The CMM accommodates large, heavy workpieces with measurement ranges of up to 3,000 millimeters in the X-axis. Source: Werth


Tactile and multisensor coordinate measuring machines (CMMs) are no longer used exclusively in the inspection lab. More and more, they are used directly in production. This means that operators must sometimes measure at temperatures that deviate greatly from calibration temperature. Measurement errors resulting from this temperature differential are often underestimated and neglected and, therefore, cause errors in measurement results.

In addition to other effects, such as thermally induced deformation of the measuring device and changes in probe lengths, the thermally induced linear measurement deviations, due to temperature of the workpiece and the scales, have been found to be a significant source of errors. Thus, appropriate corrective measures must be taken when installing measuring devices in production.

Thermally Induced Measurement Deviation

Temperatures that deviate from 20 C cause the scales in the CMM, and the part to be measured, to expand by different amounts because of their different materials. The influence of different temperatures compounds this problem. Because these expansions have the same direction in length- measuring machines, the only effect is the difference in expansion of the physical scale and the workpiece. The influence of thermal expansion is largely linear. A simple linear correction in each measurement axis can be implemented at a low cost. This is sufficient for small measured lengths.

Thermally induced change in length is principally calculated as follows:
ΔL = α • L0• Δt

ΔL = thermally induced change in length
α    = thermal expansion coefficient
L0  = Reference length; in practice, the measured length
Δt  = Temperature deviation     Δt = t – 20° C

  Expansion of the scale:
ΔLM= αM• L0• ΔtM
Expansion of the workpiece:
ΔLW= αW• L0• ΔtW

The thermally induced length measurement deviation (Fig. 1) is the difference between ΔLMand ΔLW:

ΔL = L0 (αW• ΔtW- αM• ΔtM)

As seen in the equation, with the same temperature deviation Dt at the workpiece and the scale assumed for the simplest case, only the difference in expansion coefficients determines the measured length deviation DL.

On a summer day at 35 C on the production floor, when measuring a 100-millimeter component made of PVDC without correction, an additional measurement error of 208 microns is expected (See Table 1). In practice, slightly different deviations are expected because the scale temperature and workpiece temperature are usually different. This does not change the fact, however, that the deviations are unacceptably large.

Lengthwise expansions of the scale and workpiece can compensate for one another if the scale and workpiece are made of the same material, such as steel-to-steel. In practice, this is usually not the case, so the expansion coefficients are different. One can conclude that an appropriate correction for the thermal influence is needed.

The CMM offers shop floor production efficiency for small measurement ranges. Source: Werth

Integrated Temperature Compensation

A new series of CMMs provides a solid design base, made of granite with encapsulated bearings. The devices are modular and can therefore be equipped to meet exact operator requirements. The equipment includes image-processing sensors, touch probes and laser probes. The machines allow simple manual measurements as well as CNC-controlled measurement with 2-D and 3-D CAD data.

All CMMs in the new series are designed to meet requirements of production floor use. They can calculate corrections based on expansion coefficients of the device and workpiece, workpiece temperature and associated temperatures of the scales. Sensors measure these temperatures, and thermal expansion of the scales is calculated automatically.

Table 1 Temperature-dependent, systematic measured length deviation, without correction, for the same temperature at the workpiece and scales.
This shows possible measurement errors associated with the thermally induced, measured-length deviation DL for workpieces of various materials at 20 C, 25 C, 30 C and 35 C ambient temperature. The values apply to a measured length of 100 mm, and for scales made of steel. It is also assumed that the workpiece and the scales are at the same temperature. Source: Werth

In the same way, the ambient temperature is measured near the workpiece, or optionally, a contact thermometer is used. For each measured value, the length-dependent correction value (DL) is calculated according to the formula and measurement results are corrected accordingly. This correction also applies to the machine diagonals because corrections are made in all three axes of the measurement volume. Thus, the projected components are considered.

Requirements are the entry of a precise value for expansion coefficients of the workpiece and the maintenance of spatial (DK/m) and time (DK/h) temperature gradients, in accordance with the manufacturer’s specifications. If the expansion coefficient of the workpiece is not precisely known, an estimate of the value will reduce the measured length deviation. This applies especially to large measurement areas.

Table 2 the remaining thermally induced measurement uncertainty with temperature correction.
Without correction at 35 C, for a 100-millimeter PVDC workpiece, there is a measurement error of 208 microns. With correction, the temperature influence is reduced as shown here. Source: Werth

Results of Temperature Correction

If temperature compensation is necessary, one cannot assume there will be no more temperature influences. Despite the correction for thermal influences, there is a remaining measurement uncertainty that is lower when the expansion coefficient of the workpiece is known and the temperature is measured more precisely. (See Table 2.)

Limit deviation is defined as the maximum possible (estimated) deviation from the true value. It is assumed to be distributed rectangularly.

According to international standards, the expanded measurement uncertainty is the standard deviation multiplied by the expansion factor k=2. Therefore, it applies to a confidence interval of 95%.

For the selected measurement example, it is assumed that the temperature can be measured at a limit deviation of 0.5 K. The expansion coefficient of the workpiece is known with a maximum deviation of 5%. A measurement uncertainty of 16 microns thus remains. Here, that is only 7.7% of the original error of 207.8 microns without correction.

The thermally induced length measurement deviation is the difference between the expansion of the scale and the expansion of the workpiece. Expansion of the scale and the workpiece have the opposite effect. Source: Werth

Tips for Practical Application

Temperature correction is more reliable and effective if the following actions are taken:

  • Allow as little temperature change as possible.

  • Avoid air drafts.

  • Enclose the devices if rapid changes in temperature occur.

  • Keep heat sources in constant operation.

  • Install devices at least 1 meter from the walls.

  • Thermally insulate the floor.

  • Do not allow direct sunlight.

  • The measured object should be at the ambient temperature.

  • Avoid touching parts with hands, or wear gloves.

  • Ensure constant temperature during a measurement cycle.

  • Carry out a drift check by reviewing the reference coordinate system, for long measurement cycles.


The CMM accommodates measurement ranges greater than 400 millimeters in the X and Y-axes. Source: Werth

CMMs can be used successfully in production, even under difficult temperature conditions, if the operator follows these steps and uses proper temperature correction. This will result in significantly fewer errors. These results could, under some conditions, be much greater than the production tolerances that are actually being inspected.

Tech tips

  • Operators must sometimes measure at temperatures that deviate greatly from calibration temperature.
  • For measuring small lengths, a simple linear correction in each measurement axis can be implemented at a low cost.

  • Lengthwise expansions of the scale and workpiece can compensate for one another if the scale and workpiece are made of the same material.

  • New modular CMMs measure temperatures with sensors and use scales to calculate thermal expansion automatically.