Getting the Most From Your Motors Kurt Heinzmann DEKA Research & Development Corp. January 2006

Getting the Most From Your Motors General Topics Manufacturers' torque curves and specification sheets How to manage power loss and temperature rise Gear ratio Review of motors from a previous Kit of Parts Which motor for which application on a robot? Batteries

Introduction Assumptions and approximations Power Power loss in the mechanism Power required at the motor Power loss in the motor

Assumptions and Approximations Steady operation We will not discuss acceleration requirements Linear systems We will represent nonlinear phenomena as linear Simple motor analysis Study only two power loss parameters Loss due to electrical resistance Loss due to friction and damping, combined in one fixed value

Example: Simplify. Assume fixed free current (combine the effects of friction and damping)

Power Power is a measure of how fast work gets done. POWER = EFFORT x FLOW “EFFORT” force torque pressure voltage thinking “FLOW” travel speed rotating speed flow of fluid flow of electrons doing

Power Loss in the Mechanism Some power from the motor is lost due to friction in the mechanism Gears, belts, cables Bearings, guides Tires, balls, or other deformable items Damage Contamination Power loss is heat

Power required at the motor Power at the motor = power required at the point of use + power lost in the mechanism Power loss is heat

Power loss in the motor Power is lost in the motor due to friction, damping, and electrical resistance Power loss is heat

Analysis Basic motor theory Important motor parameters Power loss in the motor Power loss in other electrical components Gear ratios Comparison Batteries

Basic Motor Theory Torque is rotating EFFORT, speed is rotating motion (“FLOW”) Torque = force x radius Voltage is electrical EFFORT, current is FLOW of electrons Power = EFFORT x FLOW Mechanical power P(out) = torque x speed Electrical power P(in) = voltage x current Shaft power = power in – power loss Power loss is sum of electrical loss and mechanical loss

Basic Motor Theory Important motor parameters Stall torque ( stall ) Stall current ( istall ) Free speed ( free ) Free current ( ifree )

Basic Motor Theory Important motor parameters Torque constant ( Kt ) Torque is proportional to current Units: (Nm/A) newton-metres ampere Voltage constant ( Ke ) Motor internal voltage is proportional to speed Units: V/(rad/s) volts _ radian/second Torque loss (loss) We will derive this from free current Unit: newtons (N) Resistance (R) Ohm’s law Unit: ohm ()

Units, Conversions International System (SI) of units Prefixes: m = milli- = one thousandth (mm, mNm) k = kilo- = one thousand (km, kW)

Why use SI units? Easier than U.S. Customary units A motor converts electrical power to mechanical power. If you express electrical power and mechanical power in watts, you know what’s happening at both ends of the motor, and inside it. Would you like to convert volts-times-amperes to horsepower? Advice: Convert to SI units before doing any other calculation. Consolation: you can always convert back.

Basic Motor Theory

Direct Current (DC), Permanent-Magnet (PM), Brush-Commutated Motor

Basic Motor Theory

Important motor parameters Given these four parameters: stall, istall, free, ifree and V, Find these four parameters: Kt, Ke, loss(free), and R.

Find torque constant Kt and voltage constant Ke

Find torque loss loss(free)

Find resistance R

Calculate current, speed, power and efficiency

stall = 0.65 Nm free = 2513 rad/s loss(free) Fisher-Price Motor (2005) stall = 0.65 Nm From data sheet: From equation 3a: From equation 3b: From equation 4: From equation 5: istall = 148 A free = 2513 rad/s ifree = 1.5 A Kt = 0.65 Nm / (148.0-1.5) A = 0.0044 Nm/A Ke = (12 V -1.5 A*0.081 )/ 2513 rad/s = 0.0047 V/(rad/s) loss(free) = 0.0044 Nm/A x 1.5 A = 0.0066 Nm R = 12 V /148 A = 0.081 

Equations 6 - 11 allow us to calculate the following performance curves as a function of torque (with constant voltage): current (6) speed (7) output power (8) input power (9) power loss (10) efficiency (11)

Fisher-Price Motor - Current

Fisher-Price Motor - Speed

Fisher-Price Motor - Power output

Fisher-Price Motor - Input Power

Fisher-Price Motor - Power loss

Fisher-Price Motor - Efficiency

Motor performance based on data sheet

Real World: Power loss 14 AWG wire: 3.0 m/ft. 12 AWG wire: 1.9 m/ft. (Copper at 65 °C)

Fisher-Price Motor, stalled for approximately 2 s Notes: This circuit was not properly protected (wrong circuit breaker) Measuring thermocouple was inserted near windings (windings got hotter than thermocouple) Brushes got hotter than windings

Fisher-Price Motor, stalled for approximately 2 s Motor resistance increased from 67 m to 96 m (43%) in two seconds Battery resistance = 18 m Resistance of wires (5 ft. of 14 AWG), connectors, breakers, etc. = 25 m Total circuit resistance increased to about twice the initial motor resistance

Performance of the system compared with motor performance based on data sheet

CIM motor (also known as Chiaphua and Atwood)

CIM motor data and curves Stall torque stall = 347 oz-in = 2.4 Nm Stall current istall = 114 A Free speed free = 5342 rpm = 560 rad/s Free current ifree = 2.4 A

CIM motor performance curves

Comparison of power available from Fisher-Price Motor and CIM motor

Simple strategy Calculate (or read from data sheet) the motor resistance R Increase R by 50% - 100% Calculate power curve Operate at half of new peak power

Performance curves re-calculated with R increased by 75%

"Gear" ratio: Mechanical power transmission efficiency is important Spur gears: 90% per pair Worm and gear: 10%-60% Nut on a screw (not ball nut): 10%-60% Twist cables: 30%-90% Chain: 85%-95% Wire rope (cables): up to 98% Rack and pinion 50%-80%

Gear ratio Example: out = 1.5 Nm; out = 100 rad/s Pmotor = Pout / g (12)

Gear ratio example Output power = 1.5 Nm • 100 rad/s = 150 W Try: Spur gears (assume 90% efficiency per stage) Power required at motor Pmotor = Pout / g one stage: Pmotor = 150 W / 0.9 = 167 W two stages: Pmotor = 150 W / 0.9 /0.9 = 185 W three stages: Pmotor = 150 W / 0.9 /0.9 /0.9 = 206 W four stages: Pmotor = 150 W /0.9/0.9/0.9/0.9 = 229 W

Gear ratio example Estimate torque by inspection, then calculate an approximate gear ratio to determine how many gear stages are required. Rule of thumb for spur gears: max. ratio per stage = 5:1

Gear ratio Fisher-Price Motor

Gear ratio - Fisher-Price Motor Check: gear ratio Ng = motor/out = 1850 / 100 = 18.5:1 = 4.3 • 4.3 Operating point looks good (comfortably to the left of the peak power point)

Gear ratio CIM motor

Gear ratio - CIM motor Gear ratio Ng = motor/out = 388 / 100 = 3.9:1 Moderately heavy load for this motor (near peak power)

Gear ratio example Calculate current Choose motors based on Should not exceed breaker current Choose motors based on Power Gearing required Possibility of stalling and heating – small motors heat up fast Weight All motor tasks

Summary of motors in the 2005 Kit of Parts Sorted by peak output power

Comparison of motors in the 2005 Kit of Parts

Keep batteries charged. Delivered capacity was only one third of rated capacity.

Keep batteries charged.

Conclusion Proper motor selection, good wiring, an appropriate gear ratio, aligned mechanical components, and a full battery will keep you alive in the heat of the battle. Power loss is often a significant fraction of the power consumed. Include all losses in analysis. Analyze, but test, too! Have fun