an introduction to manual numerical control, version 2

R. G. Sparber January 13, 2010 of 29

An Introduction to

Manual Numerical Control, version 2.1

By R. G. Sparber

January 13, 2010

Copyleft protects this document1.

Version What changed?

1 n/a

2 Added filing tricks

Table of Contents

Introduction ........................................................................................................... 1

A Simple Example On my Lathe .............................................................................. 2

Finishing ................................................................................................................. 5

The finer Points of MNC ........................................................................................ 7

Who’s In Charge Here?......................................................................................... 13

Enough Talking, Let’s Make Chips ........................................................................ 22

What Next? .......................................................................................................... 29

Acknowledgements .............................................................................................. 29

Introduction

There is much discussion about manual machining and also of Computer

Numerical Control (CNC). Yet before we enlisted computers to do numerical

1 You are free to copy this document but please do not change it.


control, it was done manually. I’m here to share with you the power of this middle

ground: Manual Numerical Control (MNC).

MNC can be used to make the same shapes cut by CNC. It will take a lot longer

and will be more demanding on your brain, but the results can be amazing. You

will need a means to generate the data. I use an Excel©

spreadsheet. Assuming

you have a manual machine, you are ready to go.

A Simple Example On my Lathe

Say I want to turn a 1” diameter

ball end on a piece of round stock.

One way to do this is with a ball

turning tool. I’m sure it does a

wonderful and efficient job, but

won’t help me demonstrate MNC.

So here is the MNC way.

Note that the ball end is just half of a

circle. We are looking at a side view

here.

The bar will be spinning in my lathe

about the red line so I really only

need to focus on half of this circle.

The other side will be a mirror

image.


The red rectangles

represent plunge cuts I can

make with my 3/16” thick

cut off tool2. I will later

explain why I prefer to use

this cutter for MNC. Three

quick plunges and I’m

done.

Here is your first

lesson in MNC.

Small effort gives

small results. The

resulting end

profile is far from

looking like a ball. But notice that each cut hits a point on the circle. Also notice

that the cut furthest to the left just kissed the outside of the stock. The middle

plunge went the full width but not very deep. The cut all the way to the right went

deeper but was not to the full width. All that matters here is that I hit the circle at

one point on each cut.

2 Cut off tools are prone to chatter. You may have to adjust the RPM and feed rate to get a good finish.


On my second pass I took cuts 0.05” wide using the same cut off tool. More effort.

Better results. It still doesn’t look like a perfect ball but my maximum error is

around 0.042”. This dimension is important because at any point I can stop

cutting and start to put a file on the ball while it is spinning to get to my final

contour. Before I get lynched for suggesting filing on a turning lathe, let me say

that it can be a dangerous thing to do. It is essential that you have a handle on the

file. If the file kicks back without a protected tang, it can rip you hand open.

Second, pay very close attention to how close you get to the chuck. If you catch a

jaw of the chuck in the file, you are in for trouble. I’ll talk more about the filing

step later.

The next pass was with a step size of 0.01”. Now it is starting to show some

promise. The maximum error is around 0.01” which is easy to file off.


We started with a roughing cut using 3/16” wide steps equal to the width of the

cut off tool. This removed a lot of material. The second roughing cut was at 0.05”.

This means I went from making 3 plunges to making 0.5”/0.05” = 10 plunges

(radius/width of cut). Making 10 plunges is about at the limit of what I call fun. If

the exact shape is just for looks, I would probably bail at this point and start filing.

But if I wanted a better result, I would drink another cup of coffee and brace

myself for 0.5”/0.01” = 50 plunges. Now this is mind numbing yet the reward

might justify the effort. Understand that each plunge you make, there is a

possibility of your mind wandering and you making a mistake. So MNC becomes

more of a challenge in concentration than in machining cleverness.

Finishing

Once you have done all of the plunge cuts you can stand, it is time to start filing. I

learned about MNC in Guy Lautard’s first Bedside Reader©

which I highly

recommend. He suggests a trick that you might find useful although I have to

admit I don’t use it every time. Before you start to file, blue the surface. The dye

will settle in the crevices. You then file the steps formed by the plunge cuts until

you get just the blue lines. If done right, you can get within a few thou of your

desired shape. This is

certainly good enough

for shapes that you just

want to look good.

After seeing version 1

of this article, Glenn N

[[email protected]]

suggested that filing as

shown here is safer and

lets you see how the

work is progressing.

Works great!

John Martin suggested


a variation on filing on top: “What makes the most sense to me is - if you are filing

on top of the workpiece - to file left handed. Left hand on the file handle, right

hand on the toe. That way, your body is out over the workpiece rather than over

the chuck or headstock. Plus, if the file points other than straight across the

workpiece - and we all have a tendency to angle the file - it will point toward the

tailstock. Pointing the toe of the file toward the headstock is what gets you into

trouble in the first place, as that is when it is most likely to be caught by the chuck

jaws.

I'm not too fond of filing backwards and underneath the workpiece - the major

drawback is that the filings remain on the surface of the file and are dragged

against the workpiece. You get a smoother finish when the filings fall away from

the file, and that smooth finish is the goal of the filing process.”

So the debate continues.


The finer Points of MNC

As with manual machining, it is prudent to made a rough cut followed by a finish

cut. With MNC this is a two dimensional problem. Not only do you want the steps

to be wide on the rough cut, you also want to hit a contour that is larger than the

finished one.

In our simple example, this

means that I cannot cut the

ball to the same diameter

as the stock. I need a bit

more to permit my rough

cut some space. The inner

red circle is 0.98” in

diameter which gives me

0.01” in radius for my rough

cut. We need to generate a

series of coordinates to guide our rough cut plunges and then a different series

for the finish cut(s).

Another challenge is finding and keeping your

reference points. This is not as important if you just

want to cut a pleasing shape. But if you want some

precision, it is essential that you establish and maintain

your (0,0) point.

For the present example, I would face the end with a

regular left hand cutter and then change to my cut off

tool. With the cut off tool just touching the end of the

stock, I set my zero on the longitudinal axis.


I would then feed over to the

centerline of the circle and reset my

zero point. This new origin is the

reference for both the rough and

finished circle.

The transverse axis zero will start out at the

surface of the bar while I do my rough cuts.

I will then reset it to the surface of the

finished circle.

Now let me modify the previous design in order to illustrate the value of setting

zero and using a cut off tool.

Rather than making just a rounded

end, this time we will cut a ball on the

end of a rod.


This time around I will put dimensions on the drawing.

I want to turn a ball 0.49” in radius from a 1” diameter piece of aluminum bar

stock. I will use my 3/16” wide cut off tool. My cutter has been positioned to the

“equator” of the ball with the surface of the bar as my zero in preparation for the

rough cut. The distance from the equator to the attachment point of the rod is

0.447”. This value was found by just drawing the shape up on CAD and

dimensioning it. No fancy math was necessary.

We have already cut a rounded end so I will just show you what the rough cut

looks like at that end.


This time I am showing the entire cut rather than just one side. Nothing new here.


Now I can explain the value of using a cut off tool.

For the end cuts, the left corner of the cutter shown here in red, was fed in until it

touched the rough cut outline. When I moved to the inner side of the ball, I have

switched to having the right corner of the cutter shown in green, touch the

outline.

Furthermore, as long as I account for the thickness of the cutter, I am able to

maintain my zero point at the equator.


For end cuts, my X axis

zero was set when the

cutter was at the

equator and lines up

with the left corner of

the tool.

For inner cuts, I

subtract 3/16”, the

cutter thickness,

from the X position

but do not have to

disturb the cutter.

This causes the X

axis to again

indicate the point

on the ball being

contacted.

The alternative

would be to use a

left hand cutter for the outer side of the ball. Then I would install a right hand

cutter. But what happened to my reference point? I just lost it. There are


techniques for reestablishing the zero but I find it easier to just avoid the hassle

by using a thick cut off tool.

Who’s In Charge Here?

I hope you now get the general idea of how to cut shapes on a lathe. But exactly

where do we get the numbers needed to set our dials? This is where a

spreadsheet comes in. Some geometry will also be needed.

I have a circle with a given radius. Knowing

the radius completely defines the circle. But

the radius is not what we need to cut this

shape. We need X and Z coordinates.

The X dimension is the longitudinal feed on

the lathe. The Z dimension is the cross slide

feed. From geometry we know that the radius

squared equals X squared plus Z squared:

R2 = X

2 + Z

2

The radius is constant but as it swings around

the circle, we will get different values for X

and Z. I want to set various values for X and know the correct value for Z. Using

algebra, I can rearrange the above equation to fit my needs.

Subtract X2 from both sides of the equation: R

2 – X

2 = Z

2


or

Z2

= R2 – X

2

My lathe can’t handle Z2 so I must now take the square root of the equation.

Z = ��

Remember that the radius, R, is constant and

we get to decide how much to advance X for

each cut. So this equation will tell us how

deep to go with the cutter.

We have one more hurdle to clear. As drawn

here, I am cutting the inside of the ball. That

is not what I wish to do. I can only cut the

outside of the ball so must slightly rethink

what these number will mean for me.

First of all, recall that my zero reference is on

the equator and at the surface of the bar

stock as shown here with the (0,0) tag. In

order to make a cut on the outer ball

surface, I must move my cutter to the right

by a distance X. This value is the same as

when I was talking about radius. But Z

dimension changes because this axis has a new zero.


We will sneak up on this problem so I hopefully don’t lose anyone.

First, recall that I am turning this part on my

lathe so as I make a cut, it is forming a circle as

I look into the headstock. In other words, when

I talk about the radius here, there will be a

second point that is the mirror image of it. This

means I can flip over my X, Z, radius triangle

and not change anything. The Z axis distance

from the center of the circle to the radius of my

circle is “Z” regardless of if I go up to the point

marked “radius” in black or down to its twin point that is marked “radius” in blue.

At the risk of insulting you, let me point out

that the distance from the center of the circle

straight down is also the radius.

But now look at the Z

axis distance

between this radius and my Z dimension associated with

the radius marked in blue. This distance turns out to be

“A”. “A” is what we really want since it tells us how far

to feed in the cutter given that our (0,0) point is as

shown here.

“A” equals the radius, R, minus Z. But we know that Z =

�� so by substitution we have A = R - �� .


A = R - �� is the key to cutting this ball. We know the desired radius, R,

and get to pick X. Out pops the required in-feed of the cutter. Here is where using

a spreadsheet lightens our load.

I have set my cutter width to 0.1” so the X increments are clearer.

Ball End

radius = 0.5

cutter width = 0.1

step X A

1 0.000 0.000

2 0.100 0.010

3 0.200 0.042

4 0.300 0.100

5 0.400 0.200

6 0.500 0.500

Note that when X = 0, A = R - �� = R-R = 0 as can be seen in the line marked step

1 in the spreadsheet.

When I have moved to the right along the X axis a distance equal to the radius of

the ball, my cutter moves all the way in to the center of the ball, a distance equal

to the radius.

If all I want to do is cut rounded ends, then this spreadsheet is all I will ever need.

Any ball radius within the limits of your lathe can be turned without any special

attachments. “But wait! There is more…”


With little effort, this same spreadsheet will guide us to cut the inner side of the

ball.

To cut the inner side of the ball, we must stop after moving 0.447” along the X

axis. Since we are moving to the left of my zero point, the display will show minus

0.447.


I must also shift my zero point to compensate for the cutter width.

My X axis is positive as I move to the right. When the cutter is set with its left

flank lined up with my X axis zero point, my X axis indicator will read 0. As I cut the

inside part of the ball, recall that I will be landing on the radius of the ball with my

right front corner of the cutter.

I can deal with the shift in cutter zero in two different ways.

1. Move the cutter to the left a distance equal to the width of the cutter and

set a new zero.

2. Leave the existing zero set alone and have the spreadsheet shift the X

value.

I like this second approach. When the right flank of my cutter is lined up with my

zero point, the X display will read negative 3/16”. So if I change my spreadsheet


to subtract 3/16” from all X values, my spreadsheet will give me X values that get

me to the correct location. For example, the spreadsheet will tell me X = - 0.188

and that will put the right flank of my cutter at X = 0.

Here is the updated spreadsheet. Note that I have changed the radius to 0.49”

and the cutter width is now 3/16” or 0.188”.

Let’s look at the outer side of the ball. At step 1 my cutter is at X = 0 and I set my

in-feed, A, to 0 such that I get a radius of 0.49”. In step 2 I move over the width of

my cutter and feed in 0.037”. Similarly I make my cut at step 3. But note that

things fall apart at step 4. This is because I have tried to move over further than

the radius so fell off the end of the bar. Subsequent steps also produce the

“#NUM!” error message. I manually added a “new 4” where I forced the X value

to be equal to the radius. Note that I then got the correct value for A which is also

the radius. In other words, I move to the right a distance of 1 radius and move in a

distance of 1 radius in order to arrive at the right most end of the ball.

Ball End

radius = 0.49

cutter width = 0.188

Outer side

step X A

1 0.000 0.000

2 0.188 0.037

3 0.375 0.175

4 0.563 #NUM!

5 0.750 #NUM!

6 0.938 #NUM!

new 4 0.49 0.490


Inner side

step X

X-cutter

width

A

1 0.000 -0.188

0.000

2 -0.188 -0.375

0.037

3 -0.375 -0.563

0.175

4 -0.563 -0.750

#NUM!

5 -0.750 -0.938

#NUM!

6 -0.938 -1.125

#NUM!

new 4 -0.447 -0.635

0.289

The inner side numbers have a few things that might be confusing. First of all, the

X values are increasing but are all negative. That is because I am cutting to the left

of my X zero point. The next column over is marked “X – cutter width”. Here is

where I am compensating for cut off tool’s thickness. When my X = 0, I will move

along my X axis until I see -0.188. That will put the right flank of my cutter at the

real X axis zero point. My last column, marked “A” runs into the same problem I

had with the outer side – I ran out of metal. All is well through step 3. But the

maximum distance I must follow the ball is 0.477” from my zero point. Step 3 has

the last X value that is smaller than this limit. Even if step 4 did not have an error

message in the “A” column, I still would not want to use it. Instead I have

manually entered “new 4” and set my X value to -0.477”. The associated number

for X – cutter width and “A” are correct.


In order to make the spreadsheet a little more flexible, I have added the ability to

easily set the step size for my X axis cuts.

Ball End

radius = 0.49

cutter width = 0.188

Outer side

X step size = 0.05

step X A

1 0.000 0.000

2 0.050 0.003

3 0.100 0.010

4 0.150 0.024

5 0.200 0.043

6 0.250 0.069

7 0.300 0.103

8 0.350 0.147

9 0.400 0.207

last cut 0.490 0.490

Note the “X step size=” entry which I have now set to 0.05”. I have let the

spreadsheet calculate the first 9 steps but then forced the last cut to be at the

right end of the bar.

Oops – I should have had a step 10 with X = 0.450 and A = 0.296. It is very easy to

make these kinds of mistakes and not find them until the chips are flying.

The inner ball is similarly modified using the same step size.

Inner side

step X

X-cutter

width

A

1 0.000 -0.188

0.000

2 -0.050 -0.238

0.003

3 -0.100 -0.288

0.010

4 -0.150 -0.338

0.024

5 -0.200 -0.388

0.043

6 -0.250 -0.438

0.069

7 -0.300 -0.488

0.103

8 -0.350 -0.538

0.147

9 -0.400 -0.588

0.207

last cut -0.447 -0.635

0.289


Enough Talking, Let’s Make Chips

I took a length of 1.000” diameter aluminum and turned the end square.


Then I used the squared up end to set my 3/16” wide cut off tool square plus set

my X=0 point.


My A = 0 point is initially set at the OD of the stock and at the initial X = 0 is at the

end.

I then moved to X = 0.500 and reset X to 0 because I am now at the “equator” of

the ball. Next I fed in until I have a diameter of 0.490. If this had been a true

roughing cut I should have set my radius at 0.495 but I forgot.


I have just finished making the roughing cuts for the outer side of the ball.


The roughing cuts for the inside of the ball are now done.


The finish cuts at 0.05” steps is now done. It is tedious and demanding work but

the results are cool.

The ball is now blued.


I’m most of the way through filing. Accuracy is not that good because filing is not

something I do all that well. But you can see the blued grooves that guide me. If I

had made my finish cuts with 0.01” steps, it would have been much easier to file a

decent ball. It is a trade off. Do I want to make 5 times the number of finish

passes or do I want to spend more time with a file?

Most of the grooves are done. Sad to say the distortion is still there.

After filing, I used 120 grit emery cloth and finished up with some 600 grit.


You can see that more filing was needed on the end.

Hopefully you do get the idea of how to do MNC and don’t

reject it just because of my poor filing skills.

What Next?

Using MNC to make a ball is not very impressive but I hope

this simple example was not too hard to follow. The real

power of MNC comes from defining complex shapes in the

spreadsheet. Once you have those columns of numbers, it is

just a matter of switching off your brain and religiously following the steps.

MNC also applies to a mill. If you follow the method on the lathe, transferring to a

mill should not be too hard.

Acknowledgements

I wish to thank Guy Lautard for writing such a clear explanation of MNC in his

first Bedside Reader. Thanks to Larry Gill for sifting through this article and

finding every typo, example of poor grammar, and each place where I was as clear

as mud. This is the mark of a true friend. I also want to thank Glenn N

[[email protected]] and John Martin for their suggestion of how to file on a

lathe.

I welcome questions and comments. They will only make this article better. All of

us are smarter than any one of us.

Rick Sparber

[email protected]

an introduction to manual numerical control, version 2

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