The CMM and Projection Errors

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Technical Support Article KB10229

Applies to: All Levels of Geomet
Last updated: Sunday January 09, 2011.

Projection Errors are often overlooked but their effect on the inspection process are tremendous.

A Coordinate Measuring Machine is a wonderful inspection tool when used by an experienced operator who has a sound knowledge of inspection processes, but when used by an operator who has limited knowledge in the inspection process, disastrous results can be delivered that undermine the confidence in the Quality Department. The ideal CMM operator is one who has in-depth knowledge in the inspection process as a result of years of manual inspection techniques.

However, we live in a world that has a shrinking pool of experienced inspectors as we rely on technology to deliver results. An experienced operator would have the "eye" to identify poor inspection techniques that result in errors such as Projection Errors.

The Measurement Process

To illustrate, let's use a rather simple test utilizing a 2" Gage Block and a Micrometer. This is a simple point-to-point measurement and we should be able produce the correct result with a properly calibrated micrometer repeatedly.

Using a CMM to perform this same measurement now involves several components that introduce uncertainty to the final results. Probe repeatability, CMM structural integrity, scale compensation, software algorithms, a Coordinate System and the operator are just some of the influences working against you to obtain the most accurate reading  possible. Please see Tech Note #2 for explanations on some of these items.

The micrometer provides a direct feedback from the anvils to the threaded, calibrated thimble. The main influence affecting the reading is the pressure applied to the anvils and work piece placement. Too much pressure, and the reading will be small. Not enough pressure or the work piece is held poorly, you report a larger reading.

The CMM isn't to simple. The touch probe makes contact with a part which informs the CMM software to capture an XYZ point. The relationship between the center of the probe and the actual scale is mechanically connected through a series of components starting with the stylus ball and ending with a scale reader head. The list below is a typical link from the XYZ measured point to the Y-Axis Scale:

  • Stylus Ball Radius
  • Stylus shaft length
  • Touch Probe
  • Probe Head
  • Z-Axis Probe Bar
  • X-Axis Bridge Structure
  • Y-Axis Main Support Base
  • Y-Axis Scale

If the CMM has a cube size of X=40" / Y=80" / Z=25" the distance between the data point and its reporting Y-Axis scale may have to travel through 70" or more of superstructure with each component adding its error to the result!

Example #1 - Measuring our Gage Block

The CMM through its software, allows you to establish coordinate systems that is not required to be in-line with the natural movement of the CMM axes. This coordinate system may even need to be outside the measuring cube as in the case of car coordinates in automotive inspections. The usage and placement of coordinate systems is one key component, that when used properly, will deliver the results you expect.

It is important to establish a Part Coordinate System (PCS) close to the desired location where the distance should be reported. As shown in the figure below, should the PCS be outside the effective location the distance is expected, the reported result will not represent the actual distance.

DistPCS.jpg (11006 bytes)
figure 11, Localization of the PCS

Referring to figure above, we have two established Part Coordinate Systems. PCS 1 is established on the base of the 2.000" gage block. PCS 2 is located 4.000" inches in the X direction from the right side of the gage block.

Two planes were measured, one representing the lower base and one on top of the gage block, The lower base plane was used to establish the XY PCS Base Plane for both PCS 1 and 2 which ensures that Z= 0.000 is common to both PCSs. The top plane has a AZ/X of 89.9943° and the AY/Z was 90.0000°. The intersection with the pierce point with the PCS1 Z Axis, d1, is reported at 1.9999". The reported pierce point on the Z axis of PCS2, d2 is 1.9995". By not having PCS localized to the actual measured surfaces we introduced 0.0004", d3, error!

Example #2 - Aligned Cylinder on Flange

Example #2 - Aligned CylinderIn this example we have a 0.25" diameter cylinder that passes through the outer wall of a larger cylinder. The center axis of the cylinder coincides with the axis of the larger cylinder.

The reporting coordinate system is the center of the cylinder identified as PC1. The cylinder has an inside diameter of 3.875" and a wall thickness of 0.25".

Once the PCS has been established on the ID of the larger cylinder, the stylus is articulated to allow entrance into the 0.25" through cylinder. Six data points are captured and the cylinder is calculated.

Problem: The cylinder is reported as:

Characteristic Actual
Diameter 0.2505"
X 0.0012"
Z 0.0001"
AX/Y 89.9828°
AY/Z 0.000°

The through cylinder is expected to be ±0.0002" in the X-Axis with a nominal of 0.0000". Clearly the reported value exceeds the allowable positioning.

Analysis: Looking at the reported projection angles we show a AX/Y of 89.9828° or 0.0172° which we can calculate the X-Axis deviation with. Projecting this over a distance of 4.000" we have a error of 0.0012"! This coincides with the reported X-Axis position. Adding to the projection error is the length of the measured cylinder which is less than the thickness of the cylinder wall.

Solution: Isolate projection error by translating PCS1 in the Y-Axis by 4.000" which creates a new PCS2. This will place the new PCS in the middle of the cylinder wall. Now measure the through cylinder which will report its position by piercing the ZX base plane of PCS2.

Press the <l>, Origin command and establish a new PCS with the ZX reported position from the just measured cylinder. Now we need to recast this position into the original PCS for reporting. This can be accomplished by recalling the original PCS, <'> Recall PCS command. Finally recall the Origin created with the previous step as a 3D Point into the current PCS. This is done with the, <shift + H> Recall Comps, command.

This recalled 3D Point will report a X= 0.000" eliminating the projection error!

Measured Feature Selection

Using a multi-point feature may not always deliver the expected results. In the case of a simple point-to-point gage block measurement, we could have used a -Z measured Point. With each -Z Point taken on top of the gage block, there will be no projection error. However, the full affect of CMM errors will be applied. In a multi-point feature, such as a plane, a single data point that has a repeatable error would be reduced by the remainder of data points in the calculation.

If a single point feature was being used and a repeatable error is introduced, the full error is used in the reporting. It is not uncommon to repeat a reading and have a spread of 0.00014" over many readings.

To test your CMM, fix a artifact on your table in the +X position of the measuring cube and clamp it down to prevent movement. Align your stylus in front of the artifact and lock the X and Z axes. Set the software up to capture +Y points and begin to make contact with the artifact. Move the CMM to different back off distances and approach speeds, but contact the artifact is normal touch probe speeds. Repeat this test by clamping the artifact at the furthest -X direction and compare the results.