voltage output V o?

Build the circuit in Figure 4.2 using V i = 10 Vdc and R1 = R2 = 10 kΩ. Measure theactual loop current and V o using a DMM and record the results in Table 4.1.

Replace R1, R2, and V i with the values in Table 4.1 and record the results for eachchange in Table 4.1.

Table 4.1: Experimental values for voltage divider circuit.

Target V i 10 V 1 V

Actual V iV o (V)

R1 10 kΩ 100 kΩ 10 kΩ

R2 10 kΩ 100 kΩ 10 kΩ

I (mA)

4.2.3 Circuit Loading

One of the limitations of the voltage divider is that it is sensitive to loading effects. Placingadditional components in parallel with R2 affects the voltage output. In the circuit shownin Figure 4.3, R3 is in parallel with R2. V o is the voltage across both of these resistors. If R3 R2, then the effect is negligible. However, when R3 is comparable to R2, then theeffect can be substantial.

R1

R2 R3 V o

V i

I

Figure 4.3: Voltage divider circuit with two resistors in parallel.




Pre-Lab Exercise

Using Ohm’s Law, predict the voltage output, V o, of the circuit shown in Fig-ure 4.3 when V i = 10 Vdc, R 1 = R 2 = 10 kΩ and R 3 = 10MΩ. Note that thetotal resistance R T = R 1 +R eq where R eq is the equivalent resistance of R 2 and

R 3 in parallel.

V o =

In-Lab Exercise

Build the circuit shown in Figure 4.3 with R1 = R2 = 10 kΩ. Keeping the input voltageV i = 10 V, measure the output voltage, V o, when values of R3 are those found in Table 4.2and record the values there.

Table 4.2: Experimental values for loaded circuit.

Target V i 10 V

Actual V i

V o (V)

R1 10 kΩ

R2 10 kΩR3 10 MΩ 10 kΩ 1 kΩ

4.2.4 Input Impedance

When making measurements of a circuit, the multimeter becomes a part of the overallcircuit. To measure the resistance of a resistor for example, the multimeter supplies a smallconstant current through the resistor and measures the voltage across the resistor. Becauseof this current, the resistor heats up due to I 2R heating. The resistor’s actual resistance

varies with temperature and thus the very act of measuring the resistance affects thevalue measured. Since the supplied current and the temperature coefficient of the resistorare typically very small, the error introduced by making the measurement is typicallynegligible. Under certain conditions however, the effect must be taken into consideration.In the voltage divider exercise in Section 4.2.2, for example, if R1 = R2 = 10 MΩ, then themultimeter would have loaded the circuit and affected the output voltage. In this exerciseyou will determine the input resistance (impedance) of the multimeter.




In-Lab Exercise

Place the DMM in series with R1, as shown in Figure 4.4, such that R2 from the voltagedivider circuit is equal to the input resistance of the DMM. Measure the voltage using theDMM when R1 = 10 kΩ, R1 = 100 kΩ, and R1 = 1 MΩ with V i = 10 Vdc, and record your

results in Table 4.3.

DMM

R1

I

V i

RDMM

Figure 4.4: A resistor in series with a digital multimeter.

Table 4.3: Experimental values for voltage drop across a DMM.

Target V i 10 V

Actual V i

V o (V) 9.9 5

R1 10 kΩ 100 kΩ 10 MΩRDMM

Using the V o measurements in Table 4.3, calculate the input resistance of the DMM,RDMM , for each value of R1 and record your results in Table 4.3.1

Now that you know the input resistance of the DMM, what is the error introduced when making the original measurement in Section 4.2.2 when R1 = R2 = 10 kΩ?

1For this case it is necessary to use the actual (measured) voltage being supplied when performing thecalculation, i.e. it is not sufficient to estimate V i to be 10 V if it is actually 9.99 V.




What if R1 = R2 = 10 MΩ?

4.2.5 Thermistors

Thermistors are resistors that are extremely sensitive to temperature. Thermistors areavailable with either a positive temperature coefficient (PTC) or negative temperaturecoefficient (NTC). NTC thermistors are commonly used in temperature measurement de-vices while PTC thermistors are commonly used to limit a current by acting as a thermalfuses. In this exercise you will build a temperature measurement circuit based on an NTCthermistor, as shown in Figure 4.5.

R1

RT V o

V i

I

Figure 4.5: Thermistor voltage divider circuit.

Pre-Lab Exercise

Using Eq. (4.1), derive an expression for the temperature as a function of V o,V i, and R 1. Generate a graph of temperature versus V o for the temperaturerange 25 to 85C over which the β value is specified. Use nominal values of V i = 1 Vdc and R 1 = 10 kΩ.2

T (V o, V i, R1) =

2When performing the calculations, use the values from Table B.1 on page 76 for type number RL1005-5744-103-K.




In-Lab Exercise

Build the voltage divider circuit, shown in Figure 4.5, using V i = 10 Vdc, R1 = 10 kΩ anduse the 10 kΩ thermistor P/N RL1005-5744-103-K for RT . Measure the voltage across thethermistor, V o, and convert the voltage to a temperature using the equation derived in the

pre-lab exercise. Record your results in Table 4.4.nSelf-heating, or Joule-heating, caused by the power being dissipated by the thermistor,

introduces an error into the temperature measurement. The temperature rise due to self-heating, ∆T , is related to the power dissipated by the thermistor, P T , by the dissipationconstant, δ , given in Table B.1 on page 76. Calculate the increase in the thermistortemperature due to self-heating (do not directly measure the current, but rather use thevoltage measurement to derive the current flowing through the thermistor) and record yourresults in Table 4.4.

What could be done to reduce the error due to self-heating?

Reduce the input voltage V i to 1 Vdc. Measure the voltage across the thermistor, V o,and convert the voltage to a temperature using the β value in the data sheet. Recordyour results in Table 4.4. Use the voltage measurement to calculate the current flowingthrough the thermistor. Record the amount of I 2R heating and the increase in thermistortemperature in Table 4.4.

Table 4.4: Experimental values for voltage drop across a DMM.

Target V i 10 V 1 V

Actual V i

V o (V)

T (C)

P T (mW)

∆T (C)

Pinch the thermistor between your fingers and hold until the voltage output stabilizes. What

is the temperature? Why is it not 98.6

F?



Lab 5

Active Circuits

5.1 Introduction

In Lab 4, a 1 Vdc supply voltage across the thermistor voltage divider generated a maximumoutput of 0.5 Vdc at 25C. Now suppose that we would like to measure and record thisthermistor voltage with a data acquisition system. The data acquisition system will havea limited number of input voltage ranges, possibly only one voltage range. In order tomaximize the resolution of the sensor signal, we would like to match the voltage outputrange of the sensor signal to the voltage input range of the data acquisition system. Inaddition, if the sensor is located in an electrically noisy environment, then we would liketo remove as much of the noise as possible.

Op amps provide the means to meet these goals. Op amps are widely used to conditionsensor signals so that they may meet the design requirements. In this lab, you will constructthe circuitry shown in Figure 5.1 to condition the thermistor sensor signal. The design goalsof this lab are:

• keep the self-heating error of the thermistor less than 0.1 K,

• maximize the use of a 0 to 5 V input range of a data acquisition system, and

• remove any 60 Hz (or greater) line noise picked up by the sensor signal.

The circuit shown in Figure 5.1 can be thought of as a series of building blocks thatultimately gives the desired output. We will build the circuit one section at a time in orderto gain a better understanding of how the overall circuit achieves the design goals.

27



LAB 5. ACTIVE CIRCUITS 28

V o

1 0 0 k Ω

1 0 k Ω

1 0 k Ω

1 0 k Ω

T h e r m i s t o r

1 0 k Ω

1 2 k Ω

3 3 k Ω

3 3 k Ω

0 . 1 µ F

0 . 1 µ F

1 0 0 k Ω

1 5 k Ω

3 3

k Ω

3 3 k Ω

0 . 1 µ F

0 . 1 µ F

1 0 k Ω

1 2 k Ω

3 3 k Ω

1 0 0 k Ω

+ 1 1 V

F i g

u r e

5 . 1

: C i r c

u i t

u s e

d t o

a m p

l i f y a

t h e r m

i s t o r r e a

d i n g

a n

d fi l t e

r o u

t n o

i s e .




Although it is not shown in the circuit, power connections are required for the op ampsto work. Each chip has a V + and a V − connection to supply power to the op amps. Youwill need to make this connection for each chip used in building this circuit. Consult thepinout diagram in Figure B.1 on page 74.

Adjust the voltage supply until you have both +11 V and -11 V coming from thesupply to the connectors. Turn the power off and connect the +, -, and GND connectionsto the breadboard area. Use the long rows on both sides of the breadboard for these powerconnections. You will want to turn the power off when making circuit connections butdon’t forget to turn the power on when making your measurements.

Troubleshooting: Work out all of your section gains and answer the questions in eachsection ahead of time so that you know what to expect after each section of circuitry.Check your voltage output after each section to verify that it is working properly. You canuse the reference voltage generated in the first part of this lab to feed into the inputs of the succeeding sections. Replace the thermistor with a 10 kΩ resistor. This will providea more stable reference voltage for comparison while building the circuit. Once all the

sections have been built and are working properly, insert the thermistor into the correctplace for taking the final measurements.

5.2 Experiment

5.2.1 Reference Voltage

The thermistor circuit developed in the previous lab used a supply voltage of 1 V tominimize the self-heating by the thermistor. In this lab, the voltage supply will be set muchhigher to power the op amps that will be used to condition the signal. The thermistor could

either be powered from the higher voltage supply and large self-heating error tolerated or alower voltage reference could be developed for the thermistor and maintain the much lowerself-heating error. In this lab you will generate a low voltage (stiff) reference from the highvoltage “rail” supplies.

Since only one split voltage power supply is available, the rail supply, a circuit willhave to be developed to generate the thermistor supply voltage. A “stiff” voltage referencecan be constructed from a voltage divider that is buffered. Recall from the previous labthe effect of loading the output of the voltage divider. Loading with a single low resistanceresistor reduced the output voltage of the divider. A buffer element will eliminate thisloading effect. A “follower” circuit attached to the output of the voltage divider has theproperty of very high input impedance and very low output impedance. The follower will

not load the divider circuit. The divider circuit is buffered from any additional circuitryattached beyond the follower.

The rail supply voltage for the entire circuitry will be ± 11 Vdc. Build the circuitshown in Figure 5.2. This circuit provides a voltage reference for the thermistor dividercircuit. Measure the value of the voltage reference, V ref to determine the gain of this circuitand record your value in Table 5.1.




100 kΩ

10 kΩ

+11 V

V ref

Figure 5.2: Diagram of a voltage divider and a follower circuit used to create a 1V referencevoltage.

5.2.2 Thermistor

Now that a steady voltage reference has been developed, the thermistor portion of the

circuit can be reconstructed. Build the thermistor circuit shown in Figure 5.3, only nowuse the output of the voltage reference block to power the thermistor circuit.

Place a follower op-amp on the output of the thermistor voltage divider circuit tostiffen the output, V therm, for additional signal conditioning circuitry. Measure the gain of this block of circuitry and record your value in Table 5.1.

Find an equation that describes temperature as a function of V therm over the range of 25 to85C. (This should be the similar to equation that was derived in Lab 4.)

T (V therm) =

5.2.3 Initial GainWorking within the limitations of our component selection, an initial gain block is requiredto achieve the overall desired gain. This block of circuitry provides a small amount of gainthat will boost the thermistor voltage before additional signal conditioning.

V therm10 kΩ

10 kΩ

Thermistor

V ref

Figure 5.3: Diagram of a voltage divider and a follower circuit used to buffer the readingfrom the thermistor.




Construct the inverting circuit configuration shown in Figure 5.4. Attach the outputof the previous section (thermistor block) to the input of this section. Measure the gain of this section of circuitry and record your value in Table 5.1.

10 kΩ

12 kΩ

V G1

V therm

Figure 5.4: Inverting amplifier circuit.

5.2.4 Active Filter

This section of circuitry is used to remove any external noise that may have been coupledonto the signal. A very common source of noise is the 60 Hz line frequency of AC circuitry.Routing the sensor signal lines near an AC power line can easily cause the line noise to bepicked up by the sensor signal.

The filter shown in Figure 5.5 is a 4 pole low-pass Butterworth filter. Componentvalues have been selected so that the cut-off frequency is below 60 Hz so that only lowfrequency signals will pass through. The actual 3db cutoff frequency for this circuit is f c

= 48.2 Hz. Frequencies greater than f c are greatly attenuated.

33 kΩ 33 kΩ

0.1 µF

0.1 µF 100 kΩ

15 kΩ

33 kΩ 33 kΩ

0.1 µF

0.1 µF 10 kΩ

12 kΩV G1

V BWF

Figure 5.5: Four pole low-pass Butterworth filter.




Two op amps are used successively in the non-inverting configuration. The first opamp provides a gain of 1.15 while the second provides a gain of 2.2. Measure the overallgain of this section and record your value in Table 5.1.

5.2.5 Final GainThis section of circuitry will again invert the incoming signal and provide a final boost toachieve the desired overall gain. This section is similar to the Initial Gain Section, howeverthe section gain is different.

Construct the circuitry shown in Figure 5.6 for the final gain section. Measure thissection’s gain and record your value in Table 5.1.

33 kΩ

100 kΩ

V BWF

V o

Figure 5.6: Inverting amplifier circuit.

Table 5.1: Experimental values for thermistor amplification and filtering.

Section Ideal Gain Measured Gain

Initial Gain Section

Active Filter Section

Final Gain Section

Ideal V ref (V)

Measured V ref (V)

Measured V therm (V)




5.2.6 Final Questions

What is the calculated overall gain of the signal conditioning circuitry? Start at the output of the thermistor section and calculate the overall gain of the thermistor signal through the signal conditioning circuitry. Remember gain is simply V o/V i.

What is the equation that describes temperature as a function of V o?

What is the output voltage of the circuitry?

What temperature does this voltage correspond to? Does this make sense? If not, recheck your equations and your circuit.



Lab 6

Digital to Analog Conversion

6.1 Introduction

In this lab some basic concepts about digital mathematics and conversion to analog willbe explored. The digital-to-analog converter, known as the D/A converter (read as D-to-A converter) or the DAC, is a major interface circuit that forms the bridge between theanalog and digital worlds. DACs are the core of many circuits and instruments: includingdigital voltmeters, plotters, oscilloscope displays, and many computer-controlled devices.This lab examines the basics of binary representation, binary algebra, Boolean logic gates,and digital-to-analog conversion.

6.2 Exercises

A DAC is an electronic component that converts digital logic levels into an analog voltage.The output of a DAC is just the sum of all the input bits weighted in a particular manner:

DAC =N i=1

wibi

where

wi = weighting factor

bi = bit value (1 or 0)

i = index of the bit number

In the case of a binary weighting scheme, wi = 2i. Therefore the complete expression foran 8-bit DAC is written as:

DAC = 128b7 + 64b6 + 32b5 + 16b4 + 8b3 + 4b2 + 2b1 + 1b0

34



LAB 6. DIGITAL TO ANALOG CONVERSION 35

Convert the decimal number 251 to binary.

Convert the binary number 10100011 to decimal.

6.2.1 Binary Addition

Perform the following binary addition operations. Check your answer by converting each

binary number to its decimal equivalent then adding the decimal numbers. Show yourwork.

00011001 → 00111100 →+01111000 → + +11000011 → +

→ →

6.2.2 Boolean (Logical) Operators

Boolean logical operators are fundamental to digital technology. The operators dealt withhere are AND, OR, XOR (exclusive OR), NAND, NOR, and NXOR gates. These digitalcomparators give a logical result (On or Off) based on two logical inputs. Complete thetruth table in Table 6.1.

Table 6.1: Logic gate truth table.

Gate Case 1 Case 2 Case 3 Case 4

Type 0 0 0 1 1 0 1 1

AND

OR

XOR

NAND

NOR

NXOR




6.2.3 DAC Circuit

The circuit shown in Figure 6.1 can be used to convert a digital signal into an analogoutput. Since the op-amps require ± 11 Vdc, the supply voltage will first be stepped downwith a voltage divider. A follower circuit will then be used to provide a hard reference

voltage, V ref .Current will be allowed to flow through one or more of the branches by closing one

or more of the switches. The voltage drop across each branch will be the same, so eachbranch will always contribute the same current if its switch is closed regardless of the stateof the other branches.

The current flowing into the node connected to the non-inverting input of the secondop-amp will have to go through the 5kΩ gain resistor. Therefore, closing additional switcheswill cause additional current to flow through the gain resistors which will cause the valueof the output voltage, V o, to rise.

The current flowing through the 128 kΩ branch will be smaller than the current flowingthrough the other branches; therefore the 128 kΩ branch will correspond to the leastsignificant bit (LSB) of the binary representation of the state of the switches.

Build the circuit shown in Figure 6.1 and use it to fill in the values in Table 6.2.

-11 V

100 kΩ

10 kΩ

V ref

1 kΩ

2 kΩ

4 kΩ

8 kΩ

16 kΩ

32 kΩ

64 kΩ

128 kΩ

5 kΩ

V o

Figure 6.1: Digital to analog conversion circuit




Table 6.2: Experimental digital to analog conversion values.

Binary DecimalIdeal V o (V) Measured V o (V)

Representation Representation

00000000

00000001

00000010

00000100

00001000

00010000

00100000

01000000

10000000

11111111

01011010

135

5.546875

Ideal V ref (V)

Measured V ref (V)



Lab 7

Pressure Sensor Calibration

7.1 Introduction

The purpose of this lab is to produce calibration functions for a bourdon tube dial pressuregauge and a membrane pressure transducer using a dead weight tester as the calibrationstandard.

7.1.1 Dead Weight Tester


A deadweight tester is a pumping device for forcing oil into a closed piping or tubingnetwork in order to increase the pressure of the oil. Oil is pumped out of a reservoir andinto the network using a hand lever. The oil cannot flow back into the reservoir because it

is blocked by a check valve. There is a bleed valve leading from the network back to thereservoir, bypassing the check valve, so that the pressure in the network may be decreasedby opening the bleed valve. Fine adjustments may be made using a screw which slightlyincreases or decreases the volume of the network, which slightly decreases or increases thepressure. On the network side of the tester is a piston, on which weights may be placed.If the piston has risen off of its supports, then the pressure at the bottom of the piston isthe total of the weights and the weight of the piston divided by the area of the piston. Anillustration of a dead weight tester is shown in Figure 7.1.

Operation

The weight of the piston is 0.5 lbs. and the area of the piston is 0.1”. Load weights on thepiston until the desired pressure is set. Pump the tester until the piston just begins to riseoff of its support. Use the bleed valve and fine adjustment screw to bring the piston to thepoint where the top line is barely visible. Do not over pump, as this may cause the pistonto disengage from the tester. The bleed valve does not have to be closed tightly. This is afine valve, and only needs light finger pressure to close it. Excess tightening will damagethe bleed valve. The neutral position of the fine adjustment screw is halfway up. There isno need to screw it either all the way in or all the way out.

38



LAB 7. PRESSURE SENSOR CALIBRATION 39

Fine Adjust Screw

F = m · g

P system

Figure 7.1: Operational diagram for a dead weight tester.

Data Reduction

The deadweight pressure, weight divided by area, is a gage pressure. The elevation of this pressure is at the face of the piston, which is level with the collar about 3” down onthe sleeve in which the piston slides. When calibrating another pressure gauge with thedeadweight tester, it is necessary to consider the difference in elevation between the faceof the piston and the other gauge. AAA tester oil is generally used, which has a specificgravity of 0.88 at room temperature.

Uncertainty

The manufacturer of the deadweight tester claims an uncertainty of 0.1% of the reading ingage pressure. However, if the deadweight tester is being used as a calibration standard,then its uncertainty must be taken as zero.

7.1.2 Bourdon Tube Dial Pressure Gauge


A bourdon tube is a tube of oval cross section which is bent into a circular arc, wherethe minor axis of the oval lies in the plane of the arc. When the inside of the tube isexposed to a pressure, the tube has a tendency to unbend. The amount of unbending isproportional to the inside pressure. The tip of the unbending tube is geared to a dial,and so the deflection of the dial is proportional to the applied pressure. A zero deflectionimplies a zero difference between the pressures internal and external to the tube. Since




the external pressure is generally atmospheric pressure, these devices read directly in gagepressure. An illustration of a bourdon tube is shown in Figure 7.2.

Inlet

Low PressureCross Section

High PressureCross Section

Figure 7.2: Operational diagram of a bourdon tube pressure gauge.

Operation

Before exposure to elevated pressure, adjust the zero of the gauge (if there is a zero adjust).Be sure that the bourdon tube inlet is freely exposed to the pressure of interest, and thatthere are no leaks.

Data Reduction

The bourdon tube pressure gauge is an analog dial gauge which reads directly in pressure.When reading the pressure from the dial, do not estimate between the tick marks.

UncertaintyReputably manufactured bourdon tube pressure gauges, which have not gone out of cali-bration, have an uncertainty equivalent to their display uncertainty.




7.1.3 Membrane Pressure Transducer


A membrane pressure transducer is comprised of an upper chamber and a lower chamber,separated by a membrane. When the pressure in one chamber exceeds that in the other,the membrane deflects towards the other chamber. A strain gauge is mounted on themembrane, so that as the membrane deflects and stretches, the strain gauge is stretched.The output of the strain gauge is a function of the difference in pressure between chambers.If the low pressure chamber is at atmospheric pressure, then the strain gauge indicates gagepressure. If the low pressure chamber is held at a vacuum, then the strain gauge indicatesabsolute pressure. An illustration of a membrane pressure transducer is shown in Figure 7.3.

P 1

P 2

P 1

P 2

P 1

P 2

P 1 < P 2 P 1 > P 2

Diaphram

UpperChamber

StrainGages

LowerChamber

Figure 7.3: Operational diagram of a pressure membrane transducer.

Operation

This lab uses pressure transducer type 746 manufactured by Precise Sensors, Inc. Eachtransducer has a model number in the format 746-50-A-P. The 50 refers to the range inpsi. The range is necessary for data reduction. If the transducer is exposed to a pressuredifferential greater than the top of its range, then the strain gauge may separate fromthe membrane, necessitating costly repair. The A defines the transducer as an absolutepressure device; i.e., the low pressure chamber is a sealed vacuum (if A were replaced byG, it would be a gage pressure transducer, and the other chamber would be exposed to

atmospheric pressure). Each transducer has a serial number, and each has been calibrated.The calibrated sensitivities are given in Table 7.1.

Membrane transducers of this type are passive devices, meaning that they do notgenerate a signal by themselves (the converse would be active, where a signal is generatedby the device). Therefore, an activation voltage must be applied to the transducer. For allof the above transducers, the nominal activation voltage is 5 Vdc.

The activation voltage is generated by a power supply. Connect the power supplyto a voltmeter and adjust the power supply voltage to the correct activation voltage by




Table 7.1: Sensitivity values for membrane transducer

Model No. Serial No. Sensitivity (mV/V)

746-50-G-P 21360 10.353

746-50-G-P 21361 9.423746-50-A-P 25592 10.123746-50-A-P 21673 10.216746-50-A-P 25695 10.294746-50-A-P 26287 10.378746-50-A-P 26288 10.288

746-200-A-P 26289 9.938746-200-A-P 26290 10.097746-200-A-P 25712 9.771746-200-A-P 25713 9.888

746-200-G-4P 46462 10.254

watching the voltmeter output, instead of by watching the hard-to-read dial on the frontof the power supply. The voltmeter reading is the actual activation voltage. The powersupply must be adjusted so that the actual activation voltage is 5 V ±0.01 V. Then connectthe power supply and voltmeter to the transducer. There are four lead wires passing out of the transducer body. The red and black wires are, respectively, the positive and negativeconnections for the activation (or excitation, or input) voltage. The green and white wiresare, respectively, the positive and negative connections for the signal (or output) voltage.

The signal produced by the transducer is voltage (usually mV) across the signal leads,which is proportional to the resistance of the strain gauge, which is proportional to the

strain of the strain gauge, which is proportional to the interchamber pressure differential.Deflection type devices (including both the strain gauge and the membrane itself) are

notoriously subject to zero drift. Therefore, it is necessary to measure the output of thetransducer at one known pressure each time it is used. This known pressure is usuallyatmospheric pressure at the time and location of the transducer operation, which must bemeasured using another pressure measurement device.

Data Reduction

The measured pressure is to the pressure range of the transducer as the measured signalvoltage is to the voltage range of the strain gauge. Therefore the data reduction formula is

P = P range ·V measured

V range(7.1)

where P is the measured pressure, P range is the pressure range of the transducer (fromTable 7.1), V measured is the voltage output by the transducer, and V range is the voltagerange,

V range = V activation · Sensitivity (7.2)




where V activation is the activation voltage and Sensitivity is the sensitivity of the transducer,which can be found in Table 7.1.

Uncertainty

The membrane pressure transducer, with locally measured offset, is most sensitive to lin-earity error. The manufacturer claims this to be 0.1% of full scale output, which shouldbe regarded as the uncertainty in the measured voltage. The uncertainty of the pressurerange may be taken as 0.5 psi, the sensitivity as 0.0005 mV/V, and the activation voltage asexperimentally determined by observing the voltmeter. The uncertainty of the known pres-sure for offset determination is the uncertainty in the atmospheric pressure measurementfor absolute pressure, and is zero for gage pressure.

7.1.4 Mercury Barometer


A mercury barometer consists of a mercury reservoir and a glass tube with one closedend and one open end. The glass tube is filled with mercury, the open end of the tubeis submerged in the reservoir, and the tube is oriented vertically. As gravity pulls themercury down the glass tube, a vacuum is created at the closed end. The height of themercury column will continue to change until the weight of the mercury column above thereservoir level exerts the same force per unit area as the atmospheric pressure. The heightof the column can then be used to determine the atmospheric pressure. An illustration of a mercury barometer is given in Figure 7.4.

OperationA Vernier scale is mounted to the glass tube which can be used to measure the height of themercury column. However, as the atmospheric pressure increases, mercury will flow fromthe reservoir into the tube, which causes the height of the mercury column rise and thelevel of the reservoir to drop. Since the height of the mercury must be measured relativeto the reservoir, it is necessary to ensure that the length scale starts at the same heightas the surface of the reservoir. This is achieved by using the thumb screw at the bottomof the barometer to raise or lower the reservoir. There is a downward pointing white conethat designates the started of the length scale. Adjust the height of the reservoir so thatthe tip of the white cone just touches the surface of the reservoir.

Data Reduction

The height of the mercury can be determined by reading the Vernier scale mounted to thetube.




Table 7.2: Measured values for pressure sensor calibration.

Dead Weight Tester Bourdon Tube Membrane Transducer(psi) (psi) (mV)

0

10

20

30

40

50

60

70

80

90

100

90

80

70

6050

40

30

20

10

0

Membrane Transducer Model Number

Membrane Transducer Serial Number

Atmospheric Pressure (inHg)




7.2.2 Report

Using the dead weight tester as the standard, follow the procedure in Appendix A to createa calibration curve for the bourdon tube and the membrane transducer. Use the mercurybarometer to convert the dead weight tester data to absolute pressures prior to calibrating

the membrane transducer. Plot each calibration curve as a deviation. Fit a linear regressionline to each calibration curve. Comment on the appropriateness of the linear regressionform. Report the calibration curve along with its uncertainty. Compare the calibrateduncertainty to the manufacturer’s stated uncertainty, as completely as it is known or canbe determined.1 Comment on any hysteresis present in the readings.

1It may be necessary to propagate the uncertainties given by the manufacturer into the data reductionprocedure.



Lab 8

PID Controls

8.1 Introduction

A control system is defined as an interconnection of components forming a system config-uration that will provide a desired system response. In your everyday life, you regularlyencounter control systems. The temperature control in your home, the cruise control onyour car, and the automatic door opener at the supermarket are a few common examples.

A controller may be a simple input-output relation, as shown in Figure 8.1. This iscalled open-loop control. A reference position is dialed into the controller and works itsway through the dynamics of the system being controlled to achieve some output. Suchcontrol designs work very well if the dynamics of the system (or plant) are well known andexternal disturbances are minimal.

Battery

dcamplifier

Turntable

dc motor

Speed

SpeedSetting

(a)

Control Device Actuator Process

Amplifier dc motor TurntableActualSpeedDesiredSpeed

(b)

Figure 8.1: Example of an open loop control system.

Most often, however, the dynamics of the plant are not known exactly (or may tend tovary over time) and external disturbances are significant. Such systems require interaction

47



LAB 8. PID CONTROLS 49

The equation that governs the tank level is based upon conservation of mass and theassumption that the liquid in incompressible.

ρAH = mo + ρV i − ρV o (8.1)

Dividing through by ρ and differentiating both sides with respect to time gives the rateequation:

C dH

dt= q i − q o (8.2)

where C = A (constant for a cylindrical tank) is the tank capacitance,

q i =dV idt

(8.3)

Generally, the outflow is a function of the water level, H . For the simulations in this lab,the outflow will be defined as

q o = H · 2 m2/s. (8.4)

Substituting Eqs. (8.3) and (8.4) into Eq. (8.2) gives

dH

dt=

1

C q i −

2 m2/s

C H (8.5)

The time constant for this system is then τ = C · 0.5 s/m2

8.2.1 Open Loop System

Set the leak rate to zero and the inflow rate to 50 m3/s. Start the simulation and open theoutflow valve.

Predict the steady state level of the fluid in the tank using Eq. ( 8.5 ).

Describe what is observed to happen to the fluid level. Does the steady level match your prediction?

From the observed tank level versus time plot, determine the system time constant.




Set the leak rate to 3 m3/s. Restart the simulation and open the out-flow valve.

Describe what happens to the tank level once the leak rate has been set.

This exercise is meant to illustrate one of the basic issues associated with feedbackcontrol systems. If no outside disturbances occur, or if they are completely known, thena simple open-loop system will adequately maintain the desired behavior, a steady tank level . That is, the inflow just offsets the outflow. However, this is not generally the case.If the leak rate is variable, or unaccounted for, the fluid level will not be steady. One wayof dealing with this issue is with a closed-loop system.

8.2.2 Closed Loop System with Proportional Feedback Only

Set the leak rate to zero and choose a non-zero value for the proportional feedback gain.Restart the simulation and turn on the outflow valve.

What happens to the liquid level in the tank?

Repeat this process with higher and lower values for the proportional feedback gain.

What happens when the proportional feedback gain is increased?

What happens when it is decreased?

Find the proportional gain that will reach steady state the quickest without oscillationin the state of the valve and restart the simulation.

What is the system time constant, as determined from the tank level versus time plot.




How does this compare to the open loop time constant calculated earlier?

Set the leak rate to 3 m3/s and restart the simulation.


You should see that the tank level reaches a steady level below that observed when theleak rate was zero. For this first order dynamic system, a closed-loop proportional controlserves to maintain a steady (and non-zero) fluid level. But, there is a steady state errorbetween the desired level and the actual level. One way of dealing with such problems isthe addition of an integral control term to the feedback controller.

8.2.3 Closed Loop System with Proportional and Integral Feed-back

Set the leak rate to zero, use the previously determined proportional feedback gain, andchoose a non-zero value for the integral feedback gain. Restart the simulation and openthe outflow valve.


How long does it take for the error between the desired value and the actual (measured value) to decrease to less than 2% of the desired steady state value?

Repeat this process with higher and lower values for the integral feedback gain.

What happens when the integral feedback gain is increased?



Lab 9

Temperature Sensor Calibration

9.1 Introduction

The purpose of this lab is to produce calibration functions and calibrated uncertainties forfour types of temperature sensors, using a platinum resistance temperature detector (RTD)as the calibration standard. The sensors to be calibrated are:

• a liquid bulb thermometer,

• a bimetallic strip thermometer,

• a thermistor, and

• a k-type thermocouple.

9.1.1 Liquid Bulb Thermometer


A liquid bulb thermometer operates on the principle of thermal expansion of liquids. Thetotal volume of liquid mercury (or any other liquid) in an evacuated enclosure is a relativelylinear function of the temperature of the liquid bulb. The enclosure is comprised of both abulb and a capillary tube. The capillary is very small and serves to amplify any volumetricchange in the liquid volume of the mercury. Any expansion/contraction of the mercurytube is graduated (linearly) and the height of mercury in the tube is calibrated againsttemperature when only the bulb is immersed (in most cases). Slight corrections can be

made for readings where the tube is also immersed.

Operation

Expose only the bulb to the medium being measured.

53



LAB 9. TEMPERATURE SENSOR CALIBRATION 54

Data Reduction

The graduation marks on the capillary tube indicate temperature directly. Do not attemptto approximate readings between the marks. Simply choose which mark is closest to thetop of the meniscus and record the temperature.

Uncertainty

The uncertainty in a research grade liquid bulb thermometer is equivalent to its displayuncertainty if properly calibrated.

9.1.2 Bimetallic Strip Thermometer


A bimetallic strip thermometer operates on the principle of thermal expansion of solids

exploiting the difference in the thermal expansion coefficient of differing metals. In abimetallic strip thermometer two different materials are bonded together. Since the metalshave distinctly different coefficients of thermal expansion one material will attempt toexpand more than the other as the device is heated. This will cause a deformation fromthe reference position, as shown in Figure 9.1. In the case of bimetallic strip thermometersthe composite strip is preformed into a coil in which heating the device will cause the coilto unwind and cooling will cause the coil to contract. A dial is attached to the coil, whichmoves relative to a scale as the coil winds and unwinds. Notice the linearity of the scale.

Figure 9.1: Bonded metals with different coefficients of thermal expansion will warp whenheated.




9.1.4 Platinum RTD


A platinum RTD operates on the principle that as the temperature of a metal changes,so does the electrical resistance. RTDs are comprised of a thin metal wire, usually woundin a coil (to increase the overall length of exposed wire) which is encased in a probe.Platinum RTDs are relatively rugged since the metallic element is not brittle. RTDs aresimilar to thermistors that use a semiconductor resistance element in place of the RTDsmetallic resistance element. The metallic element is less sensitive to temperature changesand therefore often less accurate than the semiconductor device; however, RTDs are usuallymore rugged that thermistors.

Operation

The electrical resistance of the RTD element wire is measured using an ohmmeter while the

end of the probe (where the platinum wire is wound) is in contact with the temperaturefield of interest.

Data Reduction

RTDs are often packaged with a readout device, which contains an ohmmeter and othersignal conditioning hardware such that the temperature is displayed directly.

Uncertainty

The uncertainty of the RTD used in this laboratory is equivalent to the display uncertaintyof the readout device.

9.1.5 Thermocouple


Under a physical mechanism known as the Seebeck effect, two dissimilar metal wires joinedtogether end-to-end produce a very small voltage source at the junction. This voltageis temperature dependent. Therefore, by immersing the junction in the temperature of interest, measuring the voltage between the two free ends of the dissimilar metal wires,and using calibration data for the two particular metals at the junction, temperature maybe measured. Unfortunately, there is also a Seebeck effect voltage at the junction betweenthe thermocouple lead wires and the voltage measuring device. To distinguish only thatvoltage at the wire junction, there must be a second, and possibly third, junction heldat a known (reference) temperature. The voltmeter Seebeck effects are then canceled,and the temperature at the non-reference junction may be determined. An example of athermocouple with cold junction compensation is shown in Figure 9.2.




Metal A

Metal B

Metal C

Ice BathCold

Junctions

HotJunction

Figure 9.2: Operational diagram of a thermocouple.

Operation

Submerge the thermocouple probe in the medium being measured and attach the plug toa thermocouple reader.

Data Reduction

The voltage generated by the thermocouple is converted into a temperature by the readoutdevice. The screen output will be in C.

Uncertainty

K-type thermocouple wire is manufactured to a standard uncertainty of 2 .2C or 0.75%of reading (in C relative to the reference temperature), whichever is greater. Uncertaintyof the signal conditioning within the readout device may be taken as insignificant to the2.2C wire/bead uncertainty.

9.2 Experiment

9.2.1 Constant Temperature Water Bath OperationThe temperature sensors will be calibrated in a circulating water bath with an incorporatedheating and cooling system. A pump causes water to be pulled into the Inflow port andpushed out of the Outflow port. The circulation of the water aids in mixing and helps tokeep the bath nearly isothermal. The control unit heats or cools the water as necessary toreach a desired set point.



Lab 10

Load Cell Use and Instrumentation

10.1 Introduction

The purpose of this lab is to understand proper use techniques and instrumentation of loadcells and the instrumentation used in conjunction with them.

10.1.1 Theory of Operation

A strain gage load cell works by measuring the strain in an elastic member of knownshape and material properties. Given the geometry and material properties, the stiffnessof the load cell is determined. The elastic member exhibits a linear relationship betweenapplied load and strain in the material so long as the elastic member is not loaded pastits yield strength. Typically four transducer quality strain gages are mounted to areas of the transducer corresponding to the location of maximum strain. The member is typically

axisymmetric and the strain gages are mounted symmetrically to maximize output of thesensor. Electrically, the gages are wired in a Wheatstone Bridge configuration as shown inFigure 10.1.

Instrumentation

As noted in Figure 10.1, an excitation voltage must be applied to the Wheatstone Bridge.The output of the transducer is analog voltage in millivolts. Several methods may be usedto instrument a load cell. A separate power supply and multimeter or voltmeter may beused to apply the excitation and measure the output voltage. The disadvantage lies in themanual data reduction. To properly reduce data using this method, the following equationsmay be used.

F = F range ·V measured

V range(10.1)

where F is the measured force, F range is the load range of the transducer , V measured is thevoltage output by the transducer, and V range is the voltage range,

V range = V activation · Sensitivity (10.2)

60



LAB 10. LOAD CELL USE AND INSTRUMENTATION 61

E o

E i

Figure 10.1: Wheatstone Bridge Configuration

where V activation is the activation voltage and Sensitivity is the sensitivity of the transducer,which can be found in the manufacturer’s specification sheet.

A data acquisition system may be used to both power the transducer and measure theoutput. The acquisition card, module, or unit will also digitize the output, relaying thedata to a computer for data reduction. A third option is the use of a panel meter. A panelmeter is basically a voltmeter, analog to digital converter, and digital display in one unit.One example is the Omega DP25B-S which will be used in this lab. A standard strain gage

load cell, or any strain gage transducer, will have four leads for electrical connection. Thecolor of these leads has been standardized as follows:

Lead Color Symbol Connection

Red +E Positive Excitation VoltageBlack −E Negative Excitation VoltageGreen +S Positive Signal Input (Positive Sense)White −S Negative Signal Input (Negative Sense)

10.2 Experiment

10.2.1 Procedure

Use the provided calibration sheet for the specific load cell in use and follow the directionsgiven. The input range that will be used for this load cell is 0-100 mV.




27

Configuring The Meter 4

3. Determine IN1and IN!2 input range and resolution. The example selects the0 to 100 mV range and 10 uV resolution (R.2=4 ).

Example: IN1= (0 mV) x (100 cts/mV) x (1.000) = 0

IN!2= (31 mV) x (100 cts/mV) x (1.000) = 3100

RD1= 0000

RD!2= 100.0

4. Press MENU button until the meter shows RD.S.O .

5. Press the∂TARE button. The meter shows IN1.

6. Press the∂TARE button again, the meter shows the last Input 1 value, with the

fourth digit flashing.

7. Press theßNT/GRS button to change the value of your digits.

8. Press the∂TARE button to scroll horizontally to the next digit.

9. Press the MENU button to store this value. The meter shows RD1.

10. Press the∂TARE button. The meter shows the last value for Read 1.

Repeat steps 7, 8 and 9 until RD1, IN!2and RD!2 have been displayed, verified,changed (if necessary) and stored.

4.4 USING READING CONFIGURATION RD.CF

Refer to Table 6-1 for a summary list of menu configuration.

You may use Reading Configuration RD.CF to configure your meter for the following:

• To select ratiometric or non-ratiometric operation

• To set the input resolution of your meter

• To display the filtered/unfiltered signal input value

• To select gross/net vs. peak reading

Note




A single type of tape will be tested at three different rates to determine the effect of strain rate on strength of the material. Record the measured data in the following tables.

Extension Rate Max Load(lb)

Tape Name

Average Max Load


Tape Name

Average Max Load


Tape Name

Average Max Load




Three different types of tape will be tested at the same rate of extension. Record themeasured data in the following tables.

Tape Name Max Load(lb)

Average Max Load

Tape Name Max Load

(lb)

Average Max Load

Tape Name Max Load(lb)

Average Max Load




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Appendix A

Sensor Calibration

One method for calibrating a sensor is through direct comparison to a known value ormeasurement. In this approach, the sensor being calibrated is used to measure a system

in which the conditions are being controlled or monitored by a more accurate sensor, orstandard. Measurements can be taken over a range of conditions and a least-squares fitcan be applied to derive a calibration curve. This calibration curve can then be used tocorrect the measurements taken by the sensor during post processing.

Following the procedure in Beckwith, et. al. [5]. The calibration curve will be of theform

f cal(x) = ax + b ± (δ ax + δ b + δ std) (A.1)

where δ a is the scale uncertainty,

δ a = ±tα/2,ν S y/x

S xx, (A.2)

δ b is the offset uncertainty,

δ b = ±tα/2,ν S y/x

1

n+

x2

S 2xx, (A.3)

δ std is the uncertainty of the standard, n is the number of measurements, tα/2,ν can befound using Table B.3, x is the mean of the uncalibrated values,

S 2xx =ni=1

(xi − x)2, (A.4)

andS y/x =

ni=1[yi − f cal(xi)]2

n − 2(A.5)

where f cal(xi) is the calibrated value. When reading the Student’s t table, use ν = n − 1and assume a confidence interval of 95%,

α/2 =1 − 0.95

2= 0.025. (A.6)

70



APPENDIX A. SENSOR CALIBRATION 72

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

78

9

10

Uncalibrated (kΩ)

S t a n

d a r d

( k Ω )

Uncalibrated DataLinear Fit:

y = 1.013 x − 0.112kΩR2 = 0.998

Figure A.1: Sample plot of standard versus uncalibrated values with a least squares linearfit applied.

Following Eq. (A.5), S y/x can be calculated as

S y/x =

ni=1[yi − f cal(xi)]2

n − 2(A.10)

=

(1kΩ − 1.00kΩ)2 + (2 kΩ − 2.02kΩ)2 + . . .

8(A.11)

= 0.137 kΩ (A.12)

From Table B.3,tα/2,ν = 2.262. (A.13)

The scale uncertainty, δ a, can be calculated with Eq. (A.2)

δ a = ±tα/2,ν S y/x

S xx(A.14)

= ±2.262 · 0.137kΩ

8.96kΩ(A.15)

= ±0.035, (A.16)



APPENDIX A. SENSOR CALIBRATION 73

and the offset uncertainty, δ b, can be calculated with Eq. (A.3)

δ b = ±tα/2,ν S y/x

1

n+

x2

S 2xx(A.17)

= ±2.262 · 0.137kΩ

1

10+

(5.54kΩ)2

(8.96kΩ)2(A.18)

= ±0.192kΩ. (A.19)

If the uncertainty of the standard is not known, then it must be assumed to be zero,and the final calibration equation with its estimated uncertainty would be,

f cal(x) = 1.013 x − 0.112kΩ ± (0.035 x + 0.192 kΩ). (A.20)

However, since the uncertainty of the standard is known to be δ std = ±0.001 kΩ, it can be

added to Eq. (A.20) to get

f cal(x) = 1.013 x − 0.112kΩ ± (0.035 x + 0.192kΩ + δ std) (A.21)

f cal(x) = 1.013 x − 0.112kΩ ± (0.035 x + 0.193 kΩ) (A.22)



Appendix B

Additional Resources

B.1 741 Operational Amplifier Pinout Diagram

-

+

Offset Null

Inverting (-)

Non-Inverting (+)

(Power) V −

Not Connected (NC)

V + (Power)

Output

Offset Null

1

2

3

4 5

6

7

8741 Op. Amp

Figure B.1: Pinout diagram for a generic 741 opamp.

74



APPENDIX B. ADDITIONAL RESOURCES 76

B.3 RL10 Thermistor Specification Sheet

Table B.1: Properties for RL10 thermistors.

Type Number Ro @ 25C Material β B δ τ (Ω) (mm) (mW/K) (sec)

RL1003-49.2-59-M 75 D5.9 3096 2.79 2.5 9RL1004-65.6-59-M 100 D5.9 3096 3.05 2.5 9

RL1005-82-59-M 125 D5.9 3096 3.30 2.5 10RL1006-98.4-59-M 150 D5.9 3096 3.56 2.7 10RL1003-238-85-K 400 D8.5 3772 2.79 2.5 9RL1003-312-73-K 500 D7.3 3468 2.79 2.5 9RL1004-297-85-K 500 D8.5 3772 3.05 2.5 9RL1005-468-73-K 750 D7.3 3468 3.30 2.5 10RL1006-475-85-K 800 D8.5 3772 3.56 2.7 10RL1007-624-73-K 1,000 D7.3 3468 3.81 2.8 10RL1007-594-85-K 1,000 D8.5 3772 3.81 2.8 10RL1003-1157-95-K 2,000 D9.5 3965 2.79 2.5 9

RL1004-1446-95-K 2,500 D9.5 3965 3.05 2.5 9RL1005-1735-95-K 2,500 D9.5 3965 3.30 2.5 10RL1003-1746-97-K 3,000 D9.5 3965 2.79 2.5 9RL1007-2313-95-K 4,000 D9.5 3965 3.81 2.8 10RL1004-2910-97-K 5,000 D9.7A 3972 3.05 2.5 9RL1003-2871-103-K 5,000 D10.3 4073 2.79 2.5 9RL1004-4019-103-K 7,000 D10.3 4073 3.05 2.5 9RL1007-4364-97-K 7,500 D9.7A 3972 3.81 2.8 10RL1009-5820-97-K 10,000 D9.7A 3972 4.32 3.0 10RL1005-5744-103-K 10,000 D10.3 4073 3.30 2.5 10RL1007-6890-103-K 12,000 D10.3 4073 3.81 2.8 10




B.4 Probability Tables




Table B.2: Areas under the Standard Normal Curve

0 z

Second Decimal Place in z

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.03590.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.07530.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.11410.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.15170.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879

0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.22240.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.25490.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852

0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.31330.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389

1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.36211.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.38301.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.40151.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.41771.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319

1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.44411.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.45451.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.46331.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.47061.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767

2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.48172.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.48572.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.48902.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.49162.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936

2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.49522.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.49642.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.49742.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.49812.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986

3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.49903.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993

3.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.49953.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.49973.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998

3.5 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.49983.6 0.4998 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.49993.7 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.49993.8 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.49993.9 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000




Table B.3: Student’s t-Distribution (Values of tα,ν )

0 tα

α

ν t0.10,ν t0.05,ν t0.025,ν t0.01,ν t0.005,ν ν

1 3.078 6.314 12.706 31.821 63.657 12 1.886 2.920 4.303 6.965 9.925 23 1.638 2.353 3.182 4.541 5.841 34 1.533 2.132 2.776 3.747 4.604 45 1.476 2.015 2.571 3.365 4.032 56 1.440 1.943 2.447 3.143 3.707 6

7 1.415 1.895 2.365 2.998 3.499 78 1.397 1.860 2.306 2.896 3.355 89 1.383 1.833 2.262 2.821 3.250 9

10 1.372 1.812 2.228 2.764 3.169 1011 1.363 1.796 2.201 2.718 3.106 1112 1.356 1.782 2.179 2.681 3.055 1213 1.350 1.771 2.160 2.650 3.012 1314 1.345 1.761 2.145 2.624 2.977 1415 1.341 1.753 2.131 2.602 2.947 1516 1.337 1.746 2.120 2.583 2.921 1617 1.333 1.740 2.110 2.567 2.898 1718 1.330 1.734 2.101 2.552 2.878 1819 1.328 1.729 2.093 2.539 2.861 1920 1.325 1.725 2.086 2.528 2.845 2021 1.323 1.721 2.080 2.518 2.831 2122 1.321 1.717 2.074 2.508 2.819 2223 1.319 1.714 2.069 2.500 2.807 2324 1.318 1.711 2.064 2.492 2.797 2425 1.316 1.708 2.060 2.485 2.787 2526 1.315 1.706 2.056 2.479 2.779 2627 1.314 1.703 2.052 2.473 2.771 27

28 1.313 1.701 2.048 2.467 2.763 2829 1.311 1.699 2.045 2.462 2.756 2930 1.310 1.697 2.042 2.457 2.750 30...

......

......

......

∞ 1.282 1.645 1.960 2.326 2.576 ∞

MECH 3050 Lab Manual

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