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{
"cells": [
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import pretty_plots # script to set up LaTex and increase line-width and font size"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [],
"source": [
"pretty_plots.setdefaults()\n",
"pi=np.pi"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"![Mass measurement cantilever](./contest_diagram.png)\n",
"\n",
"*Figure 1: Diagram of cantilever with unknown mass in position 2 out of 3 total positions. Measure changes in the natural frequencies to determine mass of object.*\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ME 3263 Introduction to Sensors and Data Analysis (Fall 2018)\n",
"\n",
"## Lab #5 Mass Measurement Device with Cantilever beam\n",
"\n",
"# Mass measurement contest\n",
"\n",
"In the mass measurement contest, you will use natural frequency shifts to determine the mass of an object. There are three locations you can mount the object as seen in Figure 1, where the object is mounted in position 2. The experimental procedure only involves measuring natural frequency with the mass mounted in different positions. You can create an *engineering model* as we will do with experimental results from Ghatkesar *et al.* 2007 [\\[1\\]](./ghatkesar-et-al-2007_higher-mode-mass-sensors.pdf), as described in section 2.\n",
"\n",
"You can use the modal analysis in **Ansys** [\\[2\\]](https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/main_page.html) and apply a point mass to get predicted changes in natural frequencies. This will create a table of values for your given cantilever for known masses for *interpolation* as described in section 3.\n",
"\n",
"**Rules of Contest**\n",
"\n",
"1. The masses must not leave the lab\n",
"\n",
"2. You cannot mount other known masses to the cantilever\n",
"\n",
"3. You must report your uncertainty in your mass measurement to enter the competition\n",
"\n",
"4. You must report your serial number \"TJM 01-TJM 12\" to enter the competition\n",
"\n",
"6. You may use the following tools and software: strain gage or accelerometer (not both), calipers, Ansys, Labview, Python, Matlab, and Excel\n",
"\n",
"**Winners of the contest**\n",
"\n",
"There will be two sets of winners for the contest:\n",
"\n",
"1. Lab group with the most accurate mass measurement calculated with $A=|m_{reported}-m_{actual}|$\n",
"\n",
"2. Lab section with the most precise mass measurement calculated with $P=\\sum_{i=1}^{N}(m_{reported}-m_{actual})^2$\n",
"\n",
"Where $A$ is the accuracy, $P$ is the precision, $m_{reported}$ is the reported mass from your experiment, and $m_{actual}$ is the actual mass of the object, and $N$ is the total number of lab groups in a section. The group and section with smallest A and P, respectively will win prizes. The prizes are as such\n",
"\n",
"1. ** \\$100 cash prize** put into your student accounts ($50/group member for group of 2)\n",
"\n",
"2. **Donuts/cookies** brought to your lab section\n",
"\n",
"**Lab #5 report** should include details of the following\n",
"\n",
"1. Your design of experiments\n",
"\n",
"2. Your measured results\n",
"\n",
"3. Your predicted results from Ansys\n",
"\n",
"4. Your final calibration process for measuring a mass based upon natural frequency changes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1. What affects natural frequencies\n",
"\n",
"The natural frequencies of a cantilever beam using Euler-Bernoulli beam theory are as such\n",
"\n",
"$\\omega_i=\\beta_i^2\\sqrt{\\frac{EI}{\\bar{m}L^4}}$ (1)\n",
"\n",
"where the $i^{th}$ natural frequency, $\\omega_i$ is given in\n",
"rad/s,$\\beta_1=1.875104$, $\\beta_2=4.694091$, $\\beta_3=7.854757$, $\\bar{m}$ is\n",
"the mass per unit length, $E$ is Young's modulus, and $I$ is the second moment\n",
"of area of the beam. Ensure that the units of $\\omega_i$ are rad/s e.g. 1/s.\n",
"\n",
"There are four variables that affect the natural frequency: stiffness (E), mass ($\\bar{m}$), second moment of area of cross-section, ($I=wt^3/12$, for rectangular cross-section of $w\\times t$), and length, $L$. \n",
"\n",
"One common use for microscale cantilever beams is to measure mass of micro- and nanoscale particles or coatings \\[[1](./ghatkesar-et-al-2007_higher-mode-mass-sensors.pdf), [3](./sharos-et-al-2004_MEMS-torsion.pdf), [4](./narducci-et-al_MEMS-mass.pdf), 4-9\\]. If a thin coating of material is applied to the surface, the mass per unit length, $\\bar{m}$ increases while the stiffness, $E$, will remain mostly unchanged for stiff cantilevers, e.g. the commonly used silicon cantilever. Consider a silicon cantilever $500\\times 100 \\times 4~\\mu m^3$. The first three bending natural frequencies are calculated below."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"natural frequency 1 = 21.4 kHz\n",
"natural frequency 2 = 134.2 kHz\n",
"natural frequency 3 = 375.8 kHz\n"
]
}
],
"source": [
"L=500 # um\n",
"w=100 # um\n",
"t=4 # um\n",
"E=160 # GPa = 160 mN/um^2\n",
"rho=2330 # kg/m^3 \n",
"# properties from https://www.memsnet.org/material/siliconsibulk/\n",
"mbar=rho*(1e-3)**3*t*w*(1e-3)**2 # kg/mm\n",
"I=w*t**3/12\n",
"beta=np.array([ 1.87510407, 4.69409113, 7.85475744])\n",
"omega=beta**2*np.sqrt(E*I/(mbar*L**4))*1000 # sqrt(kg-mm/s^2/um^2 *mm/kg) = 1000 rad/s\n",
"for i,w in enumerate(omega):\n",
" print('natural frequency %i = %3.1f kHz'%(i+1,w/2000/pi))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2. Creating an engineering model from experimental data\n",
"\n",
"Now, if we monitor gold coatings as seen in Ghatkesar *et al.* 2007 [\\[1\\]](./ghatkesar-et-al-2007_higher-mode-mass-sensors.pdf), the gold coating will decrease the first three bending mode natural frequencies. The results for the 4$\\mu m$ cantilever coated with 40, 80, and 120 nm of gold are shown in the \"Experimental Data\" figure. We can use these experimental results to create a model that relates thickness (increase in mass) to frequency shift. The model will have three inputs, $\\Delta f_1$, $\\Delta f_2$, and $\\Delta f_3$ and one output of thickness, $t$ as such\n",
"\n",
"$t = A \\Delta f_1+ B \\Delta f_2 + C \\Delta f_3$ (2)\n",
"\n",
"where the constants A, B, and C are fitting parameters that depend upon the cantilever. The fitting process and results are shown in the next cell with a plot titled \"Best fit model for Au thickness detection\". Here, we use a linear fit because we only have 4 data points per mode, we could add quadratic or cubic terms if the slope of the results was not constant."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f112e450160>"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f1_shift=np.loadtxt('./f1_shift.csv',delimiter=',',skiprows=1) # load Ghatkesar mode 1 shift\n",
"plt.plot(f1_shift[:,0],f1_shift[:,1],'s-',label='mode 1') # plot Ghatkesar mode 1 shift\n",
"f2_shift=np.loadtxt('./f2_shift.csv',delimiter=',',skiprows=1) # load Ghatkesar mode 2 shift\n",
"plt.plot(f2_shift[:,0],f2_shift[:,1],'o-',label='mode 2') # plot Ghatkesar mode 2 shift\n",
"f3_shift=np.loadtxt('./f3_shift.csv',delimiter=',',skiprows=1) # load Ghatkesar mode 3 shift\n",
"plt.plot(f3_shift[:,0],f3_shift[:,1],'^-',label='mode 3') # plot Ghatkesar mode 3 shift\n",
"plt.title('Experimental Data')\n",
"plt.xlabel('Au thickness (nm)')\n",
"plt.ylabel('frequency shift (kHz)')\n",
"plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"best-fit model constants are:\n",
"A=-1.53+/-1.1e-12\n",
"B=-92.27+/-1.9e-12\n",
"C=31.13+/-6.7e-13\n"
]
}
],
"source": [
"from scipy.optimize import curve_fit\n",
"def thickness_func(df,A,B,C):\n",
" df1,df2,df3=df # input is a list of three frequency shifts (df1,df2,df3)\n",
" return A*df1+B*df2+C*df3 # output is a thickness of gold in nm\n",
"\n",
"t_meas=f1_shift[:,0] # grab thickness measurements from data\n",
"df_meas=(f1_shift[:,1],f2_shift[:,1],f3_shift[:,1]) # format frequency shift measures for fitting\n",
"CSTS,pcov=curve_fit(thickness_func, df_meas, t_meas)# least-squares curve-fit using function, df-values, and thickness measures\n",
"A,B,C=CSTS # get best-fit constants\n",
"Aerr=np.sqrt(pcov[0,0]) # get error in best-fit constant A\n",
"Berr=np.sqrt(pcov[1,1]) # get error in best-fit constant B\n",
"Cerr=np.sqrt(pcov[2,2]) # get error in best-fit constant C\n",
"df_model=(np.linspace(0,f1_shift[-1,1]),\\\n",
" np.linspace(0,f2_shift[-1,1]),\\\n",
" np.linspace(0,f3_shift[-1,1])) # format model inputs to plot results from min-max of df1=df3\n",
"\n",
"print('best-fit model constants are:') \n",
"print('A=%1.2f+/-%1.1e'%(A,Aerr))\n",
"print('B=%1.2f+/-%1.1e'%(B,Berr))\n",
"print('C=%1.2f+/-%1.1e'%(C,Cerr))\n",
"\n",
"t_model=thickness_func(df_model,A,B,C) # get model predictions from best-fit constants"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f112e289710>"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot experimental data and best fit model\n",
"plt.plot(f1_shift[:,0],f1_shift[:,1],'s-',label='mode 1')\n",
"plt.plot(f2_shift[:,0],f2_shift[:,1],'o-',label='mode 2')\n",
"plt.plot(f3_shift[:,0],f3_shift[:,1],'^-',label='mode 3')\n",
"plt.plot(t_model,df_model[0],'r-',label='model')\n",
"plt.plot(t_model,df_model[1],'r-')\n",
"plt.plot(t_model,df_model[2],'r-')\n",
"plt.xlabel('Au thickness (nm)')\n",
"plt.ylabel('frequency shift (kHz)')\n",
"plt.title(r'Best fit model for Au thickness detection')\n",
"plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3. Interpolating data from a numerical model\n",
"\n",
"In the previous example, we used a least-squares regression to create a model that reduces noise in our prediction based upon experiments. If, we have a numerical model that we do not want to solve with 100 or 1,000 different input configurations, we can use interpolation to estimate points in between calculated values. Let's use a set of calculated data using Eqn (1) as seen in the table below. The values in Table 1 are calculated based upon the density of gold (19.32 g/cm^3) and deposited volume ($500\\times400\\times t~\\mu m^3$), but we could have also tabulated these with an Ansys model that incorporated the stiffness of the gold coating. \n",
"\n",
"*Table 1: Tabulated data for change in frequency and gold coating thickness.*\n",
"\n",
"|Au thickness (nm)| $\\Delta f_1 (kHz)$| $\\Delta f_2 (kHz)$| $\\Delta f_3 (kHz)$|\n",
"|---|---|---|---|\n",
"|0| 0.0| 0.0|0.0 |\n",
"|20| -0.2| -1.4|-3.8 |\n",
"|40| -0.4| -2.7|-7.6 |\n",
"|60| -0.6| -4.0|-11.2 |\n",
"|80| -0.8| -5.2|-14.7 |\n",
"|100| -1.0| -6.5|-18.1 |\n",
"|120| -1.2| -7.6|-21.4 |\n",
"\n",
"Now, we can use an interpolation function to estimate points in between the predicted values of our model as seen in the next cell.\n"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f112dfba160>"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.interpolate import griddata\n",
"data = np.loadtxt('./df_model.csv',skiprows=1,delimiter=',')\n",
"t_pred=data[:,0]\n",
"plt.plot(t_pred,data[:,1],'s',label='mode 1')\n",
"plt.plot(t_pred,data[:,2],'o',label='mode 2')\n",
"plt.plot(t_pred,data[:,3],'^',label='mode 3')\n",
"df1=np.linspace(0,np.min(data[:,1]))\n",
"df2=np.linspace(0,np.min(data[:,2]))\n",
"df3=np.linspace(0,np.min(data[:,3]))\n",
"\n",
"t_int_l = griddata(data[:,1:], t_pred, (df1,df2,df3), method='linear')\n",
"plt.plot(t_int_l,df1,'r-',label='linear interp.')\n",
"plt.plot(t_int_l,df2,'r-')\n",
"plt.plot(t_int_l,df3,'r-')\n",
"plt.xlabel('Au thickness (nm)')\n",
"plt.ylabel('frequency shift (kHz)')\n",
"plt.title(r'Linear interpolation for Au thickness detection')\n",
"plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# References\n",
"\n",
"3. Ghatkesar, Murali Krishna, et al. \"Higher modes of vibration increase mass sensitivity in nanomechanical microcantilevers.\" Nanotechnology 18.44 (2007): 445502.\n",
"\n",
"0. [Ansys help topic: Modal Analysis](https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/corp/main_page.html)\n",
"\n",
"1. Narducci, Margarita, et al. \"A high sensitivity silicon microcantilever based mass sensor.\" Sensors, 2008 IEEE. IEEE, 2008.\n",
"\n",
"2. Sharos, L. B., et al. \"Enhanced mass sensing using torsional and lateral resonances in microcantilevers.\" Applied Physics Letters 84.23 (2004): 4638-4640.\n",
"\n",
"4. Chen G Y, Thundat T, Wachter E A and Warmack R J 1995\n",
"Adsorption-induced surface stress and its effects on\n",
"resonance frequency of micocantilevers J. Appl. Phys. 77\n",
"3816\n",
"\n",
"5. Wachter E A and Thundat T 1995 Micromechanical sensors for\n",
"chemical and physical measurements Rev. Sci. Instrum.\n",
"66 3662\n",
"\n",
"6. Pinnaduwage L A, Hawk J E, Boiadjiev V, Yi D and\n",
"Thundat T 2003 Use of microcantilevers for the monitoring\n",
"of molecular binding to self-assembled monolayers\n",
"Langmuir 19 7841\n",
"\n",
"7. Nugaeva N, Gfeller K Y, Backmann N, Lang H P,\n",
"Duggelin M and Hegner M 2005 Micromechanical\n",
"cantilever array sensors for selective fungal immobilization\n",
"and fast growth detection Biosens. Bioelectron. 21 849\n",
"\n",
"8. Battiston F M, Ramseyer J P, Lang H P, Baller M K,\n",
"Gerber Ch, Gimzewski J K, Meyer E and\n",
"G¨untherodt H-J 2001 A chemical sensor based on a\n",
"microfabricated cantilever array with simultaneous\n",
"resonance-frequency and binding readout Sensors Actuators\n",
"B 77 122\n",
"\n",
"9. Gfeller K Y, Nugaeva N and Hegner M 2005 Micromechanical\n",
"oscillators as rapid biosensor for the detection of active\n",
"growth of escherichia coli Biosens. Bioelectron. 21 528\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 2
}