Sine bar errors

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.

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".

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.

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

Quote:

---

Originally Posted by 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

---

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.

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.

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.

Quote:

---

Originally Posted by 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.

---

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.

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

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.

Thanks Marv and everybody! I've been lurking hear since Marv started it and Learned a lot. Thought I might chime in here with a relevant experience.

I had an experience last year where I picked up an across the pond variety of Angle blocks (45-45-90 & 30-60-90) for set up and granite work on my meager budget. The specs said, "back then" that they were good to ±20 arc second and for $30, even if they were ±50 arc seconds I would be thrilled. First thing I did was set them against a known good 123 block and checked for daylight...Oh My. Was able to put a 6 thou feeler gauge on the far end of most sides. I contacted them and they sent me another pair...and ask if I would change my initial review of them because they didn't respond to my contacting them. When I checked the new ones they were only slightly better on one angle and worse on the others. The 45 was the best but the 30-60-90 was something on the order of ~400 arc seconds. And worse was the two sets were different in size fairly significantly. The difficult thing was the Obliqueness of the triangles and trying with my meager tools to measure and calculate the real error.

Had lunch with my son a week after and he said to give them to him and he'd measure them on their Hi-End Keyance IM-620 visual measuring system good to <.5µm...and calibrated regularly. Here are the print outs from his test.

Attachment 9817Attachment 9818

Basically these show that the 30-60-90 were out of spec by 25-41 times the spec, but the 45-45-90's were only out by 1-2.5 times. Obviously the 45's were Very usable for my meager shop but the lopsidedness of the 30-60-90 were pretty much paper weights (or maybe a chip scraper as Paul suggests)...unless I could use Marv's idea of compensation. It would mean needing to mark them permanently some how and having a way to use them with some method of compensation. Would love to hear your thoughts on this Marv.

Hemingway, there were several other things with this experience but interestingly they have now changed the specs on the website to show a tolerance of: "Accuracy +/-20 seconds, 0.0001" per inch. " These things are about 3" long. @¿@ Obviously they didn't get it Or Did, but were tired of me as some do get. They are still for sale if you want some. Doubt I will purchase their incremental angle block set though (same new spec) even if it's only $40 instead of hundreds for a good set of B&S.

Thanks again Marv for starting this great thread! ~PJ

PJs,

Perhaps there is a way to lap the surface by clamping the 30-60-90 to the correct angle (kind of a catch 22 but can be done) and systematically remove the taper. There are ways to set up the lapping so the part (the 30-60-90 angle block) is lapped but not the reference surface.

I have bought several pairs of 1-2-3 blocks with specs of +/- 0.0002 or +/- 0.0003 on parallel surfaces and 0.0003" over-sized on all three parallel sides. The interesting thing is the manufacturer (three different companies) states they purposely make the 1-2-3 blocks slightly over-sized to allow for manual lapping to precise dimensions. This is not high on my priorities but could be done. By the way, of all pairs of 1-2-3 blocks I have, the solid ones without any holes are my most useful pair. Most of my set-ups just require a precise spacer without bolting on or through the block. I find the ones with holes collect the metal shavings and have to be cleaned and inspected for chips. It is so much easier to just use your hand to wipe of the solid blocks. So if you need a second pair, buy the solid kind.

I like the discussion here and have learned a lot from all of you.

Paul

This is a bit off-topic but may be useful for current and future readers.

Most of you know that measuring a taper involves measuring the part diameter at two locations a known and precise distance apart. With a tapered part this can be a 'fidgety' task at best. But 1-2-3 blocks can make it easy.

Lay the blocks so the 1" dimension is vertical. With the tapered part held vertical between the two blocks lay your caliper's jaws flat on the horizontal 2-3 surface on the blocks and measure the part diameter.

Now arrange the blocks so the 2" dimension is vertical and the caliper jaws lie on the horizontal 1-3 surface. Take another reading and, voila, you have two diameters separated by exactly one inch.

Thanks Paul. I have considered lapping them by holding the long side (hypotenuse) as a reference and work on the 90, but feels difficult to adjust the obliqueness with any thing I have to accurately hold the correct angle and allow the slow whittling away till I get there. The other thing is my height gauge only measures to 3 places plus a floater half, and the long side of 30-60-90 is just slightly bigger than my 3" 10'th mic, which is my largest. It would be difficult to check to any accuracy as I go along and wouldn't want to bug my son. Need to crunch some numbers to see what I "could" hit with 3 decimals and how I might hold it to get there. I'd love to salvage them as the 30-60-90 is the one I really wanted but just couldn't justify sending them out or much more time on them.

Interestingly, both sets of these have one side that is ground perpendicular to the plane and the other two are ground in the run. Definitely Friday units while the QA people were out to lunch.

I only have one set of 123 blocks and believe it or not they are from the same people. When I got them I measured and swept them every way I could thing of and they are withing 2 tenths in all directions and parallel. They are oversize by 2 tenths but are definitely matched, but like you say it's not a priority...Straight/square/parallel is workable for my meager needs. I use them more on the granite than for setup but do use them occasionally for a set up for lapping perpendicular to a small granite I have. I do like your idea of a solid block though, as the threaded holes on these are worthless and cobby but for $20 I can live with that. I'll keep an eye out for them.

Me too on the learning and fun! ~PJ