What is Cosine Error?

What is cosine error? Let's put a dial test indicator on the plunger of a dial indicator to SHOW why the angle of measure affects in the measurement!

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[iPadApprentice]

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.

[joepie]

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.

[EVguru]

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.

[danb]

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.

[jasonholm]

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.

[patricksullivan]

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!!!

[BrickTactical]

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.

[massquantities]

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.

[edrees]

Excellent demonstration. The dial indicator visualization made it finally click.

[AntimatePcCustom]

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!

[msek]

Studying engineering: We usually approximate up to 3-5°. It is also called linearisation meaning sin(phi) = phi and cosine(phi) = 1

[MorganOliff]

Perfect timing as usual.
Came up today in the shop. Probably within 30 min of this hitting the channel.

[Stephen]

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.

[Perryman]

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.

[pewpew]

Excellent video man!!!! so informative and with properly set up demonstrations!!!!

[wayned]

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.

[brunohougaard]

@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 :)

[thedraggon]

Very interesting. I can certainly see where cosine error would cause some issues in the shop. Thanks for sharing

[ScottMoyse]

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.

[Nobody-ldmk]

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.