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# Ultimate Benchtop CNC Mini Mill Part 5: Acceleration and Cutting Forces

*This is the fifth installment of our Ultimate Benchtop CNC Mini Mill series. The series is dedicated to helping DIY CNC’ers work through the design considerations and tradeoffs for their CNC Mill projects. Here are the installments so far:*

*Part 2: CNC Mechanicals (Ballscrews and Such)*

*Part 3: Close Loop vs Open Loops (Servos vs Steppers)*

*We’re working towards Motor Sizing, but before we can do that properly, we have one more aspect we need to understand, and that is the role of acceleration and cutting forces on motor torque requirements.*

The last thing we want to consider before I wrap up axis motor selection in installment 6 is the role of acceleration and cutting forces. To put it simply, the faster you want to accelerate the axes of your machine, the more motor torque will be needed. Similarly, the bigger the cuts you want to make, the more cutting forces will be generated, and once again, the bigger the axis stepper or servo you will need. I’ve put together an Excel Spreadsheet you can download to play with these various factors (just click the link to download). There’s a lot of math there, and you’re welcome to go through it to try to understand how it works, but following all that math is not a requirement to make use of the spreadsheet.

The various inputs used by the spreadsheet are marked with Blue text. The rest is black and bold and should not be edited unless you understand and want to change the math involved. Let’s take a look at the inputs:

**Motor Sizing Inputs…**

If you like, download the spreadsheet and follow along.

**Motor Sizing Worksheet Inputs**

Let’s have a look at each input and describe what it means:

– Table Weight: How heavy is the axis being moved? Is there a saddle moving as well? If so, include the weight of the saddle.

– Part and Fixture Weight: Just moving an empty table on the mill is not very helpful. Put in an allowance for fixtures such as vises and your workpiece. I put a big number in because that’s the weight my mill’s table is rated for.

– Friction Coefficient of the Ways: This is a plug-in. Just use 0.2 for box or dovetail ways. If your machine has Turcite (Tormach’s and many others do, for example), it lowers the friction. If you are using linear ways with ball bearings, the coefficient is very low indeed.

– Max. Thrust Force: This is the amount of cutting force used. You can get this from our G-Wizard Calculator. The 428 lbs I am using is based on a beefy 3″ Face Mill cut–they use a lot of power. This one is a 7.5 HP cut. I just wanted to give something that would definitely be an upper bound for a hobby machine.

– Max Linear Speed: What are your rapids?

– Max Cutting Speed: Max speed for accurate cutting is often less than rapids.

– Ballscrew Lead: How far does your ballscrew move the axis per revolution?

– Drive Ratio: Are you running timing pulleys? How many revolutions does the motor make to turn the ballscrew 1 revolution?

– Diameter: What’s the diameter of your ballscrew? That 1.5″ is really big for a hobby ballscrew. Yours is likely much smaller.

– Length: How long is your ballscrew?

– Efficiency: Ballscrews are typically 85-90% efficient.

– Resolution: How many steps per revolution does your motor offer? Use encoder resolution for servos and steps/revolution for stepper motors. 4000 is definitely a servo number.

– Target Motor Torque: Thinking of a particular motor? Put it’s torque in here and we’ll see how well it’ll work for your axes.

– Travel Distance: (Just off bottom of screen shot) To calculate reasonable acceleration values needed, we look at a travel distance and figure out how much we need to accelerate if we spend no more than 25% of that distance accelerating to your rapids speed. This gives some idea of what minimum acceleration makes sense for your machine. Too little acceleration and the rapids won’t matter because the machine never gets going that fast.

**Results**

Having keyed in all of those inputs, you’re ready to see the results. A lot of intermediate values are computed that can be safely ignored by most.

This is where it gets interesting. We get to see what the motor rpms will be at rapids and cutting speeds: 3000 for rapids and 1200 for cutting. Recall from our earlier articles that 3000 is a pretty high rpm for a stepper–it’ll likely have fallen off in torque there. This makes this more likely a servo application.

More interesting is the bottom line acceleration value. This combination, with an 800 oz-in motor, can accelerate at a rate of 80.8 inches per second squared. Is that good or bad? Let’s look at the acceleration worksheet just above:

Recall that what this part of the spreadsheet is doing is taking your travels (24 inches in the example) together with your rapids (400 IPM from the original assumptions) and determining how much acceleration is needed to reach the rapids speed in 25% of the travels. BTW, what that means is that from a stop, if you’re moving less than 25% of full travels, you’ll never get the machine up to its maximum rapids. Acceleration is one of the most important determinants of machine performance. It’s actually more important than the rapids because you may never get up to full rapids on many jobs–the distances are just too short and the acceleration capability of many machines is too low.

In this case, we have a predicted acceleration capability of 80.8 in/sec^2 and a desired acceleration rate of 92.6 in/sec^2. We’re not doing terribly badly, at least in the ballpark, but we can clearly see we need stronger axis motors to achieve the desired performance. About 900 oz-in would do it. Suppose we have linear slides instead of box or dovetail ways? The much lower friction gives us an acceleration of 103.7 in/sec^2. That’s about 30% more acceleration than with the box ways. This is one reason why machines with fast rapids and smaller machines (less room to accelerate in) often prefer linear slides to box ways.

Next installment, we’ll bring all this together and finish describing the process for selecting your motors.

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Brad2014/02/27 at 10:48 amWould be neat for you to look at a Tormach 1100

Michael2014/02/28 at 5:40 amI’m having trouble finding the cutting force (“Max Thrust Force”) output in G-Wizard. Can anyone point me to it?

“Max. Thrust Force: This is the amount of cutting force used. You can get this from our G-Wizard Calculator. The 428 lbs I am using is based on a beefy 3″ Face Mill cut–they use a lot of power. This one is a 7.5 HP cut. I just wanted to give something that would definitely be an upper bound for a hobby machine.”

Brian2014/03/02 at 11:16 pmHi Bob,

Did you weigh, calculate or guesstimate your table weight? Seems a bit light??? I have a Hardinge UM mill in parts and the much smaller table (26″ x 6″) weighs over 90lbs with leadscrew and handwheels etc.

Cheers

Brian

Bob Warfield2014/03/03 at 8:07 amBrian, the table weight is just a round number for a pretty small mill. You’ll have to come up with a number suited to your particular mill.

Steve Simpson2014/03/08 at 1:59 amBravo. Well done.

I would only add the caveat that you cannot rely on the torque ratings of servo motors without an ‘adjustment factor’ because there is a vast difference in how manufacturers rate their motors. An example most readers would be familiar with is the trend to rate consumer level electric motors at their stall HP, which is an unrealistic an useless number. So a compressor ‘rated’ with this method at 3HP only produces 6 or 7 CuFt, whereas a compressor rated at true running 2 HP produces 11 CuFt. Recently I have noted some consumer tools rated specifically at ‘running’ HP.

Industrial AC servos can output 2.5 to 3x their rated torque momentarily, which is what is needed for acceleration. On the other hand, some popular hobby servo motors are rated extremely optimistically and at their absolute maximum potential output.

i.e. an industrial AC servo can easily have 4x the actual torque output of an identically ‘rated’ hobby servo motor. This is not so say one is ‘better’ than the other, only that the calculations will not produce the predicted results if the motor is selected based on the manufacturers rating alone.

Put another way, if the calculations demand 800 oz/in for the desired accel, then you should select (in my opinion) at least a 1,000 oz/in rated hobby servo or a 300 oz/in rated AC industrial servo. They will perform the same.

Steve Simpson2014/03/08 at 2:07 amIncidentally, your table weight is accurate. I weighed an actual IH hobbies ‘long’ table off the machine with a crane scale. It was exactly 150lbs.

Also, I found that the ground ways on the IH have extreme ‘sticktion’ which can be very significantly reduced by cutting shallow slots into one face of the mating surfaces. You would probably be surprised how much effect this has on accell from a stop.

Steve Simpson2014/03/08 at 2:20 amThe IH mill table is very light. While I do not know this for a fact, I would speculate that they ‘stretched’ the table by simply adding a section the existing core or duplicating the existing core with extra length only. The table height and structure appear to be the same as a shorter ‘normal’ bench mill table. i.e. they did not beef up in proportion to the additional length.

I found two weak points in the IH frame and the table was by far the worst. It has a very significant amount of flex. It is fine for the kind of work most users would require of it, but for heavy duty work or long work pieces, I would add stiffeners to the sides.

For contrast, my next mill build will use an actual Bridgeport table that I purchased for that project. It is close in surface dimension to the IH table, but has almost exactly twice the mass.

Elmo2014/04/21 at 11:49 pmYes, this is the single thing that I’ve missed. Some Android calcs give numbers, but I don’t really trust them. For my sizing needs, I think I just calculated them myself using the given torque, but having the maximum/continuous cutting force output by GWCalc would be very useful.

Also, do you plan on adding all this into GWCalc itself? I’ve used Delta’s (the servo maker) sizing calculator, which has sane units (metric customizable).

Elmo2014/04/21 at 11:51 pmYes, this is the single thing that I’ve missed. Some Android calcs give numbers, but I don’t really trust them. For my sizing needs, I think I just calculated them myself using the given torque, but having the maximum/continuous cutting force output by GWCalc would be very useful.

Also, do you plan on adding all this into GWCalc itself? I’ve used Delta’s (the servo maker) sizing calculator, which has sane units (metric customizable).

Steve Wanamaker2014/05/16 at 4:02 pmThanks Bob. This spreadsheet is very useful.

Steve Simpson said:

“Put another way, if the calculations demand 800 oz/in for the desired accel, then you should select (in my opinion) at least a 1,000 oz/in rated hobby servo or a 300 oz/in rated AC industrial servo. They will perform the same”

I’m looking at DMM Tech AC servos: 880-DST-A4K1. These are “.75KW” 2.39 N (338 oz/in) continuous, 7.15 (1012 oz in) Peak. Can I use 1000 for Target Motor Torque?

A question on the acceleration calculations. I see that when I change the ballscrew lead from .197 to .394 (5 -> 10mm), the acceleration almost doubles. I thought that with a lower gear ratio you would have faster accelerations, but a lower top speed. This doesn’t seem to be the case! I’m trying to wrap my brain around this!

Table weight 110 (is actually half of the gantry weight, makes almost no difference, inertia is in the ball screw), part weight 0, Friction .01, Max Thrust Force 40, Max linear 400, Cutting 200, Lead .197 or .394, drive ratio 2, Diameter .985, Length 57.3, Efficiency 90%, target motor torque 1000 oz

Acceleration (bottom of spreadsheet):

Lead .197 gives acceleration 96.18 in/sec^2 (.249 G)

Lead .394 gives acceleration 187.48 in/sec^2 (.485 G)