G
In late April I posted questions about the importance of motor to load inertia ratio. I received numerous responses & sincerely thank
everyone who contributed. I would like to offer a summary of those responses, my belief in the matter, and finally end with a question (or two).
It seems everybody agreed on a couple themes:
1) Bandwidth (system response) is a function of system inertia, load to motor inertia ratio, and the drivetrain/mechanics.
2) A 1:1 ratio is ideal.
3) A system's bandwidth can be no better than the
mechanical bandwidth the motor is attached to.
4) If an infinitely stiff system is coupled to a motor and it does not require a high degree of responsiveness, it can handle a higher load
to rotor inertia ratio.
5) The inertia reflected to the motor is critical for proper sizing of the motor.
6) Most loads are not infinitely stiff. Stiffness can be a very subjective/relative term; ie, what one person considers stiff, another
may consider sloppy.
7) When elements are added to reduce reflected inertia (gearheads, belt & pullies, etc.), the stiffness of the system is reduced. Therefore these elements reduce the maximum bandwidth of the system.
8) Higher inertia mismatches are harder to properly tune. When they are tuned properly, the gains are lower than they would be with a 1:1 ratio.
9) As our servo systems get higher in performance, a mechanical system's resonant frequency will play more of a factor.
Many manufacturers have begun introducing low-pass & notch filters to address the possibility of instability caused by exciting resonant frequencies.
There were a couple of comments that I feel were incorrect:
1) Inertia ratios that are not equal to 1:1 make tuning a nightmare.
The desired response dictates how tightly the system has to be tuned. One could literally spend hours or days on tuning a system (I've done it). Many times however, default gains give the desired response. The application dictates how difficult tuning is.
2) Inertia isn't dependant upon where devices are mounted, it's how they are shaped.
The shape is critical to the inertia of a load, but so is the position of the load. The position is also used to calculate the reflected inertia. The parallel axis theorem is used to reflect inertias that are rotating in a different plane than the motor's shaft.
3) Elements added to reduce reflected inertia (gearheads, belt & pullies, etc.) dramatically reduce the systems performance.
When they are added, slop is introduced & therefore the system repeatability, response, & longevity had been sacrificed.
Many precision gearheads that are available have efficiencies higher than 95% & backlash less than 2 arc-minutes. Certainly
using a device such as this will be completely different than using a belt & pulley.
4) The only reason inertia is important is to size the motor.
That's definitely one aspect of inertia. However, there are several other reasons. Regen calculations and how responsive the system can be are two obvious factors.
5) Inertia ratio is a guideline that says a motor's design torque is probably capable of driving an assembly of rotating elements whose load inertia is "x" times the motor's rotor inertia.
This can't be used reliably, because motors have different design characterstics. It is very common for manufacturers to have a high inertia motor & a low inertia motor that produce similar torques. I can't recall ever seeing a manufacture spec out an inertia ratio that relates to the torque it can produce. I have
seen it spec'd for regen purposes however.
There were a couple of comments that were only made by one person, but I found them to be extremely valuable & agree completely:
1) A motor's bandwidth is a function of the motor's torque to motor's inertia ratio. A higher ratio means higher bandwidth.
Therefore motors w/ a higher bandwidth can tolerate higher load to rotor inertia ratio with good response.
2) The goal of tuning is maximize responsiveness & minimize instability
3) The ideal solution for tuning would be to include more parameters in the PID loop structure. If we could accurately determine a particular element's characteristics (stiffness as an example), it would allow us to better model the system. The only draw back is, the more complex we make a PID loop the longer it would take to tune. We have seen more "tools" added in for tuning however: feedforward, integral limits, system bandwidth, etc.
My take on the matter is as follows:
Inertia ratio is important. However, the importance of the ratio is relative to how responsive the system needs to be and how stiff the system is. Obviously a directly driven load could respond faster w/ a 10:1 ratio than a chain & sprocket could.
Inertia ratio should be considered when extremely high accelerations & decelerations are necessary; settling times & regen could comprimise such a system. Guidelines are there for a reason, but there are exceptions to them. 10:1 for servos
& 5:1 for steppers are the maximum ratios that I've always gone by and I see no reason to change unless that range can't be achieved.
One question still hasn't been answered to my satisfaction: Why do some manufacturers offer inertia slugs on motors?
There were several attempts to address the question. I think we all agree that these slugs do increase the system's inertia (motor inertia plus load inertia). I think most of us would also agree that this increase in inertia lowers the system's bandwidth. The disagreement still remains though, does this lower the motor to load inertia ratio? In other words, is the slug part of the motor inertia? The manufacturers that offer these slugs certainly state that it is. Those of you that responded were split on this one.
Personally, I do not believe it does add to the motor's rotor inertia. The motor's rotor inertia is just what it says......ROTOR INERTIA. The slug's coupling may be infinitely stiff, but it is
still a load and therefore not part of the motor's rotor.
Please let me know what you guys think. Does a slug help? If so, why? If not, why offer it?
Regards,
Guy H. Looney
Sales Engineer
Regan Controls, Inc.
475 Metroplex Dr.
Suite 212
Nashville, TN 37211
phone: (615) 333-1940
fax: (615) 333-1941
email: [email protected]
web: www.regancontrols.com
everyone who contributed. I would like to offer a summary of those responses, my belief in the matter, and finally end with a question (or two).
It seems everybody agreed on a couple themes:
1) Bandwidth (system response) is a function of system inertia, load to motor inertia ratio, and the drivetrain/mechanics.
2) A 1:1 ratio is ideal.
3) A system's bandwidth can be no better than the
mechanical bandwidth the motor is attached to.
4) If an infinitely stiff system is coupled to a motor and it does not require a high degree of responsiveness, it can handle a higher load
to rotor inertia ratio.
5) The inertia reflected to the motor is critical for proper sizing of the motor.
6) Most loads are not infinitely stiff. Stiffness can be a very subjective/relative term; ie, what one person considers stiff, another
may consider sloppy.
7) When elements are added to reduce reflected inertia (gearheads, belt & pullies, etc.), the stiffness of the system is reduced. Therefore these elements reduce the maximum bandwidth of the system.
8) Higher inertia mismatches are harder to properly tune. When they are tuned properly, the gains are lower than they would be with a 1:1 ratio.
9) As our servo systems get higher in performance, a mechanical system's resonant frequency will play more of a factor.
Many manufacturers have begun introducing low-pass & notch filters to address the possibility of instability caused by exciting resonant frequencies.
There were a couple of comments that I feel were incorrect:
1) Inertia ratios that are not equal to 1:1 make tuning a nightmare.
The desired response dictates how tightly the system has to be tuned. One could literally spend hours or days on tuning a system (I've done it). Many times however, default gains give the desired response. The application dictates how difficult tuning is.
2) Inertia isn't dependant upon where devices are mounted, it's how they are shaped.
The shape is critical to the inertia of a load, but so is the position of the load. The position is also used to calculate the reflected inertia. The parallel axis theorem is used to reflect inertias that are rotating in a different plane than the motor's shaft.
3) Elements added to reduce reflected inertia (gearheads, belt & pullies, etc.) dramatically reduce the systems performance.
When they are added, slop is introduced & therefore the system repeatability, response, & longevity had been sacrificed.
Many precision gearheads that are available have efficiencies higher than 95% & backlash less than 2 arc-minutes. Certainly
using a device such as this will be completely different than using a belt & pulley.
4) The only reason inertia is important is to size the motor.
That's definitely one aspect of inertia. However, there are several other reasons. Regen calculations and how responsive the system can be are two obvious factors.
5) Inertia ratio is a guideline that says a motor's design torque is probably capable of driving an assembly of rotating elements whose load inertia is "x" times the motor's rotor inertia.
This can't be used reliably, because motors have different design characterstics. It is very common for manufacturers to have a high inertia motor & a low inertia motor that produce similar torques. I can't recall ever seeing a manufacture spec out an inertia ratio that relates to the torque it can produce. I have
seen it spec'd for regen purposes however.
There were a couple of comments that were only made by one person, but I found them to be extremely valuable & agree completely:
1) A motor's bandwidth is a function of the motor's torque to motor's inertia ratio. A higher ratio means higher bandwidth.
Therefore motors w/ a higher bandwidth can tolerate higher load to rotor inertia ratio with good response.
2) The goal of tuning is maximize responsiveness & minimize instability
3) The ideal solution for tuning would be to include more parameters in the PID loop structure. If we could accurately determine a particular element's characteristics (stiffness as an example), it would allow us to better model the system. The only draw back is, the more complex we make a PID loop the longer it would take to tune. We have seen more "tools" added in for tuning however: feedforward, integral limits, system bandwidth, etc.
My take on the matter is as follows:
Inertia ratio is important. However, the importance of the ratio is relative to how responsive the system needs to be and how stiff the system is. Obviously a directly driven load could respond faster w/ a 10:1 ratio than a chain & sprocket could.
Inertia ratio should be considered when extremely high accelerations & decelerations are necessary; settling times & regen could comprimise such a system. Guidelines are there for a reason, but there are exceptions to them. 10:1 for servos
& 5:1 for steppers are the maximum ratios that I've always gone by and I see no reason to change unless that range can't be achieved.
One question still hasn't been answered to my satisfaction: Why do some manufacturers offer inertia slugs on motors?
There were several attempts to address the question. I think we all agree that these slugs do increase the system's inertia (motor inertia plus load inertia). I think most of us would also agree that this increase in inertia lowers the system's bandwidth. The disagreement still remains though, does this lower the motor to load inertia ratio? In other words, is the slug part of the motor inertia? The manufacturers that offer these slugs certainly state that it is. Those of you that responded were split on this one.
Personally, I do not believe it does add to the motor's rotor inertia. The motor's rotor inertia is just what it says......ROTOR INERTIA. The slug's coupling may be infinitely stiff, but it is
still a load and therefore not part of the motor's rotor.
Please let me know what you guys think. Does a slug help? If so, why? If not, why offer it?
Regards,
Guy H. Looney
Sales Engineer
Regan Controls, Inc.
475 Metroplex Dr.
Suite 212
Nashville, TN 37211
phone: (615) 333-1940
fax: (615) 333-1941
email: [email protected]
web: www.regancontrols.com