Sine bar errors

[mklotz]

In the metalworking books, when you see a picture of a sinebar in use, the
stack used to form the angles is generally composed of gage blocks, the
accuracy of which is measured in millionths of an inch. Are gage blocks, a
moderately expensive item for the amateur, really needed? Or is it possible to
get by with a homeshop-made stack that's only accurate to a thou?

The equation for a sinebar is:

sin(A) = S/L

where:

A = desired angle
S = stack height
L = sinebar length (i.e., roller center-to-center distance)

With a little bit of differential calculus, it's possible to write the error
equation for the angle due to errors in the stack height.

dA = (1/cos(A)) * dS/L

where:

dA = the error in the angle due to an error of 'dS' in the stack height.
(For purposes of this discussion, we'll ignore the effect of any error in 'L'.)

Let's plug in some numbers...

A = 10 deg
L = 5 in
dS = 0.005 in

Then:

dA = 1.01543 * 0.005 / 5 = 1.01543E-3 rad = 0.0582 deg

or about one milliradian error. That's pretty small. Think about it this
way...If I make a one milliradian error pointing my rifle at a target 100 yards
away, I'll miss the bullseye by 3.6 in.

If I'm any kind of machinist, I should be able to machine the block I'm using
for the stack to within 0.001 in, which would reduce the error to 0.2
milliradian, or a target miss of 0.72 in at 100 yards.

The error depends on the angle for which the sinebar is set. For:

L = 5 in
ds = 0.001 in

it looks like this:

5 0.0115029
10 0.0116359
15 0.0118634
20 0.0121946
25 0.0126438
30 0.0132319
35 0.013989
40 0.0149589
45 0.0162057
50 0.0178273
55 0.0199784
60 0.0229183
65 0.0271147
70 0.0335043
75 0.0442748
80 0.0659906
85 0.131479

where the first column is the angle, A, in degrees and the second column is
the error in A, dA, in degrees.

Since a sinebar is seldom used for angles greater than 40 degrees, we can
count on an angle error of less than 0.015 deg (0.25 mrad) if we can machine
the stack block to an accuracy of one thou. Unless you're making highly
critical components, don't be afraid to machine your own blocks for setting
the sine bar.

[Paul Jones]

Marv,

Great analysis of the error and discussion. Years ago I bought a 81 block set of "economy" grade gage blocks from Enco when they had them at half price ($99). The over all specs list +or-0.000050" accuracy but the QC inspection sheet report for each block shows it is much better. Your 0.001" error analysis helps me realize the "economy" set is overkill for what I do.

I did use the gage blocks to check an old 6" Mitutoyo dial indicator I bought new in 1970 because I thought the fine tooth rack maybe wearing out. The only measurable error was 0.001" too large between 0.450 and 0.560. I have a new Mitutoyo Absolute electronic caliper but I still love to using the old light green faced analog dial indicator for most of my general purpose work and save the new one for measurements where I really need the precision or use my micrometers.

Thanks for the posting.

Paul

P.S. Stan Z at Bar Z Industrial just published a great YouTube video on the errors associated with distance between the centers of the sine bar roll bars. His was out by 0.0005 but perfectly parallel so used the new value in the calculations instead of 5".

[mklotz]

The equation for the angle error resulting from an error in the sine bar length, i.e. distance between roll center-lines, is:

dA = -(S/cos(A)) * (dL/L^2)

If we substitute the sine bar relation, S = L * sin(A), into this we obtain:

dA = -tan(A) * (dL/L)

Using

A = 10 deg
L = 5 in
dL = 0.005 in

we have:

dA = -tan(10) * 0.005/5 = 0.000176 rad = 0.01 deg

An error of 0.005 in 5 inches is a rather big error in this application and, as you can see from the above, causes a relatively tiny error in the angle.

If you have access to a precision angle plate, you can calibrate the value of 'L' for your sine bar. Mount the angle bar on the sine bar in such a way that placing a stack under the sine bar will bring the angle plate horizontal. (In effect, you're using the sine bar to "cancel out" the angle of the precision plate.) Once this is achieved, measure the stack height, 'S'. Then the value of 'L' for your sine bar is:

L = S/sin(A)

where 'A' is the angle of the precision angle plate.

[Paul Jones]

Marv,
Good analysis, however the accual error was an order of magnitude smaller at 0.0005" and didn't have a significant effect.

Thanks, Paul

[mklotz]

Marv,
Good analysis, however the accual error was an order of magnitude smaller at 0.0005" and didn't have a significant effect.

Thanks, Paul

I purposely used an (unrealistically) large error to demonstrate that even large errors in the roll spacing don't affect the angle accuracy significantly.

Sine bars are viewed by many as only measurement tools, meant to be treated with extreme care. What these analyses show is that it's perfectly possible to make a sine bar and stack blocks in a home shop that will serve for almost any but the most demanding angle work. This opens up the possibility to make the sine bar part of the milling setup, not just a measurement tool.

I've already described one of my homemade sine bars here...

http://www.homemadetools.net/forum/b...8996#post39492

It's supported many a setup in the milling machine over the years.

[Paul Jones]

Marv,

I totally agree with your analysis. I realized I didn't need the super precise sine bar for my work and could either make my own like you did or buy a used one on eBay. I bought a "previously owned" 5" sine bar on eBay because used sine bars seem to be highly discounted despite being of the highly precise variety and no obvious signs of wear or corrosion.

I like your approach of building your own sine bar for general use around the shop but I took the easy way out. However, for a lot of my small part machining, I could also used a 2.5" sine bar which would be a fun project.

Thank you,

Paul

Post Script - I put the sine bar project on hold because I bought a new, never used, 2.5" sine bar manufactured by Fischer Machine Products for $25.75 on eBay. I have bought other Fischer Machine Products and they are very precise and well made.

[C-Bag]

Thanks Marv and Paul. Thanks for breaking this all down.

As a machinist wannabe who most of the setups and processes are still idle curiosity I take for granted things like you need a Starrett Sinebar and a set of gauge blocks. That's what Mr.Pete used so it must be so. But seeing the Blue Collar Sinebar and now this thread have changed all that. And in so many ways exemplifies what Homemade tools is and should be about.

[mklotz]

Thanks Marv and Paul. Thanks for breaking this all down.

As a machinist wannabe who most of the setups and processes are still idle curiosity I take for granted things like you need a Starrett Sinebar and a set of gauge blocks. That's what Mr.Pete used so it must be so. But seeing the Blue Collar Sinebar and now this thread have changed all that. And in so many ways exemplifies what Homemade tools is and should be about.

It's very unlikely that you'll ever achieve metrology lab conditions in your home shop so having super-accurate measuring equipment is not terribly economical. However, that doesn't mean a set of gage blocks isn't a worthwhile thing to have. Checking your other measuring gear is one important use.

If you're going to check a micrometer for accuracy, it's important to use a set of gage blocks that cause the spindle to seat at different orientations so drunken thread errors will be noticed. The preferred set for inch micrometers is: 0.105, 0.210, 0.315, 0.420, 0.500, 0.605, 0.710, 0.815, 0.920, 1.000. For metric micrometers the preferred set is: 3.1, 6.5, 9.7, 12.5, 15.8, 19.0, 21.9, 25.0.

[Paul Jones]

Marv,

Good reminder about the drunken thread errors. I remember reading about this measurement technique when buying used micrometers. In the case of the rack and pinion on my old 6" Mitutoyo dial indicator (bought new in 1970), the rack teeth worn very slightly in a range just before and after the 0.5 position. I used the gage blocks set at 0.2" increments from 0" to 2" to check the measurements. I also checked at 0.5" increments to the 6" capacity but didn'y expect to see errors. Today most dial calipers spec +/- 0.001" accuracy over the 6" length but I had checked this dial indicator when new and several times over the years and it was reading correctly but no longer. I contacted Mitutoyo for spare parts but their response was the model is no longer supported and to buy a used one on eBay and use the parts (not likely). I still use the dial indicator for sentimental reasons but have high-end Mitutoyo digital calipers and micrometers when I need more accuracy. If you can afford them, the Mitutoyo 0"-1" and 1" to 2" digital micrometers with a fast adjusting thread are an excellent addition to the shop and it is hard to make a measurement mistake.

Thank you for the preferred measurement locations for checking micrometers.

Paul

[mklotz]

DIs whose absolute accuracy can no longer be trusted can always be used as comparators. I had one such; made an aluminum tool holder for my QCTP and mounted the DI to that to use when centering stock in the 4jaw. In that application only its repeatability counts, not its absolute accuracy.