Sensor Evaluation for Silver Plating Process

By David Christofalo

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Table of ContentsI. Executive Summary_____________________________________________________________2

II. Project overview and Requirements-_____________________________________________3, 4

III. Discussion__________________________________________________________________5-22

A. Sensor Research and Selection______________________________________________5-7

B. Simulink Description_____________________________________________________8-17

C. Financial Analysis______________________________________________________18-22

IV. Conclusions and Recommendations____________________________________________23,24

V. Appendices ________________________________________________________________25-31

A. Gantt Chart________________________________________________________________25

B. Block diagram______________________________________________________________26

C. Labeled Block Diagram_______________________________________________________27

D. M-File____________________________________________________________________28

E. Sensor 1 Info_______________________________________________________________29

F. Sensor 1 Info_______________________________________________________________30

G. Sensor 1 Info______________________________________________________________31

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VI. Executive Summary:

Abstract:

Copper spheres were to be plated with silver up to a minimum thickness requirement. This was done by submerging them in a tank full of plating solution, including Trichloroethylene. The thickness of the plating on the spheres was calculated as a function of the height of plating solution in the tank. A sensor had to be selected which would monitor the height of plating solution in the tank.

The inlet and outlet flow of plating solution through this tank was modeled using the Simulink component of the MATLAB software. Three sensors were researched and selected based on their price, accuracy, durability and ease of installation. These sensors were modeled within the Simulink model of the plating tank. The Simulink model generated the following data for each of the three sensors:

I. Thickness of silver plating on each sphereII. Number of loads that can be plated per year

III. Cost per year of the plating operation, including the cost of the sensor and any wasted silver

A QFD matrix and a Cost benefit Analysis were made based on the generated data from the 3 Simulink models. A recommendation was made for the optimal sensor based on the Simulink data, price, accuracy, durability and ease of installation. This report covers the research of liquid level sensors, completely details the construction of the Simulink model(s) of the plating process, the associated equations, as well as project management aspects like a Gantt chart and work breakdown structure.

Results:

The Omega® LVU-2001 Ultrasonic level transmitter was recommended, based on the data generated from the Simulink models. This was based on the final QFD matrix which ranked each sensor for its accuracy, projected annual cost, and projected production quality.

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Project Overview & Requirements:

The purpose of this experiment was to develop a program using the SIMULINK features of the MATLAB software which modeled the process of plating copper spheres, 2.4in in diameter, with silver. The process of plating these spheres with silver involved the chemical Trichloroethylene. The spheres were to be submerged in a cylindrical tank, 5 ft. in diameter and 6ft. 8in. high, filled with Trichloroethylene.

The thickness of the plating on the spheres was assumed to be controlled by the height of the Trichloroethylene in the tank. Trichloroethylene was pumped into the tank via an inlet butterfly valve, which could be closed or open to a maximum of 20 degrees. The tank also featured drain valve, which could be fully open (0 degrees) or fully closed (90 degrees). The level of Trichloroethylene in the tank was dynamically changing; a function for the height of the Trichloroethylene in the tank was assigned by the instructor. The dynamically changing height was centered about a height of 6 ft.

The thickness of the silver plating on the copper spheres, θ, was governed by the following equation:

1. θ=∫0

t

[(A∗Ha ( t )−B¿)+(C|Hd ( t )−Ha ( t )|)]dt ¿

Where Ha(t) was the actual height of the plating solution in the tank, and Hd(t) was a function of the dynamically changing height of plating solution in the tank, and A, B and C were constants with values of

4.26410-5

in/(ft-min), 1.89710-4

in/min, and 2.35710-4

in/(ft*min) respectively.

The functions Ha(t) and Hd(t) were governed by the following three equations:

2.dVdt

=Qin

3. c dhdt

=(1− Ain90 )Qin

4. Qout=(1− Aout90 )K out√h

For equation 2, the inlet flow rate, Qin, was the change in volume per unit time (gallons/sec). Equation 3 was the base equation modeling the height of plating solution in the tank, where Ain was the angle of the inlet butterfly valve and c was the cross sectional area of the tank. Equation 4 governed the drain

valve, where Aout was the angle of the outlet valve, Kout was a given constant of 0.4824 ft.5/2, h was the height (derived from equation 2, and Qout was the outlet flow rate in gallons/sec.

Using these equations, the group was to model the flow of plating solution in the tank, and create a model in SIMULINK which took into account several parameters. These parameters are bulleted below.

The thickness of the plating, θ, was to be greater than 0.00075in., and less than 0.00125in thick.

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The number of spheres per load was not to exceed 1% of the minimum height given from the Hd(t) function.

A PID controller was required to operate the inlet valve to maintain the appropriate plating solution level in the tank. The model was to take into account that after each load of spheres were plated; the tank had to be pumped empty, cleaned, and then filled back up. It took 3 min to clean the tank, and 33% more time to pump the tank empty than to fill the tank.

Finally, the height of the plating solution in the tank was not to exceed 6’8”, as Trichloroethylene is toxic and any spill would be a financial and economic disaster.

Taking into account all said parameters, 3 Simulink models were to be created, each modeling a unique liquid level sensor. Each model was to calculate the following:

I. Thickness, θ, of silver plating on each sphereII. Time (in seconds) to plate the sphere

III. Number of spheres per loadIV. Number of loads that can be plated in an 8 hour work dayV. Cost per year of the plating operation, including the cost of the sensor and any wasted silver

Using the generated data above, the group was to create a QFD matrix which rated each sensor-system with respect to cost, sensor durability, quality (accuracy of the sensor), and ease of installation. The optimal sensor-system was to be chosen based on these criteria.

Finally, the group was to develop a brief, 10 slide presentation overviewing the results of the report.

The overall goal of the group was to develop the 3 Simulink models and to determine which sensor was most cost effective, accurate and produced the highest quality product.

To solve this complex problem, the group first created a Gantt chart, which broke down the various tasks, goals and milestones associated with project completion (See Gantt Chart in Appendix A). The group followed the work breakdown structure assigned within the Gantt chart, and meet weekly in class to work on the project. The group first brainstormed, and then wrote a proposal briefly describing the problem and the method by which it would be solved. Next, instrumentation was researched by Maggie and Christian, and the group collectively decided on three unique sensors to model. The main Simulink model was then developed by David. This model was closely de-bugged and scrutinized for accuracy. Next, the three unique sensors were modeled, each with its own separate Simulink model created from the aforementioned main model. The data generated from these 3 models was used to develop QFD and a cost benefit analysis for the sensors, for which Theresa was responsible. The written report was then compiled, which ultimately recommended the optimal senor of the given 3. Finally, an oral presentation was given by the group which summarized the findings of the report.

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Discussion:

Research Process:

Researching the sensors to utilize in this project was fairly straightforward. Primary research was done online, contacting companies and reading up on the various types of liquid level sensors. This project was meant to simulate an actual process in which a harmful substance could potentially cause damage, the accuracy and durability of the sensors chosen was crucial. The major concerns in choosing the sensors included the lifespan, the cost (actual sensor and extra purchases that would be needed), and the accuracy of such a device. Below is QFD Matrix detailing the 6 primary types of liquid level sensors found during research. The three sensors to be modeled were selected based on this matrix.

Quality Functional Development for 3 Level Sensors

Criteria

Importance Ranking

Liquid Level

Pressure

Ultrasonic

Buoyancy float

Continuous Radar

Radio Freq.

Sensor Cost 4 3 2 1 5 2 3Accuracy 6 1 3 5 0 3 2Ease of Installation 2 1 4 2 3 3 2Durability/Lifespan 3 2 3 4 2 2 2Contact w/ plating soln? 1 0 1 1 0 0 1Calibration needed? 2 1 0 1 1 0 0Warrantee length 1 2 2 2 1 2 0Sensor Range (full scale is close to 6ft.)

5 4 5 6 1 1 3

Quality Points Total 50 46 85 40 45 19

Three different types of sensors were chosen – Universal Liquid Level sensor, Pressure sensor, and a Non-Contact Ultrasonic Sensor.

Universal Liquid Level sensor : Omega® LV140

This sensor was chosen from the Omega® company which makes a wide range of sensors for a multitude of applications. The LV140 universal liquid level sensor operates on a direct, simple principle. A float is equipped with powerful, permanent magnets. As the float rises or lowers with liquid level, it actuates a magnetic reed switch mounted within the stem. This condition either opens or closes the electrical circuit to operate an external alarm or control circuit. When mounted vertically, this basic design provides a consistent accuracy of ± 1 /8 inch. Costing a relatively small $105.00, this sensor was designed to operate in harsh environments, requires no calibration, and can be mounted directly on the bottom of the tank. After calling the Omega® directly, it was

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found that the expected life time of this switch was about 10,000 hours in ideal conditions (about 416 days of continuous use). However, it was unknown if the toxic effects of the Trichloroethylene plating solution could be classified under these ideal conditions. However the low price, ease of installation and accuracy justified its use.

Pressure Sensor: Omega® PX429-005GV

The pressure sensor the group selected was the Omega® company’s PX429-005GV Gauge pressure sensor. This sensor utilizes a piezoresistive transducer capable of accuracy to +0.25% of full scale, with a response time of 1 millisecond. It is capable of measuring pressures between 0-5psi, and this range could be calibrated further. The sensor is mounted outside the tank, which is beneficial for both ease of installation and so that the caustic effects of the plating solution would not affect the lifespan of the sensor. At a list price of $475 dollars, it seemed a good choice, especially considering the accuracy, response time and ease of installation.

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Ultrasonic Sensor

Like the pressure sensor, it was also non-contact, and thus the material need not be safe against the plating solution. The group chose the Omega® LVU-2001 Ultrasonic level transmitter. This sensor functioned by sending high frequency ultrasonic sound wave, pulsed three times per second, from the base of the transducer. The sound wave reflects against the process medium below and returns to the transducer. The microprocessor based electronics measure the time of flight between the sound generation and receipt, and translates this figure into the distance between the transmitter and liquid below. This sensor was the most expensive selected, at $645.00, but the trade-off for that price was a relatively high accuracy of 0.25% of full scale. Additionally, no programming was required. The sensor could be mounted at the top of the plating tank. The only draw backs to this sensor were its high price, and the fact that the accuracy would decrease as the level of the plating solution in the tank decreased (liquid got farther away from the sensor. But since the overwhelming concern with these sensors was to ensure that the height of the solution did not exceed 6’8”, it was selected.

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Simulink Description:

This section is broken up into 4 Sections: Tank Filling and Senor Modeling, PID Controller, Thickness Calculation, and Financial Calculations. See Appendix B for the Unabridged Block Diagrams for each sensor, as well as the common “m” file listing all the constants used.

Tank Filling &Sensor Modeling:

To model the tank plating operation, the MATLAB software was used. A functional block diagram was created with the Simulink component of MATLAB, and MATLAB was used to create an “m” file which listed all the variables used in the block diagram.

The block diagram modeled the following three equations:

2.dVdt

=Qin

3. c dhdt

=(1− Ain90 )Qin

4. Qout=(1− Aout90 )K out √h

These equations were manipulated as shown below to solve for h. The bolded equation was actually modeled in the block diagram, shown in the picture below.

c dhdt

=(1− Ain90 )∗(Qin−Qout )

c dhdt

=(1− Ain90 )∗{Qin−[(1− Aout

90 )K out √h ]}h=1

c∫(1− Ain90 )∗{Qin−[(1− Aout

90 )K out √h]}

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The green and purple rectangles were drawn simply to emphasize the Qin and Qout functions, they are not a part of the program. This function, Ha(t), (also referred to as the actual height of plating solution) outputted data to a scope(see red arrow) where the height could be observed vs. time. The accuracies of each sensor are listed in the table below.

Sensor Accuracy (ft)Accuracy (+-)

Sensor 1: Liquid Level 0.010%

Sensor 2: Pressure 0.025%

Sensor 3: Ultrasonic 0.005%

The Ha(t)function then went into the “sensor”, a uniform random number generator which modeled the accuracy of the given sensor by choosing a random number in the range, in feet, of the sensors accuracy. In the block diagram below, the Sensor is indicated by the blue arrow. Each sensor’s accuracy was simulated by entering its accuracy into this this function block. Three separate models were created, but all differed only in the range of the uniform random number generator (and also the PID constants, to be mentioned shortly).

Ha(t) output scope (red arrow), Qin and Qout fns. (green and purple rectangles, respectively)

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The function Hd(t) is shown above in the blue oval. This function was given by the instructor, was the dynamically changing height of the fluid. This function was a “saw tooth” signal centered around 6 ft with amplitude of 8 inches (5’8” to 6’4”) and a frequency of 1.2Hz. This was constructed using a signal generating block, shown above in the blue oval.

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Simulink Description:

PID Controller

A PID controller, shown below in the red oval, was used to control the inlet valve and account for the difference between the Hd(t) and Ha(t) functions. The value of Hd(t) – Ha(t) was inputted into the PID controller.

PID stands for the Proportional, Integral and Derivative components of the controller. The Proportional component calculates a control signal that is directly proportional to the current error. The Integral component calculates a control signal based upon the sum of past errors. The Derivative component calculates a control signal based upon the rate at which the error signal has been changing. The three resulting individual signal are added together and relayed back into to actuator, in this case the height calculation.

The effect of each component of the PID was weighted by individual gain factors, shown in the previous picture as triangles. These gain factors, termed Kp, Ki and Kd needed to be varied for each sensor, so that the system (specifically the inlet valve) can react and compensate for the disturbances brought about by the Hd(t) function and the inherent inaccuracy of the height sensor. Said another way, the PID was meant to keep the error, the difference between Ha(t) and Hd(t) as close to 0 as possible. Specifically, the Kp, Ki and Kd values were changed to decrease the following disturbances:

Proportional

Integral

Summation

Derivative

Output Signal

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Rise Time: The time required for the system to change from a specified low value to a specified high value

Overshoot: The magnitude by which the system goes above the desired set point (6ft) when transitioning between high and low values

Settling Time: The time it takes a system to maintain a specified error about the desired set point

Steady State Error: Magnitude of error, the offset between the desired and actual heights, when steady state conditions have been achieved

The following chart was available to the group via Moodle, the Stevens Institute of Technology’s online class room of sorts. It was used as reference to tune the Kp, Ki and Kd values for each model.

Effect of Increasing GainParamete

r Rise time Overshot Settling Time

Steady Sate Error

Kp Decrease Increase Decrease DecreaseKi Decrease Increase Increase EliminateKd small change Decrease Decrease None

A scope was created in the block diagram which displayed both Ha(t) and Hd(t) simultaneously. This was used in the tuning of the PID for each sensor. An example of this scope output is shown below.

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The yellow line was Hd(t), the dynamically changing height of the plating solution. The Purple line was Ha(t). One can see that for this graph, there was significant overshoot error, likely the result of a Kp value that was too small. It was found by the group that the Kp value had the strongest effect on the Ha(t) graph for all sensor models. This overshoot could have been adjusted by increasing the Kp value.

The saw tooth signal of our Hd(t) function proved very difficult to tune, several hours were spent finding the optimal values. Though the chart above was very helpful, it still took a significant amount of time to find the optimal gain values. Once found, the scope showing both functions looked like this:

The Scope outputs for each sensor were additionally compiled in Appendix B.

The output of the PID was treated as a flow rate, and was added to the Qin-Qout value in the height calculator (green rectangle). Ideally, the PID would actually change the value of Ain, the angle to which the inlet butterfly valve was open. However this proved to be too tedious, and at our instructors suggestion the group simply considered it a flow rate. The values arrived at after tuning for each sensor was listed in the proceeding table.

Kp, Ki and Kd Values used for Each sensor/modelParamete

rSensor 1:

Liquid LevelSensor 2: Pressure

Sensor 3: Ultrasonic

Kp 3000 30 15Ki 1000 30 15Kd 2000 100 15

Ha(t) and Hd(t) scope outputs, in yellow and purple respectively:

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-Liquid Level:

-Pressure Sensor:

.

-Ultrasonic:

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Simulink Discussion:

Thickness Calculation

Next, the Hd(t) and Ha(t) values were inputted into the θ calculator, shown previously in the yellow rectangle. As previously stated, these functional blocks modeled the given equation for θ:

θ=∫0

t

[(A∗Ha ( t )−B¿)+(C|Hd (t )−Ha ( t )|)]dt ¿

The values for the constants A, B and C were 4.26410-5

in/(ft-min), 1.89710-4

in/min, and

2.35710-4

in/(ft*min) respectively. This equation is represented in the picture below.

The display box in the far right showed the real time thickness of the plating on each sphere. When this value reached or exceeded 0.00075”, the simulation was stopped. A clock out plating to a display showed the time, in seconds, for the plating to occur. This was also the value of t in the equation above for the thickness calculation.

Once the thickness of the plaint was calculated, and the time to plate the spheres was known, these values were used to calculate the financial aspects of the plating operation.

The thicknesses of the plating on each sphere and the plating time, by sensor were as follows:

-Liquid Level: 0.0007509 in.; 669 seconds

-Pressure Sensor: 0.0007507 in.; 670 seconds

-Ultrasonic: 0.0007521 in.; 675 seconds

The scope outputs for the thickness as a function of time were compiled, and were shown below.

Ha(t) Hd(t)

Block Diagram of the Thickness (θ) calculation

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Liquid Level Sensor:

Pressure Sensor θ Scope:

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Ultrasonic Sensor θ Scope:

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Simulink Discussion: Financial Calculations

The Simulink model was required to calculate the following information based on the time to plate the spheres and the thickness of each spheres’ plating:

1. Amount of and cost of silver used to plate each sphere2. Number of spheres per load3. Amount and Cost of sphere per load4. Number of loads that can be processed in an 8 hour day5. Amount and Cost of silver per Year6. Total cost of the plating operation per year (including sensor cost and wasted silver)

This was the criteria by which the three sensors would be judged and from which one would be chosen.

To calculate the amount of silver used to plate each sphere, the volume ( in inches^3) of each sphere (Vc) was first calculated in the Simulink model. This calculation is shown below.

Vc=43π ¿)^3

Next the thickness of the plating, θ, was added to the radius of the copper sphere, 1.2 in, and that value was used to find the volume of the plated sphere (Vp).

Vp= 43π (1.2+θ)3

The amount of silver used was found by subtracting the copper sphere volume from the plated sphere volume.

Vsilver=Vp−Vc=43π (1.2+θ )3−4

3π (1.2 )3

The block diagram version of this calculation is highlighted in the red rectangle below.

Copper sphere volume calculation (red)

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Having the volume of silver used, the given density of silver, 656 lbm/ft^3, was multiplied by the volume of silver to find the pounds of silver used per sphere. This value was then converted into ounces by multiplying by 16. The amount of silver in ounces was then multiplied by the cost of silver per ounce. It was assumed that the silver used was pure silver (.999% purity). The cost of silver at the time this report was written was $30.87 per oz. This resulted in the cost of plating one sphere with silver. This process is highlighted in the green rectangle below.

The number of spheres per load was governed by the Hd(t) function. The minimum volume of the spheres in the tank was not to exceed 1% of the minimum height of Hd(t). The minimum height of our function was 5’8”. Shown below is the calculation of the volume of the spheres as well as the number of spheres per load.

Vc=43π (1.2 )3

Vmin=5.666∗π∗(2.5 )2

V (load )=1 %∗Vmin=0.01∗5.666∗π∗(2.5 )2

Spheresload

=V ( load )Vc

=0.01∗5.666∗π∗(2.5 )2

43π (1.2 )3

The number of spheres per load was rounded down the nearest whole number, resulting in roughly 248 spheres per load. The block diagram below displays this calculation. The number of spheres per load was then multiplied by the cost per sphere to get the cost per load. This calculation is shown in the next block diagram except, highlighted in the orange oval.

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The purple rectangle above highlights the functional blocks which calculated the downtime after each load of spheres was plated. The project description stated that numerous loads could be process per day, but after each load there was downtime where the tank was to be pumped empty, cleaned and then refilled. It took an average of 3 minutes to clean the tank after it was pumped empty, and it took 33% more time to pump the tank empty than it did to fill the tank. For the filling of the tank, the PID controller was to be bypassed.

The block diagram above has one function block that is colored red, along with the wires associated with it. This block was time, in seconds, to fill the tank. To find this value, a simplified tank filling block diagram was created which did not feature a PID controller, so that the time to fill the tank could be found.

Tank Filling Model: Block diagram modeling the filling of the empty tank after cleaning; PID bypassed

Downtime Calculation (purple) and Spheres per load Calc.

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This model was duplicated for each sensor, with the accuracy of each sensor entered into the uniform random number box. It was important to change the parameters of the integrator block in this model. The initial condition was normally set at 6 (ft.), which was the initial height of the plating solution. This block diagram however, modeled that the tank was empty, so the initial condition was set to 0. Additionally, the outlet valve was considered closed, to the value of Aout was set to 90 degrees. This time was uniform for all sensor models, at 1110s.

The time to fill the empty tank was entered as a constant into the main block diagram. This value was multiplied by 1.333, to find the time to pump the tank empty. The tank emptying time was added to the tank filling time, which was then added with 180s, the cleaning time in seconds. The derivation of the total time, including downtime, for each load is shown below

tp = time to plate spheres

tf = time to fill tank=1110s

tE = time to empty tank

tC = time to clean tank =180s

8Hrs*60min/hr.*60sec/min=28800s

Total time per load=t p+180+tf +tE

Total time per load=t p+180+2.333∗tf

Loads Per Day= 28800 stotal time per load

= 28800 stp+180+2.333∗tf

The number of loads per day was multiplied by the cost per load, resulting in the cost to run the entire plating operation per day. It was assumed that the average year has 260 work days (after

Financial Block diagram: brown rectangle shows the annual cost construct

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weekends, holidays, etc.) so the annual cost was calculated by multiplying the daily cost by 260 (See the brown rectangle in the block diagram above).

The values that were used to ultimately calculate the cost per year of the plating process for each sensor model were tabulated in a Cost analysis QFD. The values and assigned quality point values, where the lower cost was associated with a lower quality point Value; the sensor with the lowest quality point total was judged to be the best sensor. Shown below is the QFD.

Cost QFD of Sensors

CriteriaQualit

y Points

Sensor 1: Liquid Level

Sensor 2: Pressure

Sensor 3:

Ultrasonic

Amount of silver/sphere (oz.)

1 0.08258 0.08253 0.08272

Cost of Silver per sphere ($)

1 2.549 2.549 2.554

Spheres per load

0 265 265 265

Cost of 1 load

1 679.65 675.49 678.30

Loads per day

0 8 8 5426.4

Cost per day ($)

1 5437.2 5403.88 5426.4

Cost per year ( $)

0.5 1413672 1405008.8 1410864

Quality Points Total

712955.482

708586.397

711539.3

In order to accurately judge the cost the cost associated with each sensor, the recurring and no-n recurring costs had to be considered. The annual recurring costs were essentially the repeatable costs; the cost to plate each sphere. The most important of which was the annual cost to plate the given number of spheres. Based on this QFD, the Pressure sensor was the optimal sensor.

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The non-recurring costs comprised the non-repeatable costs, specifically the cost of the sensors. These costs were estimated by the lifespan of sensors, and how long the sensors could function before either breaking or losing accuracy.

Unfortunately, there was insufficient data to accurately judge the non-recurring costs of the individual sensors. Upon calling the Omega Company (which produced all three sensors), the group was only able to find an average time to failure for the first sensor, the Liquid Level sensor, which was 10,000 hours or a year and 3 months. And this value did not account for the caustic nature of the Trichloroethylene plating solution, which would likely reduce the time to failure. No data was available for the other two sensors, so the non-recurring costs could not be assed.

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Conclusions & Recommendations:

The purpose of this project was ultimately to make a recommendation on which sensor should be used to monitor the height of plating solution in a tank used to plate copper spheres with silver.

Many sensors were researched, and three were chosen to be modeled in the MATLAB simulation for the plating process. The sensors to be modeled were chosen based on their accuracy, cost, ease of installation and life span, among other things. These sensors were the Liquid Level Sensor, the Pressure Sensor and the Ultrasonic Sensor.

These sensors were modeled using the Simulink component of the MATLAB software, along with the plating process itself. The Simulink sensor models generated data for the thickness of the silver plating, the time to plate the spheres and ultimately the annual cost of running the process with that sensor.

These values were used to generate the final Recommendation QFD (shown below), which was used to make the recommendation on the optimal sensor. Lower quality points were associated with desirable attributes.

Final QFD Matrix

Quality Points

Sensor 1: Liquid Level

Sensor 2: Pressure

Sensor 3: Ultrasonic

Annual Plating cost

3 3 1 2

Accuracy 7 1 2 3

Quality (plating thickness)

1 3 1 2

Total: 19 18 29

Based on our data, the Omega ® LVU-2001 Ultrasonic level transmitter Sensor was the optimal sensor.

The Ultrasomic sensor had the highest accuracy, which was stipulated by the instructor to be the most important quality of the chosen sensors. I had the second highest projected annual cost and accuracy, as well as the second highest projected θ quality. Though the first sensor had a projected lower paltin cost and a higher quality palting, the low accuracy of that sensor made its projected results less relyable than those of the Ultrasonic sensor.

Recommendations:

In the course of constructing the Simulink model, several recommendations were noted to increase the accuracy of the generated data. The PID should have controlled the value of Ain, as this was the way the height of the plating solution in the tank would have actually been controlled.

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Also, the saw tooth signal proved difficult in regard to the PID tuning, other signal types would have been easier to model, specifically the sine wave.

Finally, in the financial calculation portion of the block diagram, the number of loads processed per day was not a round number. It was worth noting that profitability might be increased if “non- full loads” or loads that were less that the calculated number of spheres could be processed to utilize the full 8 hour day, and ultimately the cost per year. This may not be the case, but it would be prudent to use the Simulink model to investigate.

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Gantt chart

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Appendix B: Block Diagram

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Appendix C: Labeled Block Diagram

Key:green = Qinyellow = θblue oval= Hd(t)red= PIDBlue arrow= SensorOrange oval = Cost per sphere calc.Blue rectangle =Financial Calculator

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Appedix D: M-File

Ain = 20; %angle of inlet butterfly valve Aout=0; %angle of outlet drain valve C=19.3650;% cross sectional area of tank Kd=15;% Derivitive constant Ki=100:% integral constant Kp=2000;% proportional constant Kout=8*10^-3;% constant for Qout calculation Qin=60*0.134/60;% flow rate in feet/sec a=7.1067*10^-7;% constast for theta calc. b=3.1617*10^-6;% constast for theta calc. c=3.9283*10^-6;%constast for theta calc.

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Appendix E: Sensor Info

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Appendix F: Sensor 2 Info

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Appendix G: Sensor 3 Info