{
"cells": [
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"cell_type": "markdown",
"metadata": {
"user_expressions": []
},
"source": [
"\n",
"\n",
"# Evaluation models: endurance of the actuator\n",
"\n",
"*Written by Marc Budinger (INSA Toulouse) and Scott Delbecq (ISAE-SUPAERO), Toulouse, France*"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
},
"tags": [],
"user_expressions": []
},
"source": [
"\n",
"## Endurance specifications\n",
"\n",
"In the description of the TVC system given in the [following article](http://esmats.eu/esmatspapers/pastpapers/pdfs/2009/vanthuyne.pdf) an endurance test profile composed of multiple sinusoidal displacements is given. \n",
"\n",
"*Endurance profile for P80 EMA*\n",
"\n",
"\n",
"\n",
"> Exercice: declare the magnitude displacement, frequency and number of cycles (divided by 100 here) informations in 1D arrays (numpy) for cycles 1 to 6 in a global a Pandas [dataframe](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html) called 'Profil'."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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" A f Nc\n",
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},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Markdown as md # enable Markdown printing\n",
"import numpy as np\n",
"import pandas as pd\n",
"from math import pi\n",
"\n",
"# Declaration of amplitude, frequency and number of cycles 1 to 6\n",
"\n",
"lever_arm = 1.35 # [m] Lever Arm\n",
"stroke = 6 * pi / 180 * lever_arm # [m] Stroke\n",
"\n",
"profil = pd.DataFrame(\n",
" {\n",
" \"A\": np.array([0.95, 0.5, 0.3, 0.1, 0.05, 0.05]) * stroke,\n",
" \"f\": np.array([0.3, 0.6, 1, 2, 5, 3]),\n",
" \"Nc\": np.array([3700, 4800, 5000, 7000, 8500, 1500]) / 100,\n",
" }\n",
")\n",
"\n",
"profil"
]
},
{
"cell_type": "markdown",
"metadata": {
"user_expressions": []
},
"source": [
"with: \n",
"- A [m], magnitude of stroke;\n",
"- f [Hz], frequency;\n",
"- Nc [-], number of cycles.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
},
"user_expressions": []
},
"source": [
"## Generation of the test profiles\n",
"\n",
"The target is now to generate from this specification a set of time vectors representing the displacement, speed and acceleration. \n",
"\n",
"> Exercice: define a [function](https://anh.cs.luc.edu/python/hands-on/3.1/handsonHtml/functions.html) which take as parameters a dataframe *profil* and a time step and return the desired time vectors.\n",
"Remark: 'arange', 'concatenate' and 'array' functions of numpy can be usefull. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
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},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def test_profiles(profil, step_size):\n",
" tmin = 0\n",
" time = np.array([])\n",
" position = np.array([])\n",
" speed = np.array([])\n",
" acceleration = np.array([])\n",
" for A, f, Nc in zip(profil.A, profil.f, profil.Nc):\n",
" tmax = Nc / f\n",
" # time vector\n",
" t = np.arange(tmin, tmin + tmax, step_size)\n",
" # Position, speed and Acceleration vectors\n",
" X = A * np.sin(2 * pi * f * t)\n",
" Xp = A * 2 * pi * f * np.cos(2 * pi * f * t)\n",
" Xpp = -A * (2 * pi * f) ** 2 * np.sin(2 * pi * f * t)\n",
" # Concatenation of multiple cycles\n",
" time = np.concatenate((time, t))\n",
" position = np.concatenate((position, X))\n",
" speed = np.concatenate((speed, Xp))\n",
" acceleration = np.concatenate((acceleration, Xpp))\n",
" # new start time for the next cycle\n",
" tmin = tmin + tmax\n",
"\n",
" d = {\n",
" \"t\": time,\n",
" \"position\": position,\n",
" \"speed\": speed,\n",
" \"acceleration\": acceleration,\n",
" }\n",
"\n",
" df = pd.DataFrame(data=d)\n",
"\n",
" return df\n",
"\n",
"\n",
"df = test_profiles(profil, 1 / max(profil.f) / 20)\n",
"\n",
"df"
]
},
{
"cell_type": "markdown",
"metadata": {
"user_expressions": []
},
"source": [
"The combination of cycles can now be plot :"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Acceleration [m/s²]')"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"# Position\n",
"plt.figure()\n",
"plt.subplot(311, xlabel=\"Time [s]\")\n",
"plt.plot(df[\"t\"], df[\"position\"])\n",
"plt.ylabel(\"Position [m]\")\n",
"\n",
"# Speed\n",
"plt.subplot(312, xlabel=\"Time [s]\")\n",
"plt.plot(df[\"t\"], df[\"speed\"])\n",
"plt.ylabel(\"Speed [m/s]\")\n",
"\n",
"# Acceleration\n",
"plt.subplot(313, xlabel=\"Time [s]\")\n",
"plt.plot(df[\"t\"], df[\"acceleration\"])\n",
"plt.ylabel(\"Acceleration [m/s²]\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"user_expressions": []
},
"source": [
"## Force mission profile\n",
"\n",
"> Exercice: Knowing the main characteristics of the nozzle (stiffness of 1.52E+04 Nm/deg, viscous damping of 1.74E+02\tNms/deg, inertia of 1.40E+03 kg.m^2), calculate and plot the mechanical force to be applied by the actuation system. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 0, 'Time (s)')"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Definition of nozzle equivalent parameters with engineering units\n",
"Jnozzle = 1.40e03 # [kg.m2] Inertia\n",
"Knozzle = 1.52e04 # [Nm/deg] Stiffness\n",
"Fnozzle = 1.74e02 # [Nms/deg] Viscous damping\n",
"\n",
"# Calculate SI unit values of Knozzle and Fnozzle\n",
"# pi value is math.pi\n",
"\n",
"Knozzle = Knozzle / (pi / 180)\n",
"Fnozzle = Fnozzle / (pi / 180)\n",
"\n",
"# Angular mission profiles (nozzle)\n",
"df[\"teta\"] = df[\"position\"] / lever_arm\n",
"df[\"tetap\"] = df[\"speed\"] / lever_arm\n",
"df[\"tetapp\"] = df[\"acceleration\"] / lever_arm\n",
"\n",
"# Torque and force calculation\n",
"df[\"Fact\"] = (Jnozzle * df[\"tetapp\"] + Fnozzle * df[\"tetap\"] + Knozzle * df[\"teta\"]) / lever_arm\n",
"\n",
"# Plot force mission profile\n",
"plt.plot(df[\"t\"], df[\"Fact\"])\n",
"plt.ylabel(\"Force (N)\")\n",
"plt.xlabel(\"Time (s)\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"user_expressions": []
},
"source": [
"## Rolling fatigue\n",
"\n",
"The rolling fatigue for a variable mission profile is evaluated in two stages:\n",
"- firstly by calculating the number of revolutions and an equivalent rolling fatigue effort called $F_{RMC}$ (RMC for RootMean Cube) \n",
"$F_{RMC}=(\\frac{1}{\\int |\\dot{x}| {d}t} \\int |F|^3 |\\dot{x}| {d}t)^{1/3}$\n",
"- then by obtaining a fatigue effort $F_d$ equivalent to 1 million rev. \n",
"$F_d^3 . N_{ref} = F_{RMC}^3. N_{cycles}$\n",
"\n",
"We will assume here that the screw/nut system has a pitch of 10 mm/rev. Examples of thrust bearings can be found [here](./PDF/MatchedBearingSKF.pdf).\n",
"\n",
"> Exercice: Calculate $F_{RMC}$ and $F_d$. Compare relative ratio between $C_0$ and $C_d$. Conclusion. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/markdown": [
"\n",
"The Root Mean Cube force is *FRMC* = 31 kN \n",
"The number of turns = 4.9e+05 \n",
"The equivalent dynamic load for one million revolutions is *Fd* = 24 kN\n"
],
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pitch = 10e-3 # [m/rev] pitch of the roller screw\n",
"\n",
"# Computation of integrals avec np.trapz\n",
"\n",
"# Global distance\n",
"distance = np.trapz(abs(df[\"speed\"]), df[\"t\"])\n",
"\n",
"# Cumulative damage\n",
"FcubeD = np.trapz(abs(df[\"Fact\"] ** 3 * df[\"speed\"]), df[\"t\"])\n",
"\n",
"# Root Mean Cube\n",
"FRMC = (FcubeD / distance) ** (1 / 3)\n",
"\n",
"# Number of rev for the mission profile\n",
"Nturn = distance * 100 / pitch\n",
"\n",
"# Dynamic equivalent load\n",
"Fd = FRMC * (Nturn / 1e6) ** (1 / 3)\n",
"\n",
"md(\n",
" \"\"\"\n",
"The Root Mean Cube force is *FRMC* = {:.0f} kN \n",
"The number of turns = {:.2g} \n",
"The equivalent dynamic load for one million revolutions is *Fd* = {:.0f} kN\n",
"\"\"\".format(\n",
" FRMC / 1e3, Nturn, Fd / 1e3\n",
" )\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"user_expressions": []
},
"source": [
"> Exercice for excel users: calculate RMC force and equivalent dynamic force with the mission profile saved in the `FatigueProfil.xlsx` file."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# Profil mission export to excel\n",
"df.to_excel(\"FatigueProfil.xlsx\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"user_expressions": []
},
"source": [
"## Analytic calculation of equivalent rolling force\n",
"\n",
"The following figures show the evolution of the actuator forces as a function of the position, speed and acceleration. \n",
"\n",
"> Exercice: Derive from it a simplified approach allowing to calculate the rolling fatigue stress in a fast way directly from the table of specifications of fatigue life cycles. Compare your results with the calculations made directly on the mission profile."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
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48GEcOXIEALBr1y6cO3cOv/zyC5o3b44ePXpg9uzZWL58OXJzX1waYuXKlfDx8cGiRYvQqFEjjB49Gm+99RYWL14sf6xvvvkGw4cPx9ChQ+Hn54eVK1fC1tYWa9as0e+LQQbn3UBPsUuQvDqfR4ldgsljr6FpWn0wRewSjIrkAtaoUaMQFhaG4OBghemJiYnIy8tTmO7r6wtPT0/Exb04n0tcXByaNm0KV1dXeZuQkBBkZ2fj7Nmz8jYllx0SEiJfRm5uLhITExXamJmZITg4WN5GmZycHGRnZyv8kXSN35ykdPq8N5rqtxAjxw09EUmVpALWpk2bcPz4cURERJSal56eDktLSzg5OSlMd3V1RXp6urxN8XBVNL9oXlltsrOz8ezZM9y7dw8FBQVK2xQtQ5mIiAg4OjrK/zw8PNR70mSQfj9xU+wSiPSGuwmJNCeZgJWWloaPP/4Yv/76K6ytrcUuR2NTpkxBVlaW/C8tLU3skkjL2NtSedyQGw5eqJyociQTsBITE3Hnzh20bNkSFhYWsLCwwL59+/Dtt9/CwsICrq6uyM3NRWZmpsL9MjIy4ObmBgBwc3MrdVRh0e3y2jg4OMDGxgY1atSAubm50jZFy1DGysoKDg4OCn8kTQwB+sHAKi5eqJyociQTsLp164bTp08jKSlJ/teqVSuEh4fL/1+lShXExsbK75OcnIzU1FQEBQUBAIKCgnD69GmFo/1iYmLg4OAAPz8/eZviyyhqU7QMS0tLBAQEKLQpLCxEbGysvA0RkbERBB7daYxcHazELsFoWYhdgLrs7e3RpEkThWlVq1ZF9erV5dOHDRuG8ePHw9nZGQ4ODhgzZgyCgoLQtm1bAED37t3h5+eHgQMHYsGCBUhPT8e0adMwatQoWFm9WMlGjhyJZcuWYdKkSXjvvfewe/dubNmyBZGR//VajB8/HoMHD0arVq3Qpk0bLFmyBE+ePMHQoUP19GqQWMZvSVI6nb0tlffm94fELoHK4DMliuu5EdoxpiNaz/1H7DKMkmQCljoWL14MMzMz9OnTBzk5OQgJCcH3338vn29ubo4dO3bgww8/RFBQEKpWrYrBgwdj1qxZ8jY+Pj6IjIzEJ598gqVLl6J27dpYtWoVQkJC5G369u2Lu3fvYvr06UhPT0fz5s0RHR1dauA7GZ/fj3Nwu64cT82U////PmRvsCG4Nj+Mu8SNXE179mDpiqQD1t69exVuW1tbY/ny5Vi+fLnK+3h5eSEqquzz7HTp0gUnTpwos83o0aMxevRotWsl48XBwNoX4OUsdglERJUimTFYRGJT9Uueg4HJVESfuS12CUSSwYBFRKLjbijDNaprXfn/R/5yXMRKiKSFAYtIDdO2nVY6nYN+tY+vqWH5NMRX7BKIJIkBi0gNvxxJFbsEIiKSEAYsogr6bSSPdNMGnl9JWs7f5nVUidTBgEVUDlXjg1p580g3bfCZUvZRvSS+rg1ryv/fY+kBESshkg4GLCIyGBx/ZZjWDm0jdglEksOARVSGOTvOKZ3OIEBERGVhwCIqw6qDKWKXQEREEiTpM7kTicGvloPYJRgNYz3/VUGhgLqflx5b9sdH7dDCs5oIFWmX9+RI9uJKjCAIWH0wBe93rCN2KSaDAYtIBVUb/6iPO+q5EtMgtQ12RcLhG98fLnP+4ckvw93JpqIl6RSvSyhtRQeTzIk8L7nPmlQxYBERqUEf4aLd/N0Kt6PHdYSvG3tMiaSIAYtIiQXRF5RO5y8/06FqN5+mhrb3xp4Ld3Dt/lON7xu65L9TIkzp4YsPOtctozURGRIGLCIlvt97RewSjJ6h7m7SpC51A/eM1xpX+nEj/r6AiL8vaPS4uhR7PgPdGrmKXQaRwWLAIiLRGUJgUCdY6bLOkssuq56ieednhcLG0lxnNZU0tWcjzI06DwAYtv6YQbxvRIaKAYuoBFUbNm5MjE/W0zz4z9pVZhux3vfij6tqnWw0PRoAkDT9FTjZWuq8puGd6sgDFhGVjQGLiExSWT1EhhamywtbzWfFlGpHpApPs6EfDFhExXwbe0np9Etze+i5EuNWUCjeBZ6lFKyUKapR2fMomiaF50Fk7BiwiIr5Juai0ulVzHnRA23SxtF5mpJ6sCqpvKA1/VU/vNfBR6c1bDtxE71bvKTTxyCSKm41iEhU+gg3ZY2rk2K4Kk7Vc5i145xOjtRc3Ndf/v9xm5O0vnwiY8GARfQvDm43Pt6TI5W+r8YQrEq6Nj8M/3uvTanp3pMjtbpL9o0WtbW2LNIfY1vfpYABi4iMkikG5k4Naip9fnU/jzLY844RGSsGLCIAK1ScWPTPUe31XInxu/PouU6XX1AomEyvlSrX5odhab/mpaYzZBHpDwMWEYCvVFwax9/DSb+FmIA2c2Pl//d1s9fqsutPjVI6gN5UglVxvZq/pPR5M2QR6QcDFhGJJnpcJ60ty3tyJPIKFMca7ZnYxSTDVXG6DlkMbNK09Via2CUYPQYsMnmmOFbH2KjaJehTo6oI1RgebYcsfjak79PfToldgtFjwCIiSVMVrkjRtflhWPhWM4Vp7H2ikq7deyJ2CUaDAYtM2qoDV8UugSqB4Uozb7fyQPKcUIVpDFlUXJev94pdgtFgwCKTNidS+YVruZHWDV2P/eH7Vj4rC/NSrxNDFpH2MWARkSgqE4YYriovJaKnwm2GLOPX5CUHsUswKQxYZLJUbVB4YWfDxnClHTKZDAlTuylMq2jIYjiThh1jOopdgklhwCIqgRd2NlwMV9rlYm+NT0MaKkxTNyzxdScqG7ckZJJ+OXJd7BJIQwxXujGqa71S09gjRVR5DFhkkqZtO6N0OjfYhonhSreUvZZ/nbwlQiWkTwzSusWARUR6UdEv83d/OlJqGsOV9pV8TcdsPCFSJaRvO7V4RQX6DwMWmRxVG/qwZrX0XInp0iQgHb5yv8L3Jc3w9A2mqaGWrwlKLzBgEf1r+bstxS6BSii5gWe40r2KhqzCQqH8RkQmhAGLTMqfSTfFLoHUxHBlOASh/PBU5/MoPVRCJB0MWGRSPt6UpHQ6N96GpWS46li/hkiVmKaSnwefKcrDEz83RKoxYBGRwft5WKDYJZgcjscyThdmh5bfiLSCAYtMBjcQ4tlyLE3tttw1aDjsrSzELoG0zLqKudglmAwGLDJ53IDr3qTfTsn/v+CtZirbMVwZltNfhijc5o8U45P9PE/sEoyWZAJWREQEWrduDXt7e7i4uKB3795ITk5WaPP8+XOMGjUK1atXh52dHfr06YOMjAyFNqmpqQgLC4OtrS1cXFzw6aefIj8/X6HN3r170bJlS1hZWaFevXpYt25dqXqWL18Ob29vWFtbIzAwEAkJCVp/zqQ9By7dFbsE+tc7rTzELoE0UDLkvr7soEiVkC40m7lL7BKMlmQC1r59+zBq1CgcOXIEMTExyMvLQ/fu3fHkyRN5m08++QR//fUXtm7din379uHWrVt488035fMLCgoQFhaG3NxcHD58GOvXr8e6deswffp0eZuUlBSEhYWha9euSEpKwrhx4/D+++9j586d8jabN2/G+PHjMWPGDBw/fhz+/v4ICQnBnTt39PNikMYGrlYegM/NClE6nfSPvVfScOpGltglEEmCZAJWdHQ0hgwZgsaNG8Pf3x/r1q1DamoqEhMTAQBZWVlYvXo1vvnmG7z88ssICAjA2rVrcfjwYRw58uJM0Lt27cK5c+fwyy+/oHnz5ujRowdmz56N5cuXIzc3FwCwcuVK+Pj4YNGiRWjUqBFGjx6Nt956C4sXL5bX8s0332D48OEYOnQo/Pz8sHLlStja2mLNmjUq68/JyUF2drbCH4nP1pJjTAwBw5VhU3fA+/O8An2UQyQJkglYJWVlvfgV5ezsDABITExEXl4egoOD5W18fX3h6emJuLg4AEBcXByaNm0KV1dXeZuQkBBkZ2fj7Nmz8jbFl1HUpmgZubm5SExMVGhjZmaG4OBgeRtlIiIi4OjoKP/z8OBuEn3huBGiynunVe1y2/h+Ea2HSoikQZI/3wsLCzFu3Di0b98eTZo0AQCkp6fD0tISTk5OCm1dXV2Rnp4ub1M8XBXNL5pXVpvs7Gw8e/YMDx8+REFBgdI2Fy5cUFnzlClTMH78ePnt7OxshiyRsZfEMBhb79XZW1kI+1azcUqX5/aAhblh/95d8JY/thy7Ib/tPTkS1+aH4dr8MP6IMSBF74XUP0fGQJIBa9SoUThz5gwOHpTOYEsrKytYWVmJXYbJOZmWKXYJpIEzXxr+mDhdhIl6U/8uc/7wjj6YGuan9cfV1OW5PcqtlcRTfN0sCsAkHskFrNGjR2PHjh3Yv38/atf+r8vazc0Nubm5yMzMVOjFysjIgJubm7xNyaP9io4yLN6m5JGHGRkZcHBwgI2NDczNzWFubq60TdEyyHD0Wn5I+fTm7nquxHSVFUhKzrMzsPMuGUrPzE8HUvDTgRSFabsndEadmnZ6raNkLxs34tL0Qac6+GH/VbHLMHqG9W1WBkEQMGbMGPzxxx/Yu3cvfHx8FOYHBASgSpUqiI2NRZ8+fQAAycnJSE1NRVBQEAAgKCgIc+fOxZ07d+Di4gIAiImJgYODA/z8/ORtoqIULwsRExMjX4alpSUCAgIQGxuL3r17A3ixyzI2NhajR4/W2fMn7Vrar4XYJZik4hvjjOznKueJRZuB6sCkrvBwti2zzdpDKfjyr3MVWv7Li/Yp3NbX63dxTg80mMZeLEO04K1mCuecu531DLUcbUq1m9KzEQOWHkgmYI0aNQobNmzAn3/+CXt7e/mYKUdHR9jY2MDR0RHDhg3D+PHj4ezsDAcHB4wZMwZBQUFo27YtAKB79+7w8/PDwIEDsWDBAqSnp2PatGkYNWqUfPfdyJEjsWzZMkyaNAnvvfcedu/ejS1btiAy8r8v3vHjx2Pw4MFo1aoV2rRpgyVLluDJkycYOnSo/l8YUslQeh9IucB5sWKXgIGr43Hg0j2N76etMDO0vQ+Gtvcps83PR67ji21nyl1W8fX994/aoaVntUrXp4ylReleLDIM77TyUAhYQRG71VpXVx1g2NIFyQSsFStWAAC6dOmiMH3t2rUYMmQIAGDx4sUwMzNDnz59kJOTg5CQEHz//ffytubm5tixYwc+/PBDBAUFoWrVqhg8eDBmzZolb+Pj44PIyEh88sknWLp0KWrXro1Vq1YhJOS/sSF9+/bF3bt3MX36dKSnp6N58+aIjo4uNfCdDJMh9JSYurO3FM+lpM/3ZPvJWxi78YTa7cVeXwa29cLAtl4K08oLNW9+f1j+f13Uv2diF3T9eq/Wl0vimBN5XuwSjJJkApYgCOW2sba2xvLly7F8+XKVbby8vErtAiypS5cuOHGi7C/g0aNHc5egAbty97HYJVAZND3KThvU7WkRO1CpQ5MLMRfNs7Oy0NpBBD41qmplOaR7HCcnHskELCJNdCsxPoUMx9NcxUtT6fLL3/eLv/E8r7DMNq/5u+O7/tIek1f8NVQVth7n5PMQfhMwtWcjzI1ij5QhYMAik8INi/j8pu8sv1ElqdNbZazrgjphSxtBS9X5r5bvuYxRXetVeLlUOcM71WHAMhAMWGR0OOhWOrQdcsp77401VKlS9Hx1GbRKWrgzmQHLwHA3oTgM+9TBRCRpeQWKu+d0FX69J0eWuez32vuY9Aam6IzrO8Z0UDrfe3IkLmY8qtByiUg5BiwyKo+e56mcx42B/tUv46zf2ng/ei07qFZoW3MoBVd54AOavOSIa/PD8NvIoFLzui/ez95fI8HvOsPAgEVGpenMXWKXQHriPTkSJ29klZr+87A2ODo1GJ+GNFSY/vKifQhfdQR/n75dqmfN1LTydla5EfaeHIlPt57Uc0Wka8Z2zU8p4BgsMgnxn3cTuwQqJnlOaIXvq6qXpY23M7YU65kZ1bUeQhq7Ivib/QAAmQw4dPk+Dl2+Dxd7K/Rr44n+bTyUnunaVKgao7U18Qa2Jt5QayPMiz0TKcceLDIaZX3JuzpY67ESKo+VhbnG9yksFFS+x9fmhymEqyIezraQyV78/4+P2uOjLnVRw84Sdx7l4NvYS+jw1R6M+N8x7L94F4WF5Z9rz1hdmx+G41+8Umo6g5N0VbUs/Rm7/zhHhEpMFwMWERk878mRqPN56RMEFw3eVsXKwhy1/g3XhYKASaG+ODy5G77t3wJtfJxRUChg17kMDFqTgJcX7cWP+6/g4ZNcnT0PQ+Zc1VLpa+k9ORL/l3hDhIqoMs7OKt1LHDDnHxEqMV0MWGQUyup94FgDw6Lp+6GsF0VVGFCm6ILLaQ+eAnhxLb3X/d2x5YMg7PqkEwYHecHeygLX7j/FvKgLCIyIxfjNSUi8/lCtK0gYG2Wv64StJ8vszeJnTDpO3cgst40prve6wIBFRkFZ7wZJ2+/HbyjdqKvanaWK578BK/X+01LzGrja48teTXDk826IeLMpGrs7IDe/EL+fuIk+Kw6j57cH8Wv8dTzJyS91X2OmqmeQuwylb/qfZ8vdHb7+8DX9FGPkGLCISG82jWirVjvvyZEYv6X0kWwV6Skp6sFKfVA6YBWpamWB/m08sWNMB/zxUTv0aVkbVhZmOH87G1P/OIPAebH4YtsZJKdrfq4oKatoyGIQMwzK3r+ktEz8ceJmmfeb+dc5XZVkUhiwSPK460I62tapXm4bVb1WFX0vPdUIWEVkMhlaeFbDonf8Ef95N0wLawSfGlXxOCcfPx+5jpAl+/H2ysP4M+kmcvILKlSP1LAny/jMj75Q5jkDSTsYsIjIYKgKV5VR1IN14+Ezje7nZGuJ9zvWQez4zvhlWCBCG7vB3EyGo9ce4uNNSWgXsRvz/74gH9tlzBiyjMvdRzn4bvdlscswegxYZLTYe2VYEso5F5kuwhXwXw/WraxnyM3X/ASjZmYydKhfAysHBuDQZy9jXHB9uDpY4f6TXKzcdwWdFu7B0LUJiD2fgQIjPtWDsvei1ZwYle3vZD/XZTmkprVDWiudvuZgCv4Z31nP1ZgWtU40eurUKY0X7OfnBwsLnseUdIu/og1X+/m7FW67lHEuMl2FKwCoYWcJmyrmeJZXgJuZz+BTo2qFl+XmaI1xwQ0wums9/HP+Dn6Nv44Dl+5hT/Jd7Em+i5ecbPBuoCfeaeWBmvZWWqnfkJQ8qei9x7l4nJMPO6vS3/Vt5sXyR44B6OrronR6fqGAWTs41kqX1EpAzZs3h0wmU/vQTTMzM1y8eBF16tSpVHFEJF03M9XbJafLcAW8GFfl6WyL5IxHSH3wtFIBq4iFuRlCm7ghtIkbUu49wYb469iaeAM3M59h4c5kLPnnIkIau2FAWy8E+jhDVnS2UyNQMmQ1mbET1+aH4fTM7rxUlcTsv3hX7BKMmtpdTPHx8ahZs2a57QRBQJMmTSpVFJE6OLhdOgJ9nJVO13W4KuLhbCMPWNrmU6Mqpob5YUL3hog8dRu/xF/HidRM7Dh1GztO3UZ9FzuEB3rizYDacLCuovXHF0PJkOU9OZKfOaIS1ApYnTt3Rr169eDk5KTWQjt16gQbG9O9vhcRKdr8QenL2OgrXAGlTzaqC9ZVzNEnoDb6BNTGmZtZ+DU+FX8m3cSlO48x869z+Co6Gb2au2NAWy80eclRZ3Xoy65POqH74v3y29xdb7hUXS/SzcEa6RwrpzNqDXLfs2eP2uEKAKKiolCrVq2K1kRUKfwlbfj0Ga6A/wa66+uIvyYvOSLizaY48nk3zOrVGPVd7PAsrwCbjqbh1e8OotfyQ9h6LA3P86R7qocGrvbltmHoMmyD2nmJXYJR41GEJEn84jZsZb0/+g5XgGbnwtImB+sqGBTkjV2fdMLmEW3xmr87qpjLcDItE5/+dgqB82Ixe8c5XL37WK91aQt/zEjbguhksUswamqPwZo1a5Za7aZPn17hYojI9OhjI138cjmCIOh90LlMJkNgneoIrFMddx/5YcuxNGyIT8XNzGdYfTAFqw+moH296hgQ6IVgP1dUMZfOb19Vu5/IsPB90j+1A9Yff/yhcp5MJkNycjKeP3/OgEU6x8Ht0lXyvdPX+1W72ouA9SgnH1nP8uBka6mXx1Wmpr0VRnWth5Gd62LfxTv45Ugq9iTfwaHL93Ho8n242FuhXxtP9G/jgVqOHMtKJFVqB6wTJ04onZ6UlITJkyfjzJkzGD58uNYKIyLjIla4AgAbS3O42FvhzqMcpD54KmrAKmJuJsPLvq542dcVaQ+eYmNCKrYcS8OdRzn4NvYSlu+5jG6+LhjQ1gsd6tWAmZnhnuqBvSNEpVW4HzolJQUDBgxA69at4ejoiLNnz2LlypXarI1II+y9MgybElJLTfth3xWF272au+urHDl1LvosFg9nW0wK9cXhyd3wbf8WaOPjjIJCAbvOZWDQmgS8vGgvftx/BQ+f5IpdKklYSkRPsUswKRoHrHv37mHMmDHw9fXF7du3cfjwYWzevBn169fXRX1ECvgr2fBN/v10qWkRf19QuL20Xwt9lSMn1kB3TVhamOF1f3ds+SAIuz7phMFBXrC3ssC1+08xL+oCAiNiMX5LEo6nPlT7xM/6ouoHDj+zhsOYTngrBWoHrCdPnuDLL79E3bp1cfjwYfz111+IjY1F69bKr3NERKSMWD2N/50LS7OLPoulgas9vuzVBEc+74aIN5uisbsDcvML8fvxm3jz+8MI+/YgNsSn4klOvtilkhE6czNL7BIkT+0xWHXr1sWjR48wZswY9O/fHzKZTOk1Cps1a6bVAomKcHC79E0LayTaY+v7XFjaUtXKAv3beKJfaw8kpWXilyOp2HHqFs7dzsbnf5zGvKjzeLPlSxjQ1kutc1ORaevX2gObjqaV227G9rP4bWQQe70qQe2AdefOHQDAggULsHDhQoXu6aLrFMpkMhQUSPfEeUSkW+93FO/6pFLYRVgWmUyGFp7V0MKzGr54tRF+S7yBX+NTkXLvCf4Xdx3/i7uONt7OCG/ridAmbrCyMBe7ZDJA8/s0UytgJV5/iG1JN/FGi9p6qMo4qR2wUlJSdFkHUYWx98pw5BcUqpwn9vtUFLBuZj5DfkEhLCR0rqmSnGwt8X7HOnivvQ8OX7mPX45cR8z5DCRce4CEaw9Qvaol3mntgXfbeMp3jRJpKiLqAl7xc4OdldpRgYpR+1Xz8uIp9Uk8HCgrDfWm/i12CSq52FvB0sIMufmFuJ31XGvBY+W+K5hfYhC/rpQMqWZmMnSoXwMd6tdAetZzbDqaio0JqcjIzsGKvVewct8VdGlQEwPaeqFLQxeYG/CpHkgzJb8Th7b3xozXGmtv+dVtce3+U3y3+xKm9BBv176UqRWwTp06hSZNmsDMTL1ffGfPnkXDhg1hYcHUS0Ti914BL8JI7Wo2uHr3CVIfPFU7YBlSuC9vHOK44AYY3bUe/jl/B7/GX8eBS/ewJ/ku9iTfxUtONng30BPvtPJATXsrPVZN+rD20DWsPXQNQPmfN3XOWzb9NT+8t+4Y1hxMwTutPFC3pp22SjUZaiWgFi1aID09HTVr1lRroUFBQUhKSkKdOuKNtyDjwcHtpC2ezra4eveJ0oHuhy7fQ/iqeBGq0o6Sn5M+LWtjz8Qu2BB/HVsTb+Bm5jMs3JmMJf9cREhjNwxo64VAH2cOYjZCRetCZb4fX/Z1RdeGNbEn+S5m/XUO64a25rqiIbUCliAI+OKLL2Brq94vvtxcngyPiAxP8YHu2u6Z0mXYP3L1Pvr9eESj+/zf8Rv4v+M35LcXve2PX+Kv40RqJnacuo0dp26jvosdwgM98WZAbThYV9F22aRD6vRCVTZoTX+tMQ5e3od9F+8i9vwdBPu5Vmg5pkqtgNWpUyckJ6t/1e2goCDY2PAaWkRkOIpvjL7fe6WMlqV9/bY/3goQ72iqtnWql7mRVCcsTth6EgBQp0ZVBNapjj+TbuLSnceY+dc5fBWdjF7N3TGgrReavOSotbpJt9S9RJGyoKXOfX1qVMWwDnWwct8VzNpxDh3q14B1FR6dqi61AtbevXt1XAaRctw9SJVRkV4qKa5XJWsu63lfvfcEV+89wcK3muFZXgF+jruOS3ceY9PRNGw6mgZ/DycMCPTEa/7uWtuYFhYKBn0tRSnT5DqQ3pMj8WlIQ4zqWk/t5Y95uR7+OHEDqQ+eYvXBFI3ua+o4Cp2IdGrVoFZ6fTxNQpUUw5Q6ij8vQRDgMyWqVJtPf3txouiUiJ5ISHmAX+JTEX3mNk6mZeJkWibmRJ7HWwG1ER7oiTqVHODc/6cj2PxBUKWWQaqpCllvtngJv5+4qTBt4c5kLNyZrPa6X9XKAlN6NMK4zUlYtvsy3mz5Emo5cg+VOhiwyGA8zyuA7xfRAMr/VWasG0YpS7z+QOl0fY3bUCdY7Z7QGS8v2gcAODWzu65LqpS9yXcwZO1RnT+Oz5QoXJsfhsA61XH3kR+2HEvDhvhU3Mx8htUHU7D6YAra16uOAYFeCPZzRZUKnD8sPkX5ukHao+w7s2S4Kk6THyK9mrvjlyPXcez6Q8yLuoDv+uv/WqLlKSwUUOfz0j8kNKXNbQsDFhmMonAFGNah8aSePiviRHnc8taVkl+YzlUt8eBJLtIePEVjd+2MN5L6+lpe/Ycu38ehy/fh6mCFvq090b+NB3sxDNC1+WHYd/EuBq9JUDqvouupTCbDzNcb47VlB/HXyVsYEOiJwDrVK1zn/cc5CJjzT4Xvr0slX6MDk7pW+Jx5DFgkOTGfdBK7BDIAZW0sdozpoHKwtoez7b8B65nSgCX1sKRLGdk5+Db2EpbvuYxuvi4YGOSF9nVrcHyVHs2NPIefDpR9ZZV/xndC8Df7FaYVH+hekXW8yUuOeLeNJ36NT8WM7WdxIf2RxsuQoo4L9lS4V4sBiySnPi9oa9I2xKfi8z9OK52n6ovw6LUHeHulYg/byF8StV6bIVH2Wvwv7hqm/3m20ssuKBSw61wGdp3LgHd1W4QHepU6yvKDznXww76rlX4s+s9P+6+WG64AlApXxRWFq/Len7JCmKGHq0tze5S7K1vdkFmZXYYVClg///wzVq5ciZSUFMTFxcHLywtLliyBj48PevXqVeFipGb58uVYuHAh0tPT4e/vj++++w5t2rQRuywio6XqS7HoVzl7n/6j7ND8QUHeGBTkrbRdybYAEBF1Hj/sV74RHhzkhd+P38S1+08xN+o8Fu5SPJUPw5X2bUhI1dqyDOH92T66PZrVdtLJsvMLCit96a4r83pW6v4aB6wVK1Zg+vTpGDduHObOnYuCggIAgJOTE5YsWWIyAWvz5s0YP348Vq5cicDAQCxZsgQhISFITk6Gi4uL2OUZrcRpwWKXQCIpKzwZerDqWL8GCgUBBYUCCgvx4v+CgMLCon8hn180vVB40VMkv5+AYssQ8CgnX+d1T+nZSGXA+rJXE0wK9cX2k7fwy5HrOHsrW+f1mLLQJfuRcu+J2GWUUt/FDhbmZqhiLoO5mQxVzMxgbiaDhbkMVcxf/L+KuQwWZmaw+He6udmL9ttO3MKOU7dfTDeTwcLcDBbm//7frOj/xaaZm8nbVjE3w9B12j8IRNRB7t999x1++ukn9O7dG/Pnz5dPb9WqFSZOnKi1wgzdN998g+HDh2Po0KEAgJUrVyIyMhJr1qzB5MmTRa5Omhq62iM5o+yu5+p2vIaaqTD00KSJA5fuiV2CWjR9zataWaB/G0/0a+2BpLRMvPH9YR1VZtykvK5fuvNY7BIqTNdHo2scsFJSUtCiRelDNK2srPDkieGla13Izc1FYmIipkyZIp9mZmaG4OBgxMUpP5IqJycHOTk58tvZ2fy1V1JeQWGZ87eO5Hl0jJk2NjINXO3gYF0Fx64/1Pi+tRyt0aVhTZjJZDCTvfg1/uJfvJhmJoP5v/+aySD/v/m/02UyvPj/v/crfl/5tH/bypdZNK9o2TLIl2n27+3/6lBc5hvfH0bWs7wKv1a9lh3EyRtZGt9P2UZJJpOhhWe1CtdizKQcnipqab/mKCgUkF8gIL9QQH5hIfIKBBQUFmJe1AVRamrj44x323gitImb3s5Gr3HA8vHxQVJSEry8vBSmR0dHo1GjRlorzJDdu3cPBQUFcHVVPL+Pq6srLlxQvvJERETgyy+/1Ed5kvQ4Jx8p98sO6G+vjOP5r4zMP+cy8P7/jml0n9Mzu8NexXXzsp7lwf/LXWXev76LHVLuPUF+oYC4KS8b9OkGCgoF1K3guX2OTg1G67n/aGUDX9nP3c/DjHds6sm0TPRafkhvj6fOe7ExIRVTfld+IIg+fLwpSW+PlfB5N1S3s8K+i3ewIT4Nuy9koFB4Mc/Jtgr6tKyN/m08UM9F/wdHaRywxo8fj1GjRuH58+cQBAEJCQnYuHEjIiIisGrVKl3UaBSmTJmC8ePHy29nZ2fDw8NDxIoMy/nb2RAEsasgfVJnw79tVHv0LrbxihzbQWW4AqA0XO36pBMauNpj67E0fPrbKQgA3J1skPrgKVLvPxUtYBUWCghduh8XM3Szi6X13IqdZ+jjbvXxySsNtFpLh3o1tLo8fVN1NnxtSpr+CpxsLbWyrP5tPNG/jafCtHdWxiHhmrRO+FpemLyd9QwbE9Kw+WgqbmU9l09v4+OM8EBPhDTWX2+VMhoHrPfffx82NjaYNm0anj59infffRfu7u5YunQp+vXrp4saDU6NGjVgbm6OjIwMhekZGRlwc3NTeh8rKytYWXH8kCpnb2q+q4Kkq6yjActSkRODdl+seMj65WJjRpb8cwkbhjtDJtP8PE65+YXYciwNX/51FnkF0v51oOue4Yq8vmLS9m49MXveDXUXZUVfk4JCAXuT72BjQip2X7ij0Fv1Vsva6NfGE/VcKndpJ22p0GkawsPDER4ejqdPn+Lx48cmd9ScpaUlAgICEBsbi969ewMACgsLERsbi9GjR4tbnESpewSS9+RI7iY0YspOLVDcn0k30av5Syrvr+lJFOOu3td5z4TYrs7rCTMzWYVDramobBDRxet4KeMRXlms+pxWpuRW5jNsOZaGzUfTcLtYb1WgjzPeNYDeKmUqNMg9Pz8f9evXh62tLWxtX5xC/tKlS6hSpQq8vb21XaNBGj9+PAYPHoxWrVqhTZs2WLJkCZ48eSI/qpA0szXxhtglkB6VF4RUzft4U5Jex3dIwf5Pu8KzuupLefCanuXTRi+PofYUadPuCZ1hZ2WBNvNi9fJ4Rb1VG+JTsSf5v96qav+OrTKk3iplNA5YQ4YMwXvvvYf69esrTI+Pj8eqVauwd+9ebdVm0Pr27Yu7d+9i+vTpSE9PR/PmzREdHV1q4DuVLye/QOwSSASVuTaaKahs+GGwoiI/DAxASGPlw1eKK+/zWHSh9LI+u2uGtELXhi74KjoZK/ddKTW/yUsO2DGmY5mPcyvzGTYfTcOWY4q9VW3rOKN/G8PsrVJG44B14sQJtG/fvtT0tm3bmtzusdGjR5vcc9aFhtOiy2/0r9m9m+iwEtI3ZRt6Ywtd+gwz5b12fVrWxqJ3/PVUDWmLoR3tWtZ1Dd9bdwzJc0IxuYcvJvfwVXuZ+QWF2Jt8FxsTSvdWvRXworeqbk3D7a1SRuOAJZPJ8OhR6ZNBZmVlyc/qTqQtRRunX45cx4C2XuW0JmOgKpBUtEfmYsYjRJ66jajTt5WeFPHk9O5wtFV9ZKIhU+e0FAB7rMqj6vWZsOUk/u/4f8MX6rvYoWfTWghrVgsNeE1UlZ/Joh/N6qx35fVWhTZxg5WF4fdWKaNxwOrUqRMiIiKwceNGmJu/eNIFBQWIiIhAhw4dtF4gEQCGK5J/WSv7Ui9rcHwDV3s0eMVefuqBgkIBQRGxuPPoxYl/Mx49l1TA0qSHj8Gqcha9488ev3+lRPSETKb6YAllVB2UlF9QiD3/9lbtLdZb5VzVEm8F1Ebf1h6S661SRuOANX/+fHTu3BkNGzZEx44v9qMeOHAA2dnZ2L17t9YLJOPGcSKkqbLGf5ScrmwdMjeT4TV/d6w+mAIASL3/1GB7Iyqyu5SfG9IFnylRuDY/DNfmh6H38kNISstU637FQ9bNot6qo2lIz/6vtyqoTnX0D/RESGNXyfZWKaNxwGrcuDFOnTqFZcuW4eTJk7CxscGgQYMwevRoODs766JGIiIFZfVmFVdy/ob3A9GuXg30av5fwLqQno1gP3EPTjHEUwSQ6fk0pCEW7kwut922US/GYau73npPjsTLvi5Ke6v6tfZAHSPorVJGo4CVl5eH0NBQrFy5EvPmzdNVTWQiun69V+U8bjBIHcXXE3W+7N9dFV9q2te7LuLrXReVLrOy/ky6qZPTSvDzQbrwUZe6agWsIur+0AGA3RfuAADa1a2O/m080d3IequU0ShgValSBadOndJVLWRiUu6ZxsXBST+Kh47TN7Lw2rKDFVqOoR3FKPUwdXVeT7FLIDWVd8Z9VWOqNAlaG4a3rVhxEqTxLsIBAwZg9erVmD9/vi7qISKqtKa1HUttCAwtOJUk9SCl6vU1M5PWZXKo4jQJWqZA44CVn5+PNWvW4J9//kFAQACqVq2qMP+bb77RWnFkvDi4nfStvPXqs99OYfOxNFEem8iYFK3vO8+m44OfE0tNNxUaB6wzZ86gZcuWAICLFy8qzJPaBT2JSHuuzOuJup+Xvq7fnUfP4WJvLUJFmvnqrWb46q1mYpchSeyxMB2aXA82pLGbyYWq4jQOWHv27NFFHWRCCooOI1HClD+MUmeuYldQ72WHcHhKNz1XQ/ry6Hme2CUQGSSzytz5xo0buHGDF+klzSjr5SDjdavY2ZnJ+DSdWf6Z5IlMkcYBq7CwELNmzYKjoyO8vLzg5eUFJycnzJ49G4WFhbqokUyEvbXGHapEJKLydg1emB2qp0pIn7hLWD0ab9GmTp0qP4qw6KLPBw8exMyZM/H8+XPMnTtX60WS8Sjrg3l6ZogeKyEiXbOuYtznOSIqi8YBa/369Vi1ahVef/11+bRmzZrhpZdewkcffcSARURkApRdlog9G0T/0XgX4YMHD+Dr61tquq+vLx48eKCVosg4cXC76eKG17goC1cHLt0VqRoSw73HOWKXYPA0Dlj+/v5YtmxZqenLli2Dvz+vOk6qcXC78eM4OuNXMlw1dncAAAxcnSBGOSSSVnP+EbsEg6fxt+GCBQsQFhaGf/75B0FBQQCAuLg4pKWlISqKG1DSXA07S7FLIC05PTNEZW+VJufPIcN0/X7py1tFju2otC3fa+PB3b8Vo3EPVufOnXHx4kW88cYbyMzMRGZmJt58800kJyejY0flHzSisj6cx6a9osdKSEz8kpa2zgv3KtxmiDINkadui12CJKndg3X16lX4+PhAJpPB3d2dg9mJiEyIsnFXZBpGbTiudDp7pcumdg9W/fr1cffuf4MY+/bti4yMDJ0URcYlv0D1+dH44TQ97MWSHoYr4nuuObUDliAoHgEWFRWFJ09K748nKqne1L/FLoFEVvLLmSFLOkq+V6dmdi/3PtwYE1XyUjlERCWp2rh++XpjhdsMWYav5Hu06G1/OFhXEakaMkT8HKumdsCSyWSQyWSlphGVpawPH3/lmpbB7bxLTeOXs+Eq+d6MC66PPgG11WpLxonf2ZpRe5C7IAgYMmQIrKysAADPnz/HyJEjUbVqVYV2v//+u3YrJCKjoexwbw6UNSwLd17A8j1XFKZtH90ezWo7iVMQkUSpHbAGDx6scHvAgAFaL4ZMBzeoposhy3Ap64m6MDuU1xSkMm05moZ3WnuIXYbBUTtgrV27Vpd1kBHibgPTVd6JCRmyDI+y90ud94Ofc9Oi7LM76f9OMWApwUHuRCQKZRtvbqzFUdFwRabjaW6+2CVIDgMW6QQHt1NxH/2aqHQ6Q5a4vCdHMlyRWvym7xS7BMlhwCIinYs6na5yHkOWOJS9xnN6N9EoXPF9Mk38zKpH44s9E1UGfxmbDp8aVZFyT72TEasak1U0j7RH1YZQW69z4rRgrSyHSOrYg0Vax18yBAB7JnZRuL1s96Uy21+bH4bvw1uWms71STtm/HlGq+Gqy8I9SqdXt7PSeFlExogBi4j04utdF8tt07NpLZW7Hxi0Ks57ciTWx10vNf3a/LAK91xdu/+0smWRhHE3YfkYsEirrt59rHIed/WQulStK96TI7Hj1C09VyNdqoLpmy1f4ueRSMc4Bou06uVF+8QugQyYJue6KmpXMiCM3nACozecYEAog66P4mVPBVH52INFenF1Xk+xSyCJKqs3ixv6/xy79qDM16QyuwPLwqBruvjel409WKQ1ZW3szMx4YXCqOFW9WcWnhTZ2w8qBAXqtyxCUFzK1vRFkqKWy8IoM/2HAIiK9qswXcFlBK/psusmc2iF81REcuny/zDb6eA1SItgzbUoYnjTDgEU6xw8kaVtZQavkdGNZ/5b8cxFL/in7VBeAbp9vyddbJmPPtKkr77qjpowBi7SCHzDShLZ+CZcXtErOk1rYUvdzJcbzujA7FAA/+1Ta3uQ76NLQRewyRMeARTp1blaI2CWQgVg3tDWGrD2qk2UXDxjqhq2S9zMEmoSVxu4OiBzbUYfVKCpZm3UV81JtrvBgFpMUPa4jQpcckN8esvaowX22xMCARTpla8lVjF4oGa50NZ6jaJmXMh7hlcX7y2wr1oWOZ/11DmsOpWh8vwCvavi/D9vpoCLNHJ2q/HI45jyYRfL2TuyCLl/v1eg+vm4OuilG4rj1o0rjLgJSRczxGfVd7dXu2SrO0NZnQ+gJKPma1LTn5XCMlXeNqmKXYDQkcR6sa9euYdiwYfDx8YGNjQ3q1q2LGTNmIDc3V6HdqVOn0LFjR1hbW8PDwwMLFiwotaytW7fC19cX1tbWaNq0KaKiohTmC4KA6dOno1atWrCxsUFwcDAuXVIcWPrgwQOEh4fDwcEBTk5OGDZsGB4/Vn0Gc1NlCBsGMiwl14nOKq5np6vHLv5nqAytTkEQFG4bQk1keLhelCaJHqwLFy6gsLAQP/zwA+rVq4czZ85g+PDhePLkCb7++msAQHZ2Nrp3747g4GCsXLkSp0+fxnvvvQcnJyeMGDECAHD48GH0798fERERePXVV7Fhwwb07t0bx48fR5MmTQAACxYswLfffov169fDx8cHX3zxBUJCQnDu3DlYW1sDAMLDw3H79m3ExMQgLy8PQ4cOxYgRI7BhwwZxXiAR9Vh6oPxGRCpcF/F6dmJfS2127yYY2NZLb49XUT5TospvREbr2LRgtJrzj9hlSJJMKPnzRCIWLlyIFStW4OrVqwCAFStWYOrUqUhPT4elpSUAYPLkydi2bRsuXLgAAOjbty+ePHmCHTt2yJfTtm1bNG/eHCtXroQgCHB3d8eECRMwceJEAEBWVhZcXV2xbt069OvXD+fPn4efnx+OHj2KVq1aAQCio6PRs2dP3LhxA+7u7mrVn52dDUdHR2RlZcHBQbr7r1VtkI5/8Qqcq1rquRrTI8Z6pOljKjuKz9AHm5fnzqPnaDM3ttR0Xzd7RI/rJEJFuqHO+1TRozSlsO6aqpLvqSbv8ZZjaXirZW2jPrm0uuuRJHqwlMnKyoKzs7P8dlxcHDp16iQPVwAQEhKCr776Cg8fPkS1atUQFxeH8ePHKywnJCQE27ZtAwCkpKQgPT0dwcH/DeB0dHREYGAg4uLi0K9fP8TFxcHJyUkergAgODgYZmZmiI+PxxtvvKG03pycHOTk5MhvZ2dnV+r5GzqGKzJmLvbWkguFRNoweE0C1r/XRuX8d1p56LEawyaJMVglXb58Gd999x0++OAD+bT09HS4uroqtCu6nZ6eXmab4vOL309VGxcXxfN7WFhYwNnZWd5GmYiICDg6Osr/PDykvxIa2mBgko6S4YTrkuHRtPeKTMO+i3fFLkEyRA1YkydPhkwmK/OvaPdekZs3byI0NBRvv/02hg8fLlLlmpsyZQqysrLkf2lpaWKXpDP8ZU/q2DGmg9glkArL91xWuH16Zvdy78PPPZEiUXcRTpgwAUOGDCmzTZ06deT/v3XrFrp27Yp27drhxx9/VGjn5uaGjIwMhWlFt93c3MpsU3x+0bRatWoptGnevLm8zZ07dxSWkZ+fjwcPHsjvr4yVlRWsrIzn0Oa7j3LKb0RUQubTXDjZvth93OQlR4V5vM6Z4Vi4M1nhtr11FZEqIZIuUXuwatasCV9f3zL/isZU3bx5E126dEFAQADWrl0LMzPF0oOCgrB//37k5eXJp8XExKBhw4aoVq2avE1srOLA1JiYGAQFBQEAfHx84ObmptAmOzsb8fHx8jZBQUHIzMxEYmKivM3u3btRWFiIwMBALb46hq31XOVHlRya/LKeKyFD95KTjfz/zWfFKMwrGaje+P6QXmoi1aR+AAKRoZDEGKyicOXp6Ymvv/4ad+/eRXp6usKYp3fffReWlpYYNmwYzp49i82bN2Pp0qUKg9o//vhjREdHY9GiRbhw4QJmzpyJY8eOYfTo0QBeXLh03LhxmDNnDrZv347Tp09j0KBBcHd3R+/evQEAjRo1QmhoKIYPH46EhAQcOnQIo0ePRr9+/dQ+gtCYFd+YEgGahe4TqZm6K4TKVTJc7TSiIyKJ9E0SASsmJgaXL19GbGwsateujVq1asn/ijg6OmLXrl1ISUlBQEAAJkyYgOnTp8vPgQUA7dq1w4YNG/Djjz/C398fv/32G7Zt2yY/BxYATJo0CWPGjMGIESPQunVrPH78GNHR0fJzYAHAr7/+Cl9fX3Tr1g09e/ZEhw4dSu2yNGYc2EraxAHvhquhm73YJRBJlmTPgyV1Uj4fi6oNIHcl6J9UziVU3nl08gsKUW/q3/LbVhZmSJ7To/LFktoqsmuwoufAAqSz7pqiku+rIAgKJ5w19e96ddcjSfRgEZFxszBX/CrKyS8UqRLTVNlwRcZNJjPek4bqEgMWaUTVlyrHalBlcVehOEq+zn1a1tZ4Gabeo2Fqsp7lld+IGLBIOzhWg7SBIUu/lB21uegdfxEqISnx/3KX2CVIAgMWqa374n1il0BGQNPQxJClG4+e55U6apM9UUTaw4BFaruY8VjpdH4pU3muzOupdltl69PT3HxtlkMAms5U7IXg55hIuxiwiEjnzM00GyRbcmPvN32nNssxeTyZKJHuMWCRWlTtpvlrNK8nR7rB8Vi6oY1wxfeCqHwMWFQpTWs7lt+IqIJSIhR3LXLDXjm6OFP7hdmhlV4GGT5/ftdrjAGLyvU8r0DsEshEyWSyUiGAIatiSr5u899sqpWjf62rmFd6GWT4/uTeCo0xYFG5fL+IVjqd4zaooi5mPFK7bUM3e/RqrnidT4YszZR8vdYMaYV+bTxFqobINDBgEZFevNniJfn/uy/er9F9l/ZrUWoaQ1b5LqRnl3qd/u/DILzs6ypSRUSmgwGLyqRqI/bnqPZ6roSk7pu+zSt1f2U9pgxZqnlPjkTokgMK0xI+74YAL+dKLZeXryUAeH/9MbFLMHgMWFQh/h5OYpdAJkhVyMor4LULi1MWPK/ND4OLg3Wll138or9kuv45nyF2CQaPAYuIJOXa/DBMCm2oMK3+1L/Zm/UvVeFKFzgOk0g1BixSSdUGi1+qJLaPutTDVSVnhzflkHXmZpZewxURlY0Bi4hE8fbKw5W6v5mZjOOy/uU9ORKvfnew1HSGK6qs3xJviF2CZDFgkVLbT95SOn3LB0F6roSMScLn3eT/P3rtoVaWqSpkmULQynqap/R5Hv/iFYYr0oqJW0/K/6/JNUWJAYtUGLvxhNLpbXwqdwQSmTZtDLJWRlWYMOaQ5T05Ev6zdpWafm1+GJyrWursMcl0aXpNUVNnIXYBRETaUBSySoaAotvG0qOjKuS08XHWaw+zsbyeRLrCgEWlcHA7Sdm1+WFK12GpB62yeo+k+pyIjBkDFhGJ5sbDp6hdzVbry1XVm1V8mlRCSVnBKiWiJ2Qy7rYhMkQcg0UKHj7JVTp9w/BAPVdCxqpd3ery/3f4ao9OH+va/DAcmxasdJ6hD4Qvq74uDWvi2vwwvYarJzn5ensskgZD/vwYAvZgkYIWs2OUTm9Xt4aeKyFjtWF4W71+Mdews8K1+WGYuf0s1h2+Vmp+8VrE7tVS53URq8bGM3aK8rhEUsWARUQmYebrjTHz9caIOn0bH/16XGkbMcKWOqHqy9cbY3A7b90Xoyaxgyjp1t6JXdDl671ilyF5DFgkx8HtZAp6Nq1V5hitIiXnaeNz8DyvAL5fRKvdnp89EoNXddXjIo9ODUbruf/osRrpYsAiIlF9F3sJY7rVF+WxiwLMT/uvYm7U+TLb6mu35r5Pu8CrelW9PBaRMmWN7atpb6XHSqSNAYvKtG5oa7FLICP048AAjPg5EQCwKOaiaAGryPBOdTC8Ux0AQE5+ARpOU7+XSRsMvaeKg5mJNMeARQBUf4F2aeii50rIFHRv7CZ2CSpZWZiXCjzaDhiGHqjKIuXaifSJAYuIqBwMFUT/4edBPTwPFnFwOxERkZYxYBGR6DjGx3DxvSGqGAYsUmrlgACxSyAjxx5S6bk4p4fYJRBJBgOWiVP16zS0ieEOQiYicVhacJNBpC5+WoiIiIi0jAHLhO04dUvpdO66ITFwrI/h4XtCVHEMWCZs9IYTYpdAJo5hXjr4XhFphgGLFCx/t6XYJRAREUkeA5aJUtX1H9aslp4rISIiMj4MWERkMDjmx3DwvSCqHAYsE5STX6B0OsdYkBi43hk+vkdEmmPAMkENp0WLXQIREZFRY8AiAMCCt5qJXQIRAOBpbr7YJZg87h4kqjzJBaycnBw0b94cMpkMSUlJCvNOnTqFjh07wtraGh4eHliwYEGp+2/duhW+vr6wtrZG06ZNERUVpTBfEARMnz4dtWrVgo2NDYKDg3Hp0iWFNg8ePEB4eDgcHBzg5OSEYcOG4fHjx1p/rrqg6ovznVYeeq6ESDm/6TvFLoGKOT2zu9glEEmS5ALWpEmT4O7uXmp6dnY2unfvDi8vLyQmJmLhwoWYOXMmfvzxR3mbw4cPo3///hg2bBhOnDiB3r17o3fv3jhz5oy8zYIFC/Dtt99i5cqViI+PR9WqVRESEoLnz5/L24SHh+Ps2bOIiYnBjh07sH//fowYMUK3T5zIiHGMj+Gyt64idglEkiSpgPX3339j165d+Prrr0vN+/XXX5Gbm4s1a9agcePG6NevH8aOHYtvvvlG3mbp0qUIDQ3Fp59+ikaNGmH27Nlo2bIlli1bBuBF79WSJUswbdo09OrVC82aNcP//vc/3Lp1C9u2bQMAnD9/HtHR0Vi1ahUCAwPRoUMHfPfdd9i0aRNu3VJ+ZnTgRc9bdna2wp+h4MaNiIpcuSuN3ngiQyeZgJWRkYHhw4fj559/hq2tban5cXFx6NSpEywtLeXTQkJCkJycjIcPH8rbBAcHK9wvJCQEcXFxAICUlBSkp6crtHF0dERgYKC8TVxcHJycnNCqVSt5m+DgYJiZmSE+Pl5l/REREXB0dJT/eXjof5ccx1WQVHBdFU+3RfvELoHIKEgiYAmCgCFDhmDkyJEKwaa49PR0uLq6Kkwrup2enl5mm+Lzi99PVRsXFxeF+RYWFnB2dpa3UWbKlCnIysqS/6WlpZX5nPXl2/4txC6BCAB7Ug0R3xOiihM1YE2ePBkymazMvwsXLuC7777Do0ePMGXKFDHLrRQrKys4ODgo/OlT7+WHlE5/3b/0eDYiMk2FhYLYJRAZDQsxH3zChAkYMmRImW3q1KmD3bt3Iy4uDlZWVgrzWrVqhfDwcKxfvx5ubm7IyMhQmF90283NTf6vsjbF5xdNq1WrlkKb5s2by9vcuXNHYRn5+fl48OCB/P6GKCktU+wSiDTy+R+nMe+NpmKXYVLqfB5VfiMiUouoPVg1a9aEr69vmX+Wlpb49ttvcfLkSSQlJSEpKUl+aoXNmzdj7ty5AICgoCDs378feXl58uXHxMSgYcOGqFatmrxNbGysQg0xMTEICgoCAPj4+MDNzU2hTXZ2NuLj4+VtgoKCkJmZicTERHmb3bt3o7CwEIGBgTp4lXSH3f9kaGa+5if//4b4VBErIX4/EFWOJMZgeXp6okmTJvK/Bg0aAADq1q2L2rVrAwDeffddWFpaYtiwYTh79iw2b96MpUuXYvz48fLlfPzxx4iOjsaiRYtw4cIFzJw5E8eOHcPo0aMBADKZDOPGjcOcOXOwfft2nD59GoMGDYK7uzt69+4NAGjUqBFCQ0MxfPhwJCQk4NChQxg9ejT69eun9PQRhoADhkkqhrT3EbsEkyUI3D1IpE2SCFjqcHR0xK5du5CSkoKAgABMmDAB06dPVzg/Vbt27bBhwwb8+OOP8Pf3x2+//YZt27ahSZMm8jaTJk3CmDFjMGLECLRu3RqPHz9GdHQ0rK2t5W1+/fVX+Pr6olu3bujZsyc6dOigcL4tKdg6MkjsEojKFX/1vtglmAyfKdw9SKRNoo7Bqihvb2+lv7aaNWuGAwcOlHnft99+G2+//bbK+TKZDLNmzcKsWbNUtnF2dsaGDRvUL1hEidcfKJ3e2ttZz5UQqcemijme5b24IHnfH49wV5UI+JpTcY+e5/GEsxVgND1YpFyfFXFil0CkkfOzQ8UuweRkZD8vvxGZrEFrEsQuQZIYsEwQf52SlGw5ahjnjDNmgfNiy29EJutEaqbYJUgSA5YR4+B2kqo2Pv/twp70f6dErMT08AcYkXYwYJmYf8Z3FrsEonJt+YAHYegLf4gR6QYDlpFSdUbmei52eq6EqPIYAvRjw/vSOpcfkSFjwDJSPCMzSd3qwcqvO0q6065eDbFLIAPhYm9VfiMqEwOWCeHYCpKSbo1cy29ElcKeQVIl6uOOYpcgeQxYRohfmmSMuF7rFn+AUXE17NiDVVkMWCbi9MzuYpdApDFu9HXnx/1XxC6ByKgxYJkInoWXjMHtrGdil2A05kVdELsEIqPGgGVkuBuFjFlQxG6xSzBK7Ckk0j4GLBPAL0+SMq6/2scfYkS6x4BlRNYdShG7BCKdYzjQLgZYIt1gwDIiM/86V2ra1Xk9RaiESLtSIrgeawsDKpF+MGAZOTMzmdglEFWaTKa4HndeuEekSozL/k+7il0CkdFiwDIS/FVKxi60sZv8/9fvPxWxEukKXbJf4bZndVuRKiEyfgxYRoxjK8iYrBwYoHD7eV6BSJVI14X0R2KXQGQyGLCMgKoLOxMZM98vosUuQVLir95XuM0fYES6xYBlBJRd2JlfnmSMuF5XXN8fj4hdApFJYcAiIsni2EP13MpUPAM+gyqR7jFgSRw3MGRqGA40124+z4BPpG8MWEaIGyAyJfyRUbaDl+4p3Ob3A5F+MGARkeQwJKhvwOp4sUsgMkkMWBKm7Jc7NzxkitiLpdzoDccVbvP7gUh/GLCISJIYFsq349RtsUsgMlkMWBJ1PPWh2CUQGRT2Yikq+XowkBLpFwOWRL35/eFS0/gFSqam5Dp/+Mo9FS1NW+cGNcUugcjkMGARkdF49ycO6AZK916tf6+NSJUQmS4GLAni4Hai/5Rc9019V2FeQaHC7ZSIniJVQmTaGLCISPIcrC3ELsFg1J/6t8JtmUwmUiVEpo0Bywh0bcjxFWTaTs0MUbhtqr1YHNhOZDgYsCRG2YZj7VCOryAqGSb+OZchUiVERAxYRGSk3v/fMbFL0Cv2XhEZFgYsCRmyNqHUNH6JEv3HVAe8M1wRGR4GLAnZm3xX7BKIDN7/fRikcDv6TLpIlRCRKWPAkrA/R7UXuwQigxPg5axwe+QviSJVoh/svSIyTAxYEqFsV4e/h5P+CyGSAFPZVchwRWS4GLCIyChdmttD4baxhaySz2fMy/VEqoRMQXrWc7FLkBwGLAkoLBRKTeMvVaKyVTEv/fW2KSFVhEq0797jnFLTJnRvKEIlZCpe/e6g2CVIDgOWBNT5PErsEogkqeQPkcm/nxapEu1qNecfhdv8wUW6pizUU9kYsCSI1xYjUp+xjcfiuCsiaZBUwIqMjERgYCBsbGxQrVo19O7dW2F+amoqwsLCYGtrCxcXF3z66afIz89XaLN37160bNkSVlZWqFevHtatW1fqcZYvXw5vb29YW1sjMDAQCQmK5596/vw5Ro0aherVq8POzg59+vRBRoZuzhrdZ8XhUtN4bTEizRhLyGK4In1q7O4gdgmSJpmA9X//938YOHAghg4dipMnT+LQoUN499135fMLCgoQFhaG3NxcHD58GOvXr8e6deswffp0eZuUlBSEhYWha9euSEpKwrhx4/D+++9j586d8jabN2/G+PHjMWPGDBw/fhz+/v4ICQnBnTt35G0++eQT/PXXX9i6dSv27duHW7du4c0339TJ8068/lAnyyUyNQcmdVW4LbWQVbLeNUNaiVQJmYotHwSV34hUkgmCUHoEtYHJz8+Ht7c3vvzySwwbNkxpm7///huvvvoqbt26BVdXVwDAypUr8dlnn+Hu3buwtLTEZ599hsjISJw5c0Z+v379+iEzMxPR0dEAgMDAQLRu3RrLli0DABQWFsLDwwNjxozB5MmTkZWVhZo1a2LDhg146623AAAXLlxAo0aNEBcXh7Zt26r1nLKzs+Ho6IisrCw4OKj+lcBfrFQWddcjqT+mtry98jCOXlP80SKFz1TJ7wHnqpY4/sUrIlWjHVx3paH4uieFz4o+qLseSaIH6/jx47h58ybMzMzQokUL1KpVCz169FAISnFxcWjatKk8XAFASEgIsrOzcfbsWXmb4OBghWWHhIQgLi4OAJCbm4vExESFNmZmZggODpa3SUxMRF5enkIbX19feHp6ytsok5OTg+zsbIW/8kjtFzaRods6sl2paYb+OVNWn9TDFZEpkETAunr1KgBg5syZmDZtGnbs2IFq1aqhS5cuePDgAQAgPT1dIVwBkN9OT08vs012djaePXuGe/fuoaCgQGmb4suwtLSEk5OTyjbKREREwNHRUf7n4eGh4avAXw9E2qDsc2SoIUtZXfweIJIGUQPW5MmTIZPJyvy7cOECCgsLAQBTp05Fnz59EBAQgLVr10Imk2Hr1q1iPgW1TZkyBVlZWfK/tLQ0sUsiMlmqQpayc86JIT3rOcMVkcRZiPngEyZMwJAhQ8psU6dOHdy+fRsA4OfnJ59uZWWFOnXqIDX1xYkD3dzcSh3tV3Rkn5ubm/zfkkf7ZWRkwMHBATY2NjA3N4e5ubnSNsWXkZubi8zMTIVerOJtlLGysoKVlVWZz7W4kl+uqwZxQCuRNl2bH4ZPt57E1sQb8mlF55wTM8goC1YL+jTDO6017/UmIvGI2oNVs2ZN+Pr6lvlnaWmJgIAAWFlZITk5WX7fvLw8XLt2DV5eXgCAoKAgnD59WuFov5iYGDg4OMiDWVBQEGJjYxVqiImJQVDQiyMlih6reJvCwkLExsbK2wQEBKBKlSoKbZKTk5GamipvowvBfq7lNyIijSx82x8XZoeWmi7WLkNlj5sS0ZPhikiCRO3BUpeDgwNGjhyJGTNmwMPDA15eXli4cCEA4O233wYAdO/eHX5+fhg4cCAWLFiA9PR0TJs2DaNGjZL3HI0cORLLli3DpEmT8N5772H37t3YsmULIiP/+1IbP348Bg8ejFatWqFNmzZYsmQJnjx5gqFDhwIAHB0dMWzYMIwfPx7Ozs5wcHDAmDFjEBQUpPYRhOX5M+mmVpZDROWzrmKOa/PDSoWbotv66M1SFei4S5BIuiQRsABg4cKFsLCwwMCBA/Hs2TMEBgZi9+7dqFatGgDA3NwcO3bswIcffoigoCBUrVoVgwcPxqxZs+TL8PHxQWRkJD755BMsXboUtWvXxqpVqxASEiJv07dvX9y9exfTp09Heno6mjdvjujoaIWB74sXL4aZmRn69OmDnJwchISE4Pvvv9fac/14U5LCbX7JEumespAFvAg/Bz/ritrVbLX+mBFR5/HD/qsq6yEi6ZLEebCMUVnn0eC5r0hdPJeQ9hUUCqir4vqfb7R4CYv7Nq/0Y5S1C9JUPu9cd6WB58EqTd31SDI9WKai88I9Cre5QhPpl7mZTGVv1h8nbuKPEy924W8f3R7Najupvdz31x/FP+fvqJzvXd0Wez/tqnI+EUkLA5aBuX7/qdglEBH++3Gjqrfp9WWHtP5YRGQ8GLAMWNJ0nq2ZSGxF4Sd0yX5cSH+kteVu+SAIbXyctbY8IjIsDFgGzMnWUuwSiOhf0eM6yf/fa/khnEzL1HgZa4e2RteGLlqsiogMFQOWgeGuAiLD9+eo9mKXQKQX3CZVnCSuRUhEREQkJQxYRERERFrGgEVERESkZQxYRERERFrGgEVERESkZQxYRERERFrGgEVERESkZQxYRERERFrGgEVERESkZQxYRERERFrGgEVERESkZQxYRERERFrGgEVERESkZQxYRERERFpmIXYBpkoQBABAdna2yJWQlBWtP0Xrkz5w3SVt4LpLUqXuusuAJZJHjx4BADw8PESuhIzBo0eP4OjoqLfHArjuknZw3SWpKm/dlQn6/PlAcoWFhbh16xbs7e0hk8m0uuzs7Gx4eHggLS0NDg4OWl22PhnD89D1cxAEAY8ePYK7uzvMzPSzx5/rbvn4PMpnbOtuEam/96y/fOquu+zBEomZmRlq166t08dwcHCQ5AekJGN4Hrp8Dvr69V+E6676+DzKZozrbhGpv/esv2zqrLsc5E5ERESkZQxYRERERFrGgGWErKysMGPGDFhZWYldSqUYw/MwhuegT8byevF5mC6pv2asX3s4yJ2IiIhIy9iDRURERKRlDFhEREREWsaARURERKRlDFhEREREWsaAZSQePHiA8PBwODg4wMnJCcOGDcPjx4/LvM+PP/6ILl26wMHBATKZDJmZmfoptpjly5fD29sb1tbWCAwMREJCQpntt27dCl9fX1hbW6Np06aIiorSU6WqafIczp49iz59+sDb2xsymQxLlizRX6EGStN198GDBxgzZgwaNmwIGxsbeHp6YuzYscjKytJj1aa37v7000/o2LEjqlWrhmrVqiE4OLjc52zqij7nxf/mz58vdlkqabpOG4qZM2eWep19fX3FLgsQyCiEhoYK/v7+wpEjR4QDBw4I9erVE/r371/mfRYvXixEREQIERERAgDh4cOH+in2X5s2bRIsLS2FNWvWCGfPnhWGDx8uODk5CRkZGUrbHzp0SDA3NxcWLFggnDt3Tpg2bZpQpUoV4fTp03qtuzhNn0NCQoIwceJEYePGjYKbm5uwePFi/RZsgDRdd0+fPi28+eabwvbt24XLly8LsbGxQv369YU+ffrorWZTXHffffddYfny5cKJEyeE8+fPC0OGDBEcHR2FGzdu6Lly6fDy8hJmzZol3L59W/73+PFjsctSStP1wZDMmDFDaNy4scLrfPfuXbHLEhiwjMC5c+cEAMLRo0fl0/7++29BJpMJN2/eLPf+e/bsESVgtWnTRhg1apT8dkFBgeDu7i5EREQobf/OO+8IYWFhCtMCAwOFDz74QKd1lkXT51Ccl5eXyQesyq67RbZs2SJYWloKeXl5uiizFFNfdwVBEPLz8wV7e3th/fr1uipR8qT0Ga/s+iCmGTNmCP7+/mKXUQp3ERqBuLg4ODk5oVWrVvJpwcHBMDMzQ3x8vIiVqZabm4vExEQEBwfLp5mZmSE4OBhxcXFK7xMXF6fQHgBCQkJUtte1ijwHUqStdTcrKwsODg6wsND95VW57r7w9OlT5OXlwdnZWVdlGoX58+ejevXqaNGiBRYuXIj8/HyxSyrFGL7LLl26BHd3d9SpUwfh4eFITU0VuyRe7NkYpKenw8XFRWGahYUFnJ2dkZ6eLlJVZbt37x4KCgrg6uqqMN3V1RUXLlxQep/09HSl7cV6jhV5DqRIG+vuvXv3MHv2bIwYMUIXJSp9PK67wGeffQZ3d/dSwZH+M3bsWLRs2RLOzs44fPgwpkyZgtu3b+Obb74RuzQFUv8uCwwMxLp169CwYUPcvn0bX375JTp27IgzZ87A3t5etLrYg2XAJk+eXGrgXsk/Kaz8ZHr0te5mZ2cjLCwMfn5+mDlzZuULJ7XMnz8fmzZtwh9//AFra2uxy9ErTdbt8ePHo0uXLmjWrBlGjhyJRYsW4bvvvkNOTo7Iz8K49OjRA2+//TaaNWuGkJAQREVFITMzE1u2bBG1LvZgGbAJEyZgyJAhZbapU6cO3NzccOfOHYXp+fn5ePDgAdzc3HRYYcXVqFED5ubmyMjIUJiekZGhsmY3NzeN2utaRZ6DqdDHuvvo0SOEhobC3t4ef/zxB6pUqVLZstVi6uvu119/jfnz5+Off/5Bs2bNdFmmQVJ33VYmMDAQ+fn5uHbtGho2bKiD6irG2L7LnJyc0KBBA1y+fFnUOtiDZcBq1qwJX1/fMv8sLS0RFBSEzMxMJCYmyu+7e/duFBYWIjAwUMRnoJqlpSUCAgIQGxsrn1ZYWIjY2FgEBQUpvU9QUJBCewCIiYlR2V7XKvIcTIWu193s7Gx0794dlpaW2L59u157UUx53V2wYAFmz56N6OhohXFzpkTddVuZpKQkmJmZldotLjZj+y57/Pgxrly5glq1aolbiNij7Ek7QkNDhRYtWgjx8fHCwYMHhfr16ysc6n7jxg2hYcOGQnx8vHza7du3hRMnTgg//fSTAEDYv3+/cOLECeH+/ft6qXnTpk2ClZWVsG7dOuHcuXPCiBEjBCcnJyE9PV0QBEEYOHCgMHnyZHn7Q4cOCRYWFsLXX38tnD9/XpgxY4ZBHOquyXPIyckRTpw4IZw4cUKoVauWMHHiROHEiRPCpUuXxHoKotN03c3KyhICAwOFpk2bCpcvX1Y4NDs/P18vNZviujt//nzB0tJS+O233xRe80ePHon1FAza4cOHhcWLFwtJSUnClStXhF9++UWoWbOmMGjQILFLU6q89cGQTZgwQdi7d6+QkpIiHDp0SAgODhZq1Kgh3LlzR9S6GLCMxP3794X+/fsLdnZ2goODgzB06FCFL76UlBQBgLBnzx75tBkzZggASv2tXbtWb3V/9913gqenp2BpaSm0adNGOHLkiHxe586dhcGDByu037Jli9CgQQPB0tJSaNy4sRAZGam3WlXR5DkUvQ8l/zp37qz/wg2Eputu0WlFlP2lpKTorW5TW3e9vLyUvuYzZszQf+ESkJiYKAQGBgqOjo6CtbW10KhRI2HevHnC8+fPxS5NpbLWB0PWt29foVatWoKlpaXw0ksvCX379hUuX74sdlmCTBAEQX/9ZURERETGj2OwiIiIiLSMAYuIiIhIyxiwiIiIiLSMAYuIiIhIyxiwiIiIiLSMAYuIiIhIyxiwiIiIiLSMAYuIiIhIyxiwSCf27t0LmUyGzMzMMtt5e3tjyZIlOq1l3bp18qvcjxs3rlLLKnpeMpkMvXv31kp9ZFyuXbsGmUyGpKQklW28vb3l61F5nxFtK3pcJycnvT4uqa9Lly6V/q6qjJkzZ6J58+Y6fxxDWxeHDBkir2nbtm2VXh4DlgkrvjJZWlqiXr16mDVrFvLz8yu97Hbt2uH27dtwdHQE8CLkKPsQHT16FCNGjKj045XHwcEBt2/fxuzZsyu1nKLn9c4772ipMqqIu3fv4sMPP4SnpyesrKzg5uaGkJAQHDp0SOzS1DZr1iyFz0hlde3aFatWrSq33e3bt3X+o8YYxMXFwdzcHGFhYWKXolPKwsTEiRNLXZxcV9auXYuLFy9qbXk+Pj74559/ymzz0Ucf4ZVXXkGjRo0wZswY+fSlS5fi9u3bWqvFQmtLIkkKDQ3F2rVrkZOTg6ioKIwaNQpVqlTBlClTKrVcS0tLuLm5lduuZs2alXocdclkMrXqKU/R87KxsUFOTo4WKqOK6NOnD3Jzc7F+/XrUqVMHGRkZiI2Nxf3798UuTW329vZaWScB4MGDBzh06BA2bdpUbls3NzethTpjtnr1aowZMwarV6/GrVu34O7uLnZJaisoKIBMJoOZWcX6UOzs7GBnZ6flqpRzcnKCi4uLVpZ16tQpPHz4EJ07dy6z3ZIlS2BpaYmcnBy4urpi3rx5sLe3h6Ojo1Y/G+zBMnFFv/69vLzw4YcfIjg4GNu3bwcAPHz4EIMGDUK1atVga2uLHj164NKlS/L7Xr9+Ha+99hqqVauGqlWronHjxoiKigKguItw7969GDp0KLKysuQ9ZjNnzgRQehdhamoqevXqBTs7Ozg4OOCdd95BRkaGfH5R1/XPP/8Mb29vODo6ol+/fnj06JHGz93b2xtz5szBoEGDYGdnBy8vL2zfvh13796V19CsWTMcO3asAq8s6UpmZiYOHDiAr776Cl27doWXlxfatGmDKVOm4PXXX5e3k8lkWLFiBXr06AEbGxvUqVMHv/32m8Ky0tLS8M4778DJyQnOzs7o1asXrl27ptBm1apVaNSoEaytreHr64vvv/9eYX5CQgJatGgBa2trtGrVCidOnKjQ8yrq5d2xYwcaNmwIW1tbvPXWW3j69CnWr18Pb29vVKtWDWPHjkVBQYHCfSMjI9GyZUu4urri4cOHCA8PR82aNWFjY4P69etj7dq1FarJVD1+/BibN2/Ghx9+iLCwMKxbt65Um7/++gutW7eGtbU1atSogTfeeEM+LycnB5999hk8PDxgZWWFevXqYfXq1fL5Z86cQY8ePWBnZwdXV1cMHDgQ9+7dU1lPTk4OJk6ciJdeeglVq1ZFYGAg9u7dK59ftO5s374dfn5+sLKyQmpqKo4ePYpXXnkFNWrUgKOjIzp37ozjx4/L7+ft7Q0AeOONNyCTyeS3S+4iLCwsxKxZs1C7dm1YWVmhefPmiI6Ols8v2i3++++/o2vXrrC1tYW/vz/i4uLUfMX/U/TYa9asgaenJ+zs7PDRRx+hoKAACxYsgJubG1xcXDB37txS9/3zzz8RGhqKKlWqlLl9srS0RH5+Pj766CN5uNIFBixSYGNjg9zcXAAvdiEeO3YM27dvR1xcHARBQM+ePZGXlwcAGDVqFHJycrB//36cPn0aX331ldJfPe3atcOSJUvku+lu376NiRMnlmpXWFiIXr164cGDB9i3bx9iYmJw9epV9O3bV6HdlStXsG3bNuzYsQM7duzAvn37MH/+/Ao938WLF6N9+/Y4ceIEwsLCMHDgQAwaNAgDBgzA8ePHUbduXQwaNAi8JrrhKPp1vW3btnJ7Eb/44gv06dMHJ0+eRHh4OPr164fz588DAPLy8hASEgJ7e3scOHAAhw4dgp2dHUJDQ+WfgV9//RXTp0/H3Llzcf78ecybNw9ffPEF1q9fD+DFhvjVV1+Fn58fEhMTMXPmTKXrtrqePn2Kb7/9Fps2bUJ0dDT27t2LN954A1FRUYiKisLPP/+MH374oVRQ3L59O3r16iV/zufOncPff/+N8+fPY8WKFahRo0aFazJFW7Zsga+vLxo2bIgBAwZgzZo1Ct8BkZGReOONN9CzZ0+cOHECsbGxaNOmjXz+oEGDsHHjRnz77bc4f/48fvjhB/l3Y2ZmJl5++WW0aNECx44dQ3R0NDIyMsocdjB69GjExcVh06ZNOHXqFN5++22EhoYq/OB9+vQpvvrqK6xatQpnz56Fi4sLHj16hMGDB+PgwYM4cuQI6tevj549e8p/kB49ehTAi910t2/flt8uaenSpVi0aBG+/vprnDp1CiEhIXj99dcVHh8Apk6diokTJyIpKQkNGjRA//79KzTk5MqVK/j7778RHR2NjRs3YvXq1QgLC8ONGzewb98+fPXVV5g2bRri4+MV7lf8c1DW9un27dvo3bs3QkND8dFHH2lcn9oEMlmDBw8WevXqJQiCIBQWFgoxMTGClZWVMHHiROHixYsCAOHQoUPy9vfu3RNsbGyELVu2CIIgCE2bNhVmzpypdNl79uwRAAgPHz4UBEEQ1q5dKzg6OpZq5+XlJSxevFgQBEHYtWuXYG5uLqSmpsrnnz17VgAgJCQkCIIgCDNmzBBsbW2F7OxseZtPP/1UCAwMVPk8y3rsAQMGyG/fvn1bACB88cUX8mlxcXECAOH27dsK9y3+2pH+/fbbb0K1atUEa2troV27dsKUKVOEkydPKrQBIIwcOVJhWmBgoPDhhx8KgiAIP//8s9CwYUOhsLBQPj8nJ0ewsbERdu7cKQiCINStW1fYsGGDwjJmz54tBAUFCYIgCD/88INQvXp14dmzZ/L5K1asEAAIJ06cUFl/8fW+yNq1awUAwuXLl+XTPvjgA8HW1lZ49OiRfFpISIjwwQcfyG8/f/5csLOzE86cOSMIgiC89tprwtChQ1U+dtFjKftM0Avt2rUTlixZIgiCIOTl5Qk1atQQ9uzZI58fFBQkhIeHK71vcnKyAECIiYlROn/27NlC9+7dFaalpaUJAITk5GRBEAShc+fOwscffywIgiBcv35dMDc3F27evKlwn27duglTpkwRBOG/dScpKanM51VQUCDY29sLf/31l3waAOGPP/5QaDdjxgzB399fftvd3V2YO3euQpvWrVsLH330kSAIgpCSkiIAEFatWiWfX/Tdff78eZX1qHrskt/xISEhgre3t1BQUCCf1rBhQyEiIkJ++8aNG4KlpaV8m1PW9qlZs2aCh4eHEBgYKAQGBgpXrlwpt66KYA+WiduxYwfs7OxgbW2NHj16oG/fvpg5cybOnz8PCwsLBAYGyttWr14dDRs2lPcAjB07FnPmzEH79u0xY8YMnDp1qlK1nD9/Hh4eHvDw8JBP8/Pzg5OTk/wxgRfd2sW7dGvVqoU7d+5U6DGbNWsm/7+rqysAoGnTpqWmVXT5pBt9+vTBrVu3sH37doSGhmLv3r1o2bJlqV05QUFBpW4XrUsnT57E5cuXYW9vL+8Vc3Z2xvPnz3HlyhU8efIEV65cwbBhw+Tz7ezsMGfOHFy5cgXAi3W2WbNmsLa2VvmYmrC1tUXdunXlt11dXeHt7a3QM+zq6qqwPu7evRsuLi5o3LgxAODDDz/Epk2b0Lx5c0yaNAmHDx+ucD2mKDk5GQkJCejfvz8AwMLCAn379lXYxZeUlIRu3bopvX9SUhLMzc1VjgM6efIk9uzZo7BO+fr6AoB8vSru9OnTKCgoQIMGDRTus2/fPoX2lpaWCt9nAJCRkYHhw4ejfv36cHR0hIODAx4/fozU1FS1X4/s7GzcunUL7du3V5jevn17he9lQPH7tFatWgAq9t1Z8jve1dUVfn5+CmPKSn4Otm/fjg4dOsgPpipr+3Ty5EmkpqbiyJEjOHLkCOrUqaNxjergIHcT17VrV6xYsQKWlpZwd3eHhYX6q8T777+PkJAQREZGYteuXYiIiMCiRYsUjsrQhSpVqijclslkKCwsrPSyZDKZymkVXT7pjrW1NV555RW88sor+OKLL/D+++9jxowZGDJkiFr3f/z4MQICAvDrr7+WmlezZk08fvwYAPDTTz8p/NAAAHNz80rXr4yydbu89X379u0KY8969OiB69evIyoqCjExMejWrRtGjRqFr7/+Wic1G5vVq1cjPz9fYVC7IAiwsrLCsmXL4OjoCBsbG5X3L2se8GK9e+211/DVV1+VmlcUSkq2Nzc3R2JiYqn1rnjwtrGxkX9fFRk8eDDu37+PpUuXwsvLC1ZWVggKCpLvAtc2bX13auNzINb2qTj2YJm4qlWrol69evD09FQIV40aNUJ+fr7CPu779+8jOTkZfn5+8mkeHh4YOXIkfv/9d0yYMAE//fST0sextLQsNTC3pEaNGiEtLQ1paWnyaefOnUNmZqbCYxIp4+fnhydPnihMO3LkSKnbjRo1AgC0bNkSly5dgouLC+rVq6fw5+joCFdXV7i7u+Pq1aul5vv4+AB4sc6eOnUKz58/V/mYuiQIAv766y/5uJMiNWvWxODBg/HLL79gyZIl+PHHH/VWk5Tl5+fjf//7HxYtWoSkpCT538mTJ+Hu7o6NGzcCeNFTo+o0Bk2bNkVhYSH27dundH7Lli1x9uxZeHt7l1qvqlatWqp9ixYtUFBQgDt37pRqX95RqIcOHcLYsWPRs2dPNG7cGFZWVqUG01epUqXM72YHBwe4u7uXOgXKoUOHDOZ7+fHjx9izZ0+pz4G62yddYcAiperXr49evXph+PDhOHjwIE6ePIkBAwbgpZdekq/E48aNw86dO5GSkoLjx49jz5498o1XSd7e3nj8+DFiY2Nx7949PH36tFSb4OBgNG3aFOHh4Th+/DgSEhIwaNAgdO7cGa1atdLp8yXpuH//Pl5++WX88ssvOHXqFFJSUrB161YsWLCg1Bfs1q1bsWbNGly8eBEzZsxAQkICRo8eDQAIDw9HjRo10KtXLxw4cAApKSnYu3cvxo4dixs3bgAAvvzyS0RERODbb7/FxYsXcfr0aaxduxbffPMNAODdd9+FTCbD8OHDce7cOURFRem1pygxMRFPnz5Fhw4d5NOmT5+OP//8E5cvX8bZs2exY8cOlZ9LUrRjxw48fPgQw4YNQ5MmTRT++vTpI99NOGPGDGzcuBEzZszA+fPn5YOogRffdYMHD8Z7772Hbdu2yderLVu2AHgx+PrBgwfo378/jh49iitXrmDnzp0YOnSo0qDToEEDhIeHY9CgQfj999+RkpKChIQEREREIDIyssznU79+ffz88884f/484uPjER4eXqqHzdvbG7GxsUhPT8fDhw+VLufTTz/FV199hc2bNyM5ORmTJ09GUlISPv74Y41fY12Ijo5GgwYN5EdBApptn3SFAYtUWrt2LQICAvDqq68iKCgIgiAgKipK3lVbUFCAUaNGoVGjRggNDUWDBg1KHcJepF27dhg5ciT69u2LmjVrYsGCBaXayGQy/Pnnn6hWrRo6deqE4OBg1KlTB5s3b9bp8yRpsbOzQ2BgIBYvXoxOnTqhSZMm+OKLLzB8+HAsW7ZMoe2XX36JTZs2oVmzZvjf//6HjRs3yn9129raYv/+/fD09MSbb76JRo0aYdiwYXj+/DkcHBwAvNjNsGrVKqxduxZNmzZF586dsW7dOnkPlp2dHf766y+cPn0aLVq0wNSpU5Xu+tGVP//8Ez179lTofba0tMSUKVPQrFkzdOrUCebm5mqdH4te7B4MDg5Wei6kPn364NixYzh16hS6dOmCrVu3Yvv27WjevDlefvllJCQkyNuuWLECb731Fj766CP4+vpi+PDh8t7Vot6ggoICdO/eHU2bNsW4cePg5OSk8rxVa9euxaBBgzBhwgQ0bNgQvXv3xtGjR+Hp6Vnu83n48CFatmyJgQMHYuzYsaXOObVo0SLExMTAw8MDLVq0ULqcsWPHYvz48ZgwYQKaNm2K6OhobN++HfXr1y/z8fXlzz//VNg9CGi2fdKZSg+TJzJwujhiikcRGj5o6UggXVB2FGFFNG3aVNi8ebPG9+NRhGQItPEZzcvLE5ydnYX4+HjtFCXwKEIijWRlZcHOzg6fffZZpZZz4MAB2NnZKR0YTaSJzz77DHZ2dsjKyqrQ/XNzc9GnTx/06NFDo/vZ2dlh5MiRFXpMIm3r378/ateuXeH7P3jwAJ988glat25d6VpGjhyp1TPYy/5Na0RG69GjR/KzwTs5OVXqpIvPnj3DzZs3AbzYUGnrUiekfTKZDH/88YdBXpT7+vXr8hP21qlTp8KXNKmIy5cvA3hxJGTRrk4iMRjaunjnzh1kZ2cDeHFEp7KDDjTBgEVERESkZdxFSERERKRlDFhEREREWsaARURERKRlDFhEREREWsaARURERKRlDFhEREREWsaARURERKRlDFhEREREWvb/nH6tK/nXZOoAAAAASUVORK5CYII=\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot force mission profile\n",
"plt.figure(3)\n",
"\n",
"plt.subplot(131)\n",
"plt.plot(df[\"position\"], df[\"Fact\"])\n",
"plt.ylabel(\"Force [N]\")\n",
"plt.xlabel(\"Position [m]\")\n",
"\n",
"plt.subplot(132)\n",
"plt.plot(df[\"speed\"], df[\"Fact\"])\n",
"plt.xlabel(\"Speed [m/s]\")\n",
"plt.gca().axes.get_yaxis().set_visible(False)\n",
"\n",
"plt.subplot(133)\n",
"plt.plot(df[\"acceleration\"], df[\"Fact\"])\n",
"plt.xlabel(\"Acceleration [m/s²]\")\n",
"plt.gca().axes.get_yaxis().set_visible(False)"
]
},
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"The force is mainly proportional to the position: therefore the effect of the stiffness of the flexible bearing dominates this fatigue cycle. In this case the calculation of the fatigue force can be carried out analytically using the following equations: \n",
"$F_{RMC}=(\\frac{1}{\\int |\\dot{x}| {d}t} \\int |F|^3 |\\dot{x}| {d}t)^{1/3}$ \n",
"where: \n",
"- $F(t)=Kx(t)=F_kcos(\\omega_kt)$ with $x(t)=X_kcos(\\omega_kt)$ and $F_k=KX_k$ \n",
"- $\\dot{x}(t)=-X_k\\omega_ksin(\\omega_kt)$ \n",
"with:\n",
"- $F_k$ magnitude of sinusoidal forces;\n",
"- $A_k$ magnitude of sinusoidal displacements;\n",
"- $N_k$ "
]
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"Thus: \n",
"$F_{RMC}^3 = \\frac{\\sum{\\frac{F_k^3}{4}A_k N_k}}{\\sum{A_k N_k}}$ \n",
"\n",
"We have used following trigonometric formula: \n",
"$cos(\\theta)^3sin(\\theta) = cos(\\theta)^2 sin(\\theta)cos(\\theta) = \\frac{1+cos(2\\theta)}{2} \\frac{sin(2\\theta)}{2} $ \n"
]
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