## (solution) Microsoft Word - ps6_f15 can you help with #1. I tried to sole it

Microsoft Word - ps6_f15

can you help with #1. I tried to sole it but i could not

ME EN 3200 MECHATRONICS I: PROBLEM SET 6

DUE FRIDAY, OCTOBER 23, 2015 BY MIDNIGHT

For all questions, show your work and include units where appropriate for full credit. 1. Four strain gages (denoted A, B, C and D are mounted on the metal beam as shown to form a

force sensor. They need to be wired together to form a Wheatstone bridge as shown.

a. Label the Wheatstone bridge, with the letters A, B, C, and D, to show how the strain

gages should be wired together to produce a positive voltage out of the instrumentation

amplifier for a downward load on the beam (the circuit should be insensitive to forces

in other directions). The arrows over the resistors indicate whether the resistance should

be increasing or decreasing when a force F is applied in the downward direction. Force F

A h B

D

C b

L +

Vs

- R+?R

Va R-?R

Vb

Vab R-?R Instrumentation

Amp R+?R DEPARTMENT OF MECHANICAL ENGINEERING, UNIVERSITY OF UTAH

PAGE 1 OF 6 ME EN 3200 MECHATRONICS I: PROBLEM SET 6

DUE FRIDAY, OCTOBER 23, 2015 BY MIDNIGHT b. Using voltage divider equations, calculate the differential voltage Vab = Vb-Va as a

function of the change in resistance, ?R of the strain gages (in this configuration, you

can assume they all experience the same ?R. c. The gauge factor of a strain gage relates the relative change in resistance to the strain:

? Using this relationship and your result from part b, write an equation for Vab as a

function of the strain. DEPARTMENT OF MECHANICAL ENGINEERING, UNIVERSITY OF UTAH

PAGE 2 OF 6 ME EN 3200 MECHATRONICS I: PROBLEM SET 6

DUE FRIDAY, OCTOBER 23, 2015 BY MIDNIGHT d. Using principles of strengths of materials, the maximum strain occurring in the beam

is given by:

6

Assume the beam width b=5mm wide, the beam thickness h=1mm, the beam length

L=20mm, and the modulus of elasticity E=70 GPa. Assuming a maximum of 0.5 kgf

load is applied to the end of the beam, calculate the maximum strain in the beam. e. Assume the gauge factor of the strain gages, GF = 2.0, the nominal strain gauge

resistance is R = 120 ?, and the supply voltage is Vs = 12 V. Given the maximum strain

you just calculated in part d, what is the maximum voltage Vab that will be output from

the Wheatstone bridge? If the range of your A/D is ±5V, what gain should you use for

the instrumentation amp? DEPARTMENT OF MECHANICAL ENGINEERING, UNIVERSITY OF UTAH

PAGE 3 OF 6 ME EN 3200 MECHATRONICS I: PROBLEM SET 6

DUE FRIDAY, OCTOBER 23, 2015 BY MIDNIGHT 2. List the three common types of electronic temperature sensors and identify two

characteristics of each one.

Sensor Type Characteristics DEPARTMENT OF MECHANICAL ENGINEERING, UNIVERSITY OF UTAH

PAGE 1 OF 6 ME EN 3200 MECHATRONICS I: PROBLEM SET 6

DUE FRIDAY, OCTOBER 23, 2015 BY MIDNIGHT 3. Suppose you are using a K-type thermocouple to measure temperature as shown in the

diagram below. According to NIST, the temperature-voltage relationship for a K-type

thermocouple can be modeled by the following polynomial equation:

?

where E is the voltage in milliVolts, and T is the temperature in degrees Celsius. For the

range 0°C to 500°C, the coefficients di are given in the table below.

d0

d1

d2

d3

d4

d5

d6

d7

d8

d9 0.000000E+00

2.508355E+01

7.860106E-02

-2.503131E-01

8.315270E-02

-1.228034E-02

9.804036E-04

-4.413030E-05

1.057734E-06

-1.052755E-08 Thermocouple @ temp T E Instrumentation

Amp Reference Junction (0°C) a. Use MATLAB to plot the temperature-voltage relationship for the stated

temperature range, which corresponds to a voltage range of 0.000 to 20.644 mV.

Use the MATLAB basic fitting tools (in the Figure window, select Tools-&gt;Basic

Fitting) to fit a straight line to this relationship. Using this straight line fit, what is

the sensitivity of the K-type thermocouple in mV/°C? DEPARTMENT OF MECHANICAL ENGINEERING, UNIVERSITY OF UTAH

PAGE 2 OF 6 ME EN 3200 MECHATRONICS I: PROBLEM SET 6

DUE FRIDAY, OCTOBER 23, 2015 BY MIDNIGHT b. Suppose you use your linear fit to approximate the temperature-voltage

relationship. What would be the accuracy of your temperature measurements in °C?

(As demonstrated in PS#5, the accuracy can be derived from the norm of the

residuals of your fit). c. Suppose you want to measure the voltage with a 16-bit A/D whose range is ±10V.

What gain would you need to choose for your instrumentation amp in order to

match the thermocouple range with that of your A/D? What would be the

temperature resolution? DEPARTMENT OF MECHANICAL ENGINEERING, UNIVERSITY OF UTAH

PAGE 3 OF 6

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