It’s a common problem for a machinist to need to find the center of a circular feature–either a boss or a hole.  There are a lot of ways to do this ranging from using a probe on a CNC to using one of the many tried-and-true methods that started out with manual machining.  Our Complete Guide to Metrology goes over a bunch of methods.

The Blake Coaxial Indicator is one of those methods left over from the days of manual machining:

blakeco-axindica

A Blake Coaxial Indicator…

You stick one of these little goodies in the spindle, position it over the feature in question, start it spinning slowly, and adjust position until the indicator needle stops swinging.  There’s an offset arm not shown in the picture that keeps the indicator facing your way.  It usually takes more time to dig out your Blake Coax and stick it in the spindle than it does to dial in the feature–they’re very convenient, in other words.  If there’s a knock on them at all, it’s about their accuracy.

If you want to measure the feature much more accurately, most machinists reach for what is typically called a “Zero Set:”

Zero Set Indicator

Zero Set-Style Indicator Holder…

The one I’ve got was made for me by a fellow from CNCZone called “Widgitmaster.”  It’s a beautifully made piece of work with a fine screw adjustment for diameter.  You stick it in the spindle and you can tell when you’re centered on the feature because you rotate the DTI (Dial Test Indicator) and get no motion on the needle.  With a nice DTI, you can measure very accurately indeed.

But just how bad is a Blake Indicator compared to a Zero Set DTI rig like this?  I tend to reach for my DTI when I want to position to a thousandth of an inch or better and use the Blake when it is less critical.  Most of the Blake’s error is due to what is called “cosine error.”  It’s possible to have cosine error even with the DTI rig.  It’s a function of the angle the measuring needle has:

CosineError

Keep as small an angle as possible on  your DTI to minimize cosine error…

The cosine error is determined by the angle of the indicator tip to the surface being swept.  No or a very small angle means no error.   A large angle means a large cosine error.   How large can the error get?  Well, we can just take the cosine of some angles to see.  Let’s try this for some real measurements.  Let’s say we want to measure a distance of 0.010″.  If our indicator tip angle is 60 degrees, we multiply the distance read off the indicator (0.010″) by the cosine of the angle:

cos( 60 ) * 0.010 = 0.005″

What that means is that with the tip at a 60 degree angle, when the indicator reads 0.010″, the real distance is 0.005″.  That’s quite a bit of difference!  Clearly we want to be sensitive to cosine error when taking such measurements.

Aside from paying attention to the angle of your measuring probe, there are some interesting ways that DTI manufacturers have worked to minimize cosine error.  To learn more, click that prior link.

Note that the Blake Coaxial Indicator is a relative measuring device, so the effect of the cosine error is largely to reduce its sensitivity.  If you wonder exactly how much error we’re talking about here, we can use G-Wizard Calculator’s Geometry module to figure it out pretty easily.  This kind of problem comes up fairly often, and it’s useful to be able to put real numbers to a solution.  For example, it is a similar calculation to figure out how accurately a DRO scale must be aligned to a machine axis to give accurate measurements.

For this problem, let’s first consider the mechanism of the Co-Axial Indicator. It basically uses a probe that swings a little lever. That lever raises or lowers a ring, and the ring is connected to an indicator. The lever on mine is about 1/2″ long. So an important question to understand is how far must that lever move in order to move the indicator a particular distance, such as 0.001″?

Here is the geometry:

CoAxGeometry

How far must the arm of a Coaxial Indicator move to make the indicator needle show 0.001″ difference?

Now let’s set up the calculation in G-Wizard that produced that 0.1146 degree figure:

RightTriangleGWC

The Right Triangle Calculator from the G-Wizard Geometry tab…

This is an easy problem to set up.  Referring to our CAD drawing, distance “A” is the 0.001″ change on the indicator.  Distance “B” is the offset of the probe tip.

Here is the result:

CosineErrorGWC

We use the Right Triangle Geometry Calculator to find the angle…

And sure enough we can see the angle is 0.1146 for that particular deflection.

Given that knowledge, its easy to use the same calculator to figure out for a given probe length, how much it deflects to generate the same angle (0.1146 degrees)?

Here is our result:

 

Indicator Motion

Probe Length

0.0010″

0.0005″

0.0001″

1″

0.0020

0.0010

0.0002

2

0.0040

0.0020

0.0004

3

0.0060

0.0030

0.0006

4

0.0080

0.0040

0.0008

5

0.0100

0.0050

0.0010

6

0.0120

0.0060

0.0012

Probe length on the left, indicator reading at top, boxes contain the level of cosine error…

We can see that the indicator’s accuracy is based on how well you can read the dial. As mentioned above, the Blake’s is calibrated to 0.0005″ increments. You can certainly see that much motion of the needle, in fact it looks huge. Can you see the wiggle of 1/5 of a division? I certainly can, which would get me to the 0.0001″ column. The longer the probe, the less accurate you will be, but I seldom use a probe longer than maybe 3″, so the accuracy of the indicator is not too bad.  Looks like a little over half a thousandth with the long probe.  

You’ll still do better with a Zero-Set and DTI, but if you can read your coaxial indicator well enough, they’re more accurate than many believe.

 

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