Application Note | Roughness Statistics
Surface Roughness Statistical Analysis Using 3D Profilometry
Turning Roughness Measurements on 30 Coupons into Quality Control Statistics
Research & Experimental Testing
Jorge Ramirez
Visual Design & Editorial
Andrew Shore
Introduction
With constant development of new materials and processes, it is often a challenge to find credible ways to properly assess material surfaces for quality control. Manufacturers have had to find or develop new ways to make sure that materials comply with specific internal or external manufacturing standards. The NANOVEA Profilometer can do much more than that: it can support developing new standards, designs of experiments (DOEs), survey sampling, predictions and forecasting.
Importance of 3D Non-Contact Profilometry for Statistical Analysis
The NANOVEA 3D non-contact profilometer is capable of measuring the widest range of surfaces to assess roughness, planarity and many other properties. Surface roughness at the micron level can often be challenging for manufacturers to assess and is vital when asked to develop new standards or DOEs. The 3D non-contact profilometer provides real measured values and lets the probability of observations be tested, unlike theoretical statistics.
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Measurement Objective
In this application, the NANOVEA ST400 Profilometer is used to measure over 30 coupons with similar surface features and only slight differences. The surfaces were analyzed for parameters such as surface roughness, maximum height, maximum peak height and root mean square. A statistical analysis was then performed using histograms, tables, control charts, box plots and scatter plots.
NANOVEA ST400 Standard
Optical 3D Profilometer
Results
The false color view, 3D image and extracted profile below are representative of the 30 samples measured for the analysis.
Statistical Analysis
A summary table is a visualization of statistical information about the data. Table 1 shows a statistical summary of the parameters measured with the NANOVEA 3D non-contact profiler for all samples.
| Parameter | Mean | Std dev | Min | Max | Range |
|---|---|---|---|---|---|
| Sa (µm) | 3.781 | 0.7091 | 3.024 | 5.368 | 2.343 |
| Sq (µm) | 4.905 | 1.037 | 3.8 | 7.468 | 3.668 |
| Sz (µm) | 31.01 | 7.98 | 22.47 | 50.01 | 27.54 |
| Ssk | 0.3805 | 0.8227 | −2.537 | 1.91 | 4.447 |
| Sku | 8.142 | 13.16 | 3.044 | 67.9 | 64.85 |
| Sp (µm) | 24.22 | 10.6 | 13.73 | 62.25 | 48.52 |
| Sv (µm) | 28.51 | 32.88 | 9.687 | 145.6 | 135.9 |
| St (µm) | 52.73 | 33.57 | 25.97 | 161.4 | 135.5 |
| Tolerance (Sa − 7) | 0.449 | 0.4974 | 0 | 1 | 1 |
Table 1: Statistical summary of all populations.
A control chart is a good statistical tool to monitor product quality and detect out-of-control processes. When assessing the skewness of the samples measured, sample 6 deviates from the average range.
Histograms are bar graphs that represent the ranges of values of a selected parameter along the horizontal axis and the number of observations in these ranges along the vertical axis. Here, the Sa (surface roughness) histogram shows the number of samples falling under specific levels of roughness.
Box plots are used to summarize large amounts of data and display the range of distribution of data along a number line. The data are ordered from least to greatest, the median splits them into equal groups, and these are split again into sub-groups. The box plot arranges Sa (surface roughness) from all 30 samples measured.
Scatter plots show the relationship between two sets of data and can be used to determine whether they are positively or negatively correlated. The two parameters plotted are Sa (surface roughness) and St (total height).
Conclusion
In this application, we have shown how the NANOVEA 3D Non-Contact Profilometer can precisely characterize surfaces of similar types and create multiple study modules to assess materials, by summarizing the data and developing control charts, box plots and histograms. These features can be a valuable tool to improve and streamline products and processes.
Frequently Asked Questions About Roughness Statistics
Why apply statistics to roughness data?
Measuring many parts and analyzing the population supports developing standards, designs of experiments (DOEs), sampling surveys, predictions and forecasting, beyond checking single parts against a specification.
What was measured?
Over 30 coupons with similar surface features and only slight differences, analyzed for Sa, Sq, Sz, Ssk, Sku, Sp, Sv and St.
What was the average roughness?
Sa averaged 3.781 µm with a standard deviation of 0.7091 µm, ranging from 3.024 to 5.368 µm.
What does a control chart show?
It monitors product quality and flags out-of-control processes; here sample 6 deviated from the average range for skewness.
What do histograms and box plots add?
Histograms show how many samples fall in each roughness range; box plots summarize the distribution and median of each population.
Which tools were used?
Summary tables, control charts, histograms, box plots and scatter plots generated from the 3D non-contact measurements.
