Volumetric Calibration

A call for a 3D standard

by Charles Wang, Ph.D.
President
Optodyne Inc.

Let's face it—we live in a 3D world. Engineers who are content with 2D drawings are fast becoming a minority. As a result, 3D is trickling down to the manufacturing floor. This has created a need for maintaining higher accuracy 3-axis machine tools. Because many more types of errors than linear displacement errors have a tremendous effect on 3D machining accuracy, the International Standards Organization (ISO) has begun the process of creating a standardized world-class definition of 3D accuracy.

Twenty years ago, the largest machine tool errors were linear displacement errors, such as lead or ball screw pitch error and thermal expansion along an axis. However, linear displacement errors have been minimized with the use of compensation and linear encoders and ball screw cooling systems.

As more components and molds are designed in 3D, additional errors, such as straightness and squareness, are superseding linear displacement errors in importance. Minimizing 3D errors has become increasingly important because machine tools are experiencing longer duty cycles and substantially faster spindle speeds, feed rates, and traverse rates, amplifying wear on machine tool positioning components and assemblies.

Creating a new world standard for defining 3D accuracy is difficult because it must include a process for measuring 3D accuracy and be easily deployed and not time- or cost-prohibitive. If the process is unwieldy or expensive, it will be ignored and ultimately forgotten. Without an accepted standard, components of a product or assembly made by different suppliers may have widely varying tolerances. This will lead to increased part rejections, longer assembly time, and additional warranty and field repair costs.

There are many theories for measuring 3D accuracy. The simplest theory calls for linear calibration or one-dimensional measurements parallel to the axis of movement. This assumes the only possible errors are lead or ball screw and thermal expansion errors. At the other extreme is Taylor's linear-expansion theory, which requires 45 measurements to determine the 3D (volumetric) accuracy of a 3-axis machine tool. Other methods, such as the rigid body and body diagonal methods are in between the two extremes. ISO must carefully consider all the methods and their tradeoffs to ensure that the standardized process for defining 3D (volumetric) accuracy is accurate and accepted by those who will be using it.

It's not practical to require 45 different measurements for determining 3D accuracy. The cost for a service technician to perform these measurements and the several days the machine would be out of service make it cost-prohibitive.

The rigid body method considers 21 errors, including:

• Three linear displacement errors

• Three vertical straightness errors

• Three horizontal straightness errors

• Three roll angular errors

• Three pitch angular errors

• Three yaw angular errors

• Three squareness errors

The 3D (volumetric) error is defined as the root-mean-square sum of the total of these errors. The maximum and minimum absolute errors can be defined as the maximum and minimum absolute errors in the volume. Using a conventional laser interferometer for measuring the straightness and squareness errors requires an excessive amount of time, which is cost prohibitive. As a result, the rigid body method has not achieved a high level of acceptance.

However, the B5.54 body diagonal displacement tests have been used by aerospace OEMs, including Boeing Aircraft Company, for many years with very good results. As a result, it has become a de facto standard.

Body diagonal displacement measurement
Measuring the displacement of only four body diagonals enables 3D accuracy to be determined. The volumetric positioning errors, including three displacement errors, six straightness errors, squareness errors, and angular errors, show up as the four body diagonal displacement errors. Therefore, body diagonal displacement is an efficient measurement of the volumetric error.

Body diagonal displacement errors are sensitive to all the volumetric error components and, therefore, make an efficient test of volumetric accuracy. A diagonal is defined by starting at one corner of the base plane and moving to the opposite corner at the top plane. These body diagonals are defined by the positive or negative axis movement. The last four body diagonals are the same corners as the first four diagonals, except the directions are reversed. Hence there are only four body diagonal directions with forward and reverse movement (bi-directional), and only four setups. Measurements are taken after each simultaneous X, Y, and Z move.

Sequential step diagonal measurement
For a machine tool with small body diagonal displacement errors, the volumetric error is small. However, if a machine has large body diagonal displacement errors, not enough data are generated to determine the errors causing the large volumetric error. In sequential step diagonal measurement, the machine spindle movement along each of the diagonals is measured by first executing X, then Y, and finally the Z portion of spindle travel. Readouts are taken and recorded at each intermediate step. This explains how three displacement errors, three vertical straightness errors, and three horizontal straightness errors are measured with only four setups.

Using Optodyne's Laser Doppler displacement meter (LDDM), the sequential step diagonal or vector measurement, 12 sets of data can be collected by the four sequential step diagonal measurements. Therefore, the three displacement errors, six straightness errors, and three squareness errors can all be determined. These measured errors can be used to compensate the volumetric positioning errors and improve the 3D positioning accuracy.

The ASME B5.54 and ISO 230-6 machine tool performance measurement standards identify the laser body diagonal displacement measurement as a quick check of the volumetric error. This body diagonal displacement measurement has been used by many aerospace companies with very good results for many years. Although, the simplest way, body diagonal measurements are not exactly volumetric error. They are related because a larger body diagonal error indicates a larger volumetric error, but the ratio is not exactly a one-to-one correspondent. The more complicated methods for measuring 3D accuracy, such as measuring 21 errors, are too time-consuming. The alternative, measuring displacement along the axis, as well as straightness and squareness errors, using the body diagonal method defined by ASME B5.54 and ISO 230-6, has been proven in the aerospace industry over many years and, therefore, should be accepted as the basis for ISO's world-class 3D accuracy standard.

Optodyne Inc.,
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