Thanks. Using a toroid as an example flywheel understanding that it's rotational inertia is larger than a flat sided flywheel let's use a 4" diameter donut with the center at 12" giving us a 24" diameter donut. And in my example I'm saying it weighs 300 lbs. So the formula from the first wiki page gives me a rotational inertia of 214.6. After that's it's pretty standard physics I think? Our time is 5 seconds and target velocity is 5.24 radians per second resulting in an acceleration of 1.05 radians per second per second. If Our force (Torque) = ma then it's 314 ft-lbs but recall I said the reduction drive was 32:1 so that works out to 9.8 ft.lbs or 1885 oz.in at 1600 RPM. Not really within the realm of a stepper motor but DC/AC Servo can do that. A quick look on the net suggests a 3.8kW motor would do the job.
> -----Original Message----- > From: Chris Albertson [mailto:albertson.ch...@gmail.com] > Sent: June-16-22 10:29 PM > To: Enhanced Machine Controller (EMC) > Subject: Re: [Emc-users] Acceleration question. > > OK, here is the problem. > > 1) we can not know the distance from the mass to the center of the wheel. > Mass is always distributed, It all cannot be at the same radius. S We > define a concept called "moment of Inertia" that tell us how much a > rotating body resists changes in rotation speed. Your first step is to > compute the wheel's moment of inertia. If the wheel has a simple shape > then there are formulas you can use. If the wheel has a complex shape > then it is more work to find the moment. > This article explains what moment of inertia is and shows how to calculate > it for various shapes > <https://en.wikipedia.org/wiki/List_of_moments_of_inertia> > https://en.wikipedia.org/wiki/List_of_moments_of_inertia > > 2) now that you know how much your wheel resists changes in rotational > speed you can compute how much torque is required to accelerate the wheel. > torque = (moment of inertia) x (rotational acceleration) > This is just like the better known "f = ma" that works for linear motion. > See here for more > <https://en.wikipedia.org/wiki/Angular_acceleration#Relation_to_torque> > https://en.wikipedia.org/wiki/Angular_acceleration#Relation_to_torque > > 3) so now you know the torque required. You need to find a mother that has > this torque at the required RPM. Moros produce less toque at higher > speedSo you can not use the motor's rated torque at stall (zero RPM) you > must look at the torque vs. RPM graph > > The trick is to watch the units. Keep the rotation units in radians per > second and acceleration in read/second squared > > > > On Thu, Jun 16, 2022 at 7:50 PM John Dammeyer < > <mailto:jo...@autoartisans.com> jo...@autoartisans.com> > wrote: > > > I'm not sure you are answering my question. > > > > Let me put it another way. Assume you know the distance of the mass from > > the center. And assume it's not possible to do any testing at this time. > > But you know the dimensions. > > > > Once the wheel is spinning it doesn't take a lot to keep it spinning. > > Friction and air resistance mostly unless it's also being asked to > > translate the spin back to some sort of work. > > > > Then let's say the need changes and now 2.5 seconds are required to bring > > it up to speed instead of 5 seconds. What size motor then? > > > > > > > > > -----Original Message----- > > > From: Chris Albertson [ <mailto:albertson.ch...@gmail.com> > > > mailto:albertson.ch...@gmail.com] > > > Sent: June-16-22 6:56 PM > > > To: Enhanced Machine Controller (EMC) > > > Subject: Re: [Emc-users] Acceleration question. > > > > > > Knowing the mass of the wheel is not enough, you need to know how far the > > > mas is from the center of rotation. They call this "Moment of inertia" > > > There are ways of calculating this for simple wheel shapes like a plain > > > disk but for anything else you are best off if you just measure it. > > > > > > The simplest way you can find your answer with not much math is to wrap a > > > string around the wheel and attach a weight to the string and time how > > long > > > it takes for the weight to fall some distance. The weight will apply a > > > torque to the wheel equal to the weight times the radius of whatever you > > > wrapped the string around. > > > > > > Make the weight bigger until it works, then buy a motor that can supply > > > that torque, plus a bit more. > > > > > > if you really want to calculate the moment, perhaps because you have not > > > yet built the wheel then remember that the wheels moment is equal to the > > > some of the moments of the parts of the wheel (the parts add up) So > > divide > > > the wheel into (say) a rim, a thin disk and a hub find the moment of each > > > and then add them. > > > > > > But the string experiment is easier. > > > > > > On Thu, Jun 16, 2022 at 5:53 PM John Dammeyer < > > > <mailto:jo...@autoartisans.com> jo...@autoartisans.com> > > > wrote: > > > > > > > OK. I realize this will be a dumb question but please bear with me > > > > especially since I've included the ability to accelerate in my > > Electronic > > > > Lead Screw project. > > > > > > > > A friend and I were discussing bringing a 300 pound flywheel up to > > speed. > > > > Vz=0 RPM, Vf=50 RPM. Reduction drive to the flywheel shaft is 32:1 so > > > > final speed of motor is 1600 RPM. > > > > > > > > Assume we're happy with 5 seconds to accelerate for Tz to Tf. Motor > > > > voltage is 12V. > > > > > > > > We have the mass, we have the velocity, we have the time and motor > > > > voltage. The question is what are the calculations to determine how > > much > > > > current the motor will require to create this acceleration? Assuming > > of > > > > course the motor is 100% efficient. > > > > > > > > We're getting all confused with F=ma and 1/2*a*t^2 etc. > > > > > > > > What size motor is actually needed to do this? > > > > > > > > Thanks. > > > > John > > > > > > > > "ELS! Nothing else works as well for your Lathe" > > > > Automation Artisans Inc. > > > > www dot autoartisans dot com > > > > > > > > > > > > _______________________________________________ > > > > Emc-users mailing list > > > > <mailto:Emc-users@lists.sourceforge.net> > > > > Emc-users@lists.sourceforge.net > > > > <https://lists.sourceforge.net/lists/listinfo/emc-users> > > > > https://lists.sourceforge.net/lists/listinfo/emc-users > > > > > > > > > > > > > -- > > > > > > Chris Albertson > > > Redondo Beach, California > > > > > > _______________________________________________ > > > Emc-users mailing list > > > <mailto:Emc-users@lists.sourceforge.net> Emc-users@lists.sourceforge.net > > > <https://lists.sourceforge.net/lists/listinfo/emc-users> > > > https://lists.sourceforge.net/lists/listinfo/emc-users > > > > > > > > _______________________________________________ > > Emc-users mailing list > > <mailto:Emc-users@lists.sourceforge.net> Emc-users@lists.sourceforge.net > > <https://lists.sourceforge.net/lists/listinfo/emc-users> > > https://lists.sourceforge.net/lists/listinfo/emc-users > > > > > -- > > Chris Albertson > Redondo Beach, California > > _______________________________________________ > Emc-users mailing list > <mailto:Emc-users@lists.sourceforge.net> Emc-users@lists.sourceforge.net > <https://lists.sourceforge.net/lists/listinfo/emc-users> > https://lists.sourceforge.net/lists/listinfo/emc-users
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