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bldc motor, esc and battery draw, nominal vs peak


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$begingroup$


I want to better understand how Electronic Speed Controllers (ESC) work for BLDC motors. Specifically, I am trying to understand battery current draw.



Question 1:
When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.



Question 2:
If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that? I'm now thinking the draw will be more along the RMS value of the output pulse wave. This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.



Question 3: (slightly off topic)
To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear. I just want to understand the theory of how ESC's work at a high level.



Much thanks!










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$endgroup$



















    2












    $begingroup$


    I want to better understand how Electronic Speed Controllers (ESC) work for BLDC motors. Specifically, I am trying to understand battery current draw.



    Question 1:
    When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.



    Question 2:
    If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that? I'm now thinking the draw will be more along the RMS value of the output pulse wave. This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.



    Question 3: (slightly off topic)
    To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear. I just want to understand the theory of how ESC's work at a high level.



    Much thanks!










    share|improve this question







    New contributor




    twegner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      2












      2








      2





      $begingroup$


      I want to better understand how Electronic Speed Controllers (ESC) work for BLDC motors. Specifically, I am trying to understand battery current draw.



      Question 1:
      When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.



      Question 2:
      If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that? I'm now thinking the draw will be more along the RMS value of the output pulse wave. This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.



      Question 3: (slightly off topic)
      To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear. I just want to understand the theory of how ESC's work at a high level.



      Much thanks!










      share|improve this question







      New contributor




      twegner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      I want to better understand how Electronic Speed Controllers (ESC) work for BLDC motors. Specifically, I am trying to understand battery current draw.



      Question 1:
      When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.



      Question 2:
      If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that? I'm now thinking the draw will be more along the RMS value of the output pulse wave. This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.



      Question 3: (slightly off topic)
      To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear. I just want to understand the theory of how ESC's work at a high level.



      Much thanks!







      current brushless-dc-motor motor-controller






      share|improve this question







      New contributor




      twegner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|improve this question







      New contributor




      twegner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|improve this question




      share|improve this question






      New contributor




      twegner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      asked 4 hours ago









      twegnertwegner

      111




      111




      New contributor




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      Check out our Code of Conduct.





      New contributor





      twegner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






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      Check out our Code of Conduct.






















          3 Answers
          3






          active

          oldest

          votes


















          3












          $begingroup$


          Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.




          Without a datasheet we're guessing but the 500 A peak current is likely to occur during start-up and this may last one or more tenths of a second. A capacitor to supply 500 A for 0.1 s at a useful voltage will be very large.



          It's much more likely that any capacitors on the DC input stage are acting as short-term filters to pass high-frequency noise to ground.




          Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?




          It will need to draw enough to power the motor. It completely depends on the load the motor is given.




          This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.




          This may be a warning sign that you have a low quality product.




          Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear.




          The ESC will operate using pulse-width modulation (PWM) as it results in very low losses in the switching transistors. PWM applies pulses of 100% voltage to the motor for a short period, switches off, waits and then repeats the process.



          enter image description here



          Figure 1. PWM signal transitioning from high pulse width (75%) to low (25%) and back again. Note amplitude remains constant.






          share|improve this answer









          $endgroup$













          • $begingroup$
            Q2 "It completely depends on the load the motor is given". Would that not be the nominal 200 amp rating? Assuming it is, would it then be drawing the RMS of the PWM wave? Also, you are likely correct that I have a low quality product, thanks for raising this point.
            $endgroup$
            – twegner
            4 hours ago










          • $begingroup$
            Both the question and to some degree this attempted answer are making the fundamental mistake of assuming that the rating is a current draw. It is not, rather it is a "rating" (likely overly optimistic) of what the FETs on the ESC can handle. This has nothing to do with what the circuit may draw, which might be far less in proper operation, or substantially more in misapplication, leading to failure of whatever part of the installation is weakest (hopefully a user-provided fuse).
            $endgroup$
            – Chris Stratton
            3 hours ago












          • $begingroup$
            @twegner: What I'm saying is that the load on the motor (bike going up a hill, winch lifting a load, etc.) determines the current requirement. If there is a light load then the current will be reduced. The maximum load that you can drive will be determined by the motor limit or ESC limit - whichever is the lower.
            $endgroup$
            – Transistor
            3 hours ago










          • $begingroup$
            @Transistor: Yes, I understand. I should have phrased that as Max Throttle and full load - like heavy acceleration against a high resistance. So in this case, I assume the 200 amp nominal rating is what is being output (if that - according to Chris Stratton) from the ESC to the motor.
            $endgroup$
            – twegner
            2 hours ago










          • $begingroup$
            @ChrisStratton: I didn't mean to imply the ESC rating is current draw. Rather I was questioning if the ESC's 200 amp output is what I should expect to be pulled from the battery pack or if it was more along the lines of the RMS of the output that would be pulled from the battery. Thanks for you input. Again, I was just looking for some high level theory, so this helps.
            $endgroup$
            – twegner
            2 hours ago



















          3












          $begingroup$

          All answers assume you're talking about "hobby" ESCs, as used in planes, boats, cars, robots, etc.




          Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps?




          No. For the most part, the ESC draws what it draws given the motor, battery and load on the motor.



          Some of the better ESC's do have current limiting, but experience in the flying field is that if you dork the thing into the dirt at full throttle, chances are that you'll damage the electronics due to overcurrent.



          An ESC could be designed to limit current in such a way (I've designed industrial motor controllers that do), but AFAIK ESC's don't.




          Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?




          See answer to question 1.




          Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage?




          Neither. At the level of the throttle command to motor, it supplies a fixed PWM to the motor -- essentially it chops the battery voltage and hands it to the motor.



          This is complicated by the fact that some ESC's have a governor function, that servos the motor speed to the signal coming in -- but they still have an internal throttle command that works as above.






          share|improve this answer









          $endgroup$













          • $begingroup$
            Your Q3 response. I'm trying to understand this better. Are you saying the current is fixed and that the PWM is just shortened? (Like Transistors PWM graph) Basically the duty cycle is reduced but the current is not, but essentially this means less power is used.
            $endgroup$
            – twegner
            2 hours ago



















          1












          $begingroup$

          The max operating temperature or heat rise above 25'C is what limits the nominal continuous current rating. The peak is an absolute maximum which may or may not be protected and should never be exceeded, such as starting a couple of these motors below at full throttle.




          One must mind the rated peak currents to prevent damage to the electronics.




          Similarily, a motor full load current rating is defined by the same method of temperature rise above 25'C for the winding hot spots. However every market does not use the same hot spot temperature for a long useful life and if no standards are given or not temp rise is specified, you might guess they don't want you to know.



          However it is quite common to give the peak motor current as surge, start or locked rotor current. These are all the same as is simply Ohm's Law applied to the DC resistance or DCR, so Imax= V/DCR. This is typically Imax = 8 to 12 times the rated current in modern BLDC, high-efficiency DC motors.



          Here they generously rate the motor current with a 180 second limit. This would be at max internal temperature.



          enter image description here






          share|improve this answer









          $endgroup$













          • $begingroup$
            If I'm reading the Tech sheet right, they are doing P=IV, so 885.4 watts = 4.2 vdc (not 3.7) * 4 cells * 52.7 amps. I understand your locked rotor 360 amp (V/R=I) calculation. So are you saying that as soon as the rotor locks, like if the parking brake was on (just go with it), that this motor should be paired with an ESC that can handle at least 360 amps? Which is way more than the Max Current on the spec sheet indicates. Also, thanks for providing a real world example. Yours and all the other answers are beginning to clear up my muddy understanding of this.
            $endgroup$
            – twegner
            1 hour ago










          • $begingroup$
            The 885W is the motor power doing work if the batteries did not drop from a full charge at 4.2V for 120s, which seems unlikely even if they were 8P4S arrays as I believe it would drop to 3.6V at this current @ 120s. The 113 watts I calculated is DCR loss that makes the inefficiency 12.8% = 113/885W that produces heat while accelerating or braking until speed induced BEMF reduces the net voltage across the winding. So the ESC must use current feedback to regulate constant current to match this motor spec. limit. I expect ESC current-mode feedback limits torque and voltage regulates speed.
            $endgroup$
            – Sunnyskyguy EE75
            25 mins ago










          • $begingroup$
            I would expect an ESC of this caliber to have current limit control and voltage control. But I can't say for sure. AWG8= 2 mohm/m or 4mOhm/m pair
            $endgroup$
            – Sunnyskyguy EE75
            23 mins ago














          Your Answer






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          3 Answers
          3






          active

          oldest

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          3 Answers
          3






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          3












          $begingroup$


          Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.




          Without a datasheet we're guessing but the 500 A peak current is likely to occur during start-up and this may last one or more tenths of a second. A capacitor to supply 500 A for 0.1 s at a useful voltage will be very large.



          It's much more likely that any capacitors on the DC input stage are acting as short-term filters to pass high-frequency noise to ground.




          Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?




          It will need to draw enough to power the motor. It completely depends on the load the motor is given.




          This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.




          This may be a warning sign that you have a low quality product.




          Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear.




          The ESC will operate using pulse-width modulation (PWM) as it results in very low losses in the switching transistors. PWM applies pulses of 100% voltage to the motor for a short period, switches off, waits and then repeats the process.



          enter image description here



          Figure 1. PWM signal transitioning from high pulse width (75%) to low (25%) and back again. Note amplitude remains constant.






          share|improve this answer









          $endgroup$













          • $begingroup$
            Q2 "It completely depends on the load the motor is given". Would that not be the nominal 200 amp rating? Assuming it is, would it then be drawing the RMS of the PWM wave? Also, you are likely correct that I have a low quality product, thanks for raising this point.
            $endgroup$
            – twegner
            4 hours ago










          • $begingroup$
            Both the question and to some degree this attempted answer are making the fundamental mistake of assuming that the rating is a current draw. It is not, rather it is a "rating" (likely overly optimistic) of what the FETs on the ESC can handle. This has nothing to do with what the circuit may draw, which might be far less in proper operation, or substantially more in misapplication, leading to failure of whatever part of the installation is weakest (hopefully a user-provided fuse).
            $endgroup$
            – Chris Stratton
            3 hours ago












          • $begingroup$
            @twegner: What I'm saying is that the load on the motor (bike going up a hill, winch lifting a load, etc.) determines the current requirement. If there is a light load then the current will be reduced. The maximum load that you can drive will be determined by the motor limit or ESC limit - whichever is the lower.
            $endgroup$
            – Transistor
            3 hours ago










          • $begingroup$
            @Transistor: Yes, I understand. I should have phrased that as Max Throttle and full load - like heavy acceleration against a high resistance. So in this case, I assume the 200 amp nominal rating is what is being output (if that - according to Chris Stratton) from the ESC to the motor.
            $endgroup$
            – twegner
            2 hours ago










          • $begingroup$
            @ChrisStratton: I didn't mean to imply the ESC rating is current draw. Rather I was questioning if the ESC's 200 amp output is what I should expect to be pulled from the battery pack or if it was more along the lines of the RMS of the output that would be pulled from the battery. Thanks for you input. Again, I was just looking for some high level theory, so this helps.
            $endgroup$
            – twegner
            2 hours ago
















          3












          $begingroup$


          Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.




          Without a datasheet we're guessing but the 500 A peak current is likely to occur during start-up and this may last one or more tenths of a second. A capacitor to supply 500 A for 0.1 s at a useful voltage will be very large.



          It's much more likely that any capacitors on the DC input stage are acting as short-term filters to pass high-frequency noise to ground.




          Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?




          It will need to draw enough to power the motor. It completely depends on the load the motor is given.




          This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.




          This may be a warning sign that you have a low quality product.




          Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear.




          The ESC will operate using pulse-width modulation (PWM) as it results in very low losses in the switching transistors. PWM applies pulses of 100% voltage to the motor for a short period, switches off, waits and then repeats the process.



          enter image description here



          Figure 1. PWM signal transitioning from high pulse width (75%) to low (25%) and back again. Note amplitude remains constant.






          share|improve this answer









          $endgroup$













          • $begingroup$
            Q2 "It completely depends on the load the motor is given". Would that not be the nominal 200 amp rating? Assuming it is, would it then be drawing the RMS of the PWM wave? Also, you are likely correct that I have a low quality product, thanks for raising this point.
            $endgroup$
            – twegner
            4 hours ago










          • $begingroup$
            Both the question and to some degree this attempted answer are making the fundamental mistake of assuming that the rating is a current draw. It is not, rather it is a "rating" (likely overly optimistic) of what the FETs on the ESC can handle. This has nothing to do with what the circuit may draw, which might be far less in proper operation, or substantially more in misapplication, leading to failure of whatever part of the installation is weakest (hopefully a user-provided fuse).
            $endgroup$
            – Chris Stratton
            3 hours ago












          • $begingroup$
            @twegner: What I'm saying is that the load on the motor (bike going up a hill, winch lifting a load, etc.) determines the current requirement. If there is a light load then the current will be reduced. The maximum load that you can drive will be determined by the motor limit or ESC limit - whichever is the lower.
            $endgroup$
            – Transistor
            3 hours ago










          • $begingroup$
            @Transistor: Yes, I understand. I should have phrased that as Max Throttle and full load - like heavy acceleration against a high resistance. So in this case, I assume the 200 amp nominal rating is what is being output (if that - according to Chris Stratton) from the ESC to the motor.
            $endgroup$
            – twegner
            2 hours ago










          • $begingroup$
            @ChrisStratton: I didn't mean to imply the ESC rating is current draw. Rather I was questioning if the ESC's 200 amp output is what I should expect to be pulled from the battery pack or if it was more along the lines of the RMS of the output that would be pulled from the battery. Thanks for you input. Again, I was just looking for some high level theory, so this helps.
            $endgroup$
            – twegner
            2 hours ago














          3












          3








          3





          $begingroup$


          Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.




          Without a datasheet we're guessing but the 500 A peak current is likely to occur during start-up and this may last one or more tenths of a second. A capacitor to supply 500 A for 0.1 s at a useful voltage will be very large.



          It's much more likely that any capacitors on the DC input stage are acting as short-term filters to pass high-frequency noise to ground.




          Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?




          It will need to draw enough to power the motor. It completely depends on the load the motor is given.




          This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.




          This may be a warning sign that you have a low quality product.




          Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear.




          The ESC will operate using pulse-width modulation (PWM) as it results in very low losses in the switching transistors. PWM applies pulses of 100% voltage to the motor for a short period, switches off, waits and then repeats the process.



          enter image description here



          Figure 1. PWM signal transitioning from high pulse width (75%) to low (25%) and back again. Note amplitude remains constant.






          share|improve this answer









          $endgroup$




          Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps? I'm rationalizing this in my head by assuming the capacitors in the ESC are just discharging more current than normal for short durations when this 'peak' value is experienced. I'm also assuming it will never try to pull 500 amps from the battery pack. If this isn't right, please explain.




          Without a datasheet we're guessing but the 500 A peak current is likely to occur during start-up and this may last one or more tenths of a second. A capacitor to supply 500 A for 0.1 s at a useful voltage will be very large.



          It's much more likely that any capacitors on the DC input stage are acting as short-term filters to pass high-frequency noise to ground.




          Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?




          It will need to draw enough to power the motor. It completely depends on the load the motor is given.




          This would explain why the ESC input wires from the battery pack are relatively small in relation to the output current rating. When I see 200 amps I think of thick 2/0 awg gauge wire, not the 6 awg or 8 awg gauge wires I see on my ESC.




          This may be a warning sign that you have a low quality product.




          Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage? I assume it is current, I just want verification. Let's say the throttle is at 10% and assume the throttle curve is linear.




          The ESC will operate using pulse-width modulation (PWM) as it results in very low losses in the switching transistors. PWM applies pulses of 100% voltage to the motor for a short period, switches off, waits and then repeats the process.



          enter image description here



          Figure 1. PWM signal transitioning from high pulse width (75%) to low (25%) and back again. Note amplitude remains constant.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 4 hours ago









          TransistorTransistor

          89.7k787193




          89.7k787193












          • $begingroup$
            Q2 "It completely depends on the load the motor is given". Would that not be the nominal 200 amp rating? Assuming it is, would it then be drawing the RMS of the PWM wave? Also, you are likely correct that I have a low quality product, thanks for raising this point.
            $endgroup$
            – twegner
            4 hours ago










          • $begingroup$
            Both the question and to some degree this attempted answer are making the fundamental mistake of assuming that the rating is a current draw. It is not, rather it is a "rating" (likely overly optimistic) of what the FETs on the ESC can handle. This has nothing to do with what the circuit may draw, which might be far less in proper operation, or substantially more in misapplication, leading to failure of whatever part of the installation is weakest (hopefully a user-provided fuse).
            $endgroup$
            – Chris Stratton
            3 hours ago












          • $begingroup$
            @twegner: What I'm saying is that the load on the motor (bike going up a hill, winch lifting a load, etc.) determines the current requirement. If there is a light load then the current will be reduced. The maximum load that you can drive will be determined by the motor limit or ESC limit - whichever is the lower.
            $endgroup$
            – Transistor
            3 hours ago










          • $begingroup$
            @Transistor: Yes, I understand. I should have phrased that as Max Throttle and full load - like heavy acceleration against a high resistance. So in this case, I assume the 200 amp nominal rating is what is being output (if that - according to Chris Stratton) from the ESC to the motor.
            $endgroup$
            – twegner
            2 hours ago










          • $begingroup$
            @ChrisStratton: I didn't mean to imply the ESC rating is current draw. Rather I was questioning if the ESC's 200 amp output is what I should expect to be pulled from the battery pack or if it was more along the lines of the RMS of the output that would be pulled from the battery. Thanks for you input. Again, I was just looking for some high level theory, so this helps.
            $endgroup$
            – twegner
            2 hours ago


















          • $begingroup$
            Q2 "It completely depends on the load the motor is given". Would that not be the nominal 200 amp rating? Assuming it is, would it then be drawing the RMS of the PWM wave? Also, you are likely correct that I have a low quality product, thanks for raising this point.
            $endgroup$
            – twegner
            4 hours ago










          • $begingroup$
            Both the question and to some degree this attempted answer are making the fundamental mistake of assuming that the rating is a current draw. It is not, rather it is a "rating" (likely overly optimistic) of what the FETs on the ESC can handle. This has nothing to do with what the circuit may draw, which might be far less in proper operation, or substantially more in misapplication, leading to failure of whatever part of the installation is weakest (hopefully a user-provided fuse).
            $endgroup$
            – Chris Stratton
            3 hours ago












          • $begingroup$
            @twegner: What I'm saying is that the load on the motor (bike going up a hill, winch lifting a load, etc.) determines the current requirement. If there is a light load then the current will be reduced. The maximum load that you can drive will be determined by the motor limit or ESC limit - whichever is the lower.
            $endgroup$
            – Transistor
            3 hours ago










          • $begingroup$
            @Transistor: Yes, I understand. I should have phrased that as Max Throttle and full load - like heavy acceleration against a high resistance. So in this case, I assume the 200 amp nominal rating is what is being output (if that - according to Chris Stratton) from the ESC to the motor.
            $endgroup$
            – twegner
            2 hours ago










          • $begingroup$
            @ChrisStratton: I didn't mean to imply the ESC rating is current draw. Rather I was questioning if the ESC's 200 amp output is what I should expect to be pulled from the battery pack or if it was more along the lines of the RMS of the output that would be pulled from the battery. Thanks for you input. Again, I was just looking for some high level theory, so this helps.
            $endgroup$
            – twegner
            2 hours ago
















          $begingroup$
          Q2 "It completely depends on the load the motor is given". Would that not be the nominal 200 amp rating? Assuming it is, would it then be drawing the RMS of the PWM wave? Also, you are likely correct that I have a low quality product, thanks for raising this point.
          $endgroup$
          – twegner
          4 hours ago




          $begingroup$
          Q2 "It completely depends on the load the motor is given". Would that not be the nominal 200 amp rating? Assuming it is, would it then be drawing the RMS of the PWM wave? Also, you are likely correct that I have a low quality product, thanks for raising this point.
          $endgroup$
          – twegner
          4 hours ago












          $begingroup$
          Both the question and to some degree this attempted answer are making the fundamental mistake of assuming that the rating is a current draw. It is not, rather it is a "rating" (likely overly optimistic) of what the FETs on the ESC can handle. This has nothing to do with what the circuit may draw, which might be far less in proper operation, or substantially more in misapplication, leading to failure of whatever part of the installation is weakest (hopefully a user-provided fuse).
          $endgroup$
          – Chris Stratton
          3 hours ago






          $begingroup$
          Both the question and to some degree this attempted answer are making the fundamental mistake of assuming that the rating is a current draw. It is not, rather it is a "rating" (likely overly optimistic) of what the FETs on the ESC can handle. This has nothing to do with what the circuit may draw, which might be far less in proper operation, or substantially more in misapplication, leading to failure of whatever part of the installation is weakest (hopefully a user-provided fuse).
          $endgroup$
          – Chris Stratton
          3 hours ago














          $begingroup$
          @twegner: What I'm saying is that the load on the motor (bike going up a hill, winch lifting a load, etc.) determines the current requirement. If there is a light load then the current will be reduced. The maximum load that you can drive will be determined by the motor limit or ESC limit - whichever is the lower.
          $endgroup$
          – Transistor
          3 hours ago




          $begingroup$
          @twegner: What I'm saying is that the load on the motor (bike going up a hill, winch lifting a load, etc.) determines the current requirement. If there is a light load then the current will be reduced. The maximum load that you can drive will be determined by the motor limit or ESC limit - whichever is the lower.
          $endgroup$
          – Transistor
          3 hours ago












          $begingroup$
          @Transistor: Yes, I understand. I should have phrased that as Max Throttle and full load - like heavy acceleration against a high resistance. So in this case, I assume the 200 amp nominal rating is what is being output (if that - according to Chris Stratton) from the ESC to the motor.
          $endgroup$
          – twegner
          2 hours ago




          $begingroup$
          @Transistor: Yes, I understand. I should have phrased that as Max Throttle and full load - like heavy acceleration against a high resistance. So in this case, I assume the 200 amp nominal rating is what is being output (if that - according to Chris Stratton) from the ESC to the motor.
          $endgroup$
          – twegner
          2 hours ago












          $begingroup$
          @ChrisStratton: I didn't mean to imply the ESC rating is current draw. Rather I was questioning if the ESC's 200 amp output is what I should expect to be pulled from the battery pack or if it was more along the lines of the RMS of the output that would be pulled from the battery. Thanks for you input. Again, I was just looking for some high level theory, so this helps.
          $endgroup$
          – twegner
          2 hours ago




          $begingroup$
          @ChrisStratton: I didn't mean to imply the ESC rating is current draw. Rather I was questioning if the ESC's 200 amp output is what I should expect to be pulled from the battery pack or if it was more along the lines of the RMS of the output that would be pulled from the battery. Thanks for you input. Again, I was just looking for some high level theory, so this helps.
          $endgroup$
          – twegner
          2 hours ago













          3












          $begingroup$

          All answers assume you're talking about "hobby" ESCs, as used in planes, boats, cars, robots, etc.




          Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps?




          No. For the most part, the ESC draws what it draws given the motor, battery and load on the motor.



          Some of the better ESC's do have current limiting, but experience in the flying field is that if you dork the thing into the dirt at full throttle, chances are that you'll damage the electronics due to overcurrent.



          An ESC could be designed to limit current in such a way (I've designed industrial motor controllers that do), but AFAIK ESC's don't.




          Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?




          See answer to question 1.




          Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage?




          Neither. At the level of the throttle command to motor, it supplies a fixed PWM to the motor -- essentially it chops the battery voltage and hands it to the motor.



          This is complicated by the fact that some ESC's have a governor function, that servos the motor speed to the signal coming in -- but they still have an internal throttle command that works as above.






          share|improve this answer









          $endgroup$













          • $begingroup$
            Your Q3 response. I'm trying to understand this better. Are you saying the current is fixed and that the PWM is just shortened? (Like Transistors PWM graph) Basically the duty cycle is reduced but the current is not, but essentially this means less power is used.
            $endgroup$
            – twegner
            2 hours ago
















          3












          $begingroup$

          All answers assume you're talking about "hobby" ESCs, as used in planes, boats, cars, robots, etc.




          Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps?




          No. For the most part, the ESC draws what it draws given the motor, battery and load on the motor.



          Some of the better ESC's do have current limiting, but experience in the flying field is that if you dork the thing into the dirt at full throttle, chances are that you'll damage the electronics due to overcurrent.



          An ESC could be designed to limit current in such a way (I've designed industrial motor controllers that do), but AFAIK ESC's don't.




          Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?




          See answer to question 1.




          Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage?




          Neither. At the level of the throttle command to motor, it supplies a fixed PWM to the motor -- essentially it chops the battery voltage and hands it to the motor.



          This is complicated by the fact that some ESC's have a governor function, that servos the motor speed to the signal coming in -- but they still have an internal throttle command that works as above.






          share|improve this answer









          $endgroup$













          • $begingroup$
            Your Q3 response. I'm trying to understand this better. Are you saying the current is fixed and that the PWM is just shortened? (Like Transistors PWM graph) Basically the duty cycle is reduced but the current is not, but essentially this means less power is used.
            $endgroup$
            – twegner
            2 hours ago














          3












          3








          3





          $begingroup$

          All answers assume you're talking about "hobby" ESCs, as used in planes, boats, cars, robots, etc.




          Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps?




          No. For the most part, the ESC draws what it draws given the motor, battery and load on the motor.



          Some of the better ESC's do have current limiting, but experience in the flying field is that if you dork the thing into the dirt at full throttle, chances are that you'll damage the electronics due to overcurrent.



          An ESC could be designed to limit current in such a way (I've designed industrial motor controllers that do), but AFAIK ESC's don't.




          Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?




          See answer to question 1.




          Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage?




          Neither. At the level of the throttle command to motor, it supplies a fixed PWM to the motor -- essentially it chops the battery voltage and hands it to the motor.



          This is complicated by the fact that some ESC's have a governor function, that servos the motor speed to the signal coming in -- but they still have an internal throttle command that works as above.






          share|improve this answer









          $endgroup$



          All answers assume you're talking about "hobby" ESCs, as used in planes, boats, cars, robots, etc.




          Question 1: When an ESC is rated at 200 amps nominal and 500 amps peak is it safe to assume that the draw on the battery pack will not exceed 200 amps?




          No. For the most part, the ESC draws what it draws given the motor, battery and load on the motor.



          Some of the better ESC's do have current limiting, but experience in the flying field is that if you dork the thing into the dirt at full throttle, chances are that you'll damage the electronics due to overcurrent.



          An ESC could be designed to limit current in such a way (I've designed industrial motor controllers that do), but AFAIK ESC's don't.




          Question 2: If the motor is run indefinitely at max throttle (theoretically) will the ESC draw 200 amps from the battery continuously or less than that?




          See answer to question 1.




          Question 3: (slightly off topic) To modulate motor speed does the ESC restrict current flow or voltage?




          Neither. At the level of the throttle command to motor, it supplies a fixed PWM to the motor -- essentially it chops the battery voltage and hands it to the motor.



          This is complicated by the fact that some ESC's have a governor function, that servos the motor speed to the signal coming in -- but they still have an internal throttle command that works as above.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 4 hours ago









          TimWescottTimWescott

          7,2391416




          7,2391416












          • $begingroup$
            Your Q3 response. I'm trying to understand this better. Are you saying the current is fixed and that the PWM is just shortened? (Like Transistors PWM graph) Basically the duty cycle is reduced but the current is not, but essentially this means less power is used.
            $endgroup$
            – twegner
            2 hours ago


















          • $begingroup$
            Your Q3 response. I'm trying to understand this better. Are you saying the current is fixed and that the PWM is just shortened? (Like Transistors PWM graph) Basically the duty cycle is reduced but the current is not, but essentially this means less power is used.
            $endgroup$
            – twegner
            2 hours ago
















          $begingroup$
          Your Q3 response. I'm trying to understand this better. Are you saying the current is fixed and that the PWM is just shortened? (Like Transistors PWM graph) Basically the duty cycle is reduced but the current is not, but essentially this means less power is used.
          $endgroup$
          – twegner
          2 hours ago




          $begingroup$
          Your Q3 response. I'm trying to understand this better. Are you saying the current is fixed and that the PWM is just shortened? (Like Transistors PWM graph) Basically the duty cycle is reduced but the current is not, but essentially this means less power is used.
          $endgroup$
          – twegner
          2 hours ago











          1












          $begingroup$

          The max operating temperature or heat rise above 25'C is what limits the nominal continuous current rating. The peak is an absolute maximum which may or may not be protected and should never be exceeded, such as starting a couple of these motors below at full throttle.




          One must mind the rated peak currents to prevent damage to the electronics.




          Similarily, a motor full load current rating is defined by the same method of temperature rise above 25'C for the winding hot spots. However every market does not use the same hot spot temperature for a long useful life and if no standards are given or not temp rise is specified, you might guess they don't want you to know.



          However it is quite common to give the peak motor current as surge, start or locked rotor current. These are all the same as is simply Ohm's Law applied to the DC resistance or DCR, so Imax= V/DCR. This is typically Imax = 8 to 12 times the rated current in modern BLDC, high-efficiency DC motors.



          Here they generously rate the motor current with a 180 second limit. This would be at max internal temperature.



          enter image description here






          share|improve this answer









          $endgroup$













          • $begingroup$
            If I'm reading the Tech sheet right, they are doing P=IV, so 885.4 watts = 4.2 vdc (not 3.7) * 4 cells * 52.7 amps. I understand your locked rotor 360 amp (V/R=I) calculation. So are you saying that as soon as the rotor locks, like if the parking brake was on (just go with it), that this motor should be paired with an ESC that can handle at least 360 amps? Which is way more than the Max Current on the spec sheet indicates. Also, thanks for providing a real world example. Yours and all the other answers are beginning to clear up my muddy understanding of this.
            $endgroup$
            – twegner
            1 hour ago










          • $begingroup$
            The 885W is the motor power doing work if the batteries did not drop from a full charge at 4.2V for 120s, which seems unlikely even if they were 8P4S arrays as I believe it would drop to 3.6V at this current @ 120s. The 113 watts I calculated is DCR loss that makes the inefficiency 12.8% = 113/885W that produces heat while accelerating or braking until speed induced BEMF reduces the net voltage across the winding. So the ESC must use current feedback to regulate constant current to match this motor spec. limit. I expect ESC current-mode feedback limits torque and voltage regulates speed.
            $endgroup$
            – Sunnyskyguy EE75
            25 mins ago










          • $begingroup$
            I would expect an ESC of this caliber to have current limit control and voltage control. But I can't say for sure. AWG8= 2 mohm/m or 4mOhm/m pair
            $endgroup$
            – Sunnyskyguy EE75
            23 mins ago


















          1












          $begingroup$

          The max operating temperature or heat rise above 25'C is what limits the nominal continuous current rating. The peak is an absolute maximum which may or may not be protected and should never be exceeded, such as starting a couple of these motors below at full throttle.




          One must mind the rated peak currents to prevent damage to the electronics.




          Similarily, a motor full load current rating is defined by the same method of temperature rise above 25'C for the winding hot spots. However every market does not use the same hot spot temperature for a long useful life and if no standards are given or not temp rise is specified, you might guess they don't want you to know.



          However it is quite common to give the peak motor current as surge, start or locked rotor current. These are all the same as is simply Ohm's Law applied to the DC resistance or DCR, so Imax= V/DCR. This is typically Imax = 8 to 12 times the rated current in modern BLDC, high-efficiency DC motors.



          Here they generously rate the motor current with a 180 second limit. This would be at max internal temperature.



          enter image description here






          share|improve this answer









          $endgroup$













          • $begingroup$
            If I'm reading the Tech sheet right, they are doing P=IV, so 885.4 watts = 4.2 vdc (not 3.7) * 4 cells * 52.7 amps. I understand your locked rotor 360 amp (V/R=I) calculation. So are you saying that as soon as the rotor locks, like if the parking brake was on (just go with it), that this motor should be paired with an ESC that can handle at least 360 amps? Which is way more than the Max Current on the spec sheet indicates. Also, thanks for providing a real world example. Yours and all the other answers are beginning to clear up my muddy understanding of this.
            $endgroup$
            – twegner
            1 hour ago










          • $begingroup$
            The 885W is the motor power doing work if the batteries did not drop from a full charge at 4.2V for 120s, which seems unlikely even if they were 8P4S arrays as I believe it would drop to 3.6V at this current @ 120s. The 113 watts I calculated is DCR loss that makes the inefficiency 12.8% = 113/885W that produces heat while accelerating or braking until speed induced BEMF reduces the net voltage across the winding. So the ESC must use current feedback to regulate constant current to match this motor spec. limit. I expect ESC current-mode feedback limits torque and voltage regulates speed.
            $endgroup$
            – Sunnyskyguy EE75
            25 mins ago










          • $begingroup$
            I would expect an ESC of this caliber to have current limit control and voltage control. But I can't say for sure. AWG8= 2 mohm/m or 4mOhm/m pair
            $endgroup$
            – Sunnyskyguy EE75
            23 mins ago
















          1












          1








          1





          $begingroup$

          The max operating temperature or heat rise above 25'C is what limits the nominal continuous current rating. The peak is an absolute maximum which may or may not be protected and should never be exceeded, such as starting a couple of these motors below at full throttle.




          One must mind the rated peak currents to prevent damage to the electronics.




          Similarily, a motor full load current rating is defined by the same method of temperature rise above 25'C for the winding hot spots. However every market does not use the same hot spot temperature for a long useful life and if no standards are given or not temp rise is specified, you might guess they don't want you to know.



          However it is quite common to give the peak motor current as surge, start or locked rotor current. These are all the same as is simply Ohm's Law applied to the DC resistance or DCR, so Imax= V/DCR. This is typically Imax = 8 to 12 times the rated current in modern BLDC, high-efficiency DC motors.



          Here they generously rate the motor current with a 180 second limit. This would be at max internal temperature.



          enter image description here






          share|improve this answer









          $endgroup$



          The max operating temperature or heat rise above 25'C is what limits the nominal continuous current rating. The peak is an absolute maximum which may or may not be protected and should never be exceeded, such as starting a couple of these motors below at full throttle.




          One must mind the rated peak currents to prevent damage to the electronics.




          Similarily, a motor full load current rating is defined by the same method of temperature rise above 25'C for the winding hot spots. However every market does not use the same hot spot temperature for a long useful life and if no standards are given or not temp rise is specified, you might guess they don't want you to know.



          However it is quite common to give the peak motor current as surge, start or locked rotor current. These are all the same as is simply Ohm's Law applied to the DC resistance or DCR, so Imax= V/DCR. This is typically Imax = 8 to 12 times the rated current in modern BLDC, high-efficiency DC motors.



          Here they generously rate the motor current with a 180 second limit. This would be at max internal temperature.



          enter image description here







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 2 hours ago









          Sunnyskyguy EE75Sunnyskyguy EE75

          72.3k227103




          72.3k227103












          • $begingroup$
            If I'm reading the Tech sheet right, they are doing P=IV, so 885.4 watts = 4.2 vdc (not 3.7) * 4 cells * 52.7 amps. I understand your locked rotor 360 amp (V/R=I) calculation. So are you saying that as soon as the rotor locks, like if the parking brake was on (just go with it), that this motor should be paired with an ESC that can handle at least 360 amps? Which is way more than the Max Current on the spec sheet indicates. Also, thanks for providing a real world example. Yours and all the other answers are beginning to clear up my muddy understanding of this.
            $endgroup$
            – twegner
            1 hour ago










          • $begingroup$
            The 885W is the motor power doing work if the batteries did not drop from a full charge at 4.2V for 120s, which seems unlikely even if they were 8P4S arrays as I believe it would drop to 3.6V at this current @ 120s. The 113 watts I calculated is DCR loss that makes the inefficiency 12.8% = 113/885W that produces heat while accelerating or braking until speed induced BEMF reduces the net voltage across the winding. So the ESC must use current feedback to regulate constant current to match this motor spec. limit. I expect ESC current-mode feedback limits torque and voltage regulates speed.
            $endgroup$
            – Sunnyskyguy EE75
            25 mins ago










          • $begingroup$
            I would expect an ESC of this caliber to have current limit control and voltage control. But I can't say for sure. AWG8= 2 mohm/m or 4mOhm/m pair
            $endgroup$
            – Sunnyskyguy EE75
            23 mins ago




















          • $begingroup$
            If I'm reading the Tech sheet right, they are doing P=IV, so 885.4 watts = 4.2 vdc (not 3.7) * 4 cells * 52.7 amps. I understand your locked rotor 360 amp (V/R=I) calculation. So are you saying that as soon as the rotor locks, like if the parking brake was on (just go with it), that this motor should be paired with an ESC that can handle at least 360 amps? Which is way more than the Max Current on the spec sheet indicates. Also, thanks for providing a real world example. Yours and all the other answers are beginning to clear up my muddy understanding of this.
            $endgroup$
            – twegner
            1 hour ago










          • $begingroup$
            The 885W is the motor power doing work if the batteries did not drop from a full charge at 4.2V for 120s, which seems unlikely even if they were 8P4S arrays as I believe it would drop to 3.6V at this current @ 120s. The 113 watts I calculated is DCR loss that makes the inefficiency 12.8% = 113/885W that produces heat while accelerating or braking until speed induced BEMF reduces the net voltage across the winding. So the ESC must use current feedback to regulate constant current to match this motor spec. limit. I expect ESC current-mode feedback limits torque and voltage regulates speed.
            $endgroup$
            – Sunnyskyguy EE75
            25 mins ago










          • $begingroup$
            I would expect an ESC of this caliber to have current limit control and voltage control. But I can't say for sure. AWG8= 2 mohm/m or 4mOhm/m pair
            $endgroup$
            – Sunnyskyguy EE75
            23 mins ago


















          $begingroup$
          If I'm reading the Tech sheet right, they are doing P=IV, so 885.4 watts = 4.2 vdc (not 3.7) * 4 cells * 52.7 amps. I understand your locked rotor 360 amp (V/R=I) calculation. So are you saying that as soon as the rotor locks, like if the parking brake was on (just go with it), that this motor should be paired with an ESC that can handle at least 360 amps? Which is way more than the Max Current on the spec sheet indicates. Also, thanks for providing a real world example. Yours and all the other answers are beginning to clear up my muddy understanding of this.
          $endgroup$
          – twegner
          1 hour ago




          $begingroup$
          If I'm reading the Tech sheet right, they are doing P=IV, so 885.4 watts = 4.2 vdc (not 3.7) * 4 cells * 52.7 amps. I understand your locked rotor 360 amp (V/R=I) calculation. So are you saying that as soon as the rotor locks, like if the parking brake was on (just go with it), that this motor should be paired with an ESC that can handle at least 360 amps? Which is way more than the Max Current on the spec sheet indicates. Also, thanks for providing a real world example. Yours and all the other answers are beginning to clear up my muddy understanding of this.
          $endgroup$
          – twegner
          1 hour ago












          $begingroup$
          The 885W is the motor power doing work if the batteries did not drop from a full charge at 4.2V for 120s, which seems unlikely even if they were 8P4S arrays as I believe it would drop to 3.6V at this current @ 120s. The 113 watts I calculated is DCR loss that makes the inefficiency 12.8% = 113/885W that produces heat while accelerating or braking until speed induced BEMF reduces the net voltage across the winding. So the ESC must use current feedback to regulate constant current to match this motor spec. limit. I expect ESC current-mode feedback limits torque and voltage regulates speed.
          $endgroup$
          – Sunnyskyguy EE75
          25 mins ago




          $begingroup$
          The 885W is the motor power doing work if the batteries did not drop from a full charge at 4.2V for 120s, which seems unlikely even if they were 8P4S arrays as I believe it would drop to 3.6V at this current @ 120s. The 113 watts I calculated is DCR loss that makes the inefficiency 12.8% = 113/885W that produces heat while accelerating or braking until speed induced BEMF reduces the net voltage across the winding. So the ESC must use current feedback to regulate constant current to match this motor spec. limit. I expect ESC current-mode feedback limits torque and voltage regulates speed.
          $endgroup$
          – Sunnyskyguy EE75
          25 mins ago












          $begingroup$
          I would expect an ESC of this caliber to have current limit control and voltage control. But I can't say for sure. AWG8= 2 mohm/m or 4mOhm/m pair
          $endgroup$
          – Sunnyskyguy EE75
          23 mins ago






          $begingroup$
          I would expect an ESC of this caliber to have current limit control and voltage control. But I can't say for sure. AWG8= 2 mohm/m or 4mOhm/m pair
          $endgroup$
          – Sunnyskyguy EE75
          23 mins ago












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