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% efficient.
Power loss is caused by friction and heat dissipation of the motor. The relation of mechanical output power to electrical input power
is defined as the efficiency. The efficiency is dependent on the required load torque.
power
Pin = VN × IN
efficiency
η = Pout / Pauf < 1
Pout = PN = (π / 30000) × (nN × TN)
The design of the magnetic circuit and the armature winding defines how the motor converts electrical power to mechanical power.
The voltage constant kE and the torque constant kt 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 / kE) × 103 × Uind 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 = kt × (IN - Io) shows that the current is proportional to the speed of the motor.
The voltage constant and the torque constant are related as follows
kt = 3 / π x kE
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.
Speed torque chart
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 = nO / TA = ∆n / ∆T
defines the slope of the curve.
Using the slope of the curve, different motors may be compared. The smaller the slope, the smaller the difference in
speed with changing load torque.
no
Speed n
The voltage is constant in the speed torque chart.
The speed declines with increasing torque. The graph can be
defined by 2 load points, i.e. by the no load point and the stall
torque point.
n
V > VN
T
VN
V < VN
Torque T
TS
Current-torque chart
The no load current is generated by the internal friction of the
motor TF = kt × IO
The maximum current (stall current) is limited by the terminal
resistance, mainly by the winding resistance.
IS
nO
V = VN
Speed n
Current and torque are directly proportional. A higher torque
requires a higher current. The current curve is defined by 2
load points, i.e. the no load current (Io) and the stall current (IS).
The stall current is defined by IS = TS/kt
IO
TF
Torque T
TS
Output power-torque chart
The output power of the motor is defined by:
nO
The maximum output power is reached at half of the stall
torque or half of the no load speed.
V < VN
Speed n
The output power can be seen in the diagram as the area of
the rectangle under the speed-torque graph.
Pout max
V = VN
Pout = PN = (π / 30000) × (nN × TN)
Pout max
The power curve is a parabola. The maximum value
is proportional to the square of the motor voltage.
TF
Torque T
TS
Torque T
TS
Efficiency chart
ηmax
η = (π / 30000) x (n × T) / (V × I)
At small torques the internal friction losses outweigh the
applied load, and the efficiency decreases steeply towards zero.
nO
V = VN
Speed n
The efficiency represents the relation between output power to
input power.
At constant voltage the efficiency increases with increasing
speed and increases with decreasing torque.
The maximum efficiency is calculated by:
ηmax = (1–(IO /IS)–1/2)2
This means the maximum efficiency is achieved at about 1/7 of
the stall torque.
TF
Technical Notes
Motor Limits
Max. Speed:
The maximum speed is limited by the commutation system and the balance of the armature.
The armature balance also has an influence 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 defined by the max. speed and max. torque.
Short cycle mode:
Exceeding continuous mode by up to one minute.
For any questions or further information, please do not hesitate to contact our sales staff.
ηN
IS
nO
Speed n
nN
Pout
IN
IO
TF
TN
Torque T
TS
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 performance 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 the
nominal torque.
Speed n
nO
nN
IS
IO
TR
Torque T
Tmax