Technical Notes

Technical Notes regarding DC motors

Conversion of electrical to mechanical energy

The DC motor converts electrical power to mechanical power. As there are some losses, this conversion is not 100% effi cient. Power loss is caused by friction and heat dissipation of the motor. The relation of mechanical output power to electrical input power is defi ned as the effi ciency. The effi ciency is dependent on the required load torque.

The design of the magnetic circuit and the armature winding defi nes how the motor converts electrical power to mechanical power. The voltage constant k

E and the torque constant k

t are relevant measures to characterize this effect.

The voltage constant is the relationship between motor speed to induced voltage in the armature winding.The related formula n = (1 / k

E) × 103 × U

ind shows that the induced voltage is proportional to the speed of the motor.

The torque constant is the relationship between torque and current.The formula T = k

t × (I

N - I

o) shows that the current is proportional to the speed of the motor.

The voltage constant and the torque constant are related as followsk

t = 3 / π x k

E

power Pin = V

N × I

NP

out = P

N = (π / 30000) × (n

N × T

N)

effi ciency η = Pout

/ Pauf

< 1

Motor charts

For any motor a speed-torque curve and a current torque curve can be calculated. The charts may be adapted to the temperature conditions in your application. If required, the tolerance limits may be calculated.

Torque T

Sp

ee

d n

no

TS

V > VN

VN

V < VN

n

T

Speed torque chart

The voltage is constant in the speed torque chart.The speed declines with increasing torque. The graph can be defi ned by 2 load points, i.e. by the no load point and the stall torque point.

The no load speed and the stall torque change is proportional to the voltage. A change in voltage causes a parallel shift of the speed – torque curve.

The speed regulation constant Rm = n

O / T

A = ∆n / ∆T

defi nes the slope of the curve.Using the slope of the curve, different motors may be com-pared. The smaller the slope, the smaller the difference in speed with changing load torque.

power Pin = V

N × I

NP

out = P

N = (π / 30000) × (n

N × T

N)

effi ciency η = Pout

/ Pauf

< 1

Current-torque chart

Current and torque are directly proportional. A higher torque requires a higher current. The current curve is defi ned by 2 load points, i.e. the no load current (I

o) and the stall current (I

S).

The no load current is generated by the internal friction of the motor T

F = k

t × I

O

The maximum current (stall current) is limited by the terminal resistance, mainly by the winding resistance.

The stall current is defi ned by IS = T

S/k

t

Output power-torque chart

The output power of the motor is defi ned by:

Pout

= PN = (π / 30000) × (n

N × T

N)

The output power can be seen in the diagram as the area of the rectangle under the speed-torque graph.

The maximum output power is reached at half of the stall torque or half of the no load speed.

The power curve is a parabola. The maximum valueis proportional to the square of the motor voltage.

Torque T

Sp

ee

d n

nO

V = VN

TS

Pout max

V < VN

TF

Pout max

Torque T

Sp

ee

d n

TSTF

nO

ηmax

V = VN

Torque T

Sp

ee

d n

V = VN

IO

nO

TS

IS

TF

Effi ciency chart

η = (π / 30000) x (n × T) / (V × I)

The effi ciency represents the relation between output power to input power.At constant voltage the effi ciency increases with increasing speed and increases with decreasing torque.

At small torques the internal friction losses outweigh the applied load, and the effi ciency decreases steeply towards zero.

The maximum effi ciency is calculated by:

ηmax

= (1–(IO /I

S)–1/2)2

This means the maximum effi ciency is achieved at about 1/7 of the stall torque.

Technical Notes

Gear Motor Notes

Buehler Motor manufactures spur, worm, and planetary gear reduction for torque requirement between 10 mNm and 10 Nm.

The gear/pinions are made from plastic, brass, nickel, silver, steel or sintered powdered metal; the gear boxes are made from plastics, aluminum, or zinc die-cast. Bearings are mostly sintered self-aligning bearings. There are some types with plastic sleeve bearings.

Dependent on duty cycle, the life of the gear boxes and motors may be from less than 100 hours up to several thousand hours. It is not possible to predict the life time without knowing the duty cycle.

The catalog states the nominal torque for each of the gear motor types. At low ratios, the nominal torque is limited by the perfor-mance of the motor; at high ratios (starting at about i > 100) the nominal torque is limited by the mechanical strength of the gear teeth.

The gear motors are generally not stall-proof, neither mechanically (gear box) nor thermally (motor). Depending on the use, a limit switch or a current limitation device will be necessary to protect the gear motor.

The gear motors are generally not to be run continuously. The max. torque at continuous run will be about 50% of thenominal torque.

Torque T

Sp

ee

d n

TRTmax

IS

IO

nO

nN

Motor Limits

For any questions or further information, please do not hesitate to contact our sales staff.

Max. Speed: The maximum speed is limited by the commutation system and the balance of the armature. The armature balance also has an infl uence on the life of the motor.

Continuous current/torque: Is limited by the max. winding temperature of the armature. If exceeded, the temperature could damage the winding insulation and would cause a short circuit in the armature.

Continuous mode: Is defi ned by the max. speed and max. torque.

Short cycle mode: Exceeding continuous mode by up to one minute.

Torque T

Sp

ee

d n

TSTF

ISnO

nN

ηN

IN

TN

Pout

IO