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Transcript
Basic electricity Some basics for FIRST Robotics ROBOTICS ACADEMY: FRC Basic electricity Safety First Q: What voltages / currents are safe and which are dangerous? A: It depends. What body parts is it running through? Are contacts with the power damp? Is the path to complete the circuit clear? Are you lucky? Completing the circuit – battery Path to complete circuit for a battery requires contact with both + and – terminals. Circuit is not completed if only one terminal is connected. ROBOTICS ACADEMY: FRC Basic electricity Completing the circuit – Household 110V/220V Ground Phase f Common Phase f+180 220V across f and f+180 110V from common to f or f+180 The common is connected to the ground wire in the box and to a stake driven in the ground outside. The circuit is completed by connecting to anything conducting to the ground outside, i.e. everything! Only have to touch one wire since whatever you stand on or sit on completes the circuit. Dampness improves the connection. What about birds? ROBOTICS ACADEMY: FRC Basic electricity Physiological response Data from NASA “Man-Systems Integration Standards” 20 M 10 M NASA-STD-300 Handbook Vol. III, August 1994, Figure 6.4.3-1 Amperes Current Milliamperes Total Circuit Resistance, Ohms 1M 100 K 10 K 5 Data are based on current flow from arm-to-arm or arm-to leg of 60 Hz AC on 150 lb human DC limits ~ 50% higher NASA-STD-300 Handbook Vol. I, Rev B, July, 1995, Table 5.4.2-2 2 1000 5 2 100 10 2 5 100 2 5 1000 Voltage, 60Hz AC 10 K 100 K Current is major factor, but voltage also important since resistance is not known ROBOTICS ACADEMY: FRC Basic electricity So what is safe? 12V DC generally considered safe if touching with hands or dry skin. (Licking terminals could give shock, lead poisoning, acid burns.) Our cordless power tools are 18V DC, so manufactures apparently see little risk with that voltage when used properly. Many people get shocked with 110V AC with just a strong jolt. Others get shocked with 110V AC and die. Investigations generally reveal a good path to ground, often blamed on moisture, but that is not the only factor. Treat 110V as if it could kill you – it can. Lightning is nearly always fatal. There are a few survivors of branch strikes. Can exceed a billion volts and 300 kA of current. ROBOTICS ACADEMY: FRC Basic electricity Complete circuits Circuits must be complete Should be able to trace current flow from battery, through switch, controller, and motor back to other pole on the battery The wire and motors in the circuits have resistance to current flow and also create magnetic fields. These are resisters and inductors in circuits. ROBOTICS ACADEMY: FRC Basic electricity Definitions Voltage – The force pushing the electricity through the circuit. Measure in volts, denoted V. “V” in equations. Also called potential and electromotive force Current – The quantity of electrons passed in a given time. Measured in Amperes (Amps), denoted A. “I” in equations. Resistance – Obstacles impeding flow of electrons, generates heat. Measured in Ohms, denoted W. “R” in equations Capacitance – Storage of electrical charge Measured in Farads, denoted F. “C” in equations Inductance – Electrical inertia to changing charge and magnetic fields Measured in Henrys, denoted H. “L” in equations ROBOTICS ACADEMY: FRC Basic electricity Power and thermal management Voltage drop (Volts) across a resistor is current (Amps) times resistance (Ohms) V IR Power (Watts) dissipated in a resistor is voltage (Volts) times current (Amps) V2 P V I I R R 2 1 HP = 745.7 Watts All wires have resistance equal to resistivity times length divided by area increases with temperature R L/A Dissipated electrical power turns to heat, and temperature must be controlled or wires will melt and components will smoke. Smoke is from burning components. Heating rate increases as wire area decreases, and ability to transfer the heat to the environment decreases as wire size decreases. Light bulb filaments have a stable glow because resistance increases with temperature, dropping the power, while heat transfer increases with temperature. Flash bulbs flare a bright white because they melt and vaporize rapidly. ROBOTICS ACADEMY: FRC Basic electricity Selecting fuse and wire sizes Check motor or controller limits and use fuse or circuit breaker at or slightly above the maximum current draw for normal use. Main breaker: 120 Amps Note that 4 motors drawing 30+ Amps Motor Controller up to 40 Amps each will trip the main breaker! Relay module up to 20 Amps Digital sidecar 20 Amps Fuses and breakers must protect the entire circuit, including the wire Select wire size based on fuse or circuit breaker amperage. Using wires thicker than required is okay. The requirements are for minimum diameter. Application Main power 30-40 Amp circuit 20-30 Amp circuit 5-10 Amp circuit Pneumatic valves Minimum wire size 6 AWG 12 AWG (2.052 mm) 14 AWG (1.628 mm) 18 AWG (1.024 mm) 24 AWG (0.5106 mm) ROBOTICS ACADEMY: FRC Basic electricity Simple circuit with potentiometer This simple circuit contains a battery, resistance from the wire and a variable resistor in the form of a potentiometer. Voltage drop across resistor is Other circuit resistance V IR f=1 Analyze voltage through entire Voltmeter R c Battery circuit. Voltage rise and drop should sum to zero Vbat Vbat I Rc I Rpot 0 Rpot f=0 Current, I Meter voltage Vmet I Rmet f Rpot Vbat Rc Rpot Voltage and resistances are known, solve for current Vmet Resistance measured across the voltmeter is Rmet f Rpot I Vbat Rc Rpot ROBOTICS ACADEMY: FRC Basic electricity Current and magnetic fields Current in a wire induces a magnetic field around the wire. Current in a loop of wire creates toroidal shaped magnetic fields Field around wire with illustration of the right hand rule Magnetic field in coils of wire is additive to create regions of strong, consistent magnetic fields in the coil interior. Electromagnet Toroidal field around a wire loop Field in a coil with different materials in core ROBOTICS ACADEMY: FRC Basic electricity Relays and solenoids Relays use a small current to move a switch handling large current Large-current switch Material within a magnetic coil will move to increase the coil inductance. A metal rod partially filling the coil will move into the coil. This strong and fast linear actuator is called a solenoid. Field around wire with illustration of the right hand rule Small current The air compressor on our test pneumatic system uses a relay Solenoids are used to engage car starters ROBOTICS ACADEMY: FRC Basic electricity Permanent-magnet motor basics Magnetic field induced by current in the armature interacts with outer magnets Permanent magnets Repulsive Repulsive-attractive Attractive Armature Commutator Brushes The magnetic field in the armature reverses when the split in the commutator reverses the current path. The torque on the armature is strongest in the repulsive-attractive configuration. ROBOTICS ACADEMY: FRC Basic electricity Increased efficiency with segmented armature Segmented armatures are used to create multiple independent circuits and magnets which are active only when near the orientation for maximum torque. Pairs of brushes contact opposite sides of the commutator to excite different coils Commutator segments are connected to independent armature coils Brushes ROBOTICS ACADEMY: FRC Basic electricity Inductance effects on motor circuit response Armature resistance Vcomsin(wt) Oscillating voltage from commutator. Volts Voltage-time curve looks like Time but will model as a sine wave Armature inductance Rarm Larm Current, I Voltage balance on circuit with inductor dI Vcom sin( wt) L R I 0 dt The current satisfying the 1st order ODE is Vcom sin( wt) wRL cos(wt) I ; R 1 (wRL )2 IRMS Vcom 1 R 2 1 (wRL ) 2 RMS voltage drop across resistor and inductor wL Vcom 1 Vcom R VR ; V L R 2 1 ( wRL ) 2 R 2 1 (wRL ) 2 Observations: As motor speed increases, current decreases and the voltage drop is primarily across the inductor. Most of the voltage goes into flipping the magnetic field. Magnetic field strength drops, motor torque drops. ROBOTICS ACADEMY: FRC Basic electricity Torque, speed and power characteristics Power analysis Notional torque-speed curve for CIM motor P t w Torque (t) Most torque at stall No torque at max speed Speed (w) Notional torque equation w t t stall1 w max Should obtain real torquespeed curve for accurate analysis Substituting notional torque relation w 1 P t stall w w max Find speed at maximum power by setting derivative to zero 2w dP 0 t stall 1 ; w w max /2 dw w max Characteristics: Max torque at stall Max power at ½ max speed Can’t have both; what is important for application? ROBOTICS ACADEMY: FRC Basic electricity Limitations on power and delivered torque Power: •Power cannot be increased from that provided by the source. •Power on an FRC robot is limited by the current of the battery ~1400 W •Power surge can be obtained from sudden release of energy stored electrically, mechanically and pneumatically. (chemical not permitted!) Torque: •Torque be increased arbitrarily mechanically through gear reduction, but rotational speed drops commensurately. •Motor torque is limited by FRC motor specifications. •Wheel friction and other factors will eventually limit performance as torque is increased. ROBOTICS ACADEMY: FRC Basic electricity Wrap up Do not be concerned about shock from 12V circuits under normal use Size motors based on application and motor characteristics Don’t forget solenoids and electromagnets in design Use circuit breakers and fuses consistent with intended load Select minimum wire size appropriate for circuit Plan wire routing to ease assembly and troubleshooting Create wiring schematic for notebook showing motor and port numbers Ensure connections are secure and bundle wires to keep neat. ROBOTICS ACADEMY: FRC Basic electricity Questions?