What is Cp and Cpk in Tightening?

We are often asked if we can control a tightening parameter, usually a torque specification, to meet a certain Cp and/or Cpk requirement with our equipment.

This is almost an impossible question to answer for there is no way of knowing without running tests. The factors, which affect these process indices, are as follows:

• The specification engineering tolerance. The narrower the tolerance, the more difficult it will be to attain high values of Cp and Cpk.
• The ability to have minimum scatter in the final torque values. Sometimes, we may experience frictional problems like “stick-slip.” This is a phenomenon where high frictional interaction between the external and internal threads causes the threads to bind up, store torsional energy then suddenly release. The result is that the torque/ angle curve will have a jagged shape with peaks and valleys. It is very difficult for any tightening system to control torque under these conditions. In other cases, the excessive friction may be occurring under the bolt head or nut bearing face. This is called “galling” and produces the same non-linear tightening relationship.
• The ability to center the mean torque value. Usually, the target torque is chosen exactly at the mean point of the engineering tolerance. This means that with a transducerized tool, we will never get a value below the mean value, so all the values will be skewed between the mean and the Upper Control Value (High Torque limit). In these circumstances, it will be difficult to get the optimum value for Cpk. Most customers will not allow the torque control point to be set below the mean of the tolerance to allow for this. Fortunately, with the Insight Controllers, we can adjust for this with the “torque overshoot” parameter.

In any normal process, the measured values will fall within a shape that can be contained within a “Bell- Curve” or Gaussian distribution. To set limits that will statistically capture 99.7% of the expected population for that process, control limits are set to be equal to ±3σ or the total tolerance is equal to 6σ.

In controlled tightening applications, comparing the process variation (final torque values) to the engineering tolerance (torque specification) is seen as a means of improving the quality of the joint. This comparison is a measurement of the Cp process index.

Cp = (engineering tolerance) / (process capability) = (torque tolerance [max - min]) / 6σ

where σ is the standard deviation of the process calculated from the tightening data generated from actual tightening cycles.

In a process where Cp equals 1, then 6σ is equal to the total tolerance and there is no room for variation. No one likes this situation and higher values of Cp are normally specified.

If we can hold a Cp value of 1.33, 6σ is equal to 0.75 which means that we have controlled the process within 75% of the total tolerance and left some room for variation. Customers like this cushion.

For a Cp of 1.6, we have controlled the process within 60% of the total, leaving a larger cushion. Customers like this even more.

Now, we also need to insure that the mean or average value of the process is centered within the range. If it is not, then the process may be controlled within the engineering tolerance, Cp ≥1, but some values may fall outside the upper or lower control limits. To do this we need to control the Cpk process index. Cpk is the distance from the calculated process mean value to the nearest, either upper or lower specification limit, divided by one half of the total scatter used to calculate Cp which is equal to 3σ.

Cpk = (process mean - nearest spec limit) / 3σ

If Cpk = 1, then the difference between the process mean and the nearest specification limit is equal to 3σ and there is no room for variation. Like Cp, customers look for a higher value for Cpk, so that not all the allowable tolerance is used within the process variation.

Some specifications look for seemingly unattainable expectations from the tightening process.

Look at the following example:

Cp and Cpk required is 1.33 for a tightening spec of 20Nm ± 1Nm.

If a 50Nm transducer with an accuracy of ± 0.5% Full Scale is used in the tool, this is equal to 0.25Nm, so the value of σ expected is equal to the transducer accuracy value. This is impracticable.

However, if the calibration of the transducer is calibrated for this particular torque target, we can sometimes get better accuracy than the ± 0.5% FSD and this will allow us to meet the Cp and Cpk specifications.

However, we also know that applying extremely accurate torques, for example with ± 0% scatter, has very limited advantages in reducing the clamp load scatter, compared to that obtained with an applied torque with an accuracy of ± 5% or even 10%. Clamp load is what we are really trying to control, but just a few percentage points of clamp load scatter reduction is all that is achieved.