Brushed DC Motor Theory - Revision history

Lynch: /* Motor Physics */

2011-02-17T00:19:16Z

Motor Physics

Lynch: /* Motor Physics */

2011-02-17T00:17:48Z

Motor Physics

Lynch: /* Motor Physics */

2011-02-17T00:17:04Z

Motor Physics

Lynch: /* Motor Physics */

2011-02-17T00:16:27Z

Motor Physics

Lynch: /* Other Effects */

2010-12-03T14:25:22Z

Other Effects

Lynch at 14:25, 3 December 2010

2010-12-03T14:25:09Z

Lynch: /* Equations */

2010-01-15T16:46:06Z

Equations

Lynch: /* Equations */

2010-01-15T16:45:08Z

Equations

Lynch: /* Datasheets and Speed-Torque Curves */

2010-01-15T16:43:53Z

Datasheets and Speed-Torque Curves

Lynch: /* Equations */

2010-01-15T16:42:58Z

Equations

@@ Line 38: / Line 38: @@
 [[image:torque graphs.png|center]]
-The process of switching current direction is called ''commutation''. To switch the direction of curent, brushed DC motors use <I>brushes</I> and <I>commutators</I>. The brushes are attached to the motor's two external wires, and the commutator segments slide over the brushes so that current through the coils switches at appropriate angles.  Commutation can also be done electronically (see [[Brushless DC Motors]]). The following diagram shows how brushes and commutators work.
+The process of switching current direction is called ''commutation''. To switch the direction of curent, brushed DC motors use <I>brushes</I> and <I>commutators</I>. The brushes are attached to the motor's two external wires, and the commutator segments slide over the brushes so that current through the coils switches at appropriate angles.  Commutation can also be done electronically (see [[Brushless DC Motors]]). The following diagram shows how brushes and commutators work.  A real commutator must have at least three segments.
 [[image:Motor Commutators.jpg|center|400px]]

@@ Line 11: / Line 11: @@
 ==Motor Physics==
-The forces inside a motor that cause the rotor to rotate are called ''Lorentz Forces''.  If an electron is moving through an electric field, it experiences a force that is perpendicular to both the magnetic field and the direction it's moving.  If we have a current <math>\vec I</math> passing through a wire in a magnetic field <math>\vec B</math>, the wire experiences a force <math>\vec F</math> proportional to the cross product of the current (expressed as a vector, including the direction of flow) and the magnetic field:
+The forces inside a motor that cause the rotor to rotate are called ''Lorentz Forces''.  If an electron is moving through a magnetic field, it experiences a force.  If we have a current <math>\vec I</math> passing through a wire in a magnetic field <math>\vec B</math>, the wire experiences a force <math>\vec F</math> proportional to the cross product of the current (expressed as a vector, including the direction of flow) and the magnetic field:
 {| align="center"

@@ Line 11: / Line 11: @@
 ==Motor Physics==
-The forces inside a motor that cause the rotor to rotate are called ''Lorentz Forces''.  If an electron is moving through an electric field, it experiences a force that is perpendicular to both the magnetic field and the direction it's moving.  If we have a current <math>\vec I</math> passing through a wire in a magnetic field <math>\vec B</math>, the wire experiences a force <math>\vec F</math> proportional to
+The forces inside a motor that cause the rotor to rotate are called ''Lorentz Forces''.  If an electron is moving through an electric field, it experiences a force that is perpendicular to both the magnetic field and the direction it's moving.  If we have a current <math>\vec I</math> passing through a wire in a magnetic field <math>\vec B</math>, the wire experiences a force <math>\vec F</math> proportional to the cross product of the current (expressed as a vector, including the direction of flow) and the magnetic field:
 {| align="center"

@@ Line 11: / Line 11: @@
 ==Motor Physics==
-The forces inside a motor that cause the rotor to rotate are called ''Lorentz Forces''.  If an electron is moving through an electric field, it experiences a force that is perpendicular to both the magnetic field and the direction it's moving.  If we have a current <math>\vec I</math> passing through a wire in a magnetic field <math>\vec B</math>, the wire experiences a force <math>\vec F</math> equal to
+The forces inside a motor that cause the rotor to rotate are called ''Lorentz Forces''.  If an electron is moving through an electric field, it experiences a force that is perpendicular to both the magnetic field and the direction it's moving.  If we have a current <math>\vec I</math> passing through a wire in a magnetic field <math>\vec B</math>, the wire experiences a force <math>\vec F</math> proportional to
 {| align="center"
-|<math>\vec F = \vec I \times \vec B\,</math>
+|<math>\vec F \propto \vec I \times \vec B\,</math>
 |}

@@ Line 205: / Line 205: @@
 ==Other Effects==
 * '''Cogging.'''  With no power to the motor, you'll feel the motor shaft bump-bump-bump as you spin it by hand, due to the orientation-dependent attraction of the rotor to the permanent magnets.
 * '''Friction losses.'''
 ==References==

@@ Line 68: / Line 68: @@
 <center><math>v_{emf} = \begin{matrix}\frac{n}{k_n}\end{matrix}\,</math></center>
-where <math>n</math> is the rotation in '''revolutions-per-minute''' (rpm) (to be consistent with the Maxon datasheet below) and <math>k_n</math> is called the '''speed constant''', the inverse of which is often called the '''electrical constant''' <math>k_e\,</math>, which depends on the motor design.  (My preference is to use SI units, using radians-per-second for angular velocity and volt-seconds/radian for the speed constant.  But speed constants are usually given in different units, and rpms are the most common angular velocity unit in motor data sheets.)  The back-emf term indicates that any motor is also a generator:  if we spin the motor shaft, we read a voltage at the motor terminals.  This is how dams create hydroelectric power.
+where <math>n</math> is the rotation in '''revolutions-per-minute''' (rpm) (to be consistent with the Maxon datasheet below) and <math>k_n</math> is called the '''speed constant''', the inverse of which is often called the '''electrical constant''' <math>k_e\,</math>, which depends on the motor design.  (My preference is to use SI units, using radians-per-second for angular velocity and volt-seconds/radians for the electrical constant and radians/volt-seconds for the speed constant.  But speed constants are usually given in different units, and rpms are the most common angular velocity unit in motor data sheets.)  The back-emf term indicates that any motor is also a generator:  if we spin the motor shaft, we read a voltage at the motor terminals.  This is how dams create hydroelectric power.
 The torque generated by the motor is proportional to the current through the windings, where the constant of proportionality is called the '''torque constant''' <math>k_t</math> or '''motor constant''' <math>k_M</math>:

@@ Line 152: / Line 152: @@
 '''12.'''  Torque (or motor) constant, <math>k_t\,</math> or <math>k_M\,</math>:  The constant of proportionality relating current to torque.  In SI units (Newton-meters per amp), the torque constant is equivalent to the inverse of the speed constant in SI units (radians per volt-second).
-'''13.'''  Speed (or electrical) constant, <math>k_n\,</math> or <math>k_e\,</math>:  The constant of proportionality relating speed to voltage.  Equivalent to the inverse of the torque constant when expressed in SI units.
+'''13.'''  Speed constant, <math>k_n\,</math> (which is the inverse of the electrical constant <math>k_e\,</math>):  The constant of proportionality relating speed to voltage.  Equivalent to the inverse of the torque constant when expressed in SI units.
 '''14.'''  Speed/torque gradient:  A representation of the slope of the speed-torque curve (see graph below), approximately equal to the no load speed divided by the stall torque.