Servo sizing, determining required acceleration


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    Default Servo sizing, determining required acceleration

    I'm trying to size some servos for an upcoming design and am having difficulties determining how much torque I need.

    The torque required is going to be related to the screw pitch and the force required. Since as we all know, F=ma, the force required is a function of the mass, the acceleration, as well as the cutting force. The mass is easy enough, and I think the cutting force is probably going to be negligible (or if not, there are formulas to calculate it). The problem is the acceleration. I All the motion controllers that I'm thinking of using use a trapezoidal speed profile for the motion plan. Therefore with faster acceleration it will spend more time at its cutting speed and less time ramping up and down. I'm trying to figure out how to best quantify this though so I can determine the optimal servo size.

    Has anyone done anything like this? It seems particularly import with the modern adaptive clearing/volumill/ profit mill toolpaths that are constantly changing direction. Anyone have any 'rules of thumb' for what sort of acceleration levels are optimal? I've heard Teknic will give some guidance if you buy clearpath servo's, presumably they are just using some sort of rule of thumb.

    As an aside, I was also reading the long thread on jerk here, and although it didn't seem like there were any conclusions there, it may be that increasing acceleration to high might cause worse jerk issues since the hobby controllers don't consider it.

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    Default Re: Servo sizing, determining required acceleration

    Quote Originally Posted by jaguar36 View Post
    I'm trying to size some servos for an upcoming design and am having difficulties determining how much torque I need.

    The torque required is going to be related to the screw pitch and the force required. Since as we all know, F=ma, the force required is a function of the mass, the acceleration, as well as the cutting force. The mass is easy enough, and I think the cutting force is probably going to be negligible (or if not, there are formulas to calculate it). The problem is the acceleration. I All the motion controllers that I'm thinking of using use a trapezoidal speed profile for the motion plan. Therefore with faster acceleration it will spend more time at its cutting speed and less time ramping up and down. I'm trying to figure out how to best quantify this though so I can determine the optimal servo size.

    Has anyone done anything like this? It seems particularly import with the modern adaptive clearing/volumill/ profit mill toolpaths that are constantly changing direction. Anyone have any 'rules of thumb' for what sort of acceleration levels are optimal? I've heard Teknic will give some guidance if you buy clearpath servo's, presumably they are just using some sort of rule of thumb.

    As an aside, I was also reading the long thread on jerk here, and although it didn't seem like there were any conclusions there, it may be that increasing acceleration to high might cause worse jerk issues since the hobby controllers don't consider it.
    All the major Servo manufacturers have all this information that you can download there sizing software, because there is no jerk control with most controls, then the next best thing is to use a minimum of 20Bit Encoders this will add another level of smoothness and higher acceleration response, so the higher the PPR the smoother the servo motors will be and watch the servo motor pole count more the better 8 Pole /12 Pole is normal anything less and you have cogging to deal with, You can't be serious if you are looking at ClearPath they have low Pole count and are not suitable for any real CNC machine

    Fanuc start with 10 Million PPR Encoder up to 32 Million PPR standard for high speed acceleration and to help smooth out the motion

    If you are serious with building a CNC, then you would not be using a trapezoidal profile you would be using a combo of advanced S-Curve or a control that can at least do corner speed control Eding CNC can do this and works well, TinyG hobby cnc control is using S-Curve not sure if it has everything.

    VoluMill runs quite smooth it moves at the max feed rate it can to keep the tool chip loading the same all the time

    Mactec54


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    Default Re: Servo sizing, determining required acceleration

    Hi Jag - Here's a spreadsheet to calculate torque if you are using ballscrews. In regard to accelerations that's up to you and what you want to do. Accelerations for a DIY or hobby level machine is rarely important. But if you have a large machine doing long rapids getting from place to place and its commercial then accals become really important to get the cycle times down and make $$$... If you describe your size of machine and what you want to do then people can comment. Peter

    Attached Files Attached Files


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    Default Re: Servo sizing, determining required acceleration

    Appreciate the responses!
    Quote Originally Posted by peteeng View Post
    Accelerations for a DIY or hobby level machine is rarely important.
    That seems like it means folks just generally oversize their motors.

    Quote Originally Posted by peteeng View Post
    But if you have a large machine doing long rapids getting from place to place and its commercial then accals become really important to get the cycle times down and make $$$...
    If its a long rapid, the acceleration time should be a negligible portion of the overall travel time. It seems like it would be more of a driver with a cutting cycle that is continually changing direction, think of milling a slot with an adaptive clearing tool path, or thread milling.

    I suppose I need to come up with a couple representative toolpaths and figure out how much accelerations change the run time.



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    Default Re: Servo sizing, determining required acceleration

    Quote Originally Posted by jaguar36 View Post
    Appreciate the responses!

    That seems like it means folks just generally oversize their motors.


    If its a long rapid, the acceleration time should be a negligible portion of the overall travel time. It seems like it would be more of a driver with a cutting cycle that is continually changing direction, think of milling a slot with an adaptive clearing tool path, or thread milling.

    I suppose I need to come up with a couple representative toolpaths and figure out how much accelerations change the run time.
    Thread milling can be done with any control, no matter what type of machine and control you are using, adaptive does not matter either as most adaptive tool paths are only roughing cuts and are finished with a regular cleanup cut.

    Here is a machine that is using quality servo sized for the machine and it can run at 2500 IPM and cut at 500 IPM Mach3 is the machine control you can see the Build

    Here https://www.cnczone.com/forums/cnc-w...ediculous.html



    Mactec54


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    Default Re: Servo sizing, determining required acceleration

    Quote Originally Posted by mactec54 View Post
    Thread milling can be done with any control, no matter what type of machine and control you are using, adaptive does not matter either as most adaptive tool paths are only roughing cuts and are finished with a regular cleanup cut.
    I'm not sure what you're getting at here. I'm not talking about the control, talking about the required accelerations. As a machine is cutting a curve the axis are continually accelerating. The sharper the curve the higher the accelerations. Machining an outside corner the velocity change would ideally be instantaneous, which would mean infinite acceleration. Ignoring things like rigidity, your servo's power is going to drive how close to that ideal you can get. That's going to add to your machining time. Adaptive type toolpaths have a ton more direction changes, if your servo's can't keep up with those accelerations you're going to see a pretty big hit in machining time.

    Look at the velocity profile of two segments of a tool path:
    Code:
    /*    BLOCK VELOCITY PROFILE DEFINITION 
              __________________________
             /|                        |\     _________________         ^
            / |                        | \   /|               |\        |
           /  |                        |  \ / |               | \       s
          /   |                        |   |  |               |  \      p
         /    |                        |   |  |               |   \     e
        +-----+------------------------+---+--+---------------+----+    e
        |               BLOCK 1            ^      BLOCK 2          |    d
    That steeper the slope, the higher the acceleration, and the less time that is wasted not being at desired cut speed.

    So what I'm trying to figure out is how your maximum acceleration rate (aka how big your servos are) effects machining time. I imagine its probably pretty non-linear as once you are ability to hit the required acceleration for a give curve radius, having more isn't going to speed things up at all.

    (And yes I'm assuming an infinitely stiff frame and a perfect controller)



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    Default Re: Servo sizing, determining required acceleration

    Quote Originally Posted by jaguar36 View Post
    I'm not sure what you're getting at here. I'm not talking about the control, talking about the required accelerations. As a machine is cutting a curve the axis are continually accelerating. The sharper the curve the higher the accelerations. Machining an outside corner the velocity change would ideally be instantaneous, which would mean infinite acceleration. Ignoring things like rigidity, your servo's power is going to drive how close to that ideal you can get. That's going to add to your machining time. Adaptive type toolpaths have a ton more direction changes, if your servo's can't keep up with those accelerations you're going to see a pretty big hit in machining time.

    Look at the velocity profile of two segments of a tool path:
    Code:
    /*    BLOCK VELOCITY PROFILE DEFINITION 
              __________________________
             /|                        |\     _________________         ^
            / |                        | \   /|               |\        |
           /  |                        |  \ / |               | \       s
          /   |                        |   |  |               |  \      p
         /    |                        |   |  |               |   \     e
        +-----+------------------------+---+--+---------------+----+    e
        |               BLOCK 1            ^      BLOCK 2          |    d
    That steeper the slope, the higher the acceleration, and the less time that is wasted not being at desired cut speed.

    So what I'm trying to figure out is how your maximum acceleration rate (aka how big your servos are) effects machining time. I imagine its probably pretty non-linear as once you are ability to hit the required acceleration for a give curve radius, having more isn't going to speed things up at all.

    (And yes I'm assuming an infinitely stiff frame and a perfect controller)
    Your head is in the clouds somewhere, the Control is everything to do with how the machine performs and does the tasks you are posting about, the motor can't accelerate unless the control gives it the instruction to do so

    Like I said, you select your servo for the work it has to do, there is good software for doing this, go to the Yaskawa site and you will find some good servo sizing software, its a simple process, not all servo are created equal if you want performance then you have to pay to get there, this means control and servo system

    Your velocity example shows the perfect Jerk movement that you were trying to avoid

    Servo sizing is important, if your control can't output the instruction to the drives then you are not going to get the desired performance from the servos, as the performance is only going to match what the control can do.

    As for corner rounding, I gave you a control which has full lookahead with corner rounding control Eding CNC does this, it controls the corner speed to maintain the same chip load as if you were doing a straight cut, this is also adjustable on the fly, in their control, there are other controls that do this

    My example was to show you that even Mach3 plus Smooth Stepper can control a machine at highspeed speed with minimal jerk plus 3D highspeed machining

    When it comes down to what you really want to build and what you can build.

    If you can build a machine that is even half as fast as what I just posted, you will be doing very well. speed costs so if you don't plan on spending lots of money, then this whole exercise is a waste of time.

    Have you built your machine or is this just a dream build, you can't size the servos unless you know your machine specs you can't even guess your servo motor size, for sizing you need to use software that you can download, here is a series of videos you can watch from Yaskawa
    https://www.mitsubishielectric.com/f...zer/index.html



    Mactec54


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    Default Re: Servo sizing, determining required acceleration

    Hi Jag - Designing a general purpose machine with no particular operational specification is nearly impossible. You need to nail down some specs to get your answers. They (the answers) become self evident once operations are defined. If you have a specific work cycle with a specific machine this becomes easy to figure out. But that's probably not the case here. Otherwise look at commercial machines that do what you want to do and use them as a basis. Increasing acceleration of a machine is easy, bigger motors lighter parts. This approach makes cost increase exponentially though. Since your interested in high accels pick 0.5g and see how it goes. Peter



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    Default Re: Servo sizing, determining required acceleration

    Hi,
    I built a mill recently using 750W servos with a rated torque of 2.4Nm, rated speed of 3000rpm, quite normal spec for servos of that size.

    I have used 32mm diameter ballscrews of 5mm pitch. 32mm is probably a bit outsize for my purposes but its what I could find at best cost.
    The pitch is such that the screws have to spin fast to get fast rapids, 3000rpm for 15m/min, but I could just not pass up these screws at the price.

    When I did the acceleration calculation I found the rotational inertia of the ballscrew is about 80% of the total inertia, the rotational inertia of the armature of the
    servo was 12.5%, and the linear momentum of the axis (115 kg of cast iron, plus vice and workpiece for 150kg total axis weight) was only 7.5% of the total.

    It turns out the inertia of a ballscrew is proportional to the fourth power of diameter and the second power of pitch. The real take-away is be very careful
    when specifying the rotating components, its very easy to overlook how much their rotational inertia determines the overall acceleration of the machine.

    As it turns out using the combination I have listed that I get 0.27g acceleration using rated torque. Its much, MUCH more than I've ever had before, and find that it follows
    toolpaths very well. For most normal work I limit the acceleration to 0.15g and am very happy with it. I doubt it would be enough for true production speed.....but then
    I didn't pay 'production' money either.

    Craig



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    Default Re: Servo sizing, determining required acceleration

    Quote Originally Posted by mactec54 View Post
    Like I said, you select your servo for the work it has to do, there is good software for doing this, go to the Yaskawa site and you will find some good servo sizing software, its a simple process
    I'm not sure if you've used that software, but it requires the desired acceleration as an input. Its really just a more advanced version of pete's spreadsheet combined with a lookup of their servo catalog. (Both of which are just the full solution of F=ma and t=mr^2a). To do either you still need to know the acceleration.

    The control is only going to have a minor impact on the answer. Sure the farther ahead it looks ahead, smoothing and different velcotiy/acceleration profiles are going to change the answer slightly, but at the end of the day its still gotta accelerate the mass up to the feed speed. The higher the acceleration, the quicker it can get to that feed speed.

    As for what I am trying to do, I'm rebuilding my cnc and am trying to optimize the new build. The question is how much money to devote to servos vs other components, so I don't want to oversize them. Primary goal is increasing MRR.



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    Default Re: Servo sizing, determining required acceleration

    Ok, so to actually calculate how acceleration affects machine time, I generated some very simplistic G-Code to mill a small, square pocket. Simple traditional machining, no fancy adaptive/volumill toolpaths to keep it simple for now. I then calculated an estimated machining time, based on different acceleration levels. For a first cut I am only looking at X-Y motion, ignoring any smoothing, using a trapezoidal motion profile and am doing some hacks to keep the math easy. Its far from perfect, but I think its a good starting point.

    So for this simple g-code, here is a graph of the acceleration level vs machine time:
    Servo sizing, determining required acceleration-graph-png
    As you would imagine its a nonlinear curve that flattens out as you get to higher acceleration levels and the machine is spending most of its time limited by feed rate rather than accelerations. It seems that the sweet spot is probably around 0.2-0.3g's and going beyond that has pretty diminished returns.

    Next, I'd like to do the same thing for a couple of other toolpaths. This one is a small part which is going to accentuate the effect of acceleration compared with a large part where it has lots of long straight moves. I'd also like to look at some more advanced paths that have near constant directional changes.

    Attached Thumbnails Attached Thumbnails Servo sizing, determining required acceleration-graph-png  


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    Default Re: Servo sizing, determining required acceleration

    Hi Jag - To improve MRR you also have to address the machine, particularly its stiffness. Some images of your machine and its current duty and typical feeds speeds etc would help the conversation. Plus do you want to double MRR? Triple it? Peter



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    Default Re: Servo sizing, determining required acceleration

    Quote Originally Posted by peteeng View Post
    Hi Jag - To improve MRR you also have to address the machine, particularly its stiffness. Some images of your machine and its current duty and typical feeds speeds etc would help the conversation. Plus do you want to double MRR? Triple it? Peter
    Yep, I'm addressing that as well. Thats why I was asking about rigidity last week. Particularly with how expensive raw materials have gotten, I want to to make sure my servo's and frame are matched appropriately (Other components aren't changing). No point in having a frame so beefy that the servos aren't strong enough to take advantage of it.



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    Default Re: Servo sizing, determining required acceleration

    Hi Jag - well that's one way of looking at it for roughing but then a machine has to be stiff and damp to do a fine finish and the motor loads are light.... but it takes a very stiff machine to do a fine cut. Peter



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    Default Re: Servo sizing, determining required acceleration

    Been digging into this a bit more I've ran through some more complicated tool paths and as expected I am finding wide variations in how much acceleration rates change runtime. Some do seem highly dependent on acceleration, while others are hardly effected.

    I've also been looking at more 'real' VMCs and found that some companies, particularly DMG Mori, do provide acceleration specs on their machines. I was surprised to see that they are lower than I expected. The top end machines have a 1.0g acceleration, while most of them look like around 0.5g. Their 'basic' machines only show 0.3g. I imagine the mass of their table and spindle are such that 1g acceleration takes a ridiculous amount of power. Slinging around ~2000lbs of table and workpiece up to 4,000 ipm is gonna take like 10,000watts.

    Therefore I think something like 0.1g is probably reasonable for a home-built machine. I'll probably still shoot for at least the capability to do more like 0.2g or 0.25g though.



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    Default Re: Servo sizing, determining required acceleration

    Hi,
    my machine is capable of 0.27g using the rated torque of the servos, and 0.75g at overload rating.

    In practice I find that even 0.25g is very aggressive. The table of my mill is 115kg, so the axis weight including the ballscrew, servo, vice and workpiece is about 150kg. I find that at 0.25g
    the machine tries to lurch around, its not the end of world, but it does move. I have found that reducing the acceleration to 0.15g still results in good toolpath following and very acceptable cycle times
    and not lurch around so dramatically, just a good compromise.

    Therefore I think something like 0.1g is probably reasonable for a home-built machine. I'll probably still shoot for at least the capability to do more like 0.2g or 0.25g though.
    This is exactly where I ended up and am happy with the result. While I was doing the initial design I had not done the detailed acceleration calculation, so I was lucky that I ended up where I did.
    The real surprise was that its the rotating components that constitute a little over 90% of the total inertia of my machine. I had thought that the axis weight would dominate, but the calculation
    shows otherwise.

    I would recommend that you study the inertia equation until you thoroughly understand the trade-offs and the dominating terms. Once you do, you will design a machine to do what you want
    as opposed to my approach, where there was a certain degree of luck that I ended up with a good result.

    Craig



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    Default Re: Servo sizing, determining required acceleration

    Quote Originally Posted by joeavaerage View Post
    Hi,
    my machine is capable of 0.27g using the rated torque of the servos, and 0.75g at overload rating.

    In practice I find that even 0.25g is very aggressive. The table of my mill is 115kg, so the axis weight including the ballscrew, servo, vice and workpiece is about 150kg. I find that at 0.25g
    the machine tries to lurch around, its not the end of world, but it does move. I have found that reducing the acceleration to 0.15g still results in good toolpath following and very acceptable cycle times
    and not lurch around so dramatically, just a good compromise.
    When you say lurch around, do you mean the whole machine moves? That's interesting and not something I've really considered. I've only been looking at the relationship between the cutter and the workpiece. I haven't really considered the support structure for the whole machine to the ground.



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    Default Re: Servo sizing, determining required acceleration

    Quote Originally Posted by jaguar36 View Post
    When you say lurch around, do you mean the whole machine moves? That's interesting and not something I've really considered. I've only been looking at the relationship between the cutter and the workpiece. I haven't really considered the support structure for the whole machine to the ground.
    Yes, that is the normal thing that happens is the machine either flexes or moves around if the base / machine is not solid enough, the machine I posted about in post 5 had concreate feet pads that were fastened to the concreate floor to stop it moving around when accelerating and decelerating, the inertia could move that 3ton machine like it was nothing,

    Mactec54


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    Default Re: Servo sizing, determining required acceleration

    Hi,
    my machine and the table on which it stands is about 800kg. If I have the X axis, 150kg, accelerating at 0.25g then the remainder of the machine will accelerate in the
    the other direction. Newtons Law.

    150 x 0.25 = (800-150) x A, where A is the acceleration of the machine in the other direction,therefore:

    A=0.058g or 580mm/s2 which is quite considerable.

    My machine is on heavy duty castoring wheels so I can move it about the workshop, which obviously means will allow the whole machine to move under acceleration.
    If it had solid feet on the table it would move less, but the general principle still applies, whatever acceleration you apply to your X axis will result in an acceleration
    of the machine in the opposite direction.

    Craig



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    Default Re: Servo sizing, determining required acceleration

    [QUOTE=joeavaerage;2512594]
    If it had solid feet on the table it would move less, but the general principle still applies, whatever acceleration you apply to your X axis will result in an acceleration
    of the machine in the opposite direction./QUOTE]

    Well usually a machine is anchored into the ground, so its only accelerating due to the flex in the frame. (And perhaps slip of the feet if its not bolted down).

    For my machine I'm assuming that the mass of the axis being accelerated is many times less than the machine mass, such that it doesn't really matter. With yours being almost 20% the mass of the machine, I can see why that would be an issue. Particularly if the machine is on casters.



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Servo sizing, determining required acceleration

Servo sizing, determining required acceleration