Microsoft Word C042503e doc Reference number ISO/TR 24857 2006(E) © ISO 2006 TECHNICAL REPORT ISO/TR 24857 First edition 2006 03 15 Synthetic industrial diamond grit products — Single particle compres[.]
General conditions
The Vollstọdt “DiaTest-SI” system effectively measures the single particle strength distributions of various grades of saw grit diamond in standard sizes To assess the machine's performance, experiments were conducted under diverse operating conditions, adhering to ISO 5725-1 and ISO 5725-2 standards This evaluation focuses on synthetic industrial diamond grit products and their single-particle compressive failure strength.
“DiaTest-SI” system b) Name and location of the laboratories:
⎯ Centre 6 Germany c) Measuring equipment: Vollstọdt “DiaTest-SI” system using unified and optimized software d) Anvil and (pneumatic) piston Each test laboratory received three sets processed from the same PCD discs:
Abrasive, monocrystalline synthetic diamond macrogrit with the following sizes, properties and sievings:
1) high-strength grade, coarse grit (narrow sieving) 30/35 US-mesh
2) high-strength grade, medium-size grit (broad sieving) 40/50 US-mesh
3) medium-strength grade, medium-size grit (broad sieving) 40/50 US-mesh
4) low-strength grade, fine grit (broad sieving) 60/70 US-mesh
Each test laboratory was provided with three samples each of the particle sizes defined in 1) to 4), each sample consisting with approximately 500 particles.
Additional conditions
In the second phase of the study, each laboratory was provided with an additional three sets of PCD anvils and three sets of each of the four diamond samples.
For all tests to be carried out, the test laboratories appointed a measuring instrument operator
Three sets of anvils were utilized for testing different strength grades: one set for high-strength grade size 30/35, another for high-strength grade size 40/50, and a third set for both medium-strength grade size 40/50 and low-strength grade size 60/70.
The test series aimed to assess the accuracy of the Vollstọdt measuring equipment by evaluating the correctness and precision of strength measurements, specifically focusing on the compressive failure force (CFF value) measured in newtons.
Results
The following values were determined a) Mean strength, S mean take out mean
= ∑ n b) Median strength, S med med take out, med
The compressive failure force (CFF), measured in newtons, is denoted as F take out This value represents the force remaining after excluding all unquantifiable particle crushes, which are assigned an arbitrary strength value of 9,999 N by the DiaTest-SI system.
F is the middle value of F take out when sorted in ascending order; n is the number of particles (quantifiably) tested
NOTE If the number of F take out values is even, the median strength is the average of the middle pair of F take out values
Four grades of saw grit diamond were used for the study:
• HS601: a high-strength grade, in size D601 (30/35 US mesh)
• HS427: the same high-strength grade, in size D427 (40/50 US mesh)
• MS427: a medium-strength grade, in size D427 (40/50 US mesh)
• LS251: a low-strength grade, in size D251 (60/70 US mesh)
In all four diamond grades, the particle sizing and particle strength distributions were typical of those found in standard industrial diamond products
For each grade, the many samples sent to the various centres were extracted from a single larger “batch”
Each sample comprised approximately 500 particles, extracted using established proprietary random-splitting equipment This process aimed to ensure that individual samples were consistent and representative of the larger batch.
Furthermore, test centres were instructed to test all particles in a sample, rather than a fixed number, to remove associated sample selection variations
Each of the six centers analyzed six samples from each grade, with three samples tested during the initial phase of the study and the remaining three samples evaluated in a later phase.
Particular efforts were made to minimise the effect of anvil variation on single particle strength results
Polycrystalline diamond discs were carefully chosen to ensure homogeneity, processed into anvils, and distributed to the test centres for use with specific diamond samples
For the first phase of the study a particular disc was processed into anvils for use with the 18 samples of
The study utilized HS601 with three samples from each center, while a second disc was created for the 18 HS427 samples, and a third disc was produced for the 18 MS427 samples and three LS251 samples This methodology guaranteed that any structural variations between discs did not influence the results, maintaining consistency within each test center.
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The study faced challenges due to the limited size of polycrystalline discs, requiring the processing of new discs for the second phase Nonetheless, the same method for distributing anvils was applied in this phase.
6 Assignable causes of variations in single particle strength
The analysis of 144 tests aimed to identify the overall variation in single particle strength measurements and the assignable causes of this variation These assignable causes can be summarized using a mnemonic for easier recall.
• Man: the effect of different machine operators
• Machine: different units giving different results
• Materials: differences or inhomogeneities in the materials used in the test
• Method: differences in the measurement procedure
Some of these assignable causes were investigated by the statistical analyses of the results, whilst other assignable causes were minimized in their effect by judicious experimental design
To minimize test variability, each test center utilized a single operator for one "DiaTest-SI" unit throughout the entire study.
The category materials can be divided into two components: test saw grit diamond samples and polycrystalline diamond anvils Test variability in diamond samples arises from systematic strength differences across grades and random strength variations within the same grade For polycrystalline diamond anvils, variability is influenced by differences in compressive strength among anvils from the same disc and between different discs To mitigate these effects, specific discs with designated diamond types were used in both phases of the study, and careful selection of polycrystalline diamond discs based on structural homogeneity minimized within-disc variations.
Finally, variations in the method were addressed by each test centre using the same, strictly defined, measurement procedure
7 Statistical analyses of the results
Analysis of variance (ANOVA) is a widely used statistical method for evaluating experimental results It assesses differences in outcomes based on various assignable causes When only one factor, such as the machine, is altered between tests, a one-factor ANOVA is appropriate Conversely, when multiple factors, like machine and material, are changed, a multi-factor ANOVA should be utilized.
In the single particle strength experiment reported here, there were three factors that changed between tests: test centre, diamond type and run (“repeat”)
ANOVA cannot be applied to this experiment due to the requirement that random variations within each test must be normally distributed In this case, the variations refer to the strength of particles in each repeat, which do not follow a normal (Gaussian) distribution Consequently, the data collected in this study violates ANOVA's assumptions, necessitating an alternative statistical method to evaluate the key factors influencing variations in single particle strength.
Non-normal single particle strength distributions are effectively characterized using non-parametric statistics, with the median serving as the key measure of distribution location To assess the statistical significance of differences between these distributions, non-parametric significance tests are employed For further insights into distribution statistics and to validate the use of non-parametric methods, please refer to Annex A.
According to Clause 6, the primary assignable cause impacting strength measurements, aside from systematic differences from various diamond types, is the interaction between man and machine Other assignable causes have been effectively minimized through meticulous experimental design.
Precision and bias are two essential characteristics of the man/machine measurement system at each test center High precision indicates that the system can perform repeated measurements with minimal variation, while low bias signifies that the measurement results closely align with the "true" value In this study, determining the "true" strength distribution of a diamond type is challenging; therefore, it is approximated as the average of the distributions obtained from all test centers.
The statistical analyses performed here fall into two basic categories: analyses of between-centre variations and analyses of within-centre variations
Between-centre variations arise from discrepancies in strength measurements among machines at different test centres, highlighting the bias of these machines To evaluate these variations, results were compared across test centres after consolidating the repeated measurements within each centre.
Within-centre variations reflect a machine's consistency in measuring results, indicating its precision To evaluate these variations, we analyzed six repetitions for each diamond type, calculating the "scatter" in their results.
Further details of the analytical approaches are given in Clause 8, together with the results and discussion
Between-centre variation: all diamond types combined
The impact of the test centre factor, specifically the assignable cause of man/machine, was assessed by aggregating all tests conducted at each centre Each centre executed 24 tests, consisting of 6 repetitions for each of the 4 diamond types When these results were combined with equal weighting, they created a comprehensive single particle strength distribution for the test centre, resulting in an overall centre median.
A comparison of the six overall centre medians, utilizing both simple percentage differences and statistical significance tests like the Mann-Whitney U test, revealed fundamental differences in results from each test centre, highlighting the underlying bias in the man/machine interactions For detailed figures related to between-centre variations, please refer to Annex C.
Table C.1 reveals that the "master" distributions from the six centres exhibit notable similarity in their principal statistics The term "P10" refers to the 10th percentile, among other abbreviations used in the table Notably, the medians of these distributions, representing the overall centre medians, are all within approximately ±2% of the average overall centre median indicated in the right column of the table.
Mann-Whitney U tests were conducted to assess the statistical differences between overall centre medians, with results detailed in Table C.6 According to Annex B, a p-value of less than 0.05 signifies a statistically significant difference at the 95% confidence level between the medians being compared.
In this study, it was observed that 5 out of 15 comparisons revealed statistically significant differences between the two medians Although this number may seem unexpectedly high considering the similarities in the distributions, it is likely attributed to the large sample size, which included many thousands of strength values.
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`,,```,,,,````-`-`,,`,,`,`,,` - © ISO 2006 – All rights reserved 7 in each “master” distribution — as the sample size increases so does the confidence in the results, and hence even minor differences can become statistically significant
In summary, Centre 1 exhibited notable bias, as its 10th, 25th, and 90th percentiles were higher than those of other centres Additionally, four out of five statistically significant differences in medians were associated with Centre 1.
Between-centre variation: individual diamond types
Analyses were conducted on specific diamond types by aggregating six repetitions from each test centre to create a comprehensive data set This allowed for the examination of bias at each test centre based on diamond type Essentially, it was assessed whether certain test centres exhibited systematic bias in measuring specific diamond types This approach is analogous to studying the interaction between test centre and diamond type in ANOVA.
Tables C.2 and C.7 present the distribution statistics and Mann-Whitney U test p-values for the diamond type HS601 Notably, the differences between the medians for HS601 were more pronounced than for all diamond types combined, with the six centre medians falling within approximately ±4% of the average centre median Centres 1 and 4 exhibited generally high strength results, while Centre 3 showed consistently low strength results This increased variability led to a higher number of statistically significant differences among the medians, with 11 out of 15 comparisons showing significant variation.
The distribution statistics and Mann-Whitney U test results for diamond type HS427 are presented in Tables C.3 and C.8 The six center medians for this diamond type were within ±3% of the average center median, with statistically significant differences observed in 7 out of 15 possible comparisons.
The distribution statistics and Mann-Whitney U test results for diamond type MS427 are presented in Tables C.4 and C.9, while those for diamond type LS251 can be found in Tables C.5 and C.10.
The strength results for the diamond type LS251 reveal that Centre 1 exhibits significantly higher values compared to other centres, with its median being approximately 15% greater than the average of Centres 2 to 6 While the medians from Centres 2 to 6 are closely aligned, only two pairs show significant differences Importantly, the consistency of results from six repeats at Centre 1 confirms that this higher median is a genuine effect rather than an anomaly.
The "p values" from Tables C.6 to C.10 can be effectively summarized in non-numerical tables of "homogeneous groups." Table C.11 presents these homogeneous groups for each diamond type, where each center's median is indicated by an X (or a row of Xs) If different centers share Xs in the same column(s), it signifies that there are no significant differences between their medians.
In Table C.11, the homogeneous groups for diamond type LS251 reveal that Centre 1's median is significantly different from the others, as indicated by the non-overlapping X values and low p values in Table C.10 In contrast, Centre 6's X overlaps with those of Centres 2, 3, and 4, suggesting their medians are not significantly different However, Centre 6's X does not overlap with Centre 5's X, indicating a significant difference between these two medians Similar observations can be drawn from the data presented.
The interaction effect between test centre and diamond type is highlighted by the varying median strengths recorded at different centres for each diamond type For instance, Centre 3 exhibited the lowest median strength for HS601 while achieving the highest for HS427 Similarly, Centre 1 showed a notably high median strength for LS251, contrasting with an average median for HS427 This indicates that the biases of the test machines, when analyzed across all diamond types, fluctuate based on the specific diamond type being tested.
The interaction is effectively illustrated by Table C.12 and Figure C.1, which display the bias percentage of the center median compared to the average center median for each diamond type, as well as for all diamond types combined These biases were derived from the median (P50) strengths presented in Tables C.1 to C.5.
The analysis of Tables C.11 and C.12 reveals two distinct cases of center bias Centre 1 exhibits five center medians that are consistently at or above the average center medians, represented by the 0% line on the y-axis In contrast, Centre 5's medians are all positioned at or below the average center medians The remaining four centers show a relatively even distribution of medians around this average.
After analyzing the measurement bias associated with each test center and how these biases vary with different diamond types, we proceeded to evaluate the measurement precision of each test center.
Within-centre variation
The analysis of within-centre variation for each diamond type involved comparing six tests conducted at each centre By focusing solely on the relationship among these six repeats within a centre, the influence of test centre bias was removed, allowing for a clear assessment of test centre precision.
The results from six repeats across six centers for diamond types HS601, HS427, MS427, and LS251 are detailed in Annex D, specifically in Tables D.1, D.2, D.3, and D.4 To maintain brevity, only the strength distribution medians are provided, as opposed to the percentiles included in previous tables The average of the six medians for each center is presented in the bottom row of each table.
This study highlights two key points: some values are missing from the tables due to measurement difficulties reported by test centers, such as computer malfunctions and equipment faults, which either hindered test completion or invalidated results Only results affected by reported equipment issues were excluded from the analysis, while unexpected results obtained under seemingly normal equipment conditions were retained.
The analysis of within-centre variations revealed a systematic difference in results for diamond type LS251 between the first phase (repeats 1 to 3) and the second phase (repeats 4 to 6), as evidenced by the median strengths presented in Table D.4.
The only variable that changed between the two experimental phases was the polycrystalline disc used to manufacture the anvils In the experimental procedure, a pair of anvils tested a sample of LS251 after previously testing a sample of MS427 It is possible that the anvils used for the two diamond types in the second phase were more susceptible to chipping than those in the first phase Consequently, the testing of MS427 may have caused additional anvil damage, leading to rough surfaces that are known to produce lower recorded particle strengths.
Most test centers reported a consistent difference, indicating that the anvil material was likely the source of the issue, prompting a modification in the analysis procedure for LS251 Importantly, this systematic difference did not affect the findings regarding between-centre variations, as all centers experienced the same impact Additionally, statistical significance tests revealed no significant differences between the results of the first and second phases for the other three diamond types: HS601, HS427, and HS251.
Statistical tests were conducted to assess the significance of differences in medians from six repeats for a specific diamond type at a designated center The Kruskal-Wallis H test, an extension of the Mann-Whitney U test for multiple samples, was employed for this analysis The findings, represented as p-values, are summarized in Annex D, Table D.5.
Table D.5 indicates that the six repeats for each of the four diamond types measured at Centre 1 showed no significant differences In contrast, Centre 3 reported p values below 0.05, suggesting statistically significant differences across all four diamond types.
The p values for the repeats of LS251 were below 0.05 for Centres 2 to 6, indicating significant scatter among the six repeats, which was attributed to a systematic difference.
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The results from phase one of the study (repeats 1 to 3) were analyzed separately from those of phase two (repeats 4 to 6) to account for differences between the two phases.
The average medians and p values for LS251 from both phases are presented in Tables D.4 and D.5 Notably, Table D.5 indicates that the test centres exhibited a high level of consistency in results for LS251, with only two out of twelve relevant p values falling below 0.05 when comparing repeats 1 to 3 and repeats 4 to 6 separately.
The consistency of results from each center is effectively illustrated in Table D.6 and Figure D.1 For each diamond type, the differences between the median strengths of individual repeats and the average of the six repeat medians were calculated and expressed as percentages of the average median This analysis revealed both negative and positive percentage differences, indicating medians below and above the average, respectively To avoid an average of zero, the absolute values of these differences were computed, converting negative values to positive, and the mean of these absolute differences was then determined.
The term "scatter" refers to the mean deviation of the median from the average median for a specific diamond type at a given center A higher scatter value indicates greater variability among the six medians, which correlates with reduced precision in measurements.
The relationship between the p values in Table D.5 and the scatter values in Table D.6 is complex, as six repeat medians may exhibit low scatter due to five similar medians, yet the presence of a single outlier can hinder the conclusion that all six medians belong to the same population.
Comparison of between-group and within-group variations
The measurement capability of each test center, which includes factors related to both personnel and equipment, can be effectively summarized for all diamond types by determining the average bias and average scatter values, with scatter being inversely related to precision.
To determine the average bias for each test centre, the bias values for HS601, HS427, MS427, and LS251 were averaged For the average scatter, the scatter values for LS251 phases 1–3 and 4–6 were first averaged, followed by averaging this result with the scatter values for HS601, HS427, and MS427 This method was employed to address the offset in LS251 results across the two study phases and to ensure equal weighting among the four diamond types.
Figure E.1 in Annex E illustrates the average bias and average scatter for each test centre Centre 2 exhibited the lowest scatter, indicating the best precision, and, along with Centre 6, had the smallest bias Centre 1's measurement bias was notably influenced by its results on LS251, which were significantly higher than those of the other centres in both phases of the study, warranting further investigation If the results on LS251 are excluded, Centre 1's average bias would be around 2%.
An intriguing finding emerged from analyzing the average bias and scatter based on diamond type instead of the center Since the average bias for each diamond type is defined as 0, individual bias values were converted to absolute values before calculating the average Figure E.2 illustrates the relationship between average absolute bias and average scatter for the four diamond types.
A notable correlation exists between bias and scatter in diamond measurements The HS427 diamond type demonstrated the highest repeatability and the lowest bias across various centers In contrast, the LS251 diamond type exhibited the greatest within-centre variation, which, even after accounting for differences between phases, corresponded to the highest between-centre variation.
Contrary to expectations, the diamond type with the widest strength distribution (HS601) does not exhibit the greatest measurement variation Additionally, the broader particle size distributions in HS427 and MS427, which could also introduce sampling variation, do not seem to negatively impact measurement variation.
The LS251 diamond type is positioned at the boundary of the DiaTest-SI system's "operating window," which relates to particle size and strength, potentially leading to increased measurement variability.
Estimation of accuracy of the single particle strength test
A final mathematical exercise was conducted to assess the overall accuracy of the single particle strength test for each type of diamond This analysis aimed to establish a definitive experimental error for each diamond type, enabling users, such as diamond manufacturers and toolmakers, to comprehend the degree of similarity in their results during everyday comparisons.
For each diamond type, 36 medians were collected, creating a theoretically normal sampling distribution In a normal distribution, 95% of data points fall within ±1.96 standard deviations from the mean Thus, when testing a diamond sample at any of the test centers, it is expected that 95% of the time, the median will be within the mean of the sampling distribution ±1.96 standard deviations This 95% interval serves as a suitable measure of the overall experimental error for the single particle strength test in this study.
The 95% confidence intervals for the sampling distributions of the medians for the four diamond types are illustrated in Figure F.1 in Annex F Additionally, the medians for diamond type LS251 have been adjusted to account for discrepancies in results from the two phases of the study.
The data in Table F.1 indicates that for diamond types HS601, HS427, and MS427, 95% of the medians are expected to fall within approximately ±8% of the true median, which is the average of all 36 medians In contrast, diamond type LS251 has a wider range of ±15% These figures provide a reliable estimation of the accuracy with which DiaTest-SI machines can measure the median single particle strength of diamonds However, in less controlled conditions, such as typical everyday scenarios involving diamond samples and anvils, the errors may be more significant.
Testing the diamond type LS 251, which has lower strength and finer particle size, approaches the limitations of the test machine While it is feasible to study this type, the potential experimental error of approximately ±15% may be too significant for obtaining reliable results.
A controlled study evaluated the feasibility of the Vollstọdt “DiaTest-SI” system for testing the single particle compressive strength of synthetic industrial diamond Six test centers conducted six tests each, providing comprehensive data on the system's effectiveness.
“repeat” measurements on each of four diamond types
Non-parametric statistics are the most suitable for characterizing strength distributions, leading to the selection of the median as the primary measure of distribution location.
Statistical analyses revealed that the experimental error for the three coarser diamond types was approximately ±8%, while the fine, weak diamond type exhibited a higher error of about ±15% This indicates that 95% of the recorded medians for the coarser types are expected to fall within this range.
This variation was analysed in terms of contributions from measurement precision and measurement bias Measurement precision (the repeatability of results within each centre) was expressed as the average
The median strengths of a specific diamond type exhibited a scatter ranging from 2% to 4%, influenced by the testing center Additionally, measurement bias, which reflects the discrepancies in results across different centers, varied between -2% and +5%.
The analysis revealed that the machines across six test centers produced statistically significant variations in results when all diamond types were considered collectively Additionally, the results varied by diamond type, indicating that the interaction between human operators and machines, as well as the specific diamond type, significantly influenced the outcomes.
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The type of material, specifically diamond, had a significant and expected impact on the results, which was not statistically tested independently In contrast, the polycrystalline diamond anvils did not notably influence the outcomes, except for the fine, weak diamond type during the second phase of the study (repeats 4 to 6) The lower strength results observed in this phase may be attributed to the use of less chip-resistant anvils, highlighting the necessity for strictly controlled conditions when assessing the strength of superhard materials.
Use of parametric and non-parametric statistics
To accurately describe the distribution of particle strengths in a sample, it is essential to select the appropriate distribution statistics These statistics provide key insights into the characteristics of the distribution, including its location, spread, and shape.
The mean and standard deviation are fundamental statistical measures that indicate the location and spread of data, respectively These parametric statistics serve as key parameters in known probability distribution functions For instance, by inputting the mean and standard deviation into the normal (Gaussian) distribution function, one can calculate the probability of any value occurring within that distribution.
Single particle strength distributions of diamond can vary widely, exhibiting characteristics such as symmetry or skewness, and may be single-peaked or multi-peaked based on product design As a result, relying solely on the mean and standard deviation to describe these distributions can lead to substantial misinterpretations of diamond strength.
Non-parametric statistics, such as percentiles, provide an effective way to summarize any distribution, regardless of its conformity to known probability distributions Percentiles indicate the values below which specific percentages of results fall, illustrating positions along the cumulative probability distribution curve For instance, the 50th percentile, or median, represents the strength value below which 50% of results lie Utilizing the median alongside the 10th, 25th, 75th, and 90th percentiles offers five key points that effectively describe the location, spread, and shape of most strength distributions In this context, the median serves as a more robust measure of location than the mean, while the interquartile range—defined as the difference between the 25th and 75th percentiles—acts as a better measure of spread than the standard deviation.