DC motor output characteristics: Speed

• Speed: Usually specified as the speed in rotations per minute (RPM) of the motor when it is unloaded, or running freely, at its specified operating voltage.

• The speed of the motor is proportional to the applied voltage. At max speed, the motor draws relatively little current.

• Typical DC motors run at high speeds up to twenty thousand RPM or more.

• Materials taken from several sources including: Building Robots with LEGO Mindstroms by Ferrari, Ferrari, and Hempel

rotational speed or angular velocity, , is typically measured in radians/second {rad/s}, revolutions/second {rps}, or revolutions/minute {rpm}.

1 revolution = 360° 1 revolution = (2*p) radians 1 radian = (180/p)° 1° = (p/180) radians

We can find the tangential velocity of a point anywhere on the rotating body; this can be used to compute the steady state (constant speed, no acceleration) speed of a vehicle if the radius and angular velocity of a wheel is known:

DC motor output characteristics: Torque

• Torque: the term we use when we talk about forces that act in a rotational manner. You apply a torque or moment when you turn a dial, flip a lightshwitch, drill a hole or tighten a screw or bolt.

• The torque of the motor is proportional to the current flowing through it. When stalled, the motor is drawing near max current.

SI: English: newton-meters {N·m} inch-pounds {in·lb} foot-pounds {ft·lb} inch-ounces {in·oz} 1 N·m = 0.738 ft·lb 1 N·m = 0.113 in·lb 1 N·m = 141.61 in·oz 1 in·lb = 0.113 N·m 1 ft·lb = 1.356 N·m 1 in·oz = 7.062E-03 N·m

One inch-ounce means that the motor is exerting a tangential force of one ounce at a radius of one inch from the center of its shaft.

DC motor output characteristics: Power • Power: When a torque T (with respect to the

axis of rotation) acts on a body that rotates with angular velocity ω, its power (rate of doing work) is the product of the torque and angular velocity. This is the analog of the relation P = F·v for particle motion.

UNITS of POWER

SI English

Watts {W} newton-meters per second {N·m/s}

1 W = 1 N·m/s

1 W = 0.738 ft·lb/s 1 W = 1.341E-03 hp

foot-pounds per second {ft·lb/s} horsepower {hp}

1 ft·lb/s = 1.818E-03 hp

1 ft·lb/s = 1.356 W

In order to effectively design with D.C. motors, it is necessary to understand their characteristic curves. For every motor, there is a specific Torque/Speed curve and Power curve.

Note that torque is inversely proportioal to the speed of the output shaft; there is a tradeoff between how much torque a motor delivers, and how fast the output shaft spins. Motor characteristics are frequently given as two points on this graph: •The stall torque, , represents the point on the graph at which the torque is a maximum, but the shaft is not rotating. •The no load speed, , is the maximum output speed of the motor (when no torque is applied to the output shaft). The curve is then approximated by connecting these two points with a line, whose equation can be written in terms of torque or angular velocity:

We defined power as the product of torque and angular velocity.

This corresponds to the area of a rectangle under the torque/speed curve with one corner at the origin and another corner at a point on the curve.

Due to the linear inverse relationship between torque and speed, the maximum power occurs at the point where = ½ , and = ½ .

power curves for a DC motor with respect to both speed and torque are quadratics:

Torque, Speed and Power

Efficiency • A DC motor is a transducer which changes voltage and

current into speed and torque. • To calculate a motor's efficiency, you measure its

mechanical output power and divide it by the electrical input power.

• Effeciency = PM / Pe ~= 50%-60% • Pe = V x I • PM = T x w • Implications:

– Efficiency is highest in the middle of the torque range so you need to oversize your motor to run with high efficiency.

– Most robots require relatively low speed and high torque so motor output is usually geared down.

Gears

• A typical DC motor operates at speeds that are far too high to be useful, and at torques that are far too low. Gear reduction is the standard method by which a motor is made useful.

• Gears are classified by the number of teeth they

have; the description of which is then shortened to form their name. For instance, a gear with 24 teeth becomes "a 24t gear."

Fundamental Properties • The gears transfer motion from one

axle to the other. • If their teeth match well, there is only a

small amount of friction. • The two axles turn in opposite

directions: one clockwise and the other counterclockwise.

• The two axles revolve at different speeds. When you turn the 8t, the 24t turns more slowly, while turning the 24t makes the 8t turn faster.

Gearing Up and Down • Gearing helps to convert torque to

velocity. The more velocity gained, the more torque is lost. The ratio is exactly the same: if you get three times the original angular velocity, you reduce the resulting torque to one third.

• This conversion is symmetric: we can also convert velocity to torque at the same ratio.

• The price of the conversion is power loss due to friction.

Gear Ratio • You can think of gear ratio as a

multiplier on speed and a divider on torque.

• You can calculate the gear ratio by using the number of teeth of the “driving gear" (a.k.a. the input gear) divided by the number of teeth of the “driven gear” (a.k.a. the output gear).

• We gear up when we increase velocity and decrease torque.

Ratio: 3:1 • We gear down when we increase torque

and reduce velocity. Ratio: 1:3

Gear Ratio = # teeth input gear / # teeth output gear = torque in / torque out = speed out / speed in

driven gear

driving gear

Gear Trains

• The larges gear may be 40t, while the smallest may be 8t, so, the highest ratio we can obtain is 8:40, or 1:5.

• If you need an even higher ratio

you can use a multistage reduction system, called a gear train.

Pulleys and Belts

• An advantage of pulleys over gear wheels is that their distance is not as critical. They can be used to transfer motion to a distant axle.

• Pulleys are not very suitable to transmitting high torque, because the belts tend to slip. The amount of slippage is not easy to estimate; it depends on many factors, including the torque and speed, the tension of the belt, the friction between the belt and the pulley, and the elasticity of the belt.

• The rule with pulleys is that the reduction ratio is determined by the ratio between their diameters.

Load torque can be determined by measuring the current drawn when the motor is attached to a machine whose actual load value is known.

As long as the motor is used in the area of high efficiency (as represented by the shaded area) long life and good performance can be expected. However, using the motor outside this range will result in high temperature rises and deterioration of motor parts.

Reducing Motor • Working voltage: 4.0-7.0 VDC • Rotation: CCW • Startup voltage: ≤1.2V • Load torque: 1500.0 g.cm • Stalling torque: ≥7.0 Kg.cm • Stalling current: ≤9.0A No Load • Current: 280mA • Speed: 310±12% r/min Load • Current: 1600mA(max) • Speed: 260±12% rpm

Our DC motor:

Similar DC motor?

Gear Motor with dust-proof enclosure, running at 6v 60rpm. Specifications •Operating Voltage: DC 2.4 ~ 6.0V •No Load Speed: 55 ~ 70rmp •No Load Current: 30 ~ 70mA •Max. Efficiency Speed: 40 ~ 52rpm •Max. Efficiency Current: 350 ~ 450mA •Torque: 0.7 ~ 1.2kg.cm •Stall Current: 500 ~ 700mA •Stall Torque: 3.0 ~ 4.0kg.cm