Rotary Table Accuracy

What is it?
How is it achieved?
How does it affect you?

In this section, we will try to answer those questions for you.

It seems like an easy-enough task, but as you will see, many relationships must be explored in the process. Furthermore, alternative words, definitions and concepts have often added to the confusion. One example is the term precision, a word which was once included in the title of earlier versions of this discussion.  That term, once frowned upon by the NIST as being too ambiguous is, nevertheless, included in the current ISA standards concerning accuracy.  So, even an era can affect perceptions.

Over the years, one concern, which often predominates discussions of rotary table accuracy, is the relationship between angular accuracy and linear accuracy.  Most people are comfortable with Cartesian coordinates, and their linear values which are expressed in 0.0001", millionths of an inch, or microns.  But, when arc seconds or even thousandths of a degree are introduced, it often becomes an abstract convention, uncomfortable for many.  We will, therefore, discuss the angular/linear relationship, as well.

It is important to realize that this document is not intended to portray itself as a standard, nor even as a defacto standard.  Its sole purpose is to provide a better awareness and understanding of the issues, and their application to rotary tables.

Table Of Contents

1. Introduction

2. Glossary of Terms

3. Accuracy vs. Resolution

4. Angular Accuracy vs. Linear Accuracy

5. Accuracy vs. Load

6. Index Accuracy vs. Radial Runout

7. Reference Data

Introduction

At INTERNATIONAL, we take the concepts of accuracy and precision very seriously–and we always have, ever since our founding in 1957.

To begin answering the headline questions, we shall start with some basics, including some of our philosophy relating to the design, manufacture and application of rotary tables.  Because we invest a great deal of pride and effort into each and every product that we manufacture and into every service which we provide, we thought that you might appreciate a little further insight. 

For us, quality is not just another buzzword, it is a commitment–and we want you to know about it and feel comfortable with it.  By providing you with the information contained in our data sheets and on the following pages, we hope that you can better evaluate our performance, and meaningfully compare our equipment with that which is offered by the competition. 

Obviously, our goal is to give you the information which you need to convince yourself, that ours is a truly superior product.  We have tried to stay away from ambiguous and vague claims such as "reads to" or "positions within."  Instead we clearly state our accuracy, and put it up front where it counts; we don't have to bury the specifications in fine print or in some obscure corner of the brochure.

Being open and concise, however, can have its drawbacks.  Over the years, we have at times provided answers when there wasn't even a question. Other times, when we answered one question, we created a new one.

Of course, this often gets us back to the beginning of this discussion.  So,  we developed a Glossary of Terms to help our customers and prospects understand what we mean by the terminology used in our catalogs, and we'll begin with them.

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Glossary Of Terms

The definitions which are provided are a compilation of both borrowed and home grown verbiage.  They may never make it to Webster's, but we think that they will help provide a mutual understanding of the terminology.

Arc Second	The prefix, arc, is used solely to differentiate this angular measurement from a second of time. By convention, it is 1 part in 1,296,000 of a circle; or 1 part in 3,600 of a degree; or 0.0002778 degree.
Backlash	The measure by which the tooth space of a gear exceeds the tooth thickness of the mating gear along the pitch circle.  It is affected by both the center distance at which the gears operate, any eccentricity in the gears, and the variation in thickness of the teeth.
Error Bandwidth	The total measure of deviation between all readings of an instrument throughout its measuring range.
Error	The difference between a measured value and the true value.
Flatness & Wobble	A composite tolerance applied to a flat surface rotating about an axis, e. g., the faceplate of a rotary table. It is defined such that the entire rotating surface lies between two parallel planes separated by a distance equal to the tolerance specified.
Hysteresis	A bias resulting from the reversal of direction.
Index Accuracy	The agreement of the result of an angle measurement between the actual reading of the instrument and the true value, that is free of other error, at that point.
Latent Motion	The measure of change, as measured at the platen in the axial and radial directions, between the unclamped and clamped condition on a table equipped with axis clamps.
Parallelism	The state of two planes parallel to each other; where two planes are equidistantly spaced in three dimensional space.
Perpendicularity	Condition of a line in which all angles to a reference plane are at right angles.
Repeatability	The measure of accuracy by which an instrument permits the return to a specific point.  In a normal or Gaussian distribution, the results are spread roughly symmetrically about the central value, and small deviations from this central value are more frequently found than the large deviations.  The normal curve can be represented by The standard deviation, denoted by is found by taking the difference between each observed particular value and the mean, then squaring the difference, adding all the squares, dividing by the number of readings, and then taking the square root.
Resolution	The smallest increment of measure to which an instrument can respond.
Rotary Axis Definition	A measurement which compares two full consecutive axis rotations to a known standard of roundness.
Roundness	A characteristic that all parts of a circle are identical.  The measurement of roundness is essentially a measurement of the change in radii, and the roundness error is the measurement between the minimum and maximum radii in one lateral plane.
Runout T.I.R.	Total indicator deflection as measured over on revolution of the spindle.
Squareness (Orthogonality)	A condition of being at a right angle to a plane or to a line.
Straightness	A deviation from a line of sight which is generated by a reflected light–as for example, an autocollimator and mirror.
Traceability	Documentation to establish that standards are known in relationship to successively higher standards, culminating with the National Institute of Standards & Technology, or equal.
Wobble (Axis)	The measure of deviation of a rotating plane to a reference plane.  The measurement is usually performed with a mirror and an autocollimator.

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Accuracy vs. Resolution

A common misconception in this age of digital positioning is that the resolution of the device must also be its accuracy. For example, if a digital readout displays to four decimal places (0.0001), then it must also be accurate to that same value. That is usually not the case.  Although high resolution is a prerequisite for high accuracy, it does not guarantee it. Consider the two graduated scales:

Both scales have 15 graduations over equal arcs; therefore, both have identical resolutions of 1/15th arc. For arc A the resolution increments are equal; however, for arc B the resolution increments are obviously not the same.  That difference, scale accuracy, is a component of position accuracy, and while both examples have the same resolution, each will provide very different results.  Unfortunately, it is not always this apparent.

The accuracy of a rotary table is influenced by many other factors, and some of these are either misunderstood or incorrectly perceived.  Often, the relative interaction of these factors is of greater consequence than the individual components.  These interactions must be considered when evaluating rotary table performance.  We will explore these relationships on the following pages, to assist you with defining the type of rotary table required for your application.

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Angular Accuracy vs. Linear Accuracy

Individuals working in the guidance and navigation industries are used to dealing with arc seconds and radians, but those working in other industrial environments must often relate these angle measurements to X-Y-Z coordinates, because most machine tools use a Cartesian coordinate reference system. This often leads to the question: Why don't you specify the accuracy of rotary tables in fractions of inches or millimeters?

The relationship between angles and linear dimensions is defined by trigonometry. Sine, cosine and tangent functions allow us to calculate these relationships. Because an angle diverges as distance from the origin increases, so too, increases the tangential component. Therefore, it is not appropriate to specify a rotary tables accuracy in linear values, unless a maximum envelope (diameter) is also specified.

It is not difficult to determine the linear relationships to their respective angles, within a specific envelope. Let's equate 1 arc second (see definition in Glossary) to some common linear measurements. For our discussion, we'll use 0.000004848 as the tangent of 1 arc second. Since the trig functions provide dimensionless ratios, 0.000004848 (usually rounded to (0.000005) applies to any unit of linear measure, just be consistent.

From the above relationship, we can see that an angle of 1 arc second diverges approximately: 60-millionths at 1-foot; or 5 microns at 1-meter; 25 yards over the distance between New York and Los Angeles; or about 2 km over the average distance between Earth and the Moon. At the point where the angle passes the Sun, the distance that the 1 arc second diverges, has grown to a whopping 450 miles!

Though the guidance people will be concerned about those longer distances, landlubbers dealing with day-to-day problems will appreciate the quick reference charts, below. We've provided both inch and metric charts, based on the working radius. For any tolerance shown, but for a longer distances than provided, simply proportion the values, e. g., for a 8-foot radius, divide the 4-foot value by 2 (8/4=2); for a 4-m radius, divide the 1-m value by 4 to obtain the required index accuracy.

To use the charts, locate your required tolerance, and the maximum radius to be worked, the resulting intersection shows the corresponding nominal index accuracy, in arc seconds (unless specified, i.e., [°] = deg.; ['] = min.), required for the application. If your tolerance zone or working radius falls between two values, use the tighter requirement. Depending on the application, you may even want a more accurate index accuracy. A traditional rule of thumb was to select equipment 3 to 10 times more accurate than the application. Today that's, of course, not always possible.

Table 1 [inch values]

Table 2 [metric values]

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Accuracy vs. Load

In most literature and data sheets, the relationship between load and accuracy is never stated. Load has a significant effect on accuracy. The rated loads which are specified in our literature is the maximum load which will not affect the accuracy of that product, in its highest standard accuracy grade, the Ultra-Supreme.

Our tables are the sturdiest and stiffest tables built–anywhere–and our ultimate load capacities far exceed any of our competitors'.  However, we see no value in stating disproportionately high load capacities which have no relation to the accuracy. Even though our tables boast axial and radial stiffness in the order of 10⁶ to 10⁷ lb/in and cantilevered moment stiffness in the order of 106 to 108 in-lb/rad, these values are far from infinite.  Many rotary table manufactures don't even state load capacity, and most that do, don't specify whether it is a radial, axial, or cantilevered (a.k.a., overhang or overturn moment) load.

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Index Accuracy vs. Radial Runout

Earlier we touched on the subject of interaction between two or more accuracy components.  The relationship between index accuracy and radial runout is often overlooked, partly because it is difficult to visualize.

When a rotating system turns in its bearings, it typically results in a radial runout; essentially the roundness of the spindle's rotation.  For air bearing spindles this can be as little as 2 or even 1 millionth T.I.R.; for some rolling contact bearings, it can be as high as 0.0003", 0.0005" or even 0.001" and more.  This runout is a linear translation along a plane which is perpendicular to the axis' centerline.

Typically, as one moves farther from the end of the spindle, or table top, coning, another radial component compounds the problem.  These errors can result in significant composite errors.

If these error values are large in proportion to the required working tolerance, this results in an additional error source, which must be corrected through number crunching and considerable bookkeeping.

Consider this situation:

Where A is the theoretical center of the rotary table, and B is the runout error.  This runout results in an offset error of ±S.  If B is small relative to the part's tolerance band, it can be ignored.  However, if B is large this error must be considered because the rotary index position is generated about A; whereas, the part's index angle is generated from its own center, which is located on B.  A part can not be centered better than the radial runout value.  If a table has a 0.0005" runout, the part can not be centered better than 0.0005".  The smaller the radius L, the greater will be the resulting difference between Æ and Æ', and the greater the tolerance error.

The following formula allows you to calculate the effective angular error, based on the runout error of the rotary table spindle, and the diameter of the part or feature:

where q_e is in arc seconds, b is the runout and D is the diameter, with both being expressed in either inches or millimeters.  For example: if b = 0.0002", and 
D = 10", then q_e = ±8 arc sec.

Consequently, at INTERNATIONAL, we have always proportioned our specifications so that there is a meaningful relationship between these factors.  As a matter of fact, because our tables are designed with integral position transducers, runout errors must be accurately controlled because it will have a direct impact on the Index Accuracy.  Under load, this condition can be further exacerbated.  That is why we make our tables structurally stiff; they have to be.  Without good stiffness, one would obtain different accuracy results under varying load conditions.

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