Machine precision

Hello again, Mechatronitians,

February 2021

Everyone knows these two words: accuracy and repeatability. Without them, nothing would be possible in today’s world – even an orange squeezer would not work.

But what do these terms mean exactly? This might be obvious to some in the industry, but not to everyone. So today we are going to talk about these two terms as applied to machines, and about all types of movement and positioning of an object in space.

Accuracy in machinery refers to the proximity of different measurements, excluding accidental errors, i.e. the ability of a system to yield the same results when several measurements are performed. These measurements must be carried out under the same conditions in order to obtain the exact desired result.

In the world of machinery, the term “accuracy” may refer to different types of measurements, such as:

–Accurate measurements, i.e. the correct reading of any physical value, such as angle, length, temperature, etc.

–Accurate positioning, movement and stopping of an object.

–Geometrical accuracy or surface accuracy, such as flatness, straightness or parallelism.

In today’s post, we are going to focus on accuracy of positioning, i.e. in making sure a mobile object (such as a linear motor) moves and positions itself in a space with certain exactitude.

Let us suppose we have a linear stage inside a profile cutting machine moving right to left on a linear shaft (Drawing 1 and 2). We start moving at point 0 on the left, and go to position 2000.00 mm on the right. If we perform a measurement with a high-precision instrument such as a laser interferometer, we will see that the stage seldom finishes exactly at position 2000.00.

Position 0

Drawing 1

Position 2000,00mm

Drawing 2

In Case 1 (below) we choose 4 measurements: 1999.7 mm, 2000.02 mm, 1999.99 mm and 2000.01 mm. If we take the most distant values from the desired position (1999.97 and 2000.02), we see that there is a tolerance between -0.03 and +0.02. This is the positioning accuracy.

In Case 2 (below), also with four measurements: 1999.90 mm, 2000.24 mm, 1999.83 mm and 2000.12 mm. If we again choose the most distant values from the target position (1999.83 and 2000.24), we could say that tolerance here is between 0.17 and 0.24 mm.

The accuracy in Case 1, from -0.03 to +0.02 mm, is accordingly higher than in Case 2, from -0.17 to +0.24 mm.

Case 1

Case 2

The desired positioning depends on each application, on the type of machines, etc. The reasons explaining the aforementioned deviations may vary significantly: a failure of the measuring system, geometrical errors, mechanical or transmission errors, etc. They may or may not be cumulative, and they may vary with the ambient temperature, or simply with the stroke. The values we get at, say, position 1000 mm may be completely different (and even show a bigger deviation) than the values for position 2000 mm.

As for applications, a positioning accuracy of +/- 0.2 mm may be regarded as very high in the wood machinery industry, but for a tooling machine it is quite low, even insufficient.

1.Manufacturing pieces for assembly

In the case of machines making pieces for assembly, in which several parts interact to make a final assembly, for example a car’s gear box (where pinions are mounted directly via the bearings on a shaft). When manufacturing the pinion, the accuracy of the outer teeth and the inner side must both be high.

2. 2D and 3D Printers

When printing by passing several times over the same spot, the head of the printer must join several points with very high accuracy, otherwise the resulting printed matter would be distorted.

3. Manufacturing measuring instruments

The manufacture of mechanical pieces for making measuring instruments such as tables, calibres, micrometers, etc. requires the highest levels of accuracy.

As a general rule, we get a machine with X accuracy when every component has an accuracy of X/10. The sum of the errors of all components with an X/10 accuracy results in the total accuracy of the machine. As an example, if we wish to have a profile cutting machine with +/- 1 mm accuracy, we need to apply a measuring system of +/- 0.1 mm. This is only a general rule, which may vary from one type of machine to another.

Here we will comment briefly on the concept of “repeatability of positioning”.

This is the ability to repeat the desired position exactly, as it was done previously, under the same conditions.

Looking at the two cases above, which we have used to clarify the concept of machine accuracy, it can be clearly seen that Case 1 has better accuracy but also better machine repeatability: the linear stage repeats the 2000.00 mm position with a lower error range. However, high accuracy does not necessarily mean better repeatability.

Let us introduce Case 3, where we have the following four measurements: 1999.87 mm, 1999.9 mm, 1999.86 mm and 1999.85 mm. We can see that any of these values are far from the desired target between -0.15 mm and -0.11 mm, although ability to repeat the position is very high: +/- 0.02 mm (0.15-0.11/2).

When comparing Case 1 and Case 3, we could say that machine accuracy and machine repeatability are high in Case 1. However, in Case 3 repeatability is high but not accuracy.

Case 1

Case 3

Generally speaking, we need high repeatability in the case of fixed positions to be with the adequate degree of correctness: a palletiser, a pick-and-place machine, etc. In this type of applications, it is important that the machine repeats positions A and B with certain exactness, while intermediate positions are not relevant.

In general, we may be in one of the three cases shown below:

High Accuracy

High Repeatability

Low Accuracy

High Repeatability

Low Accuracy

Low Repeatability

The concepts discussed above are easy to understand. Every manufacturer must be clear about which of these are central to their applications. Producing highly precise machines is expensive and time-consuming. High precision is not always an essential requisite to a project, as sometimes high repeatability is enough.

So that’s it for today, dear readers. As usual, you can post your comments or contact us for more information. Don’t forget to subscribe to our blog so you’ll be immediately updated about new content.

See you in the next chapter or the blog.

Your SINADRIVES Team