Establishing Conformity to Tolerances by Coordinate Measuring Machines: A First Step for a Statistical Approach

2006 ◽  
Vol 7 (1) ◽  
pp. 81-84
Author(s):  
Giulio Barbato ◽  
Daniela D’Agostino ◽  
Raffaello Levi
Keyword(s):  
Technical Committee ◽  
Small Sample ◽  
Coordinate Measuring Machines ◽  
Actual Surface ◽  
Statistical Confidence ◽  
Material Condition ◽  
Grooved Surface ◽  
Surface Profiles ◽  
Product Specifications ◽  
Uncertainty Of Results

Conformity to tolerances is currently assessed taking into account the maximum material condition. Coordinate measuring machines do not however operate accordingly, a small sample only of points on workpiece surface being actually contacted, with a fairly low chance of hitting the outmost point. That problem should therefore be properly addressed using statistical methods, as currently considered also by the ISO Technical Committee on “Geometrical Product Specifications and Verification.” This paper proposes to associate maximum material with the statistical distribution of maximum; typical examples of saw-tooth and round grooved surface profiles are theoretically examined. An actual surface with a good finish, representing the common case of normal distribution, was experimentally evaluated, showing that the method proposed produces consistent results. Furthermore, the method proposed readily associates results obtained with a statistical confidence interval; the uncertainty of results obtained can thus be assessed at any given confidence level.

Geometrical consideration for mechanical contact between rolling circle and surface roughness as an improvement to the surface profile

2021 ◽  
Vol 15 (1) ◽  
pp. 7846-7859
Author(s):  
Tsuyoshi Shimizu ◽  
Yasutake Hramiishi ◽  
Takaaki Ishii ◽  
Yuzairi Abdul Rahim ◽  
Mohd Fadzil Ali Ahmad ◽  
...  
Keyword(s):  
Contact Point ◽  
Surface Profile ◽  
Displacement Sensor ◽  
Nose Radius ◽  
Rolling Circle ◽  
Actual Surface ◽  
Contact Type ◽  
Measurement Surface ◽  
Surface Profiles ◽  
Tip Radius

This paper describes measurement methods of surface profiles that improve contact-type displacement sensor outputs by focusing on the contact point between the sphere tip of the sensor and the rough surface. We examined the geometry of a surface profile model and compared measurements using various methods with the measurement using a roughness meter. The spherical tip of the contact type displacement sensor touches the measurement surface and detects the displacement. The sphere tip radius of a typical contact-type displacement sensor ranges from 1–3 mm, causing the roughness curve to be “filtered” by the radius of the sphere.  Three methods for estimating the valley portion of the surface profile are evaluated in this study: a) linear approximation of the concave portion of the surface profile, b) function approximation of the concave portion, and c) using the known nose radius of the machining tool. The following sphere tip radii were used to measure actual surface profiles: 0.25 mm, 0.5 mm, 1.0 mm and 1.5 mm. Given the conditions of the experimental model, we found that surface profiles with a roughness that approximates a predictable curve can be measured with a high degree of accuracy.

scholarly journals How many grains are needed for quantifying catchment erosion from tracer thermochronology?

2021 ◽  
Author(s):  
Andrea Madella ◽  
Christoph Glotzbach ◽  
Todd A. Ehlers
Keyword(s):  
Sample Size ◽  
Confidence Level ◽  
Small Sample Size ◽  
Age Distribution ◽  
Monte Carlo Sampling ◽  
Sample Volume ◽  
Small Sample ◽  
Statistical Confidence ◽  
Spatial Changes ◽  
Kolmogorov Smirnov

Abstract. Detrital tracer thermochronology exploits the relationship between bedrock thermochronometric age-elevation profiles and a distribution of detrital grain-ages collected from river, glacial, or other sediment to study spatial changes in the distribution of catchment erosion. If ages increase linearly with elevation, spatially uniform erosion is expected to yield a detrital age distribution that mirrors the catchment's hypsometric curve. Alternatively, a mismatch between detrital and hypsometric distributions may indicate non-uniform erosion within a catchment. For studies seeking to identify the pattern of erosion, measured grain-age populations rarely exceed 100 grains due largely to the time and costs related to individual measurements. With sample sizes of this order, discerning between two detrital age distributions produced by different catchment erosion scenarios can be difficult at a high statistical confidence level. However, there is no established method to quantify the sample-size-dependent uncertainty inherent to detrital tracer thermochronology, and practitioners are often left wondering how many grains is enough?. Here, we investigate how sample size affects the uncertainty of detrital age distributions and how such uncertainty affects the ability to uniquely infer the erosional pattern of the upstream area. We do this using the Kolmogorov-Smirnov statistic as metric of dissimilarity among distributions, based on which the statistical confidence of detecting an erosional pattern is determined through Monte Carlo sampling. The techniques are implemented in a new tool (ESD_thermotrace) to consistently report confidence levels as a function of sample size and application-specific variables. The proposed tool is made available as a new open-source Python-based script along with test data. Testing between different hypothesized erosion scenarios with this tool provides thermochronologists with the minimum sample size (i.e. number of bedrock and detrital grain-ages) required to answer their specific scientific question, at their desired level of statistical confidence. Furthermore, in cases of unavoidably small sample size (e.g., due to poor grain quality or low sample volume), we provide a means to calculate the confidence level of interpretations made from the data.

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