Why is MC2 LR so different from the others???
The previous measurements were made from the coil driver output monitors. To investigate why the MC2 LR coil has less noise than the other coils, I also measured the noise at the output to the coils.
The circuit diagram for the coil driver board is given in D010001 and a picture of the rack is on the 40m wiki here. The coil driver boards are in the upper left quadrant of the rack. The input to the board is the column of LEMOs which are the "Coil Test In" inputs on the schematic. The output monitors are the row of LEMOs to the right of the input LEMOs and are the "FP Coil Volt Mon" outputs on the schematic. The output to the coils "Coil Out" in the schematic are carried through a DB15 connector.
The attachment shows the voltage noise for the MC2 LR coil as well as the UL coil which is similar to all of the other coils measured in the previous measurement. While the LR coil is less noisy than the UL coil as measured at the output monitor, they have the same noise spectrum as measured at the output to the coils themselves. So there must be something wrong with the buffer circuit for the MC2 LR voltage monitor, but the output to the coils themselves is the same as for the other coils.
I've been looking into recovering the seismic BLRMs for the BS Trillium seismometer. It looks like the problem is probably in the anti-aliasing board. There's some heavy stuff sitting on top of it in the rack, so I'll take a look at it later when someone can give me a hand getting it out.
In detail, after verifying that there are signals coming directly out of the seismometer, I tried to inject a signal into the AA board and see it appear in one of the seismometer channels.
Steve, the pictures you posted are not the AA board I was referring to. The attached pictures show the board which is sitting beneath the GPS time server.
Steve secured the GPS time server in the rack above the AA board and removed the wooden block that it was resting on. The new rack is shown in attachment 1.
I then opened the AA board to see why the channels aren't working. Even though the board was powered and outputting 4.6 V, none of the chips were getting power. I must have shorted something while trying to diagnose this and the board is no longer powered either.
The schematic is given in D990147. The D68L8EX filter is bypassed on all the channels, as can be seen in attachment 3, so the board isn't really doing anything. Rana suggested that we could just bypass the whole circuit by wiring the IN channels directly to the OUT channels going to the ADC. I'll try that next for a single channel.
In the ongoing attempt to recover the seismometer BLRMS, I removed the AA board from the rack and modified the BS seismometer Z channel. The BS_Z BLRMs seem to be recovered after this modification.
I removed the three resistors from the output of the circuit and wired the input and from the seismometer directly to the input to the ADC. The modified schematic is shown in attachment 1. Attachments 2 and 3 show the top and bottom of the modified board. The board is doing nothing now other than serving as a connector for this channel.
I put the board back in the rack and injected a 2 Vpp signal into the BS_Z channel and saw +/- 1600 cts in C1PEM-SEIS_BS_Z. I then plugged the seismometer back into the board and took the spectrum shown in attachment 4. This shows the working Z channel giving a reasonable seismic spectrum. Note that X and Y are not modified yet.
If there are no objections, I will modify all the other channels on the board in the same way tomorrow.
I wired all 32 channels going to the AA board directly to the ADC as described in the previous log. However, instead of using the old AA board and bypassing the whole circuit, I just used a breakout board as is shown in the first attachment. I put the board back in the rack and reconnected all of the cables.
The seismic BLRMs appear to be working again. A PSD of the BS seismometers is shown in attachment 2. Tomorrow I'll look at how much the ADC alone is suppressing the common mode 60 Hz noise on each of the channels.
Steve: 5 of ADC DAC In Line Test Boards [ D060124 ] ordered. They should be here within 10 days.
Yesterday I wired the outputs from the seismometers directly to the ADC input bypassing the old AA board circuit as is described in this elog. The old circuit converted the single-ended output from the seismometers to a differential signal. Today I looked at whether 60 Hz noise is worse going directly into the ADC due to the loss of the common mode rejection previously provided by the conversion to differential signals.
I split the output from the BS Z seismometer to the new board and to an SR785. On the SR785 I measured the difference between the inner and outer conductors of the seismometer output, i.e. A-B with A the center conductor and B the outer conductor, with grounded input. At the same time I took a DTT spectrum of C1:PEM-SEIS_BS_Z_IN1. Both spectra were taken with 1 Hz bandwidth and 25 averages. The setup is shown in attachment 1.
The spectra are shown in attachment 2. The DTT spectrum was converted from counts to volts by multiplying by 2 * 10 V/32768 cts where the extra factor of 2 is from converting from single-ended to differential input. If there was common 60 Hz noise that the ADC was picking up we would expect to see less noise at 60 Hz in the SR785 spectrum measured directly at the output from the seismometer since that was a differential measurement. Since both spectra have the same 60 Hz noise, this noise is differential.
I was trying to plot trends (min, 10 min, and hour) in DataViewer and got the following error message
mjd = 58235
Open of leapsecs.dat failed
leapsecs_read() returning 0
frameMemRead - gpstimest = 1208844718
thoough the plots showed up fine after. Do we need to fix something with the leapsecs.dat file?
In light of the discussion at today's meeting, Guantanamo and I looked at how the series resistance for the test mass coil drivers limits the amount of squeezing we could detect.
The parameters used for the following calculations are:
Since we need to operate very close to signal recycling, instead of the current signal extraction setup, we will need to change the macroscopic length of the SRC. This will change the mode matching requirements such that the current SRM does not have the correct radius of curvature. One solution is to use the spare PRM which has the correct radius of curvature but a transmissivity of 0.05 instead of 0.1. So using this spare PRM for the SRM and changing the length of the SRC to be the same as the PRC we can get
This lower transmissivity for the SRM also reduces the achievable squeezing from the current transmissivity of 0.1. For an SRM with a transmissivity of 0.15 (which is roughly the optimal) we can get
The minimum achievable squeezing moves up from around 205 Hz at 1 W to 255 Hz at 5 W because the extra power increases the radiation pressure at lower frequencies.
Note that for Signal Recycling, which is what Kevin tells us we need to do, there is a DARM pole at ~150 Hz.
To be quantitative, since we are looking at smaller squeezing levels and considering the possibility of using 5 W input power, it is possible to see a small amount of squeezing below vacuum with no SRM.
Attachment 1 shows the amount of squeezing below vacuum obtainable as a function of homodyne angle with no SRM and 5 W incident on the back of PRM. The optimum homodyne angle at 210 Hz is 89.2 deg which gives -0.38 dBvac of squeezing. Figure 2 is the displacement noise at this optimal homodyne angle and attachment 3 is the same noise budget shown as the ratio of the various noise sources to the unsqueezed vacuum.
The other parameters used for these calculations are:
So maybe it's worth considering going for less squeezing with no SRM if that makes it technically more feasible.
As described in this elog, the ADC for the seismometers now has the signals wired directly to the ADC instead of going through an AA board or other circuit to remove any common mode noise. This elog describes one test of the common mode rejection of this setup. Guantanamo suggested comparing directly with a recent spectrum taken a few months before the new setup described in this elog.
Today I took a spectrum (attachment 1) of C1:PEM-MIC_2 (Ch17) and C1:PEM-MIC_3 (Ch18) with input to the ADC terminated with 50 Ohms. These are two of the channels plotted in the previous spectrum, though I don't know how that plot was normalized. It's clear that there are now strong 60 Hz harmonic peaks that were not there before, so this new setup does have worse common mode rejection.
Earlier today Kira and I reconnected the EX seismometer. I just took some spectra of all three seismometers, shown in the attachments, to compare with past data and to do a rough check of the calibration.
This elog has a spectra from 2010 (GUR1 is now EY) and this elog has one for BS at lower frequencies from 2017. Note that the EX seismometers now have strong peaks that are not at 60 Hz harmonics. Other than these peaks, these old spectra roughly match up with the ones taken today, so the callibration is still roughly the same. I couldn't find any old data for EX (GUR2) though so I don't know for sure that these peaks weren't there before.
gautam 20180517 0930: In 2017, Gur2 (now EX) looked like this. Still peaky, but the peaks seem shifted in frequency. Steve also informed me that the Gur1 and Gur2 cables were swapped n times, so perhaps we shouldn't read too much into that.
This goal of this test was to measure and map the AC (at 60 Hz) and DC magnetic fields around the interferometer. I've attached the final products which were drawn up with Google SketchUp.
The notes on the maps make them more or less self explanatory: for each numbered point there's an X, Y, and Z measurement produced by the magnetometer. For the AC numbers I measured the Peak-to-Peak value, while for the DC I simply measured the Mean. The magnetometer's axes were always oriented about the same way, with the X arrow on the magnetometer pointing north. I tried to keep variables such as the lights constant as much as possible (they were all on for most measurements, with the exception of a few noted DC ones) and all measurements had the top of the magnetometer at about 32 inches. The map is pretty close to scale and all the walls and numbered locations were measured out (though the location of objects and the laser tubes is somewhat estimated). I added "landmarks" in the room, which were pretty much the laser tubes, computer racks, and ISC tables.
For each laser room measurement I also took a screenshot using the oscilloscope as a means of recording the shape of the wave for each measurement. Ch1 corresponds to the X value, Ch2 to the Y, and Ch3 to the Z. The screenshots are numbered 1-29 corresponding to the numbers on the map. The zip folders containing the screenshots can be found on the wiki: PEM:Magnetometers
I should also mention that there is no point #24 and accordingly no 24 screenshot. I realized after I was done that I had messed up the location of that one and instead of risking bad data decided to just remove it.
I decided on the location of the points mainly based on the location of outlets in the room (since I had to plug in the oscilloscope for the AC numbers to set it to 60 Hz). After an initial pass of the room, I went back and filled in some of the larger gaps by moving the magnetometer as far as I could while the oscilloscope remained plugged in to the wall. I used the same points for DC numbers.
Prior to measuring the laser room, I measured the field in other rooms as well. I have
AC numbers and screenshots for the control room and the adjoining office room.
DC numbers for the entry room and the office room, not including the control room. The X-axis arrow is pointed south (instead of north) for these numbers.
These numbers were sort of a warm up for me to figure out the process and how I would go about recording my data. Since they're not in really important locations and aren't guaranteed to be accurate, I decided not to map them, though the screenshots are still on this Dell Inspiron 1300 Laptop and the measurements in my notebook.
Here are the settings I used on the oscilloscope for all measurements (I merely changed the Vertical Coupling between DC and AC depending on what I was measuring):
Impedance: 1M ohms
Probe Setup: Voltage 1X
Trigger Type: Edge
Trigger Coupling: DC
Fast Trig: Normal
Trigger Mode: Auto
Trigger Source: AC Line
Acquire Mode: 512 Average
The notebook that I used contains some additional info that I didn't include in the map, most importantly more precise descriptions of where each of the points is located and the measured distance between each of them (as well as slight changes I made to my measured distances in order to make the room a rectangle; the changes are slight enough that they shouldn't have any real effect on the data).
Since Kevin used our 3-axis Bartington Fluxgate magnetometer, we can guess that we can convert his voltage measurements (below) into magnetic field
by using the manual's guess of 10 uT /V or 10 V/Gauss. This is probably ok at the factor of 2 level, but one day we should calibrate it with a coil.
The punchline is that the DC fields in the lab are roughly what we expect from the Earth's field plus the rebar in our floors: ~1 Gauss. The 60 Hz fields are ~50-500 nT peak-peak.
Goal is to build a temperature sensor accurate to 1 mK. Schematic is shown below. This does not take into account the DC gain that occurs.
Parts that would be used for this: LM317 regulator, AD592 temperature transducer, OP amp (low input noise and high impedance), 100K (or maybe 10k) resistor. This is what is currently proposed, but the exact parts we use could be changed to better fit the sensor. The resistor and the OP amp will be decided depending on the output of the AD592.
Once this is built, I would like to create a few copies of it and put them into an insulated container and measure the output from each one. This would allow us to calculate the temperature noise of the circuit, as we can take out the variations due to temperature changes inside the container by comparing the outputs.
I can also model the noise in the circuit to see how much noise there is before building it. There are three terms to the noise that we have, and we need to decide which one dominates at low frequencies.
Our final goal is to create an additional circuit that could cancel out the DC gain. I have attached an additional schematic proposed by Rana that would help with this issue. I will leave this second half for when the first part works.
I decided to see what was inside the sensor that had been previously made. According to elog 1102, the temperature sensor is LM34, the specs of which can be found here:
The wiring of this sensor confused me, as it appears that the +Vs end (white) connects to the input, but both the ground (left) and the Vout (middle) pins are connected to the box itself. I don't see how the signal can be read.
Since there seems to be little difference between AD590 and AD592, I guess we could just go with the AD590. The temperature noise spectrum in the first graph are for the AD590, so if we want to reproduce those results, we should use AD590.
For the AD581/AD587, we could go with a few varieties that have the least output voltage drift, although I am not sure what precision we will need. So maybe we could try AD587U and AD581L. We could also try AD587K and AD581K and see if those work as well.
We will also need to calibrate the sensor, as it takes an input of 5V, but the AD581/AD587 provides 10V, which will give about a 1 degree error according to the datasheet. It does state that this is only a calibration error, so it shouldn't be too much of an issue.
I will figure out the packaging once I construct the sensor and verify that it works. Maybe we could use a box similar to the existing sensor, but it depends on the size of the finished circuit.
Quick update: we actually have AD587KRZ and AD592, so we could start by using that and seeing how it works.
Used AD592CNZ and AD586 (5V output) to create a circuit that works and is responsive to temperature changes. At room temp, using ~1K resistor, it showed ~0.3V across it, as expected. The voltage went up when we heated it with a heating gun. Next step will be to add in an OP amp and design some experiments to check to see how accurate it is. Thanks to Gautam for helping me with it!
I have attached the working circuit and a close up of the connections.
Decided to try adding in an OP amp just to see if it would work. Added LT1012 and a 100k resistor to the circuit (I originally wanted to do AD743 as it seems to be the best choice according to Zach's elog here, but it said that they are very precious so I went with LT1012 for testing purposes). When heating it with a heating gun, the output voltage went down by a few 0.01V. The maximum voltage was 0.686V. Similar thing happened when I switched to a 10k resistor, where the maximum was 0.705V and it also went down by a few 0.01V upon heating.
I've attached a few pictures showing the circuit.
I didn't realize that the LT1012 needed an additional input to function. I added in +15V and -15V to pins 7 and 4, respectively and placed a 10k resistor and the numbers make more sense now. The voltage showed a negative value, but it became more negative as I heated it up (it's negative due to how a transimpedance amplifier works).
I have attached the new setup and the value it shows (~-3V). It became more negative by about 0.4V, which translates to about a 40K increase in temperature, which makes sense.
In addition, I have attached an updated sketch of the circuit. I will need to do more testing to determine how accurate this is. The next step would be to calculate how much noise there is currently and figure out how to remove this circuit from the breadboard and use a PCB or something like that for final testing in an insulated container.
The reason I chose AD743 initially for the OP amp is because at low frequencies (which is what we are working with), a FET amp such as AD743 will have a low current noise at high impedance, which is what we have in this case. While a FET amp has high voltage noise compared to other OP amps, the current noise becomes more important at high impedance, so it will work better. According to Zach's graphs, the AD743 is best at high impedances, followed by LT1012.
For the final packaging/mounting of the sensor to the seismometer, I have thought of two options.
1. Attach circuit to a PCB board and place it inside the can, while leaving the AD590 open to the air inside the can.
2. Attach the AD590 to a copper plate with thermal paste and put it into a pomona box.
If anyone has input on which method is preferred or any additional options that we may have, I would appreciate it.
q = k A dT / s
For copper, k = 401 W/mK, x = 1.27 mm, A = 2.66x10^-3 m^2 (for the particular copper plate I measured), dT = 1K (assume). Thus the heat transfer will be 839 J/s.
I'm not completely sure what to do with this yet, but it could help us decide whether the copper plate option will be useful for us.
Tested to make sure that even when only the AD586 was heated that there was no change in the reading. I did so by placing the AD586 away from the rest of the circuit and blowing hot air only on it. There was, in fact, no change.
Tried taking the circuit from the breadboard to the PCB. I attached all the components to adapters that would allow them to be connected to the PCB. From the first picture, the first component is AD586, the second is AD590, and the third is LT1012, along with a resistor across it. I then soldered the connections between the components, as can be seen in the second picture. When I tested out this version of the circuit by hooking it up to the DC source, I got a reading of ~-15V. I will have to check all the connections to make sure there is contact where there should be one, and no contact where there shouldn't be. I had issues attaching the tiny AD590 and LT1012 to its adaptor, so the issue may lie there as well. I'll also check that each component is in working order as well.
Once I figure out where my error is, my plan is to build two more of these and place a metal object such that it contacts only the surface of the AD590s. This would allow me to compare the three values to the actual temperature of the metal, which would then tell me how accurate this setup is.
Note on the resistor: I measured all the resistors and chose three that had exactly 10.00k Ohm. The voltage detected is dependent on the resistor, so if we are to take three identical copies, I ensured that there would be no error due to the resistors being a little different.
Got it to work. One of the connections was faulty. I decided to check the temperature measured against a thermometer. The sensor showed 26.1 C, but the thermometer showed 25.8 C after I let them both cool down after heating them up. The temperature of the thermometer was dropping at the time of measurement, but the temperature of the sensor was not. This is still a rough version of the final sensor, so I'm not sure what exactly causes this discrepancy.
On Friday, I cleaned up the circuit so that there are only three connections needed (+15V, -15V, GND) and a BNC connector for reading the output. Today, I added in bypass capacitors. The small yellow ones are 0.1 microF ceramic, and the large ones are 100 microF electrolytic. They are used to stabilize the +15V and -15V inputs to the OP amp and minimize fluctuations, since it doesn't have a regulator for stability. I have also attached the circuit diagram for the OP amp only, where 1 are the electrolytic and 2 are the ceramic. The temperature is still about 2 degrees off, but if that difference is constant for all temperatures in our range we can just calibrate it later.
Here is a helpful link on bypass capacitors (thanks to Kevin for sending it to me).
As a note, the electrolytic capacitors do have a polarity, so it is important to place them correctly (the negative side is towards the lower voltage potential, and not always towards ground).
I worked with Kevin and Gautam to create a heater circuit. The first attachment is Kevin's schematic of the circuit. The OP amp connects to the gate of the power MOSFET, and the power supply connects to the drain, while the source goes into the heater. We set the power supply voltage to 22V and varied the voltage of the input to the OP amp. At 6V to the OP amp, we got a current of 0.35A flowing through the heater and resistor. This was the peak current we got due to the OP amp being saturated (an increase in either of the power supplies did not change the current), but when we increased the voltage of the supply rails of the OP amp from 15V to 20V, we got a current of 0.5A. We would want a higher current than this, so we will need to get a different OP amp with a higher max voltage rating, and a resistor that can take more power than this one (it currently takes 5W of power, and is the best one we could find).
Kevin and I created a simulation of this circuit using CircuitLab to understand why the current was so low (second attachment). The horizontal axis is the voltage we supply to the OP amp. The blue line shows the voltage at the point between the output of the OP amp and the gate of the MOSFET. The orange line is the voltage at the point between the source of the MOSFET and the heater. The brown line is the voltage at the point between the heater and resistor. Thus, we can see that saturation occurs at about 2.1V. At that point, the gate-source voltage is the difference between the blue curve and the orange curve, which is about 4V, which is what we measured. Likewise, the voltage across the heater is the difference between the orange curve and the brown curve, which comes out to around 8V, which is also what we measured. Lastly, the voltage across the resistor is the brown curve, which is about 2V, which matches our observations. The circuit works as it should, but saturates too soon to get a high enough current out of it.
Gautam noted that it is important to measure the current correctly. We can't just use an ammeter and place it across the resistor or heater, because the internal resistance of the ammeter (~0.5 ohm) is comparable to the resistance we want to measure, so the current gets split between the circuit and the ammeter and we get an equivalent resistance of 1/R = 1/R0 + 1/Ra, where R0 is the resistance of the part we want to measure the current across, and Ra is the ammeter resistance. Thus, the new resistance will be lower and the ammeter will show a higher current value than what is actually there. So to accurately measure the current, we must place the ammeter in series with the part we want to measure. We initially got a 1A reading on the heater, which was not correct, and our setup did not heat up at all basically. When we placed the ammeter in series with the heater, we got only 0.35A.
The last two images are the setup for testing of the heater. We wrapped it around an aluminum piece and covered it with a few layers of insulating material. We can stick a thermometer in between the insulation and heater to see the temperature change. In later tests, we may insulate the whole piece so that less heat gets dissipated. In addition, we used a heat sink and thermal paste to secure the MOSFET to it, as it got very hot.
Our next steps will be to get a resistor and an OP amp that are better suited for our purposes. We will also run simulations with components that we choose to make sure that it can provide the desired current of 1A (the maximum output of the power supply is 24V, and the heater is 24 ohm, so max current is 1A). Kevin is working on that now.
I took off the AD590 and attached it to two long wires leading out from the board. This will allow us to attach the sensor to a metal block and not have to stick the whole board to it. I have also completed three identical copies of this and it's pretty much ready to be tested. According to Craig and Andrew's elog here, the sensor is very noisy and they added in a low pass filter to fix that, so that's something to consider for the final version of the circuit. I'll test what I have so far and see how that goes. We still need to figure out how to get readings from the sensors.
To attach the sensor to the metal block, I'll use some thermal paste and fasteners. I'll also put a thermometer on the block to record the actual temperature. I'll then wrap it in some insulation we have in the lab and have only some wires leading out of it to make measurements. I'll leave this setup overnight and record the outputs for about a full day. The fluctuations between the sensors will then indicate the noise of each individual sensor.
I decided to calculate the fluctuation in power that we will have in the heater circuit. The resistors we ordered have 50 ppm/C and it would be useful to know what kind of fluctuation we would expect. For this, I assumed that the heater itself is an ideal resistor that has no temperature variation. The circuit diagram is found in Kevin's elog here. At saturation, the total resistance (we will have a resistor instead of for our new design) will be . Therefore, with a 24V input, the saturation current should be . Therefore, the power in the heater should be (in the ideal case)
Now, in the case where the resistor is not ideal, let's assume the temperature of the resistor changes by 10C (which is about how much we would like to heat the whole thing). Therefore, the resistor will have a new value of . The new current will then be and the new power will be . So the difference in power going through the heater is about 0.00088W.
We can use this power difference to calculate how much the temperature of the metal can we wish to heat up will change. where is the thermal conductivity and x is the thickness of the material. For our seismometer, I calculated it to be 0.012K.
Today, I stuck on the sensors to a metal block using a flag, rubber bands, and some thermal paste (1st attachment). I then wrapped the whole thing in about 4 layers of insulation and a lot of tape (2nd attachment). The only things leading out of the box were the three connections to the sensors and a thermometer. I then connected the wires to their respective places on the board of the sensor. To get the readings out we would need to use an ADC. Gautam and I checked to make sure the ADC we have inside the lab goes from -10V to 10V so that it would be able to measure the 3V value the sensor typically measures. We then tried to connect all three sensors to a DC source simultaneously, but unfortunately one of them seems to have disconnected somewhere during the process, as it only showed 1.2V instead of 3V. I plan to fix this tomorrow morning so that we can hopefully set this up soon.
to get the sensors to read the same values they have to be in direct thermal contact with the metal block - there can't be any adapter board in-between
for the 2nd attempt, I also recommend encasing it in a metal block rather than just one side. You can drill some 7-10 mm diameter holes in an aluminum or copper block. Then put the sensors in there and plug it up with some thermal paste.
Got it to work. A cable was broken and the AD586 also broke at the same time so it took a while to find the problem. I had to create a makeshift cable out of three parts so once I replace it for an actual cable, it will be good to go for a test.
Gautam and I measured the noise of the ADC for channels 17, 18, and 19. We plan to use those channels for measuring the noise of the temperature sensors, and we need to figure out whether or not we will need whitening and if so, how much. The figure below shows the actual measurements (red, green and blue lines), and a rough fit. I used Gautam's elog here and used the same function, (with units of nV/sqrt(Hz)) to fit our results. I used a = 1, b = 1e6, c = 2000. Since we are interested in measuring at lower frequencies, we must whiten the signal from the temperature sensors enough to have the ADC noise be negligible.
We want to be able to measure to accuracy at 1Hz, which translates to about current from the AD590 (because it gives ). Since we have a 10K resistor and V=IR, the voltage accuracy we want to measure will be . We would need whitening for lower frequencies to see such fluctuations.
To do the measurements, we put a BNC end cap on the channels we wanted to measure, then took measurements from 0-900Hz with a bandwidth of 0.001Hz. This setup is shown in the last two attachments. We used the ADC in 1X7.
I made a model for our seismometer can using actual data so that we know approximately what the time constant should be when we test it out. I used the appendix in Megan Kelley's report to make a relation for the temperature in terms of time.
In our case, we will heat the can to a certain temerature and wait for it to cool on its own so
We know that where k is the k-factor of the insulation we are using, A is the area of the surface through which heat is flowing, is the change in temperature, d is the thickness of the insulation.
We can take the derivative of this to get
We can guess the solution to be
where tau is the time constant, which we would like to find.
The boundary conditions are and . I assumed we would heat up the can to 40 celcius while the room temp is about 24. Plugging this into our equations,
We can plug everything back into the derivative T'(t)
Equating the exponential terms on both sides, we can solve for tau
Plugging in the values that we have, m = 12.2 kg, c = 500 J/kg*k (stainless steel), d = 0.1 m, k = 0.26 W/(m^2*K), A = 2 m^2, we get that the time constant is 0.326hr. I have attached the plot that I made using these values. I would expect to see something similar to this when I actually do the test.
To set up the experiment, I removed the can (with Steve's help) and will place a few heating pads on the outside and wrap the whole thing in a few layers of insulation to make the total thickness 0.1m. Then, we will attach the heaters to a DC source and heat the can up to 40 celcius. We will wait for it to cool on its own and monitor the temperature to create a plot and find the experimental time constant. Later, we can use the heatng circuit we used for the PSL lab and modify the parts as needed to drive a few amps through the circuit. I calculated that we'd need about 6A to get the can to 50 celcius using the setup we used previously, but we could drive a smaller current by using a higher heater resistance.
I performed a test with the can last week with one layer of insulation to see how well it worked. First, I soldered two heaters together in series so that the total resistance was 48.6 ohms. I placed the heaters on the sides of the can and secured them. Then I wrapped the sides and top of the can in insulation and sealed the edges with tape, only leavng the handles open. I didn't insulate the bottom. I connected the two ends of the heater directly into the DC source and drove the current as high as possible (around 0.6A). I let the can heat up to a final value of 37.5C, turned off the current and manually measured the temperature, recoding the time every half degree. I then plotted the results, along with a fit. The intersection of the red line with the data marks the time constant and the temperature at which we get the time constant. This came out to be about 1.6 hours, much longer than expected considering that onle one layer instead of four was used. With only one layer, we would expect the time constant to be about 13 min, while for 4 layers it should be 53 min (the area A is 0.74 m^2 and not 2 m^2).
Updated some values, most importantly, the k-factor. I had assumed that it was in the correct units already, but when converting it to 0.046 W/(m^2*K) from 0.26 BTU/(h*ft^2*F), I got the following plot. The time constant is still a bit larger than what we'd expect, but it's much better with these adjustments.
For our next steps, I will measure the time constant of the heater without any insulation and then decide how many layers of it we will need. I'll need to construct and calibrate a temperature sensor like the ones I've made before and use it to record the values more accurately.
For the insulation, I have decided to use this one (Buna-N/PVC Foam Insulation Sheets). We will need 3 of the 1 inch plain backing ones (9349K4) to wrap a few layers around it. I'll try two layers for now, since the insulation seems to be doing quite well according to initial testing.
Gautam and I set up the insulated seismometer can in the lab today. I had previously wired up the two heaters I placed onto the sides of the can in parallel to get a total resistance of 12.5 ohms and then I wrapped the whole can in 3 layers of insulation (k-factor 0.25). We placed it on a large sheet of insulation as to not crush the wires leading out the bottom of the can. I stuck on one of my AD590 sensors to the inside of the can onto the copper lining using duct tape, though this is only a temporary solution. In the future, it would be nice to have some sort of thermal clamp to secure the sensor to the can. To provide power to the heater circuit board and the temperature sensor board, we got a powerstrip and plugged in two power supplies and a function generator into it. The heater circuit (attachment 3) is powered by one of the power supplies and the function generator, while the temperature sensor (attachment 5) is stuck to the side of the can and is powered by the second power supply. The heater circuit's MOSFET (IRF640, attachment 4) is placed on a metal block and sandwiched between two more to make sure it doesn't move around. The temperature sensor is connected by a long BNC cable to the channels in attachment 6.
gautam: we plugged the BNC output of Kira's temperature sensor circuit to J7 on the AA input chassis in 1X2 - this corresponds to ADC1 input 12 in c1ioo. I then made a "PEM" namespace block inside the c1als model, and placed a single CDS filter module inside it (this can be used for calibration purposes). The filter module is named "C1:PEM-SEIS_EX_TEMP", and has the usual CDSfilt channels available. I DQ'ed the output of the filter module (@256 Hz, probably too high, but I'm holding off on a recompile for now). Recompilation and model restart of c1als went smoothly.
2 bench power supplies are being used for this test, we can think of a more permanent solution later.
**25 Jan noon: Added another filter module, "C1:PEM-SEIS_EX_TEMP", to which Kira is hooking up a second temperature sensor, which will serve as a monitor of the "Ambient" lab temperature. Added DQ channel for the output of this filter module, fixed sampling to 32Hz. Compile and restart went smooth.
We started the actual heating test today and it seems to be working so far. Hoping to heat it to about 40C. We also set up another temperature sensor to measure the lab temperature and connected it to J7, bottom.
After almost 3 hours the temperature rose by about 3.5C. Seems a bit slow, but we can drive it more if necssary. The heating curve itself is exponentiial, which is a good sign.
The final temperature reached in about 4.5 hours is 30.5C, while the starting temperature is about 24C. I can't seem to screenshot the data for some reason.
Also, I will calibrate the lab temperature sensor to Celcius in the near future so that we would have a working sensor inside the lab.
After taking the measurements, calibrating them (approximately), and filterting them, I created the following plot. The exponential fit is quite good, as the error is not more than 0.03 C. I used the python function curve_fit in order to get this, and it gave me the time constant as well, which came out to 0.357 hr. From my previous calculations here, I plugged in the values we have (m = 12.2 kg, c = 500 J/kg*k, d = 0.0762 m, k = 0.26 W/(m^2*K), A = 1 m^2), and got that
This is a bit off, but it's probably due to the parameters not being exactly what I supposed them to be, and heat losses through the bottom of the can.
Attached the program I used to create the plot
from scipy.optimize import curve_fit
from scipy.signal import decimate
import cdsutils as cds
import numpy as np
import matplotlib.pyplot as plt
channel = ['C1:PEM-SEIS_EX_TEMP_OUT_DQ']
tstart = 1200962230
tend = 1201041084
I decided to plot the temperatures measured over two days for the sensor inside the can and inside the lab just to see if there was any significant difference between the two, and obtained the following plot. This shows that there is a difference in measurements of a few 0.01 C. The insulated seismometer can didn't change temperature as much as the lab did, which is as expected. I'll work on properly calibrating the sensors sometime in the future so that we can use the sensor that's just in the lab as an accurate thermometer.
I subtracted out the lab temperature change during the period of cooling to see if it would have a significant effect on the time constant, but when I fit the new data, the time constant came out to 0.355 hr, which is not a significant change from the value of 0.357 that I got earlier.
Some points before we can set up the can:
Also, I need to eventually remake the connections on my circuit board because they are all currently test points. I also need to find a box for the heater circuit and figure out what to do with the MOSFET and heat sink for it. This can either be done before setting everything up, or we can just change it later once we have the final setup for the can ready.
If all of this looks good then we can begin the setup.
We set up a new rail for the Sorensens (attachment 1) and placed one of them down on this new rail (attachment 2). Unfortunately the older rail that had been used to support the other Sorensens (the top one in attachment 1) is thick and does not allow another one of the Sorensens to slide in between the current ones. So we will have to support all the ones on top with a temporary support, take out the old rail, and then insert the new ones before letting the new bottom rail carry the weight of all of the Sorensens. We will do that tomorrow.
In addition, we have to figure out how to lead all the cables to the can, but there are no holders on the side of the lab to do so. So, we decided that we would have a new one installed on the side shown in attachment 3 so that we wouldn't have to place the wires along the floor.
Also, there has been some space made for the can along with the new insulation. The stuff mounted on the wall was removed and will be reattached tomorrow so that it doesn't get in the way of the can anymore.
We installed and labeled the Sorensens today.
I checked channels 6 and 7 on the ADC and they have long wires leading to BNC ends and are currently not being used, so we could probably just attach the temperature sensors to those channels.
Rewired the temperature sensor inputs to Molex connectors so that we can now attach them to the +/- 15V Sorensens for input instead of using a power supply.
We began the setup for the lab temperature sensor today. First, we needed to add in a DIN fuse for both temperature sensors, which required us to shut down everything else first. To avoid having to do that next time, we made three instead of two spaces where we have + and - 15V. Attachment 1 shows the new fuses we installed, along with the fuses they connect to. Attachment 2 shows the wiring that we used to connect all the fuses. Attachment 3 shows the labeled long wires that are attached to the lab temperature sensor. The other end is labeled as well. I measured the voltage at the other end of the long cables, and while the -15V one looks good, the +15V one shows only about 13.5V.
edit (Tuesday) - I set up the other set of cables that will eventually lead to the sensor in the can, but neither of them are showing any voltage on the other end. I'll work on this issue tomorrow.
gautam: some additional remarks about the procedure followed: