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maxon DC motor and maxon EC motor Key information

The motor as an energy converter The electrical motor converts electrical power P el (current I mot and voltage U mot ) into mechanical power P mech (speed n and torque M ). The losses that arise are divided into frictional losses, attributable to P mech and in Joule power losses P J of the winding (resistance R ) . Iron losses do not occur in the coreless maxon DC motors. In maxon EC motors, they are treated formally like an additional friction torque. The power balance can there- fore be formulated as: P el = P mech + P J The detailed result is as follows � U mot · I mot = 30 000 n · M + R · I mot 2 Electromechanical motor constants The geometric arrangement of the magnetic circuit and winding defines in detail how the motor converts the electrical input power (current, voltage) into mechanical output power (speed, torque). Two important characteristic values of this energy conversion are the speed constant k n and the torque constant k M . The speed constant combines the speed n with the voltage induced in the winding U ind (= EMF). U ind is proportional to the speed; the following applies: n = k n · U ind Similarly, the torque constant links the mechanical torque M with the electrical current I mot . M = k M · I mot The main point of this proportionality is that torque and current are equivalent for the maxon motor. The current axis in the motor diagrams is therefore shown as parallel to the torque axis as well. Motor diagrams A diagram can be drawn for every maxon DC and EC motor, from which key motor data can be taken. Although tolerances and temperature influences are not taken into consideration, the values are sufficient for a first estimation in most applications. In the diagram, speed n , current I mot , power output P 2 and efficiency h are applied as a function of torque M at constant voltage U mot . Speed-torque line This curve describes the mechanical behavior of the motor at a constant voltage U mot : − Speed decreases linearly with increasing torque. − The faster the motor turns, the less torque it can provide. The curve can be described with the help of the two end points, no load speed n 0 and stall torque M H (cf. lines 2 and 7 in the motor data). DC motors can be operated at any voltage. No load speed and stall torque change proportionally to the applied voltage. This is equivalent to a parallel shift of the speed-torque line in the diagram. Between the no load speed and voltage, the following proportionality applies in good approximation n 0 ≈ k n · U mot where k n is the speed constant (line 13 of the motor data). Independent of the voltage, the speed-torque line is described most practically by the slope or gradient of the curve (line 14 of the motor data). n 0 = M H Δ n Δ M

See also: explanation of the motor

Units In all formulas, the variables are to be used in the units according to the catalog (cf. physical variables and their units on page 64). The following applies in particular: − All torques in mNm − All currents in A (even no load currents) − Speeds (rpm) instead of angular velocity (rad/s)

P el = U mot · I mot

P mech = 30 000 M · n

P J = R · I mot 2

Motor constants Speed constant k n and torque constant k M are not independent of one another. The following applies: 30 000 The speed constant is also called specific speed. Specific voltage, gen- erator or voltage constants are mainly the reciprocal value of the speed constant and describe the voltage induced in the motor per speed. The torque constant is also called specific torque. The reciprocal value is called specific current or current constant. � k n · k M =

Speed n

Torque M

Derivation of the speed-torque line The following occurs if one replaces current I mot with torque M using the torque constant in the detailed power balance: U mot · n · M + R · � = 30 000 M k M M k M 2 Transformed and taking account of the close relationship of k M and k n , an equation is produced of a straight line between speed n and torque M. n = k n · U mot − 30 000 � R k M 2 · · M or with the gradient and the no load speed n 0 · M Δ n Δ n = n M 0 −

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maxon

September 2020 edition / subject to change

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