John. Yes, this is simple trig. Something that will help you visualize what's happening is to realize that the dial indicator does not really measure distance - it measures an *angle*. If you could have the tip at 0 degrees, then the angle subtended during the measurement (assuming it is relatively small) will be accurate - because the tip length of the dial indicator is part of the design of the indicator (cos(angle) * length of tip.) Now, to help visualize the error, imagine that the tip is angled at, say, 80 degrees instead. The angle subtended in this configuration must be much greater than when the tip is within about 5 degrees (as you know) to move the *same dimension in the direction of the material being measured*, so the dial indicates a much larger *angle*, and this is reflected in a larger number of mils on the dial. Conversely, if the tip is at 45 degrees, then you can multiply the value read on the dial by ~ 0.71 (the cosine value of 45 degrees) to adjust the artificially high reading on the dial. (This works for any angle. If the angle was 30 degrees, you'd multiply by cos(30) = 0.87.) Hope this helps.
Respect to a man who knows math and how a dial indicator works. I'd advice anyone interested in the matter to not just watch this one video, but to take a paper and solve this little trigonometrical exercise thoroughly by themselves, since the problem is a little bit more nuanced and involves approximation.
HI John, The cosine correcting tips use an involute curve shape. With a spherical tip the effective lever length is always the same no matter at what angle the lever contacts the surface. With the involute shape, the effective length does change. At steep angles the more pointed tip would contact and the longer effective lever length results in a lower reading.
Hi John. Good demo here. I have encountered this in many mechanical instances and can guarantee a lot of engineers don't fully understand what is happening. I especially liked the stacking of the indicators to show the difference in readings. Well done.
I’ve known about cosine error my entire career as a Tool and Die maker. I assumed this was common knowledge. Perhaps I just got lucky and had a good journeyman teaching me. Great video, as are all your Fusion 360 videos.
Remind me of armor plating on tanks. How you can have a 1 inch plate and put it at an angle and its "thicker" and has more stopping power vs straight walls and 90 degree angles.
Good to keep in mind. I'm a industrial Mechanic which maintains large 5 axis gantry mills for trimming and drilling composites. When they crash we do the alignments and geometry checks of the heads.
Gotta love that feeling of finally getting your mind wrapped around a concept after it's been stumping ya for so long. I remember finding out about this phenomenon while centering work in a 4 jaw, you can purposely angle the indicator to get more cosine error which can give the indicator a perceived higher resolution. Dialing in that last thousandth with the indicator angled then becomes a few thousandths on the dial. Makes it easier to get closer to zero but not good for metrology, lol.. Interesting to see that the test indicators only increase the reading with the more cosine error they're set with. Thanks.
John, as someone just advancing into machine work, these are the tips and demos that I find helpful, fascinating, and just fun to watch. Nicely presented, oh BTW, loved the new shop sign video, nice!!!
oh jesus. thanks for making me rethink my whole career 😂 only had 5 years of exsperience as a cnc operator. and never heard of this stuff. man my mentor sucks... thanks for saving my ass!
I worked with a couple of other CNC technicians who had long experience (over 30 years for one of them, and 41 years for the other). The more experienced one was even our "tool guy". Out of 12 guys in my department, I'm the only one that uses trig on a regular basis to make my job quicker and easier, the rest of them do a lot more sample and adjust stuff, but end up in the same place usually. I've taught a couple of the department pups a little useful trig, but honestly, I just don't think anybody else in the department actually has a good grasp of trigonometry or how easy and useful it is in our work, no matter how many times I tell them "Some old hippie, Caught another hippie, Tripping on acid".
I like this demo. The interesting thing to me is you can find the correct angle to put your indicator by simply changing the contact angle to minimize the indicated reading. This is similar to checking flatness of a surface that is not necessarily parallel to your indicator or surface plate; you can use a leveling table until you get the smallest total indicated reading, or until your measurement is within tolerance requirements.
you get the same effect with car suspension as the wheel travels through its arc. The wheelbase changes effectively as it moves through from extension to compression, and you get lateral scrub at the contact patch between the tyre and the tarmac.
Hi John. Let me give you a related topic, that can come into importance when you are lifting equipment. Figure the weight a lifting strap is exposed to when moved out at an angle other than 90 degrees to the load. Two lifting straps hanging straight down from a hook, (90 degrees to the load) lifting a 1,000 pound load each strap will see 500 pounds a piece. Now move the straps out to a 60 degree angle to the load, then out to 45 degrees, then to a 30 degree angle with the load. I'll give you a hint, the 30 degree angle is against the law when operating a crane!
you can calculate the cosine error with trigonometry if you know the angle of the indicator. in the case of your example, the tilted indicators are measuring the hypoteneuse of the triangle. you can use this to your advantage and measure tenths or smaller on larger scale instruments. similar to the old fashioned method of turning the top slide of a lathe such that you get half thou increments to a thou increment dial. an indicator perpendicular to a known angle will give a calculated dimension. test indicators become more laborious to calculate the arc but still doable and accurately.
Is it a Skewed test with the radius of the top of the plunger and the angle that the test dial indicator is in relative to the dial indicator? So therefore possibly not giving the correct answer to the question?
So glad you did this, sometime ago I questioned how an indicator had been set up saying there would a cosine error, I was derided as a nut! Even though I have the small explanation paper from Brown and Sharpe .000!" indicator! In a job I had inspection we had carbide tips but still kept a look out for a wear flat.
@NYC CNC - Actually .. the plunger, atleast the ball, is always moving the same distance. However, the angle between the measuring surface and the plunger causes the axle in the indicator, that the plunger is attached to, to rotate a bigger number of degrees under the same measurement. The problem is, that cosine error causes the mathematical length of the plunger to vary - while the indicator is only calibrated to the operational length of the plunger (distance between plunger ball center and axle of rotation in the indicator), when the plunger is level to the surface of measurement. I hope that made sense :s ... Keep up the good videos :)
I thought I read somewhere that lever indicators are calibrated to read correctly when the lever is at 22.5˚ - the shallowest possible lever angle which didn't let the "knuckle" (where the lever pivots) hit the piece to be measured. This let you take accurate measurements out in the middle of a flat test piece. I recently got a digital lever test indicator (Fowler/Sylvac) and the instructions said that the instrument was calibrated to be correct when the lever was dead horizontal. This makes me wonder whether my original recollection was true or not; I suspect not. As it is, the only way to get absolute measurements with a lever indicator out in the middle of a large flat surface without trig calculations or lookup table would be to place a gauge block on the surface to be tested, indicate on the gauge block, and then subtract its thickness.
Nice demonstration of cosine error. The Increased Angle shortens the external working length of the lever to fulcrum point vs. lever's distance to the fulcrum cannot change internally because it is mechanically fixed within the body of the indicator. The short end of the stick upon a fulcrum will produce more travel at the longer opposite end of the lever. With proper consideration the external stylus length from it's fulcrum point could be changed to accommodate using the indicator at an angle. All boils down to the simplicity of lever length's and fulcrum positioning, calibration. Error leads right back to the... Angle of the dangle.
Howzit John, The error is actually a sine error when using your straight plunge DTI. You have it placed at approximately 60 Deg to the surface table. So for the feeler gauge to lift it 15 thou. The plunger can only travel longitudinally in the 60 deg plane so using the sine rule of Sine@ = opp/Hyp. Sine 60 = 0.015"/Hyp. Hyp = 0.01732". The Hyp is the travel of the plunger.
I don't think that is right, there will be no cosine error at zero degrees (or 90 degrees depending on how you look at it) the greater the angle the greater the cosine error.
end of the indicator moves on a circular path, you are not bringing the measured object under it normal to this circle. thus you are not measuring the thickness perpendicular to the material, instead at an angle. Example: the picture you have with the mitutoyo paper, draw a line through the material you are measuring at right angles, then draw the same line slightly slanted, the slanted one will be longer.
We use a plunger clock as a dial indicator, useful for actual measurement. We use a finger click as a dial comparator, not useful for actual measurements, but good to compare for things like clocking up.
And just to provide a big REMINDER when you are checking tool runout: Remember cosine error. If you are trying to check the runout on the small unfluted portion of an end mill sticking out from a ER collet it is easy to get a DTI at a lot more than 10 degrees to parallel to the tool. So... do you really have .001 runout or is it actually a LOT less? 30% as shown in this video is a huge difference when talking about tool runout. It would be very easy to get a measurement that shows a lot more than you actually have.
advil000 this shouldn't be a problem when measuring tool runout, because you're measuring the distance to the center of the chuck relative to other sides of the mill.
nice video. can u plz make a video about touch propes with mach3. to be able to find centers and edges easier. i have built a diy touch probe and cant find a way to make it work with mach3
Thats why you don't measure parts with a dial indicator. You use the indicator to establish the hight and transfer that height to a hight master. (The tall thing behind him.)
question... can you use this quirk to make your test indicator more sensitive, intentionally? say, for a relative measurement, I set my angle at 45° to get more needle deflection?
angular vs radial measurements.. examine a clock face and the difference between time setting for a give horizontal line moved vertically.. the change is most drastic at top and bottom of the clock. the angular displacement is greater for the hands the farther you get from the 3 o clock position.
BUT. Does the "error"make it more accurate in showing deviation ? Or in other words make it easier to show deviation like using a higher definition indicator ?
thats is only completely necessary when using the indicator as a measuring tool, not really as necessary when using it as a comparison tool for checking for concentricity or tramming a mill
Nice lesson, well taught, well demo'ed. I was taught pretty much the same thing when as an apprentice did my rotation through layout and inspection. "Two Tenths" Tommy Thompson, a notorious anal retentive and hair splitter ran me through a mini training course where it was my responsibility to think through and demonstrate to Tommy's satisfaction the many traps and misperceptions of Euclidian geometry as appliepd to the machinist's trade along with physics, materials, reporting, planning. He was a bastard but he taught me a lot. Glad you are passing along a few of these same lessons in a far more palatable form. I would like to have seen the simple right triangle from which "cosine error' was derived; how the inclined axis of the travel indicator's plunger follows the hypotenuse; how the corrected reading equals the reading along the inclination angle divided by the cosine of the inclination. Then relate that to a DTI which actually measures angles of rotation but is calibrated on the dial in thousandths on the contact's arc. You can't pass off essential shop math as too bothersome to learn. Sorry - picky, picky
Isn't the cosine error in regards to a test indicator (or the like) really just a function of the fulcrum lengths of the arm/nib (or whatever they're called)?
It is the same as a right triangle....it is just a really small triangle. So, when you have a triangle, you have 3 sides. One side is flat on the table. Two, is the height (this is represented by the height of the feeler gauge). The last side of the triangle is the hypotenuse....or the long side. The long side is representative of the error you see. If your gauge is correctly positioned, you read the actual height (90 deg) from the surface. If your gauge is at an incorrect angle, let's say 20 deg off, (the hypotenuse is at 20 deg off 90 deg.....or basicly 70deg from the surface. That line is longer than a straight distance from the tip of the gauge to the surface.....and that is the distance your gauge tip is actually traveling.....thus the error.
The top indicator is reading 15 because its at the same angle as the table and feeler guage. The issue is when you dont have the axis vertical to the part being measured your reading the part's thickness at an angle which means you have more material to pass though. Just like if you drilled a hole though a peice of material, the more the angle of the hole off 90 degree the longer bolt you will need to reach the other side.
I think the main issue is that it's hard to see the angle when measuring with that type of guage. Your reading the distance to the table at a 90 degree angle from the tip not directly 90 degrees from the table.
The easy answer to visually understand what's causing the error is if the stylus is not parallel to the material being measured it cannot measure vertically through the material thickness it will instead measure the material diagonally through the material thickness. The greater the angle the longer the diagonal plain through the material.
I love the setups to demonstrate what is happening. However, the idea of cosine "error" is not really accurate, but a misunderstanding of what a test/lever indicator actually measures. It gives the length of the hypotenuse of a triangle, not the vertical distance of change. IF it is positioned accurately, then these two numbers are the same (cosine of 0deg=1 or 100%). +/- 10deg gives an accuracy of about 98.5% (cosine of 10deg = .985). That means a .015" feeler measures .0152" at 10deg and .0148 at -10deg. At 30deg, the same feeler will measure .173". Assuming your feeler is perfect and your measurements are perfect, your indicator is set at a 33.56deg angle: .015"/.018" = 0.833, inverse cosine of 0.833=33.56deg. That is a far more accurate measurement than guessing and then using a poorly constructed table. (I say poorly constructed because of the poor rounding skills involved where 0.866 rounds to 0.86.) Using very easy and basic trig (cosine), the measurements are more accurate, and the resulting work is more precise. Love the videos, especially short videos like this one!
So the stylus needs to be parallel to whatever piece you're indicating. Now what about the stylus in relation to the test indicator? I put the stylus at 90° (with the indicator horizontal, the stylus will be either straight up or down) a lot to check faces. Is there any margin of error in any of the indicator positions? I'll try to clarify if needed.
you're actually getting 2 different flavors of error with those 2 indicators. the straight dial indicator is measuring the hypotenuse of a right triangle. the further from vertical it is, the worse the error. the other indicator is angle based. the angular change caused by the same feeler gauge varies as the angular pre-load AND body angle vary. thus, the measurement read will vary in accuracy.
And sometimes this is used as a feature. The same effect you get here with the cosine error (longer travel) is what is used in armoring of vehicles. By setting it to an angle, you (besides the obvious chance of ricochets) increase the effective thickness of the material. Oh before I forget: Excellent demonstration!
Also most people don't realize is that you cannot use a longer or shorter needle on a test indicator than the length of the needle it was supplied with you will get different readings, ie. cannot swap a 1/2" long needle with a 3/4" or 1" ( I've seen guys try this to get into tight spots) if you do you get a completely different reading. I believe that is considered the same thing as cosign error, yes? do you agree?
This is not quite the same as cosine error, though I suppose they are somewhat related. As long as you know what you are doing you can use a longer or shorter tip, but you can not read the indicator directly. If you use a tip that is double the length for instance the indicator will read half the real measurement (since the angle now only has to change half as much to move the tip the same distance).
This is true and I do know this... but its good to point out and make people aware.... I guess the length of the needle could be considered the cosine leg of a triangle (if you draw it out on paper to be so...so if the cosine changes of the triangle (ie. the needle length) the reading in the mechanism of the indicator will be different... cosine error.... or something somewhat related... LOL... Honestly after 32 years in this trade this is the first time I heard the term "Cosine Error"...
not a triangle, but actually an arc. by the length of stylus you change the radius of the arc... so you maybe can call it "arc error"? no idea if thats a technical correct term or not ;)
Lenny Sweet you can. You do change the read out though. Whatever factor you change the stylus by you change the read out by So if you go from a 1" length to a 1/2" length, the indicator reads 1/2 it's original measurement. Vise versa if you go from a 1/2" to a 1". The indicator reads double its original. That's why I buy long stylus indicators and have 1/2 length styluses to put on it. Effectively makes the indicator twice as accurate
I CAN`T BELIEVE THIS !! I`m teaching myself how to use a lathe and small mill I bought..Just last week I bought a cheap dial test indicator and used a .015 feeler gauge to test it the same exact way you did. It showed @.018. I thought I received a bad indicator so I bought a Starrett, did the same test and can up with .018-.019. I thought WTF !? What`s going on here ? My mic shows .015 but the indicators are off. Could they both be bad ? Well thanks to you now I know and I`m going to try it at the new angle and see what happens..I bet they`re both dead on...LMAO...Thanks so much for this John !
Not understanding this before you bought two indicators actually helped you. Now you have a cheap indicator to use on things you would hate to put a good instrument through, plus you have one you can trust if you treat it right.
I was thinking that also...Plus I also have a mill and now I don`t need to run back and forth between the two for a indicator...Yeah me for being an idiot ! lol
I think the instructions that came with my Interapid test indicator said 12° is the angle the stylus should be at compared to the measuring surface. I find it to be too much of a bother to actually set that angle, and just attach the indicator to a height gauge, or use the machine's scale for taking any actual measurements. The swivel points have enough friction that repeat-ability is within a couple tenths of a thousandth of an inch.
servant74 It's just like a lever and fulcrum. If you have a fulcrum dead in the middle, and push down an inch on one side, the other side will go up an inch. If the fulcrum is moved half way between the mid point and end of the lever, pushing down an inch on the long side, will only raise the short side half an inch. And pushing an inch down on the short side, will raise the long side 2"
collin simpson truing or traming is relative measurements. As long as you maintain the same tip angle for all measurements, the relative distance from one spot to another will be correct, Cosine error only effects absolute measurements when you're trying to measure the actual distance from a known point to an unknown.
So its akin to the measurement sensor moving up a ramp compared to moving up a ladder its measuring X and Z movement while your only expecting it to measure Z movement.
A) Trig is a thing, and cosine error is all about the trig of a right triangle (darn you Pythagoras). B) Here is a quick trick to calculate cosine ahead of time if your not sure you trust your setup... Run your gauge over a gauge block with a know (and certified) size.. if you know the block is X, and your getting Y, you can work backwards to your cosine error... and either keep mucking with the needle to get to 90 degrees or just dance with the one you brought and do math to find your true result (though calculation will mean your resolution is off, which will also mean you may loose a significant digit in your calculation so... YMMV..
Attach both indicators at different angles to the same height stand and make them deflect half of the dial capacity, you'll see the same without messing with a feeler gage.
For a builder, when we take the dimensions of a room we don't take measure them diagonally but at right angles. Who knew it was because of COSINE error, or was that the reason why Norm always said measure twice, cut once.
A couple tenths over just scrapped my part dude. Interrapid wants 12deg Some starret wants 15 deg Most others I can name want the stem parallel. Welll explained though.
I don't think it's that complicated. Whether the indicator is close to perpendicular or way off, it moves 15 thou up, but at 45 degrees it moves 1.41 times the distance in. Also, I think cosine error for runout indicating is useful, since it accentuates the error, making your tolerances smaller. It's not that complicated, but it does sometimes need to be worked around. Bore gauges and OD gauges don't have cosine error, but it could be an issue if your indicator setup is moved between measurements.
Just thinking out loud here, but if you were tramming then wouldn't the increased deflection increase your accuracy? Couldn't cosine error actually work out to be a tool to improve accuracy?
yes, just like tramming in a head on a Bridgeport manual milling machine. swing a bigger radius and you're head is more precisely perpendicular. .0005" over 12" radius versus .0005" over 6" radius is twice as precise.
Does anyone know if the cosine error through an indicator's standard range is accounted for in it's reading when they make the mechanism? Also, arn't (some? most?) dial indicators built to read true with about a 12 degree probe angle to the part?
Joel Cresswell the 12 deg is only true for interapids as far as I know. They're designed for no cosine error at 12deg. Past 12deg they will still get a cosine error. Calculating the error requires an additional step of subtracting 12 def from your overall angle first. So if your at 45deg with an interapid, you would calculate the cosine error using 33deg rather than 45 deg.
Ahh I didn't know that was only the interapid. So with most dial indicators your only correct when the probe shaft is perpendicular to the axis of movement (might be a bit of a funny way of putting it)? Seems like having a offset like 12 degrees would be more convenient in a lot of places.
Joel Cresswell I dunno if it's only interapid. But I know that's interapids claim to fame. Reality is the cosine error of most indicators at about 10deg is smaller than the accuracy of the indicator itself so the cosine error that small is essentially canceled out by other, greater errors in the instrument or simply the intrinsic accuracy of the indicator itself.
I think a key bit of understanding is that cosine error exists the moment the stylus moves. It is tuned to be the LEAST at 12° (or whatever the manufacturer specifies). But you are converting linear motion to rotational and the two just aren't constants to each other.
to call the indicator perpendicular, you would want it perpendicular in the x and y axis, this is also called "normal" to a surface in math. ya weird name, but that is what you would call something perpendicular in two axis with a 90* separation.
using advantage of cosini error give you more acurate data (if you not need measure something) good if you find center point. more cosini error more needle move. more acurate it will be. . if need dial part to lathe its better put needle allmost 90 degree. you get more needle move and you only measure is part turning centre. MORE ACURATE. i have never needed dial to measure lenght. allways use for difference
Andre Gross gage blocks + test indicator beats drop indicator any day. Drop indicators have substantial hysteresis error for one, second they are rather prone to temperature shifts
John, I highly suggest checking out the Khan Academy Trigonometry videos here on YT (bit.ly/2mV19gS). Trig is relatively simple to learn and I think it is the most important form of mathematics for a machinist and CAD person to know. As others have said, cosine is a basic function of trigonometry and you will probably be able to solve this problem after watching just a few of the KA basic trig videos.
Every time I adjust the aim of the chute of my snow blower I think about cosine error, also when I see a police radar set up far away from shoulder of the road.
and if you just measure like center point of hole try put it biggest angle you get. you will get better .not need even 1 tik error and you beat automate systems
Do you really understand it if you can't reproduce the maths? This is really basic trigonometry. If I were you I'd insist until I can recompute the numbers in the table myself (tip: assume the thickness of the measuring tip and the radius of the end ball is an ideal zero).
Jérôme Vuarand Except the radius of the ball tip has zero effect of the indicators measurements. You could triple the ball size of the tip and still read exactly the same.
Occams Sawzall That's absolutely not true. The ball size may have a small impact, negligible even, but it's not zero. It's impact is inversely proportional to the arm length. Again it's basic trigonometry. If you want to follow these old-school machinist guidelines blindly it's fine, but you should keep in mind that they are approximations, and for each digit of extra precision you want to achieve they become increasingly irrelevant if not dangerously wrong.
Jérôme Vuarand No it has no impact because the indicator stylus length is measured from the center of the ball. Because it's a sphere, force and force vector from the spheres surface to its center always remains the same no matter what the size. It's an identical 1:1 movement ratio regardless of the sphere size. Unless the sphere is so large and heavy it causes hysteresis error in the indicator. But that's just due to the weight not the shape or size.
Just for the sake of clarity I'm talking about indicators with a rotating stylus, not a plunging one (which moves linearly). Just draw the stuff and you'll see you're wrong.
Jérôme Vuarand a sphere maintains tangency to a surface at all times. No matter what size the sphere the tangency point is the same, and the angle from the tangency point to the center is the same. Hence the vector of measurement is always the same It's a linear movement, just like a linear drop indicator. The size of the sphere doesn't matter. The movement of the sphere removes the arc angle error because as the surface the sphere is tangent to rises or falls, the tangent point on the sphere shifts, but the distance AND vector of the sphere center and surface tangency point remain the same. The sphere rotates against the surface in order to maintain a vertical linear vector from surface to the spherical center. This is why the angle of the stylus matters. The angle of the stylus to the surface changes the tangency point between the surface and the sphere. But the error is only effected by the stylus angle, not the ball size.
John. Yes, this is simple trig. Something that will help you visualize what's happening is to realize that the dial indicator does not really measure distance - it measures an *angle*. If you could have the tip at 0 degrees, then the angle subtended during the measurement (assuming it is relatively small) will be accurate - because the tip length of the dial indicator is part of the design of the indicator (cos(angle) * length of tip.) Now, to help visualize the error, imagine that the tip is angled at, say, 80 degrees instead. The angle subtended in this configuration must be much greater than when the tip is within about 5 degrees (as you know) to move the *same dimension in the direction of the material being measured*, so the dial indicates a much larger *angle*, and this is reflected in a larger number of mils on the dial. Conversely, if the tip is at 45 degrees, then you can multiply the value read on the dial by ~ 0.71 (the cosine value of 45 degrees) to adjust the artificially high reading on the dial. (This works for any angle. If the angle was 30 degrees, you'd multiply by cos(30) = 0.87.) Hope this helps.
Respect to a man who knows math and how a dial indicator works. I'd advice anyone interested in the matter to not just watch this one video, but to take a paper and solve this little trigonometrical exercise thoroughly by themselves, since the problem is a little bit more nuanced and involves approximation.
HI John,
The cosine correcting tips use an involute curve shape. With a spherical tip the effective lever length is always the same no matter at what angle the lever contacts the surface. With the involute shape, the effective length does change. At steep angles the more pointed tip would contact and the longer effective lever length results in a lower reading.
Hi John. Good demo here. I have encountered this in many mechanical instances and can guarantee a lot of engineers don't fully understand what is happening. I especially liked the stacking of the indicators to show the difference in readings. Well done.
I’ve known about cosine error my entire career as a Tool and Die maker. I assumed this was common knowledge. Perhaps I just got lucky and had a good journeyman teaching me. Great video, as are all your Fusion 360 videos.
Just came across this video. I'm a hobbyist. Thought everyone knew about cosine error.
Remind me of armor plating on tanks. How you can have a 1 inch plate and put it at an angle and its "thicker" and has more stopping power vs straight walls and 90 degree angles.
how can you skate on ice,but not through it, right?
Good to keep in mind. I'm a industrial Mechanic which maintains large 5 axis gantry mills for trimming and drilling composites. When they crash we do the alignments and geometry checks of the heads.
Gotta love that feeling of finally getting your mind wrapped around a concept after it's been stumping ya for so long. I remember finding out about this phenomenon while centering work in a 4 jaw, you can purposely angle the indicator to get more cosine error which can give the indicator a perceived higher resolution. Dialing in that last thousandth with the indicator angled then becomes a few thousandths on the dial. Makes it easier to get closer to zero but not good for metrology, lol.. Interesting to see that the test indicators only increase the reading with the more cosine error they're set with. Thanks.
Studying engineering: We usually approximate up to 3-5°. It is also called linearisation meaning sin(phi) = phi and cosine(phi) = 1
Atlantic Film cool
Nice....
John, as someone just advancing into machine work, these are the tips and demos that I find helpful, fascinating, and just fun to watch. Nicely presented, oh BTW, loved the new shop sign video, nice!!!
oh jesus. thanks for making me rethink my whole career 😂 only had 5 years of exsperience as a cnc operator. and never heard of this stuff. man my mentor sucks... thanks for saving my ass!
Buckminster Florptron yes it is.
I worked with a couple of other CNC technicians who had long experience (over 30 years for one of them, and 41 years for the other). The more experienced one was even our "tool guy". Out of 12 guys in my department, I'm the only one that uses trig on a regular basis to make my job quicker and easier, the rest of them do a lot more sample and adjust stuff, but end up in the same place usually. I've taught a couple of the department pups a little useful trig, but honestly, I just don't think anybody else in the department actually has a good grasp of trigonometry or how easy and useful it is in our work, no matter how many times I tell them "Some old hippie, Caught another hippie, Tripping on acid".
Perfect timing as usual.
Came up today in the shop. Probably within 30 min of this hitting the channel.
I like this demo. The interesting thing to me is you can find the correct angle to put your indicator by simply changing the contact angle to minimize the indicated reading. This is similar to checking flatness of a surface that is not necessarily parallel to your indicator or surface plate; you can use a leveling table until you get the smallest total indicated reading, or until your measurement is within tolerance requirements.
you get the same effect with car suspension as the wheel travels through its arc. The wheelbase changes effectively as it moves through from extension to compression, and you get lateral scrub at the contact patch between the tyre and the tarmac.
Hi John. Let me give you a related topic, that can come into importance when you are lifting equipment. Figure the weight a lifting strap is exposed to when moved out at an angle other than 90 degrees to the load. Two lifting straps hanging straight down from a hook, (90 degrees to the load) lifting a 1,000 pound load each strap will see 500 pounds a piece. Now move the straps out to a 60 degree angle to the load, then out to 45 degrees, then to a 30 degree angle with the load. I'll give you a hint, the 30 degree angle is against the law when operating a crane!
you can calculate the cosine error with trigonometry if you know the angle of the indicator. in the case of your example, the tilted indicators are measuring the hypoteneuse of the triangle. you can use this to your advantage and measure tenths or smaller on larger scale instruments. similar to the old fashioned method of turning the top slide of a lathe such that you get half thou increments to a thou increment dial. an indicator perpendicular to a known angle will give a calculated dimension. test indicators become more laborious to calculate the arc but still doable and accurately.
Excellent demonstration. The dial indicator visualization made it finally click.
Is it a Skewed test with the radius of the top of the plunger and the angle that the test dial indicator is in relative to the dial indicator? So therefore possibly not giving the correct answer to the question?
So glad you did this, sometime ago I questioned how an indicator had been set up saying there would a cosine error, I was derided as a nut! Even though I have the small explanation paper from Brown and Sharpe .000!" indicator! In a job I had inspection we had carbide tips but still kept a look out for a wear flat.
@NYC CNC - Actually .. the plunger, atleast the ball, is always moving the same distance. However, the angle between the measuring surface and the plunger causes the axle in the indicator, that the plunger is attached to, to rotate a bigger number of degrees under the same measurement. The problem is, that cosine error causes the mathematical length of the plunger to vary - while the indicator is only calibrated to the operational length of the plunger (distance between plunger ball center and axle of rotation in the indicator), when the plunger is level to the surface of measurement. I hope that made sense :s ... Keep up the good videos :)
I was always taught that a dial indicator should never be used to measure, only to indicate a position or surface. Your example is the reason why.
I thought I read somewhere that lever indicators are calibrated to read correctly when the lever is at 22.5˚ - the shallowest possible lever angle which didn't let the "knuckle" (where the lever pivots) hit the piece to be measured. This let you take accurate measurements out in the middle of a flat test piece. I recently got a digital lever test indicator (Fowler/Sylvac) and the instructions said that the instrument was calibrated to be correct when the lever was dead horizontal. This makes me wonder whether my original recollection was true or not; I suspect not.
As it is, the only way to get absolute measurements with a lever indicator out in the middle of a large flat surface without trig calculations or lookup table would be to place a gauge block on the surface to be tested, indicate on the gauge block, and then subtract its thickness.
Nice demonstration of cosine error. The Increased Angle shortens the external working length of the lever to fulcrum point vs. lever's distance to the fulcrum cannot change internally because it is mechanically fixed within the body of the indicator. The short end of the stick upon a fulcrum will produce more travel at the longer opposite end of the lever. With proper consideration the external stylus length from it's fulcrum point could be changed to accommodate using the indicator at an angle. All boils down to the simplicity of lever length's and fulcrum positioning, calibration. Error leads right back to the... Angle of the dangle.
Howzit John,
The error is actually a sine error when using your straight plunge DTI. You have it placed at approximately 60 Deg to the surface table. So for the feeler gauge to lift it 15 thou. The plunger can only travel longitudinally in the 60 deg plane so using the sine rule of Sine@ = opp/Hyp. Sine 60 = 0.015"/Hyp. Hyp = 0.01732". The Hyp is the travel of the plunger.
hi sir, I learnt that the tip of the indicator should make a twelve degrees angle the datum. When you do that you humbly overcome the cosine error.
I don't think that is right, there will be no cosine error at zero degrees (or 90 degrees depending on how you look at it) the greater the angle the greater the cosine error.
Where did you get that handy dandy paper with the chart and indicator illustration on it?
Excellent video man!!!! so informative and with properly set up demonstrations!!!!
So when traming a vertical mill head in, would it matter the angle of your last word? Being that there are interruptions on the table?
So you can use cosine error to actually increase the resolution of your dial test indicator?
end of the indicator moves on a circular path, you are not bringing the measured object under it normal to this circle. thus you are not measuring the thickness perpendicular to the material, instead at an angle. Example: the picture you have with the mitutoyo paper, draw a line through the material you are measuring at right angles, then draw the same line slightly slanted, the slanted one will be longer.
We use a plunger clock as a dial indicator, useful for actual measurement. We use a finger click as a dial comparator, not useful for actual measurements, but good to compare for things like clocking up.
And just to provide a big REMINDER when you are checking tool runout: Remember cosine error. If you are trying to check the runout on the small unfluted portion of an end mill sticking out from a ER collet it is easy to get a DTI at a lot more than 10 degrees to parallel to the tool. So... do you really have .001 runout or is it actually a LOT less? 30% as shown in this video is a huge difference when talking about tool runout. It would be very easy to get a measurement that shows a lot more than you actually have.
advil000 this shouldn't be a problem when measuring tool runout, because you're measuring the distance to the center of the chuck relative to other sides of the mill.
nice video. can u plz make a video about touch propes with mach3. to be able to find centers and edges easier. i have built a diy touch probe and cant find a way to make it work with mach3
Thats why you don't measure parts with a dial indicator. You use the indicator to establish the hight and transfer that height to a hight master. (The tall thing behind him.)
question... can you use this quirk to make your test indicator more sensitive, intentionally? say, for a relative measurement, I set my angle at 45° to get more needle deflection?
angular vs radial measurements.. examine a clock face and the difference between time setting for a give horizontal line moved vertically.. the change is most drastic at top and bottom of the clock. the angular displacement is greater for the hands the farther you get from the 3 o clock position.
Hey John, Excellent demo on showing and proving cosine error! Once understood its easy to avoid/correct!
Cheers,
Ray
Learned something new today.
BUT. Does the "error"make it more accurate in showing deviation ? Or in other words make it easier to show deviation like using a higher definition indicator ?
thats is only completely necessary when using the indicator as a measuring tool, not really as necessary when using it as a comparison tool for checking for concentricity or tramming a mill
Nice lesson, well taught, well demo'ed. I was taught pretty much the same thing when as an apprentice did my rotation through layout and inspection. "Two Tenths" Tommy Thompson, a notorious anal retentive and hair splitter ran me through a mini training course where it was my responsibility to think through and demonstrate to Tommy's satisfaction the many traps and misperceptions of Euclidian geometry as appliepd to the machinist's trade along with physics, materials, reporting, planning. He was a bastard but he taught me a lot. Glad you are passing along a few of these same lessons in a far more palatable form.
I would like to have seen the simple right triangle from which "cosine error' was derived; how the inclined axis of the travel indicator's plunger follows the hypotenuse; how the corrected reading equals the reading along the inclination angle divided by the cosine of the inclination. Then relate that to a DTI which actually measures angles of rotation but is calibrated on the dial in thousandths on the contact's arc.
You can't pass off essential shop math as too bothersome to learn.
Sorry - picky, picky
Isn't the cosine error in regards to a test indicator (or the like) really just a function of the fulcrum lengths of the arm/nib (or whatever they're called)?
Picky point but the indicator isn't "wrong" it's just measuring an angular deflection you asked it to :)
Chris Brent makes it sound like it's the cosine's fault. Hmm.
Off topic, what do you think of the kress 800 kit for engraving serial numbers or any type of engravings?
It is the same as a right triangle....it is just a really small triangle. So, when you have a triangle, you have 3 sides. One side is flat on the table. Two, is the height (this is represented by the height of the feeler gauge). The last side of the triangle is the hypotenuse....or the long side. The long side is representative of the error you see.
If your gauge is correctly positioned, you read the actual height (90 deg) from the surface. If your gauge is at an incorrect angle, let's say 20 deg off, (the hypotenuse is at 20 deg off 90 deg.....or basicly 70deg from the surface. That line is longer than a straight distance from the tip of the gauge to the surface.....and that is the distance your gauge tip is actually traveling.....thus the error.
Very interesting. I can certainly see where cosine error would cause some issues in the shop. Thanks for sharing
The top indicator is reading 15 because its at the same angle as the table and feeler guage. The issue is when you dont have the axis vertical to the part being measured your reading the part's thickness at an angle which means you have more material to pass though. Just like if you drilled a hole though a peice of material, the more the angle of the hole off 90 degree the longer bolt you will need to reach the other side.
I think the main issue is that it's hard to see the angle when measuring with that type of guage. Your reading the distance to the table at a 90 degree angle from the tip not directly 90 degrees from the table.
Learned something new again.... Love YT.. Thanks buddy.. Grt Marcel
The easy answer to visually understand what's causing the error is if the stylus is not parallel to the material being measured it cannot measure vertically through the material thickness it will instead measure the material diagonally through the material thickness. The greater the angle the longer the diagonal plain through the material.
not only you show us cosine error but also a paralax error :)
Wow, this just explained so many mysteries that have been driving me crazy for years.
I love the setups to demonstrate what is happening. However, the idea of cosine "error" is not really accurate, but a misunderstanding of what a test/lever indicator actually measures.
It gives the length of the hypotenuse of a triangle, not the vertical distance of change. IF it is positioned accurately, then these two numbers are the same (cosine of 0deg=1 or 100%). +/- 10deg gives an accuracy of about 98.5% (cosine of 10deg = .985). That means a .015" feeler measures .0152" at 10deg and .0148 at -10deg. At 30deg, the same feeler will measure .173". Assuming your feeler is perfect and your measurements are perfect, your indicator is set at a 33.56deg angle: .015"/.018" = 0.833, inverse cosine of 0.833=33.56deg. That is a far more accurate measurement than guessing and then using a poorly constructed table. (I say poorly constructed because of the poor rounding skills involved where 0.866 rounds to 0.86.) Using very easy and basic trig (cosine), the measurements are more accurate, and the resulting work is more precise.
Love the videos, especially short videos like this one!
super clean shop you have
So the stylus needs to be parallel to whatever piece you're indicating. Now what about the stylus in relation to the test indicator? I put the stylus at 90° (with the indicator horizontal, the stylus will be either straight up or down) a lot to check faces. Is there any margin of error in any of the indicator positions? I'll try to clarify if needed.
Ed M stylus to indicator doesn't matter. Just stylus to part.
you're actually getting 2 different flavors of error with those 2 indicators. the straight dial indicator is measuring the hypotenuse of a right triangle. the further from vertical it is, the worse the error. the other indicator is angle based. the angular change caused by the same feeler gauge varies as the angular pre-load AND body angle vary. thus, the measurement read will vary in accuracy.
And sometimes this is used as a feature. The same effect you get here with the cosine error (longer travel) is what is used in armoring of vehicles. By setting it to an angle, you (besides the obvious chance of ricochets) increase the effective thickness of the material.
Oh before I forget: Excellent demonstration!
Also most people don't realize is that you cannot use a longer or shorter needle on a test indicator than the length of the needle it was supplied with you will get different readings, ie. cannot swap a 1/2" long needle with a 3/4" or 1" ( I've seen guys try this to get into tight spots) if you do you get a completely different reading. I believe that is considered the same thing as cosign error, yes? do you agree?
This is not quite the same as cosine error, though I suppose they are somewhat related. As long as you know what you are doing you can use a longer or shorter tip, but you can not read the indicator directly. If you use a tip that is double the length for instance the indicator will read half the real measurement (since the angle now only has to change half as much to move the tip the same distance).
This is true and I do know this... but its good to point out and make people aware.... I guess the length of the needle could be considered the cosine leg of a triangle (if you draw it out on paper to be so...so if the cosine changes of the triangle (ie. the needle length) the reading in the mechanism of the indicator will be different... cosine error.... or something somewhat related... LOL... Honestly after 32 years in this trade this is the first time I heard the term "Cosine Error"...
not a triangle, but actually an arc. by the length of stylus you change the radius of the arc... so you maybe can call it "arc error"? no idea if thats a technical correct term or not ;)
Lenny Sweet you can. You do change the read out though. Whatever factor you change the stylus by you change the read out by
So if you go from a 1" length to a 1/2" length, the indicator reads 1/2 it's original measurement. Vise versa if you go from a 1/2" to a 1". The indicator reads double its original.
That's why I buy long stylus indicators and have 1/2 length styluses to put on it. Effectively makes the indicator twice as accurate
First time for me, too, Lenny.
I CAN`T BELIEVE THIS !! I`m teaching myself how to use a lathe and small mill I bought..Just last week I bought a cheap dial test indicator and used a .015 feeler gauge to test it the same exact way you did. It showed @.018. I thought I received a bad indicator so I bought a Starrett, did the same test and can up with .018-.019. I thought WTF !? What`s going on here ? My mic shows .015 but the indicators are off. Could they both be bad ? Well thanks to you now I know and I`m going to try it at the new angle and see what happens..I bet they`re both dead on...LMAO...Thanks so much for this John !
Not understanding this before you bought two indicators actually helped you. Now you have a cheap indicator to use on things you would hate to put a good instrument through, plus you have one you can trust if you treat it right.
I was thinking that also...Plus I also have a mill and now I don`t need to run back and forth between the two for a indicator...Yeah me for being an idiot ! lol
Almost all of my best moments involved me being an idiot at some point in the process.
It's like axial offsets on a 5 axis grinder. A few tenths add up to almost a thou.
I think the instructions that came with my Interapid test indicator said 12° is the angle the stylus should be at compared to the measuring surface. I find it to be too much of a bother to actually set that angle, and just attach the indicator to a height gauge, or use the machine's scale for taking any actual measurements. The swivel points have enough friction that repeat-ability is within a couple tenths of a thousandth of an inch.
you'r good teacher .. i love ur video it short and direct to the point
very cool video.
I just had a conversation with one of the guys in machine shop about that
Not soaking in yet... but it will start my mulling-it-over process. Thanks for the info.
servant74
It's just like a lever and fulcrum.
If you have a fulcrum dead in the middle, and push down an inch on one side, the other side will go up an inch.
If the fulcrum is moved half way between the mid point and end of the lever, pushing down an inch on the long side, will only raise the short side half an inch. And pushing an inch down on the short side, will raise the long side 2"
Can I deliberate a cosine error to more accurately indicate my part on the lathe for concentricity?
ImpactoDelSur Enterprise
Run out would be a relative measurement. That's not effected by cosine errors
True its relative, but you should see a larger deflection for the same runout, making the dial more sensitive and easier to spot runout! Cool cosines!
will cosine error effect truing up? or as long as the it looks true it is true ?
collin simpson truing or traming is relative measurements. As long as you maintain the same tip angle for all measurements, the relative distance from one spot to another will be correct,
Cosine error only effects absolute measurements when you're trying to measure the actual distance from a known point to an unknown.
So its akin to the measurement sensor moving up a ramp compared to moving up a ladder its measuring X and Z movement while your only expecting it to measure Z movement.
Cool could you make a video on the Abbe Error (Sine error I think is its other name).
God bless.
Very good example. Thanks for sharing.
How to understand cosine error? Just marry an engineer. :) Nice video John!
A) Trig is a thing, and cosine error is all about the trig of a right triangle (darn you Pythagoras). B) Here is a quick trick to calculate cosine ahead of time if your not sure you trust your setup... Run your gauge over a gauge block with a know (and certified) size.. if you know the block is X, and your getting Y, you can work backwards to your cosine error... and either keep mucking with the needle to get to 90 degrees or just dance with the one you brought and do math to find your true result (though calculation will mean your resolution is off, which will also mean you may loose a significant digit in your calculation so... YMMV..
Nice presentation.
Attach both indicators at different angles to the same height stand and make them deflect half of the dial capacity, you'll see the same without messing with a feeler gage.
For a builder, when we take the dimensions of a room we don't take measure them diagonally but at right angles. Who knew it was because of COSINE error, or was that the reason why Norm always said measure twice, cut once.
A couple tenths over just scrapped my part dude.
Interrapid wants 12deg
Some starret wants 15 deg
Most others I can name want the stem parallel.
Welll explained though.
This same error can also occur in police speed radar guns.
Thank you.Best explination ever👍
I don't think it's that complicated. Whether the indicator is close to perpendicular or way off, it moves 15 thou up, but at 45 degrees it moves 1.41 times the distance in.
Also, I think cosine error for runout indicating is useful, since it accentuates the error, making your tolerances smaller.
It's not that complicated, but it does sometimes need to be worked around. Bore gauges and OD gauges don't have cosine error, but it could be an issue if your indicator setup is moved between measurements.
How many degrees of travel do those indicators have?
Pul5ar
Depends on the make/model. But typically around 200-210deg
Just thinking out loud here, but if you were tramming then wouldn't the increased deflection increase your accuracy? Couldn't cosine error actually work out to be a tool to improve accuracy?
yes, just like tramming in a head on a Bridgeport manual milling machine. swing a bigger radius and you're head is more precisely perpendicular. .0005" over 12" radius versus .0005" over 6" radius is twice as precise.
Does anyone know if the cosine error through an indicator's standard range is accounted for in it's reading when they make the mechanism? Also, arn't (some? most?) dial indicators built to read true with about a 12 degree probe angle to the part?
Joel Cresswell yes. That is the chart he holds up in the Mitutoyo catalog.
Joel Cresswell the 12 deg is only true for interapids as far as I know. They're designed for no cosine error at 12deg. Past 12deg they will still get a cosine error. Calculating the error requires an additional step of subtracting 12 def from your overall angle first.
So if your at 45deg with an interapid, you would calculate the cosine error using 33deg rather than 45 deg.
Ahh I didn't know that was only the interapid. So with most dial indicators your only correct when the probe shaft is perpendicular to the axis of movement (might be a bit of a funny way of putting it)? Seems like having a offset like 12 degrees would be more convenient in a lot of places.
Joel Cresswell
I dunno if it's only interapid. But I know that's interapids claim to fame.
Reality is the cosine error of most indicators at about 10deg is smaller than the accuracy of the indicator itself so the cosine error that small is essentially canceled out by other, greater errors in the instrument or simply the intrinsic accuracy of the indicator itself.
I think a key bit of understanding is that cosine error exists the moment the stylus moves. It is tuned to be the LEAST at 12° (or whatever the manufacturer specifies). But you are converting linear motion to rotational and the two just aren't constants to each other.
to call the indicator perpendicular, you would want it perpendicular in the x and y axis, this is also called "normal" to a surface in math.
ya weird name, but that is what you would call something perpendicular in two axis with a 90* separation.
great and informative video!
Basic trig.... I love the passion! I feel the same when maths click. Hypotenuse will always be greater than the height.
Great explanation.
finnaly a way to explain that to someone.
thanks a lot, now i can show them theyer faults xD
regards from swizerland :)
Nice explication very useful
john nice tip.
using advantage of cosini error give you more acurate data (if you not need measure something) good if you find center point. more cosini error more needle move. more acurate it will be. . if need dial part to lathe its better put needle allmost 90 degree. you get more needle move and you only measure is part turning centre. MORE ACURATE. i have never needed dial to measure lenght. allways use for difference
good tips thanks
You never explained WHY/HOW it happens you just explained THAT it happens.
DTI's are not meant for inspection measurements, you should use drop dials for absolute measurements.
Andre Gross yes they are in fact with gage blocks there is no better way to measure for .0001 accuracy.
J H but it will never be as accurate as a drop dial.
Andre Gross gage blocks + test indicator beats drop indicator any day.
Drop indicators have substantial hysteresis error for one, second they are rather prone to temperature shifts
The cool thing is when you understand what's going on. Your 0.001" indicator just became a 0.0001" for dialing in parts on the lathe.
Thanks. Great video!
Anyone notice the tool changer on the tormach
John, I highly suggest checking out the Khan Academy Trigonometry videos here on YT (bit.ly/2mV19gS). Trig is relatively simple to learn and I think it is the most important form of mathematics for a machinist and CAD person to know. As others have said, cosine is a basic function of trigonometry and you will probably be able to solve this problem after watching just a few of the KA basic trig videos.
Every time I adjust the aim of the chute of my snow blower I think about cosine error, also when I see a police radar set up far away from shoulder of the road.
Excellent!!!
and if you just measure like center point of hole try put it biggest angle you get. you will get better .not need even 1 tik error and you beat automate systems
This is why you needed to pay more attention to trigonometries at school
Great video - but such dial indicators should not be used for absolute measurement - only for comparison.
Do you really understand it if you can't reproduce the maths? This is really basic trigonometry. If I were you I'd insist until I can recompute the numbers in the table myself (tip: assume the thickness of the measuring tip and the radius of the end ball is an ideal zero).
Jérôme Vuarand
Except the radius of the ball tip has zero effect of the indicators measurements. You could triple the ball size of the tip and still read exactly the same.
Occams Sawzall That's absolutely not true. The ball size may have a small impact, negligible even, but it's not zero. It's impact is inversely proportional to the arm length. Again it's basic trigonometry. If you want to follow these old-school machinist guidelines blindly it's fine, but you should keep in mind that they are approximations, and for each digit of extra precision you want to achieve they become increasingly irrelevant if not dangerously wrong.
Jérôme Vuarand
No it has no impact because the indicator stylus length is measured from the center of the ball.
Because it's a sphere, force and force vector from the spheres surface to its center always remains the same no matter what the size.
It's an identical 1:1 movement ratio regardless of the sphere size.
Unless the sphere is so large and heavy it causes hysteresis error in the indicator. But that's just due to the weight not the shape or size.
Just for the sake of clarity I'm talking about indicators with a rotating stylus, not a plunging one (which moves linearly). Just draw the stuff and you'll see you're wrong.
Jérôme Vuarand a sphere maintains tangency to a surface at all times. No matter what size the sphere the tangency point is the same, and the angle from the tangency point to the center is the same. Hence the vector of measurement is always the same It's a linear movement, just like a linear drop indicator.
The size of the sphere doesn't matter. The movement of the sphere removes the arc angle error because as the surface the sphere is tangent to rises or falls, the tangent point on the sphere shifts, but the distance AND vector of the sphere center and surface tangency point remain the same. The sphere rotates against the surface in order to maintain a vertical linear vector from surface to the spherical center.
This is why the angle of the stylus matters. The angle of the stylus to the surface changes the tangency point between the surface and the sphere. But the error is only effected by the stylus angle, not the ball size.