example of a torque graph below: for GL1 motor brushless/gearless at 48volts.
Below I've drawn over the original graph to make the colours highlighted (some graphs are black and with some with colour, this graph was in colour).
Torque Graphs
How are they made? glad you asked
I would put some pictures here of the machines but I lost alot of pics from china when a hardrive was accidentally erased.
Basically the machine is a large metal box about 5ft high and 4or5 feet wide and are very expensive machines. They have a rotating shaft coming out of the box (similar to a lathe), there are arms at the end of the rotating shaft (a thick steel shaft maybe 4cm in diameter). The hub motor is attached to the shaft these arms with some pins which go into the spoke holes of the motor). The torque of the motor is transferred to the machine via the spoke holes and only two spoke holes (one on each side of the motor) have pins which go into them to transfer the torque. The two pins can be adjusted to fit different size motors.
One thing I'm not clear on is this: whether the torque figures done during testing, give the torque obtainable for the radius of the hub motor being tested or whether the final results are adjusted to a certain size rim (eg 20" or 24" etc). I suspect that the results are adjusted for a given rim size but I need to check on that, torque graphs I have received have a rim size written on the graph so I think they adjust the figures to a given rim size.
The torque testing machine is hooked up to another big metal box ( 5ft high by 3ft wide) which houses the electricity supply unit, there are alot of knobs and things on it which can be used when testing to adjust voltage/amps etc. In a basic torque graph test the electricity supply unit is simply set for 24v, 36v or 48volts which is then fed to the controller that is being used with the motor. The machine keeps this voltage constant so you dont get any voltage sag.
Once the motor is in place, the controller is hooked up to the power supply , the controller is also hooked up to the hubmotor. Also a throttle is hooked up to the controller. The throttle is turned on full , the hub motor starts rotating and because its joined to the machine it starts the large shaft spinning, initially the shaft spins very easily and the motor reaches its no load rpm i.e. its maximum rpm. So at the beginning of the test the motor is spinning at its fatest rpm with no load on the motor.
The machine then starts applying a load to the shaft (how it does this I have no idea) this load slowly increases and the motor begins to slow down as the load is increased. When the motor reaches a certain rpm (about 70rpm) the machine stops the test as going down to stall speeds is probably not desireable for the motor being tested, but I think the machine could be adjusted to do that.
The two parts of the testing machine (the large metal boxes) are connected to
a computer and all the graphing is done automatically by the computer. At the
end of the test the operator will adjust the scales on the graph (on the
computer) so that the data is presented in a usable format. Then they hit the
print button and thats it. It takes maybe 5 or 10 minutes to do the test from
setting up of the motor to getting the graph printed out.
A few notes on the interpreting what the graphs mean: to be honest I'm certainly
no expert on how to read these graphs, I'm still learning about them, there is
alot of information can be gathered about the motor from these graphs. So what I
put up on the website is really what i'm learning as I go along and no doubt I
will make some mistakes but will rectify when I become aware of them.
It seems there is alot of variation in how the machines are operated eg. the
point when the test ends is not at stall speed (i.e. when the motor stops
turning) , it seems to be always stopped before this point. But just where the
test is stopped does not seem to be at a given point if comparing graphs from
different testing machines.
But I am learning that motors are really complex little beasties, there is
certainly a real art and a huge amount of skill involved in building them, and
understanding their different properties also is proving to be quite complex
(for me anyway!!).
example of a torque graph below: for GL1 motor brushless/gearless at 48volts.
Below I've drawn over the original graph to make the colours highlighted (some graphs
are black and with some with colour, this graph was in colour).
About the graphs
1.Current (amps) and Torque (Nm):
Torque is directly related to amps, the current flowing to the motor. On a
torque graph the torque is along the horizontal axis and all other parameters
are put on the y-axis of the graph. The line that describes the relationship
between the current and the torque is a straight line, this means there is a
linear relationship between torque and current.
{slightly off topic: y=kx describes a straight line, if y is current in amps,
and x is torque in Nm, then there is some constant k, that relates the two
together. So using an ammeter on your bike to measure the current you are also
really getting a readout of what your torque is at any time. If you could find
the value of k then you could very accurately measure what your torque is at any
time as long as you are below the maximum amps of the controller (see graph
below). To find 'k' you would need to know just one value of current (y) and one
value of torque (x) at any time,( how to measure a value of torque (x) I haven't
put much thought into it, but is quite possible to do it ) then your ammeter
could be used to get torque figures.)
Below the picture shows the GL1 motor torque graph and I've highlighted the
amps in red on y-axis and the torque is on the x-axis at the bottom.
Remembering that the machine allows the motor to rotate at its full speed
initially then slows it down by applying a load (the load applied is really used
by the machine to determine the torque values, so load and torque are also
directly related), you can see if we go from left to right that there is a
direct linear reliationship between the amps the motor uses and the amount of
torque it can supply.
Although a bit hard to see on this graph the amps does not start at zero, it
starts at some value (usually between about 0.5 to 2amps for hub motors)
which is the current needed to make the motor spin under no load conditions, it
indicates the power needed to overcome the resistance of the bearings (and other
friction forces) and the cogging forces in the motor.
Going from left to right you can see the amps increase as the torque
increases (more load is being applied) until you get to the maximum amps the
controller can supply in this case its 18amps. After this point the amps cannot
increase any more above 18amps as the controller is limited to supply only this
amount of amps. Also (although not very clear in this picture) this is the point
at which the motor reaches its peak power output.
(Note that there is a small curve in the line where it approached maximum amps
and turns into a horizontal line).
One thing that I dont understand is that once the amps reaches 18amps, it
remains at this value. Though as more load is applied the torque continues to
increase. I really dont understand that part of the graph and how that occurs.
Also when the amps first reaches it maximum value is where the motor puts out
its peak power, after that point the power output of the motor begins to
decrease though the torque of the motor continues to increase.........I really
dont understand that part of the graph as yet....how can the torque continue to
increase when the amps is remaining constant????
The Practical Side of Amps: So you can say that the torque of a motor (eg
ability to go up a hill or ability to accelerate ) depends on how much current
you can supply to the motor (the motor will have a limit to how much current it
can use due to the resistance of its copper windings but will almost always be
higher than the current the controller can supply). So if you want to change the
torque of your motor you need to change the current that can be supplied to it
by the controller. How that relates to the graph above I have no idea!!!
2. Power Output and Torque:
Power is measured in Watts and watts is defined as Joules per second. Joules is
a measure of the energy of a system (some other units also used are BTU's and
calories). So its really measuring the energy used or produced per second.
The graph below is the same GL-1 graph again but I've highlighted the Output
Power in purple. The graphs also record the input power which is the amount of
energy going into the motor via the controller (i.e. the amount of power being
supplied by the electricity source). Power is measured in Watts and is a measure
of how much energy is being used or produced. In this case the power out is
measuring how much energy is being converted into movement of the motor. The
input energy is always higher than the output energy (seems obvious!!) and the
difference between the two is used to determine the efficiency of the motor. The
input power is simply determined by P=Volts * Amps .
The output power I am not sure on how the machine calculates it but its possible
that a generator is being used to determine the output power of the shaft being
rotated by the hub motor (that may also be the way the load is applied through a
generator on the shaft but I really have no idea about that).
I'm actually finding it quite difficult to describe what the output power is in
practical terms, hence describing it in terms of energy. It is quite important
though to know the power output, especially in australia where we have a 200watt
peak output power limit for electric bikes.
In the graph you can see that as we go from left to right the power output
begins at zero. So at the beginning of the test the motor is running at full
speed and using energy to rotate but there is no load on the motor so the power
output is zero, its not being measured, no power output is measured until the
motor has some load applied to it. The power input (not highlighted on
the graph below) though, does not start at zero as energy is being used to
rotate the motor at its top speed (overcoming friction and magnetic losses in
the motor). confused???? ........I am!!!
The purple line shows a symmetrical curve which represents the power output of
the motor. The power output increases as load is applied and reaches a maximum
value in this case 654watts at the same time that the amps first reaches its
peak value. It should be noted that most motors will have a rated output
power written on them (also called the continuous power rating), this is
different to the peak power output of the motor. I am not sure on how the rated
power is calculated but some torque machines will print the rated power value of
the motor on the graph, in this case the rated power was 350watts (I think from
memory). (There is a method for determining the rated output power of a motor
from these torque graphs but I cant remember off the top of my head how done
will put some info up after some reading up on it.)
Most ebikes in australia will state the rated or continuous power on the
motor, not the peak power.
You can see on the graph that as we continue to the right after the peak power
is reached (more load is being applied still to slow the motor and increase its
torque) that the power output starts to decline, I really dont have much of an
understanding of why this occurs but I think its related to losses in the motor
windings and other losses that I dont understand. It may be related to increased
back emf which increases as load increases.
But on a basic level the higher the load on the motor the hotter it will get, so
it becomes more inefficient and energy is wasted as heat energy rather than
being used by the motor to overcome the load being applied.
You can also see that the test stops before the motor slows down to zero rpm. In
this case the test stops when the motor reaches about 70rpm.
At that point the power output of the motor is 300watts (compared to 654 watts
at the peak output power) and the torque being produced is 42Nm. I have
continued the curve as a dotted line (extrapolated as the curve is symmetrical)
and you can see the torque would continue to increase beyond 42Nm. When the
motor stalls (stops rotating due to the load being applied) the output power
would be zero again (what the???) and the torque would be around 50Nm.
At stalled rpm the torque is higher than the maximum torque given in this graph
as 42Nm. So this poses a problem when comparing the maximum torque values given
for different motors. The point at which the test is stopped will determine the
maximum torque value you get and other torque graphs I have received for motors
certainly stop at different points making comparisons between motors somewhat
difficult.
3. Input Power
Input Power is the Power in Watts supplied by the batteries or in this case
the testing machine. The difference between the input power and the output power
(above) gives the efficiency of the motor. The testing machine holds the input
voltage constant in this case at 48volts. So its slightly different to in an
ebike where the voltage will drop when the motor is under load (called voltage
sag of the batteries). The reason why gel cells are not used in ebikes is
because they have a very big voltage sag, so sealed lead acid absorbed glass mat
type batteries are much better as they only have a small voltage sag in
comparison to gel cells. The voltage sag is I think caused by the time it takes
electrons to flow to plates in the batteries, in gel cells it takes longer for
the electrons to flow across the gel and hence the voltage sag, in absorbed
glass matt type the electrons can flow faster ( I think!!)
On the graph below you can see the power input increases as the load increases
(makes sense), the motor is using more current.
The graph doesn't show it but it doesn't start from zero the input power it
starts from some small value usually around 20 to 50watts which is the power
used to spin the motor under no load conditons (fastest rpm). For the GL-1 graph
below the peak power input was 864 watts.
Once the maximum amps of the controller is reached the power cannot increase any
more (P=V*I) as the voltage is constant (48v) and the amps is constant also at
this point (18amps).
If you compare the graph below and the graph above where the torque is 42Nm,
you can see the power input is 864watts and the power output is about 300watts.
So there is 564watts of power (energy) being lost and much of it being converted
into heat.
[300/864*100= 35% so at 42Nm the motor is only running at 35% efficiency]
So under high load conditions the motor wastes alot of energy and runs
inefficiently, typically high load conditions occur at low rpm eg hill
climbing or starting off , so thats the time when you use alot of energy from
the batteries but waste alot of it as heat, so is best to help the motor with
some pedal assist at those times.
4. RPM (revolution per minute)
The rpm line is really a measure of what speed the hub motor is revolving at and
is a measure of what speed the wheel will rotate at, and the speed of the bike
can be determined for different wheel sizes.
The graph below shows the rpm for the GL-1 motor during the torque test. At the
start under no load the motor was rotating at about 350rpm.
[ on a 26" tyre that would equate to a speed of:
diameter: 26" = 66cm =0.6m ; circumference of tyre = pi*d =
1.88m (each one revolution of the tyre the bike would move 1.88m) ;
If the motor can rotate at 350revs per minute converting to revs per hour is
350*60 = 21, 000 revs per hour ;
So in one hour the wheel would rotate 21,000 times each revolution moving the
bike 1.88m forward, so a total distance of 39,480m would be covered,
converting to km gives 39.48km in one hour or 39.48km/hr.]
So the rpm of the graph can be used to determine the maximum speed of the motor
on different rim sizes.
The graph below shows that the rpm is a straight line which changes direction at
a point, that point where it changes direction is where the maximum amps of the
controller is reached. Also I've put a dotted line to extend the graph on the
right hand side.The point where the dotted line for rpm crosses the torque axis
will be where the motor reaches zero rpm (stalls) and max. torque should be at
that point. In this case around 50Nm.
Just a note on rpm not shown on this graph, to increase the maxim rpm (speed) of
a motor the voltage can be increased to achieve that. Most motors will have
quite a large safety margin built in so many motors can be overvolted to
increase the top speed. But increasing the voltage of a motor may cause heat to
be generated in the windings especially when under load, so an eye needs to be
kept on the temperature of the motor so that the windings wont overheat and burn
out. If a motor can be kept cool it will allow higher voltages to be used, so
its probably possible to overvolt a motor by a long way as long as the motor can
be kept cool. Also just on overvolting : the higher the volts you go the less
amps that are needed to get the same power. So increasing your voltage will
decrease your amp usage generally.
5. Efficiency:
Efficiency shows how much power that goes into your motor is actually being used
to make the motor rotate and is not being lost as heat or other losses.
Efficiency of a motor is quite important in getting the most range out of
your batteries. If a hub motor seller advertises a motor has a certain
efficiency it should be realised that the value they give is a peak efficiency.
The efficiency of a hub motor varies alot depending on what torque is being
applied and at what rpm the motor is turning at. Below shows the efficiency curve
for the GL-1 motor, during the test the max, efficiency reading was about 87%.
Thats a very high efficiency and I think is probably not the true efficiency.
With these graphs you rarely get straight lines for efficiency you get a wobbly
line , I'm not sure why but you really need a line of best fit to get more
accurate maximum efficiency. So although in this test the maximum efficiency was
recorded as 87% its more likely to be around 83% (so there is some error needs
to be taken into account).
The efficiency line shows a curved line that rises very steeply when load is
first applied. This section of the curve is not particularly important as the
actual power levels are extremely low. It then curves towards the maximum
efficiency as load is further applied and then tapers off in a less steep
manner. Motors which have a high efficiency over a wide range of torque values
will be better than ones that have a high efficiency in a small area of the
graph. This motor seems to have a good efficiency over a wide range up to about
30Nm, after that point the efficiency drops off rapidly, so under high load
conditions (low rpm also) you can see this motor would be quite inefficient and
not the best for hill climbing. All hub motors show a similar curve, even the
top of range wavecrest motor shows a similar curve where at times it will run at
very low efficiencies.
For the motor below lets say we take 80% efficiency as a good efficiency to
run the motor at. This corresponds to torque values between about 2Nm up to
about 20Nm. Since the left side of the graph is at very low power levels you can
really say that under 20Nm of torque this motor will run at over 80% efficiency.
So if your the type of rider that likes to feel the acceleration and power of a
hub motor (which is quite fun!) then you'll likely be running the motor over
20Nm of torque frequently and will waste alot of energy. So smooth acceleration
and generally keeping the load on the motor to moderate levels will
greatly increase your efficiency and hence your range.
Final comment:
I've found that every motor will have a slightly different graph even if made by the same company. Each motor is hand wound and for whatever reasons each motor is unique to some degree the differences will only be slight but each motor has its own unique curve. It seems to be often the case that wobbly lines are produced in the curves (especially for geared motors) and a line of best fit gives a better indication that following the wobbly lines. There are also times when for whatever reason you get some glitch on the graph. Furthermore they dont seem to help a terrible lot with maximum torque values as it seems to depend on where the test is stopped what the max, torque obtained is., but they can give a rough idea of torque values.
I think the best test of a motor is how it goes in a bike, but the graphs
maybe useful for some one wanting to check some aspect of a motors
characteristics.
beware of spray ebike company:
more info