01 Nov Defining Brushless DC Motors #2 of 4: Relationship between Motor Sensitivity (Kt) & back emf (Kb)
Defining Brushless DC Motors #2 of 4:
Relationship between Motor Sensitivity (Kt) & back emf (Kb)
By John Knott, President of JD Technologies, LLC
In my first blog I presented an overview of a simple six-step procedure for defining a permanent magnet BDCM. In this second blog, I will show you how to establish the relationship between motor sensitivity (Kt) & back emf (Kb).
The expressions for torque and emf (electro-motive force) in a DC motor are [REF 1]
This can be determined from:
where z = number of conductors, and p1 = number of parallel paths.
The DC current motor is an energy converter: i.e. electrical energy is converted to mechanical energy. The developed mechanical power is equal to the generated electrical power (neglecting friction) or
The value of ? can be derived as follows:
For Ns conductors in series, the average emf is: [REF1]
Now substitute EQU (4) into EQU (2) to get:
As a result we see that ? is a constant determined by the number of poles and conductors in the motor.
For a permanent magnet DC motor (e.g. samarium cobalt) ?, air gap flux per pole is constant since the field current and, thereby, flux density is constant.
Therefore, the expressions for torque and EMF in a DC permanent magnet
In EQUs (7) and (8):
Substituting EQUs (7) and (8) into EQU (3) we see that
ad 1 Joule = 1 Newton-meter by definition
More to come
We now have established the relationship between motor sensitivity (Kt) & back emf (Kb). In the upcoming blogs we will derive the constants and finally give an example.
I am confident that Composite Motors, Inc. with their Team and resources would be an essential foundation for supporting your BDCM development. All of Composite Motors, Inc.’s products are made on American soil. Let’s talk! Email me at firstname.lastname@example.org or call me at 781-864-2220 or visit Composite Motors, Inc.’s website at www.compositemotors.com
About JD Technologies, LLC
JD Technologies LLC provides premium sales and marketing services to a group of high quality, complementary manufacturers of engineered services and products who serve the aerospace, military & defense, industrial, and medical industries. They develop long term relationships with key customers who value the consultative style of selling and who wish to interface with sales professionals of high integrity. Their approach is to use proven consultative selling techniques. Consultative selling is a collaborative process that leads customers/prospects through an analysis of their current situation to a resulting improvement. For more information on JD Technologies, LLC, their products, services and their consultative selling methodology, visit www.jdtechsales.com.