Basic electricity Some basics for FIRST Robotics

Basic electricity

Some basics for FIRST Robotics

ROBOTICS ACADEMY: FRC Basic electricity

Safety FirstQ: 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.


Completing the circuit – Household 110V/220V

220V across f and f+180110V 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.

Phase f+180

Phase f

Common

Ground

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?


Data from NASA “Man-Systems Integration Standards”

NASA-STD-300 Handbook Vol. III,August 1994, Figure 6.4.3-1

Data are based on current flow from arm-to-arm or arm-to leg of 60 Hz AC on 150 lb human

NASA-STD-300 Handbook Vol. I,Rev B, July, 1995, Table 5.4.2-2

DC limits ~ 50% higher

10 100 1000 10 K 100 K22 5 5

10 M

1 M

20 M

1000

10 K

100 K

100

2

2

5

5

Tota

l Circ

uit R

esis

tanc

e, O

hms

Voltage, 60Hz AC

Am

pere

s C

urre

nt M

illia

mpe

res

1 mA

10 m

A3 m

A

30 m

A

100 mA

240

mA

1 A

5 A

10 A

100 A

Heart

para

lysis

Muscu

lar

para

lysis

No-let

-go

thre

shold

Painfu

l sho

ck

Mild

shoc

k

Perce

ption

thre

shold

Asphy

xiatio

n

Tissue

burn

ing

Fibrilla

tion

Physiological response

Current is major factor, but voltage also important since resistance is not known


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.


Complete circuits

Circuits must be complete

Should be able to trace current flow frombattery, through switch, controller, and motor back to other pole on the battery

The wire and motors in thecircuits have resistance tocurrent flow and also create magnetic fields. These are resisters and inductors in circuits.


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 chargeMeasured in Farads, denoted F. “C” in equations

Inductance – Electrical inertia to changing charge and magnetic fieldsMeasured in Henrys, denoted H. “L” in equations


Power and thermal management

€

V = I × RVoltage drop (Volts) across a resistor is current (Amps) times resistance (Ohms)

€

P =V × I = I2 × R =V 2

R

Power (Watts) dissipated in a resistor is voltage (Volts) times current (Amps)

All wires have resistance equal to resistivity times length divided by area

€

R = ρ × L /A r increases with temperature

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.

1 HP = 745.7 Watts


Selecting fuse and wire sizes

Fuses and breakers must protect the entire circuit, including the wire

Check motor or controller limits and use fuse or circuit breaker at or slightly above the maximum current draw for normal use.

Select wire size based on fuse or circuit breaker amperage. Using wires thicker than required is okay. The requirements are for minimum diameter.

Main breaker: 120 AmpsMotor Controller up to 40 AmpsRelay module up to 20 AmpsDigital sidecar 20 Amps

Note that 4 motors drawing 30+ Amps each will trip the main breaker!

Application Minimum wire sizeMain power 6 AWG 30-40 Amp circuit 12 AWG (2.052 mm)20-30 Amp circuit 14 AWG (1.628 mm) 5-10 Amp circuit 18 AWG (1.024 mm)Pneumatic valves 24 AWG (0.5106 mm)


Simple circuit with potentiometer This simple circuit contains a battery, resistance from the wire and a variable resistor in the form of a potentiometer.

€

Vbat − I × Rc − I × Rpot = 0

Battery

Other circuit resistance

Rc

Rpot

Voltmeter

Vbat

f=0

f=1

Current, I

Voltage drop across resistor is

€

I =Vbat

Rc + Rpot

Voltage and resistances are known, solve for current

€

V = I × RAnalyze voltage through entire circuit. Voltage rise and drop should sum to zero

Resistance measured across the voltmeter is

€

Rmet = φ × Rpot

Meter voltage

€

Vmet = I × Rmet =φ × Rpot ×VbatRc + Rpot

Vmet


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

Magnetic field in coils of wire is additive to create regions of strong, consistent magnetic fields in the coil interior.

Field around wire with illustration of the right hand rule

Toroidal field around a wire loop Field in a coil with different materials in core

Electro-magnet


Relays and solenoids Relays use a small current to move a switch handling large current

Field around wire with illustration of the right hand rule

The air compressor on our test pneumatic system uses a relay

Solenoids are used to engage car starters

Large-current switch

Small current

Material within a magnetic coil will move to increase the coil inductance.A metal rod partially filling the coil willmove into the coil. This strong and fast linear actuator is called a solenoid.


Permanent-magnet motor basics

Permanent magnets

Commutator

Brushes

Repulsive Repulsive-attractive Attractive

Magnetic field induced by current in the armature interacts with outer magnets

Armature

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.


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


Inductance effects on motor circuit response

Oscillating voltage from commutator.

Armature resistance

Rarm

Larm

Vcomsin(wt)

Current, I

Time

Vol

ts

Voltage-timecurve looks like

but will model as a sine wave

Armature inductance

€

I =VcomR

sin(ωt) − ωLR cos(ωt)

1+ (ωLR )2 ; IRMS =VcomR 2

1

1+ (ωLR )2

Voltage balance on circuit with inductor

€

Vcom sin(ωt) − L ×dI

dt− R × I = 0

RMS voltage drop across resistor and inductor

The current satisfying the 1st order ODE is

€

VR =VcomR 2

1

1+ (ωLR )2; VL =

VcomR 2

ωLR

1+ (ωLR )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.


Torque, speed and power characteristicsTo

rque

(t)

Speed (w)

Notional torque-speed curve for CIM motor

Most torque at stall

No torque at max speed

Power analysis

€

P = τ ×ω

€

τ =τstall 1−ω

ωmax

⎛

⎝ ⎜

⎞

⎠ ⎟

Notional torque equation €

P = τ stall ×ω × 1 −ω

ωmax

⎛

⎝ ⎜

⎞

⎠ ⎟

Substituting notional torque relation

Find speed at maximum power by setting derivative to zero

€

dP

dω= 0 = τ stall × 1−

2ω

ωmax

⎛

⎝ ⎜

⎞

⎠ ⎟ ; ω =ωmax /2

Characteristics:

Should obtain real torque-speed curve for accurate analysis

Max torque at stallMax power at ½ max speed

Can’t have both; what is important for application?


Limitations on power and delivered torquePower:

•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.


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.

Wrap up


Questions?

???

Documents

Basic electricity Some basics for FIRST Robotics