{ "cells": [ { "cell_type": "markdown", "id": "b16f6916", "metadata": {}, "source": [ "# Motor DC (theory)\n", "\n", "DC motors convert electrical energy into mechanical torque and rotational motion. The fundamental equations are:\n", "\n", "- Torque generated: \n", " \n", " $$ \n", " \\tau = k_t \\cdot I\n", " $$ \n", "\n", "- Voltage across the motor: \n", "\n", " $$ \n", " V = k_e \\cdot \\omega + I \\cdot R\n", " $$ \n", "\n", "\n", "Where:\n", "- $\\tau$: torque (N·m) \n", "- $I$: current (A) \n", "- $V$: voltage (V) \n", "- $\\omega$: angular velocity (rad/s) \n", "- $k_t$: torque constant (N·m/A) \n", "- $k_e$: back-EMF constant (V·s/rad) \n", "- $R$: motor coil resistance (Ω)" ] }, { "cell_type": "markdown", "id": "5f22d4d4", "metadata": {}, "source": [ "**DC motor model**\n", "\n", "![DC motor diagrams](img/dcmotor.png)\n", "\n", "Parameter\n", "\n", "- `va` - Applied Voltage\n", "- `R` - Resistance\n", "- `L` - Inductance\n", "- `i` - Current\n", "- `b` - Damping coefficient\n", "- `J` - Rotor Inertia\n", "- `ke` - Back EMF constant\n", "- `kt` - Torque constant\n", "- `θ` - Rotor shaft angle\n" ] }, { "cell_type": "markdown", "id": "964727b9", "metadata": {}, "source": [ "**Typical Parameters for steady-state**\n", "\n", "To correctly simulate and use a DC motor in a control system, you must know or estimate the following key parameters:\n", "\n", "| Symbol | Quantity | Units | Typical Range (Lab Motors) |\n", "|-------------|--------------------------|--------------|----------------------------|\n", "| $\\tau$ | Torque | N·m | 0.01 – 0.2 N·m |\n", "| $I$ | Current | A | 0.2 – 2 A |\n", "| $V$ | Voltage | V | 3 – 24 V |\n", "| $\\omega$ | Angular speed | rad/s | 100 – 2000 rad/s |\n", "| $k_t$ | Torque constant | N·m/A | 0.01 – 0.1 N·m/A |\n", "| $k_e$ | Back-EMF constant | V·s/rad | 0.01 – 0.1 V·s/rad |\n", "| $R$ | Coil resistance | Ω | 0.5 – 10 Ω |\n", "\n", "\n", "Most of these values are provided in the motor's datasheet:\n", "\n", "- **$k_t$** and **$k_e$**: Often given directly. For brushed motors, these are numerically equal ($k_t = k_e$) if using SI units.\n", "- **Stall torque** ($\\tau_{\\text{stall}}$): Maximum torque at zero speed.\n", "- **No-load speed** ($\\omega_{\\text{free}}$): Speed at zero torque.\n", "- **Stall current** ($I_{\\text{stall}}$): Current at zero speed and maximum torque.\n", "- **Resistance**: $R = V_{\\text{stall}} / I_{\\text{stall}}$\n", "\n", "From these, you can compute:\n", "- $k_t = \\tau_{\\text{stall}} / I_{\\text{stall}}$\n", "- $k_e = V_{\\text{free}} / \\omega_{\\text{free}}$\n", " \n", "**Trade-Offs in Motor Selection**\n", "\n", "The performance of a DC motor is a balance between torque and speed. Key considerations:\n", "- Higher torque → requires more current.\n", "- Higher speed → increases back-EMF and voltage needs.\n", "- Higher current → increases resistive losses ($I^2 R$) and risk of overheating.\n", "- Motor constants ($k_t$, $k_e$) are typically fixed for a given model.\n", "\n", "> Always respect **maximum ratings**: exceeding current, voltage, or power may permanently damage the motor.\n", "\n" ] }, { "cell_type": "markdown", "id": "3cbc6149", "metadata": {}, "source": [ "**Dynamical model**\n", "\n", "Electrical part\n", "\n", "  $va = R i + L \\frac{di}{dt} + k_e \\frac{dθ}{dt}$\n", "\n", "Electromechanical Conversion\n", "\n", "  $T_{m} = k_t i$\n", "\n", "Mechanical Part (inertia plus load)\n", "\n", "  $T_{m} = b \\frac{dθ}{dt} + J\\frac{d^2θ}{dt^2}$\n", "\n", "If required, mechanical part can also include Coulomb (static) or Reynolds (aerodynamic) friction\n" ] }, { "cell_type": "markdown", "id": "c7bc471f", "metadata": {}, "source": [ "\n", "**DC motor - regime estacionário**\n", "\n", "There are two time constants associated to DC motors in the second order model: \n", "\n", "- the electrical time constant $tau_{el}=L/R$, of order 0.1 ms\n", "- the mechanical time constant $tau_{mech}=J/B$, of order 100 ms\n", "\n", "In many if not most control projects, a stationary (steady state) model is adequate. \n", "\n", "By zeroing the time variations (dynamic derivatives):\n", "\n", "$$ L \\frac{di}{dt}=0 $$\n", "\n", "$$ J\\frac{dω}{dt}=0 $$\n", "\n", "The electrical part becomes\n", "\n", "$$ va = R i + k_e ω $$\n", "\n", "The mechanical part becomes\n", "\n", "$$ T_{m} = k_t i $$\n", "\n", "A typical (minimal) load: \n", "\n", "$$ T_{m} = b ω $$" ] }, { "cell_type": "markdown", "id": "53b6a56a", "metadata": {}, "source": [ "**Speed-voltage transfer curve**\n", "\n", "$$ va = R \\frac{b ω}{k_t} + k_e ω = (1+\\frac{Rb}{k_e k_t}) k_e ω $$\n", "\n", "$$ \\boxed{ ω = \\frac{va}{(1+\\frac{Rb}{k_e k_t}) k_e}}$$\n", "\n", "This linear correlation between speed $\\omega$ and applied Voltage $va$ is called the **speed-voltage transfer curve**.\n", "\n", "For a given motor, the proportionality constant is given by $$\\frac{1}{(1+\\frac{R b}{k_e k_t})k_e}$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "id": "e7c999a6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1165.5011655011656\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Voltage range\n", "va = np.linspace(0, 5, 100)\n", "\n", "# Electrical & mechanical parameters (typical/representative)\n", "R = 2.7e0 # Armature resistance [ohm]\n", "B = 3.0e-8 # Viscous damping coeff. [N·m·s/rad]\n", "ke = 7.5e-4 # Back-EMF constant [V·s/rad] (== V/(rad/s))\n", "kt = 7.5e-4 # Torque constant [N·m/A] (≈ ke in SI)\n", "\n", "# Speed-voltage static transfer curve\n", "propconst= 1 / ((1 + (R * B) / (ke * kt)) * ke)\n", "print(propconst)\n", "omega = propconst*va*60/6.28 \n", "\n", "plt.figure(figsize=(7, 5))\n", "plt.plot(va, omega*60/6.28)\n", "plt.xlabel('Voltage $v_a$ (V)')\n", "plt.ylabel('Speed $\\\\omega$ (rpm)')\n", "plt.title('Example of Speed-Voltage Transfer Curve')\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "7ab11551", "metadata": {}, "source": [ "**Speed-Torque Curve (load line)**\n", "\n", "$$ T_{m} = \\frac{k_t}{R} (va-k_e ω) $$\n", "\n", "$$ \\boxed{ω = \\frac{va}{k_e}-\\frac{R}{k_e k_t}T_m} $$\n", "\n", "This linear inverse correlation between speed $\\omega$ and torque $T_m$ is called the **load line**.\n", "\n", "For a given motor:\n", "\n", "- the slope $-\\frac{R}{k_e k_t}$ is constant.\n", " \n", "- the vertical offset $\\frac{va}{k_e}$ is proportional to the applied Voltage \n", "\n", "\n", "Load line reference points:\n", "\n", "Maximum speed at zero load and torque:\n", "\n", "$$ ω(T_m=0) = \\frac{va}{k_e} = ω_{max} $$\n", "\n", "Maximum torque at full load and zero speed:\n", "\n", "$$ T_m(ω=0) = \\frac{k_t}{R} va = k_t I_{stall}= Tm_{max} $$\n", "\n", "\n", "The point of maximum energy transfer is in the center point of the load line: \n", "\n", "$$ P_{max} = \\frac{ω_{max}} {2} \\frac{Tm_{max}} {2} $$\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "14f9385e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Parameters\n", "va = 5 #applied voltage\n", "\n", "# Torque range\n", "Tm = np.linspace(0,kt*va/R , 100)\n", "\n", "# Electrical & mechanical parameters (typical/representative)\n", "R = 2.7e0 # Armature resistance [ohm]\n", "B = 3.0e-8 # Viscous damping coeff. [N·m·s/rad]\n", "ke = 7.5e-4 # Back-EMF constant [V·s/rad] (== V/(rad/s))\n", "kt = 7.5e-4 # Torque constant [N·m/A] (≈ ke in SI)\n", "\n", "# Speed-torque curve\n", "omega = va/ke - R / (ke * kt) * Tm\n", "\n", "# Current curve\n", "Im=Tm/kt\n", "\n", "# Power curve\n", "P = omega * Tm\n", "\n", "# Set axis limits\n", "x_min, x_max = Tm.min(), Tm.max()\n", "y_min, y_max = omega.min()*60/6.28, omega.max()*60/6.28\n", "p_min, p_max = P.min(), P.max()\n", "I_min, I_max = Im.min(), Im.max()\n", "\n", "fig, ax1 = plt.subplots(figsize=(9, 6))\n", "\n", "# Main plot: Torque vs Speed\n", "ax1.plot(Tm, omega*60/6.28, label='Load line', color='b')\n", "ax1.plot(Tm, Tm/B*60/6.28, label='Actual load', color='b', linestyle='--')\n", "ax1.set_ylabel('Speed $\\\\omega$ (rpm)', color='b')\n", "ax1.tick_params(axis='y', labelcolor='b')\n", "ax1.set_xlabel('Torque $T_m$ (Nm)', loc='right')\n", "ax1.xaxis.set_label_position('bottom')\n", "ax1.xaxis.set_ticks_position('bottom')\n", "ax1.spines['bottom'].set_position(('outward', 0))\n", "ax1.set_xlim(x_min, x_max)\n", "ax1.set_ylim(y_min, y_max)\n", "\n", "# Additional y-axis for Current\n", "ax3 = ax1.twinx()\n", "ax3.plot(Tm, Im, label='Current', color='g', linestyle='--')\n", "ax3.spines['right'].set_position(('outward', 60))\n", "ax3.yaxis.set_label_position('right')\n", "ax3.yaxis.set_ticks_position('right')\n", "ax3.set_ylim(ax1.get_ylim())\n", "#omega_ticks = ax1.get_yticks()\n", "#ax3.set_yticks(omega_ticks)\n", "#ax3.set_yticklabels([f\"{(ke*tick/(60/6.28) ):.1f}\" for tick in omega_ticks])\n", "ax3.set_ylabel('Current $I$ (A)', color='g')\n", "ax3.tick_params(axis='y', labelcolor='g')\n", "ax3.set_ylim(I_min, I_max) # restrict power axis to min/max\n", "\n", "# Additional y-axis for Power\n", "ax4 = ax1.twinx()\n", "ax4.plot(Tm, P, label='Power', color='r')\n", "ax4.set_ylabel('Power $P$ (W)', color='r')\n", "ax4.tick_params(axis='y', labelcolor='r')\n", "ax4.set_ylim(p_min, p_max) # restrict power axis to min/max\n", "\n", "# Grid on both x and y axes\n", "ax1.grid(True, which='both', axis='both')\n", "ax1.legend()\n", "#ax4.legend()\n", "plt.title('Example of Speed-Torque Curve (load line)')\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "\n" ] }, { "cell_type": "markdown", "id": "bc99b78d", "metadata": {}, "source": [ "**Gears**\n", "\n", "Gears can be used to **adapt motor output** to desired speed and torque levels.\n", "\n", "**Basic Gear Equations**\n", "\n", "- Gear ratio: \n", "\n", " $$ \n", " R = \\frac{N_{\\text{out}}}{N_{\\text{in}}}\n", " $$ \n", "\n", " where $N$ is the number of teeth or diameter.\n", "\n", "- Output torque: \n", " \n", " $$ \n", " \\tau_{\\text{out}} = R \\cdot \\tau_{\\text{in}}\n", " $$ \n", "\n", "\n", "- Output speed: \n", " \n", " $$ \n", " \\omega_{\\text{out}} = \\frac{\\omega_{\\text{in}}}{R}\n", " $$ \n", "\n", "\n", "**Why Use Gears?**\n", "\n", "- **Increase torque** at the cost of lower speed.\n", "- **Reduce load** on the motor to avoid overheating.\n", "- **Match the dynamics** of the controlled system (e.g. pendulum).\n", "\n", "**Pulleys (with belts)** provide similar mechanical advantages as gears.They are quieter than gears, and the distance between shafts is more flexible, so systems with pulleys and belts are more simple to design and align. At the same time, they are less precise (risk of belt slippage), and limited to moderate torque applications.\n", "\n", "**Numerical Example: Gear Matching**\n", "\n", "Suppose your pendulum needs:\n", "- Torque of $0.1$ N·m\n", "- Speed around $30$ rad/s\n", "\n", "But your available motor produces:\n", "- Torque of $0.02$ N·m\n", "- Speed of $150$ rad/s\n", "\n", "Then use a gear ratio of:\n", "\n", " $$ \n", "R = \\frac{0.1}{0.02} = 5\n", " $$ \n", "\n", "This brings output torque up to $0.1$ N·m, and reduces speed to:\n", "\n", " $$ \n", "\\omega_{\\text{out}} = \\frac{150}{5} = 30 \\ \\text{rad/s}\n", " $$ \n", "\n" ] }, { "cell_type": "markdown", "id": "ebf9fd48", "metadata": {}, "source": [ "**Typical values**" ] }, { "cell_type": "code", "execution_count": 9, "id": "da0b3499", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "R_ohm: 2.7\n", "B_Nm_s_per_rad: 3e-08\n", "ke_Vs_per_rad: 0.00075\n", "kt_Nm_per_A: 0.00075\n", "omega_per_volt_rad_s_per_V: 1165.5\n", "rpm_per_volt_RPM_per_V: 11129.7\n", "no_load_speed_rpm_at_3p7V: 41180\n", "stall_current_A_at_3p7V: 1.37037\n", "stall_torque_Nm_at_3p7V: 0.00102778\n", "no_load_current_A_est: 0.172494\n", "friction_torque_Nm_est: 0.000129371\n" ] } ], "source": [ "# Typical small 3.7 V brushed coreless drone motor (e.g., 8.5×20 mm “8520”)\n", "# SI units throughout.\n", "\n", "# Electrical & mechanical parameters (typical/representative)\n", "R = 2.7e0 # Armature resistance [ohm]\n", "B = 3.0e-8 # Viscous damping coeff. [N·m·s/rad]\n", "ke = 7.5e-4 # Back-EMF constant [V·s/rad] (== V/(rad/s))\n", "kt = 7.5e-4 # Torque constant [N·m/A] (≈ ke in SI)\n", "\n", "# Convenience\n", "import math\n", "V_nom = 3.7 # nominal test voltage [V]\n", "\n", "# Proportionality from DC voltage to angular speed at no external load:\n", "# Steady-state with viscous friction only:\n", "# V = I*R + ke*ω, kt*I = B*ω → I = (B/kt)*ω\n", "# ⇒ V = (R*B/kt + ke) * ω ⇒ ω/V = 1 / (ke + R*B/kt)\n", "omega_per_volt = 1.0 / (ke + R*B/kt) # [rad/s per V]\n", "rpm_per_volt = omega_per_volt * 60.0 / (2*math.pi) # [RPM per V]\n", "\n", "# Nominal no-load speed at V_nom\n", "omega_0 = omega_per_volt * V_nom\n", "rpm_0 = rpm_per_volt * V_nom\n", "\n", "# Some sanity checks\n", "I_stall = V_nom / R # [A]\n", "T_stall = kt * I_stall # [N·m]\n", "# At no-load, I ≈ (B/kt)*ω\n", "I_noload = (B/kt) * omega_0 # [A]\n", "T_friction= kt * I_noload # [N·m] (equals B*ω0)\n", "\n", "vals = {\n", " \"R_ohm\": R,\n", " \"B_Nm_s_per_rad\": B,\n", " \"ke_Vs_per_rad\": ke,\n", " \"kt_Nm_per_A\": kt,\n", " \"omega_per_volt_rad_s_per_V\": omega_per_volt,\n", " \"rpm_per_volt_RPM_per_V\": rpm_per_volt,\n", " \"no_load_speed_rpm_at_3p7V\": rpm_0,\n", " \"stall_current_A_at_3p7V\": I_stall,\n", " \"stall_torque_Nm_at_3p7V\": T_stall,\n", " \"no_load_current_A_est\": I_noload,\n", " \"friction_torque_Nm_est\": T_friction,\n", "}\n", "\n", "for k, v in vals.items():\n", " print(f\"{k}: {v:.6g}\")\n" ] } ], "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": "3.13.3" } }, "nbformat": 4, "nbformat_minor": 5 }