Below I have made a reverse image of the graph so that I can use the power out line mirror image to extrapolate the graph.
The graphs are then lined up (pushed together so that a symmetrical parabola is created for the power out curve).
Extrapolating the Torque Graphs:
I'll use the 408 Torque graph from a motor testing company as an example of
how I extrapolated the graphs (extrapolate means to extend the graphs beyond
what is given):
Below is a graph as given to me by the testing company. The power out curve
stops at a certain point probably near the torque limit of the testing machine.
So its necessary for me to extend the graph so that I can get the maximum torque
value of the motor and a better picture of the whole torque graph (what i've
been given really only represents about half of the torque graph!). Fortunately
the power out curve is a symmetrical parabolic shape which as it goes left to
right it eventually reaches a peak value and then begins to decline to zero
(where the torque is maximum).
So what I did was using a photoediting program I took the power out curve as
given below and flipped it horizontally to get the right hand side of the curve.
In the example below I have to extend the power out curve till it reaches its
maximum point, that could introduce a small amount of error but would be quite
negligible I think. Fortunately the peak of the power out curve coincides
vertically in line with the point where the current (in amps) hits its maximum
value (as limited by the controller), when it reaches 20amps the current line
then goes horizontally (in
the graph below the controller limits the maximum amps to 20amps which is quite
a bit beyond where the currrent line ( I ) ends. But I will run through the
process of how to get the complete curve on this page.
Below I have made a reverse image of the graph so that I can use the power out
line mirror image to extrapolate the graph.
The graphs are then lined up (pushed together so that a symmetrical parabola is
created for the power out curve).
The current line can be extended as its a straight line, the controller for the
408 has a 20amp limit so when the purple line below (extended current line) hits
the 20amp point (shown by red line) . The blue line shows where the maximum of
the power output will occur. So the power out curve can be extended following
the parabolic curve till it hits the blue dotted line (the extended part of the
power out curve is shown in green).
Because I'm guessing to some degree the shape of the top of this parabola there
may be some error in the maximum power out figure probably an error of
plus or minus 10watts or so ( i.e. not much inaccuracy).
Once I've got the top of the parabola of the power out curve drawn then I made a mirror image and aligned the two sides together as shown below. Fortunately the power out graph is symmetrical and this should give quite an accurate measure of the maximum torque values.
Below shows how the rpm line can be extrapolated. The rpm falls as torque
increases in a linear fashion in the testing machine as load is increased.
It follows a straight line so that can be easily extended. I've extended it till
it reaches the vertical blue line ( from the 20amp maximum current limit).
The point at which it intercepts the blue line gives the rpm at peak output
power, after that point the rpm continues to fall in a straight line but at a
steeper angle, it reaches zero at the point where power output reaches zero, so
a straight line can be drawn as show below and that should be quite an accurate
reading of the rpm of the motor under varying load.
So up to this point the graph will look like below:
Next is extrapolating the efficiency curve, this one is a bit more tricky. On
other graphs that I've looked at the efficiency curve looks like a skewed graph
with a peak to the left hand side then tapering off to the right . But just
before reaching very low efficiencies the line drops down almost vertically. So
I think my extrapolated efficiency curve will not be particularly accurate but
enough to give some rough idea of the motor efficiency at different load values
( i.e. torque values).
Power out can be extrapolated quite accurately as its a straight line until it
reaches the dotted blue line then it goes horizontally.
So the final extrapolated graph will look like below
The axes labels (y- axis) can then be put back on the graph as below, and so
thats how I did it. I think this gives a very accurate representation of the
motor torque excepting the efficiency line which after about 30Nm I'm pretty
much guessing its shape.
beware of spray ebike company: more info
back
to home page
Copyright 1998-2006 by Brett White on all images/text/information and
graphical materials on this website.