Calculated Decisions: Turning Performance

Courtesy of Walter USA

Statistical analysis of metalcutting data can help shops select the right indexable insert geometry.

Statistical analysis of metalcutting data, such as tool life and cutting edge wear, is an important scientific and engineering method because it defines the relationship between the limited test data (“sample”) and large quantity of real data (“population”). Testing time and cost prevent conducting a large number of repeated tests (specimens). It is critical, then, to understand how a sample of data represents an approximation of the real population of data.

For example, Walter USA LLC, Waukesha, Wis., conducted field tests for finishing drive shafts made of AISI 1050 carbon steel using the following tool and cutting parameters.

Indexable insert: DNMG 432-xxx WPP10S (geometry A)

Feed rate: 0.012 ipr

DOC: 0.032 ”

Cutting speed: 800 sfm

The field test results (Table 1) show the calculated average number of drive shafts (sample mean) machined with Walter’s indexable inserts is 28 percent larger than the number of drive shafts machined with a competitor’s inserts. However, to calculate only the sample mean is not enough to conclude that these values are statistically significant. Therefore, in addition to the sample mean, the following parameters are required to perform statistical analysis. These parameters must be calculated to determine how the sample size, or limited data, reflects the population size, or unlimited data.

Sample Standard Deviation

Sample standard deviation (σ) is a measure of the dispersion of data about its standard mean. Sample standard deviation is calculated with the formula:

Where x_i is an individual data point, X is a sample mean and – 1 is the number of degrees of freedom.

In our case, degrees of freedom can be defined as the number of tests conducted in excess of the minimum needed to estimate a statistical parameter or quantity. For example, one field test identified the quantity of the drive shafts machined with a certain cutting insert. If a field test was repeated four times, then the sample variance of the quantity of the drive shafts has three degrees of freedom, because three more tests were conducted to observe the difference in quantity per test.

To calculate sample standard deviation for each sample mean, the treatment of field test data was performed by the author’s calculator developed in Microsoft Excel (Tables 2 and 3).

Absolute Error

The absolute error of the sample mean (α) is calculated by dividing the sample standard deviation (σ) by the square root of the number of data (). The result is expressed in the same unit of measure as the sample standard deviation and sample mean:

Absolute error of the sample mean in Group 1 is:

Absolute error of the sample mean in Group 2 is:

Critical Value

The concept of t-Distribution was introduced in 1908 by William Sealy Gosset (1876 to 1937), who is best known by his pen name Student for his work on Student’s t-Distribution.

The critical value of t depends on the number of degrees of freedom and the probability of error. If a 95 percent two-sided confidence is used for statistical analysis, then the probability of error is ±5 percent, or ±2.5 percent per side. A 5 percent probability of error provides practical accuracy, which is commonly acceptable in various engineering calculations.