For a long time, tactile CMM was the first choice for Geometric Dimensioning and Tolerance (GD&T) measurement due to its universality and high accuracy. So far, no other measuring equipment has such a wide application in the field of geometric measurement.

As versatile as the CMM is, a work piece with a free-form surface, for example a turbine blade, can still pose significant challenges. Although tactile CMM has been widely used in the turbine blade manufacturing segment for decades for quality control of aeronautical blades, there are shortcomings worth examining.

Non-contact methods can be used to solve some of the challenges.  Some of these shortcomings, however, like the cosine error, can be compensated for if the operator can recognise the inherent errors in tactile measurements and manage them to produce accurate results.  

Taking Error Into Account

The measurement of blade airfoil is normally performed by evaluating its specific section profiles regarding their profile/positioning deviations. These section profiles have specific heights referring to a certain datum, and are generated by intersecting the airfoil with planes.

These resulting closed 3D planar curves are the section profiles, which are to be inspected. Although these curves are planar, they cannot be treated as 2D curves, because the normal direction of each point is always changing in 3D. Due to this feature, the tactile method has the shortcoming defined as cosine error (radius compensation error).

While measuring section profiles, there are two approaches. One way is to scan the profile as an unknown curve, while the other way is to measure it as a known curve. However, both have their own problems. For unknown curve scanning, software can lock the measuring height and set the component as k=0 with respect to the measuring vector i,j,k. As a result, all the delivered points will have the same z coordinate.

When a ball stylus is used to scan the section profile, the actual touching point with the airfoil is not the expected one (Figure 1). The measuring software records the stylus centre point coordinates, and does a radius compensation afterwards to get the actual point coordinates. In this case, the probe is already triggered before the stylus touches the expected point. Therefore, the compensated coordinates will have the cosine error.

In order to quantify the cosine error, we take the Ø1 and Ø2 styli under the condition of 15 deg and 30 deg incline angle to calculate the error value.

We can conclude that with the same stylus, a larger incline angle will generate a greater cosine error. Under the same incline angle, the stylus with a bigger diameter will also generate greater cosine error.

The Ø1 and Ø2 styli are the most commonly used configuration for blade measurement. When the airfoil incline angle reaches 30 deg, the resulting cosine error is up to 0.3 mm, which already exceeds the profile tolerance zone, and is also far beyond the accuracy of the CMM itself.

The above problem is under the condition of scanning the section profile that is referred to as the unknown curve. In order to overcome this effect, another method is sometimes used where every measuring point is probed along its normal vector i,j,k as a known curve.

It is common sense that no part can match the nominal to a 100 percent, and there is more or less a certain deviation. When the k component of the measuring vector is not 0, and the airfoil has some deviations, the actual point heights will have a certain offset (Figure 2).

We also take 15 deg and 30 deg incline angle to simulate the situation. When the point is probed along its normal vector, the stylus radius does not affect the result. Therefore, different stylus radii are not considered here. The offset value is as the following:

We can draw the conclusion that the resulting curve is a 3D spatial curve instead of a 3D planar curve. This curve cannot be used for the evaluation of the blade parameters, unless it is post-processed by a software to convert it into a planar curve, but the conversion will certainly affect the curve accuracy as a result.

Hammer & Knot

Sometimes profile distortion could also happen under certain conditions. As stated previously, the CMM records the coordinates of the stylus centre point while measuring. Radius compensation will be conducted afterwards to achieve the actual point coordinates for the following geometric element construction (Figures 3, 3a, 3b).

One situation is that the radius compensation direction of some measuring points are wrongly adopted when the actual profile has a relatively bigger deviation compared to the nominal. The cause is that the stylus radius is compensated according to the nearest nominal point and the wrong vector is used. The resulting profile will have a ‘hammer’ form at the edge.

Another situation is the discrete measuring point number, which jumps all of a sudden to a latter position. This will cause the curve to follow a back and forth route and generate a ‘knot’ form. This  also happens normally under the condition of a relatively big profile deviation, and with quite a few missing points at the leading edge/trailing edge.

In conclusion, although tactile CMM is capable of producing high accuracy, it can generate big error while measuring turbine blades, especially those with big twist and tilt. The error has nothing to do with CMM accuracy, but comes from the principle of tactile measurement. So, is there any solution to alleviate or even fully overcome these problems?

Compensating For Error

Although there is more than one way to solve this issue, we shall concentrate on the tactile method based on the CMM and aim to find a method to eliminate the influence of cosine error. First of all, we need to add the thickness of the stylus radius to the surface and get a thickness-compensated airfoil.

To be more illustrative, it is like using a sphere, whose diameter is the radius of the stylus, to roll over the airfoil. The outer enveloping surface is the new airfoil (Figure 4). To carry out section profile measurement, switch off the radius compensation functionality in the measuring software. It has the same effect of using a sharp-tip stylus to carry out measurement. The measuring vector has to be set horizontally (k=0). This way, the influence of the cosine error is already taken into account through airfoil thickness compensation.

Although this method can avoid accuracy loss caused by cosine error, it is still not an ideal solution. The modified section profile with thickness compensation is no longer the original nominal.

All the measurements and evaluations are also done according to the modified profiles. Since the new profiles have one-to-one correspondence with the original ones, it is logical to use the modified curve to reflect the original design regarding its profile and position tolerance, but then the evaluation of all the section profile parameters becomes meaningless.

To sum it up, tactile CMM is by far the first choice for geometric measurement. Although it has been tested and acknowledged, it is still very meaningful to explore its uses in special applications such as turbine blade measurement, and to discuss its potential problems.