Direct current motor#

The Direct current motor block is a direct current motor (DC motor), which has the possibility to select a separate circuit or permanent magnets as exciter, specifying their flux linkage.

The equation of DC motor motion is based on the formula (1):

(1)#\[М_{ЭМ}-М_{Н}=J\cdot \frac {\Delta \omega }{\Delta t}\]

where the electromagnetic torque \(М_{ЭМ}\) is calculated according to (2)

(2)#\[М_{ЭМ}=c\cdot Ф_{ОВ}\cdot I_{якорь}\]

where

c - design constant of the motor;

\(Ф_{ОВ}\) - magnetic flux of excitation winding, [Wb], which is calculated by the following formula (3):

(3)#\[Ф_{ОВ}=L_{ОВ}\cdot N_{ОВ} \cdot I_{ОВ}\]

where

\(L_{ОВ}\), \(N_{ОВ}\) - excitation winding inductance, [H], and its amount.

\(I_{ОВ}\), \(I_{якорь}\) - currents in the excitation winding and armature, [A].

The equation of DCM motion is based on the formula (4):

(4)#\[c=\frac{p\cdot N}{2\cdot П \cdot a}\]

where

p - number of magnetic pole pairs;

N - number of active conductors in the armature winding;

a - number of pairs of parallel branches in the armature winding.

The back-EMF in this block is determined by the formula (5):

(5)#\[E=c\cdot Ф_{ОВ}\cdot \omega\]

where

c - design constant of the motor;

Ф\(_{ОВ}\) - field winding magnetic flux, [Wb];

\(\omega\) - angular velocity, [rad/s].

Important

In many sources of literature, the constants of the motor c\(_m\), “c\(_e\) are used to calculate the electromagnetic torque and counter-EMF. However the formula c\(_м\)=\(\frac{p\cdot N}{2 \cdot П \cdot a}\) differs from c\(_е\)=\(\frac{p\cdot N}{60 \cdot a}\) only in additional multiplier \(\frac{2\cdot П}{60}\) for calculation of counter-EMF relative to the number of revolutions per minute (rpm) E=c\(_е\) \(\cdot\) Ф\(_{ОВ}\) \(\cdot\) n. And to calculate the counter-EMF relative to the angular velocity (rad/s), a structural coefficient is used, calculated by the formula \(\frac{p\cdot N}{2\cdot П \cdot a}\). Therefore, in this block, the structural coefficient is general, since the counter-EMF is considered relative to the angular velocity.

It is also possible to implement a motor with permanent magnets instead of an excitation circuit, the magnetic flux value is entered by the user.

When the armature and excitation windings are connected in series, the motor operates in series excitation mode. A distinctive feature of this excitation type is the nonlinear characteristic of the motor magnetic flux from the current Fig. 1 :

As there is no clear analytical expression for this curve, in this block it is possible to calculate the magnetic flow through the angular coefficient α. It is necessary to switch on the toggle switch Series wound DC motor. It is also possible to set the maximum magnetic flow crooked.

1. Properties#

Property	Default value	Description	Units of measurement
Armature resistance	1.1	–	Ohm
Armature inductance	1e-3	–	H
Motor constant	0.34	–	–
Field resistance	1e-3	–	Ohm
Field inductance	1e-3	–	H
Number of windings	10	–	–
Inertia	0.005	Rotor inertia	kg\(\cdot\) m\(^2\)
Friction coefficient	100e-3	–	N\(\cdot\) m\(\cdot\) s
Permanent magnet excited DC motor	Off	Permanent magnet excitation	–
Series wound DC motor	Off	Field circuit and armature in series connection	–
Magnets’ flux linkage	0.1	Available, when `Permanent magnet excited DC motor` - `On`	Wb
Saturation curve coefficient, available, when `Series wound DC motor` - `On`	0.01	Saturation curve slope coefficient	Wb/A
Flux saturation value, available, when `Series wound DC motor` - `On`	0.1	Maximum flux value	Wb

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
+ Обмотка возбуждения	Input	–	–	Electronics
+ Якорь	Input	–	–	Electronics
Applied torque	Input	External moment of shaft drag force	N\(\cdot\) m	Automation
- Обмотка возбуждения	Output	–	–	Electronics
- Якорь	Output	–	–	Electronics
Angular velocity	Output	–	rad/s	Rotational motion

In order to see the connection capabilities of the block, you need to go to page Description of block ports