maxon EC flat and EC-i motors Multi-pole maxon flat motors and EC-i motors require a greater number of commutation steps per revolution (6 x number of pole pairs). Due to their wound stator teeth, they have a higher terminal inductance than motors with an ironless winding. At high speeds, the current cannot fully develop due to the short commutation intervals. The torque is therefore less. In addition, some current is returned to the controller power stage. As a result, the behavior deviates from the ideal linear characteristic depending on voltage and speed: The apparent speed/torque gradient is steeper at higher speeds and flatter at very low speeds. Mostly, flat motors are operated in the continuous operation range where the achievable speed-torque gradient at nominal voltage can be approxi- mated by a straight line between no load speed and nominal operating point. The achievable speed-torque gradient is approximate.

Speed n

U>U N

U N ideal Nominal operating point

U<U N U=U N

calculated stall torque

Torque M

actual stall torque

0 −

Δ n Δ M

n

n N

≈

M N

The stall torque specified on the product page is equal to the linearly calculated load torque (without magnetic saturation effect) which causes the shaft to stall at nominal voltage. With EC-flat and EC-i motors, this torque often cannot be achieved due to saturation effects.

Acceleration In accordance with the electrical boundary conditions (power supply, control, battery), a distinction is primarily made between two different starting processes: − Start at constant voltage (without current limitation) − Start at constant current (with current limitation) Start under constant current A current limit always means that the motor can only deliver a limited torque. In the speed-torque diagram, the speed increases on a vertical line with a constant torque. Acceleration is also constant, thus simpli- fying the calculation. Start at constant current is usually found in applica- tions with servo amplifiers, where acceleration torques are limited by the amplifier’s peak current. n n

Start with constant terminal voltage Here, the speed increases from the stall torque along the speed- torque line. The greatest torque and thus the greatest acceleration is effective at the start. The faster the motor turns, the lower the accelera- tion. The speed increases more slowly. This exponentially flattening increase is described by the mechanical time constant τ m (line 15 of the motor data). After this time, the rotor at the free shaft end has attained 63% of the no load speed. After roughly three mechanical time constants, the rotor has almost reached the no load speed. n n ∅ t n n 0 n L n 0 M L , n L M H M l = constant Time

n 0 n L n

n 0

U = constant

M L , n L

Time

M H M

τ ’ m

l = constant

n 0

n 0 n L

M L , n L

− Mechanical time constant τ m (in ms) of the unloaded motor: J R · R k M 2 τ m = 100 · − Mechanical time constants τ m’ (in ms) with an additional load J L J R − Maximum angular acceleration α max (in rad/s2) of the unloaded motor: M H J R α max = 10 4 · − Maximum angular acceleration α max (in rad/s2) with an additional load inertia J L : M H J R + J L α max = 10 4 · Speeding up to an operation point with constant load torque M L and load speed n L follows an exponential law. n( t) = n L 1 – e / τ ' m inertia J L : τ m ' = 100 · 1 + J R · R k M 2 The motor voltage U must be selected to achieve this operation point. Faster acceleration requires a higher voltage that eventually must be reduced for reaching the required operation speed (see the thin dashed line).

Time

M H M

∅ t

n 0 n L n

n

n 0 − Angular acceleration α (in rad/s 2 ) at constant current I or constant torque M with an additional load of inertia J L : U = constant

M L , n L

k M · I mot J R + J L

M J R + J L

α = 10 4 ·

= 10 4 ·

Time

M H M

τ ’ m

− Run-up time ∆ t (in ms) at a speed change ∆ n with an additional load inertia J L : � 300 J R + J L k M · I mot Δ t = · Δ n ·

(all variables in units according to the catalog)

maxon 81

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