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Tolerance-Dependent Inspection Disagreement Between a Fixed CMM and a Portable Articulated-Arm CMM
Md Manjurul Ahsan, Hamidreza Samadi, Shivakumar Raman
TL;DR
Instrument specifications alone do not establish whether substituting a fixed CMM with a portable articulated-arm CMM preserves inspection decisions. Using recorded dimensional and form profiles, the paper maps tolerance intervals where labels disagree and finds disagreement across all four retained form characteristics.
Problem
Instrument specifications do not establish whether substituting CMMs preserves the inspection decision for a feature at its assigned tolerance.
Method
The study derives tolerance-specific disagreement intervals from recorded CMM means and analyzes six dimensional and four form profiles under 20 °C and 30 °C labels.
Results
All four form characteristics fell on opposite sides of the 10 μm limit, while dimensional disagreement intervals averaged 6.573 μm at 20 °C and 4.995 μm at 30 °C.
Takeaways & Limitations
The tolerance map identifies feature-tolerance combinations where instrument choice can alter recorded labels and where focused equivalence studies and task-specific uncertainty budgets should precede substitution.
Takeaways & Limitations
The small deterministic record cannot be generalized across instruments, operators, parts, or facilities, and lacks matched procedures, traceable references, and numerical uncertainty budgets.
Abstract
from arXiv · showhide
Fixed coordinate measuring machines (CMMs) and portable articulated-arm CMMs are often assigned to the same inspection task, but their nominal accuracy specifications do not show whether a change of instrument will preserve the disposition of a part. The question is not simply how far the two results differ, but whether that difference crosses the tolerance boundary. We examined this issue with recorded measurements of cylindrical, cubic, and spherical features under nominal 20 °C and 30 °C conditions. Repeated records and two roughness profiles without sufficient acquisition information were removed, leaving six dimensional and four form profiles. For each dimensional feature, the distances of the two system means from nominal define the exact tolerance interval in which the systems receive opposite direct labels. The fixed-CMM stream was approximately 11.2 μm higher than the articulated-arm stream at both conditions. All four form profiles fell on opposite sides of the recorded 10 μm upper limit. The dimensional disagreement intervals also overlapped strongly; their mean widths were 6.573 μm at 20 °C and 4.995 μm at 30 °C. The results clarify why an average difference between instruments is not, by itself, a measure of substitution risk. The proposed tolerance map identifies the feature-tolerance combinations for which instrument choice can change the recorded inspection label and, therefore, where a controlled equivalence study and a task-specific uncertainty budget are needed before substitution.
1. Introduction
The introduction frames instrument substitution as a decision-level equivalence problem: fixed and portable CMMs may serve overlapping needs, but specifications and mean differences alone cannot show whether inspection labels are preserved. The study therefore derives feature-specific tolerance intervals where the two systems receive opposite labels and extends the analysis to guard-banded decisions.
- Motivation: Fixed and portable articulated-arm CMMs serve overlapping inspection needs, creating interest in substitution only when the accept, rework, or reject decision is preserved.Fixed CMMs provide controlled measurement conditions, while portable arms support large or difficult-to-fixture components near manufacturing.
- Problem: Instrument specifications alone cannot determine interchangeability because workpiece decisions depend on measured value, nominal, tolerance, procedure, and uncertainty.A persistent inter-system difference may be irrelevant for a wide tolerance but decisive for a tight one.
- Related work: Existing standards establish frameworks for system verification, conformity decisions, uncertainty evaluation, and decision risk, but do not directly identify substitution-sensitive tolerances.The cited standards include ISO 10360-2, ISO 10360-12, ISO 10360-5, ISO 14253-1, JCGM 100, and JCGM 106.
- Problem: The key gap is determining at what tolerance the choice of measurement system changes the direct inspection label, since mean difference alone omits each result’s position relative to nominal.Prior studies address individual-system quality, capability, calibration, posture, human factors, environmental effects, traceability, and conformity.
- Contribution: The study derives the tolerance interval producing opposite direct labels for fixed-CMM and articulated-arm means, relates its width to raw inter-system difference, and extends the logic to guard-banded decisions.The records come from a broader metrology and manufacturing-integrated digital-twin project, while the present question is narrower.
2. Materials and methods
The study compares recorded fixed-CMM and FARO articulated-arm measurements from consolidated dimensional and form profiles under nominal 20 °C and 30 °C conditions. It maps deviations from nominal to tolerance values producing different direct arithmetic labels, while excluding unsupported uncertainty-based conformity claims.
- Data and measurement systems: The workbook contains cylindrical, cubic, and spherical characteristics measured by a Brown & Sharpe fixed CMM and FARO Quantum S articulated arm at 20 °C and 30 °C.Test conditions were controlled at 20 ± 0.5 °C and 30 ± 0.5 °C, with humidity control and randomized measurement order reported in the project documentation.
- Data and measurement systems: Repeated geometry-characteristic entries were consolidated into 12 unique profiles, and two roughness profiles were excluded because acquisition information was insufficient.The retained dataset comprised six dimensional and four form profiles.
- Scope and limitations: Missing probe, datum, sampling, fitting, filtering, repositioning, report-linkage, and uncertainty-budget details limit the analysis to the two recorded result streams.No numerical guard-band result is reported because the necessary uncertainty budgets are unavailable.
- Data reduction: Each system mean was computed from two recorded values, but the workbook structure does not establish two independent experimental replications.The analysis therefore uses recorded result streams rather than independent part-level variation.
- Tolerance mapping: For dimensional profiles, direct labels were assigned by comparing each system mean’s absolute deviation from the shared nominal with bilateral half-width t.Tolerance intervals identify values at which the two recorded means receive different arithmetic labels; this is not an ISO 14253-1 conformity decision.
- Tolerance mapping: For form profiles, cylindricity, flatness, perpendicularity, and sphericity were evaluated against the recorded one-sided upper limit U = 10 μm.Form labels were assigned arithmetically using f(s,j,c) ≤ U, without interpreting condition-label changes as thermal coefficients.
3. Results
The fixed-CMM mean exceeded the articulated-arm mean across all retained profiles, while form and dimensional results showed tolerance-dependent opposite direct labels. Disagreement intervals narrowed at 30 °C despite nearly unchanged average inter-system separation, and arithmetic agreement outside those intervals did not establish measurement equivalence.
- Inter-system differences: 11.175 μm at 20 °C and 11.202 μm at 30 °C were the across-profile mean differences, with the fixed-CMM mean higher for every retained profile.The corresponding standard deviations were 0.035 and 0.039 μm.
- Form characteristics: All eight form characteristic-condition pairs received opposite direct labels: fixed-CMM means exceeded the recorded 10 μm upper limit, while articulated-arm means remained below it.This arithmetic threshold comparison did not apply an uncertainty-aware conformity rule or indicate which instrument was correct.
- Dimensional characteristics: 6.573 μm at 20 °C and 4.995 μm at 30 °C were the mean dimensional disagreement-interval widths.The decision-sensitive range became narrower at the second condition label although the average raw difference changed very little.
- Dimensional characteristics: At 20 °C, at least one dimensional characteristic disagreed for 2.275 ≤ t < 8.900 μm, while all six disagreed for 2.335 ≤ t < 8.825 μm.At 30 °C, the corresponding regions were 3.080 ≤ t < 8.135 μm and 3.165 ≤ t < 8.090 μm.
- Interpretation and limitation: Agreement occurred below the smallest lower endpoint or at or above the largest upper endpoint only for the arithmetic labels of the recorded values, not as evidence of measurement equivalence.Each dimensional characteristic produced a finite disagreement interval, with strong overlap among profiles at each condition.
4. Discussion
The discussion reframes instrument disagreement as tolerance-dependent: the observed separation matters only when readings straddle a decision boundary, while opposite form labels demonstrate practical substitution risk. The tolerance map guides where controlled equivalence studies and task-specific uncertainty analyses are needed.
- Tolerance-dependent disagreement: Approximately 11.2 μm separation affects inspection labels only according to the readings’ positions relative to nominal.The interval between the smaller and larger absolute deviations identifies the tolerance half-widths for which labels differ.
- Practical inspection consequence: 10 μm limit placed the fixed-CMM and articulated-arm means on opposite sides for all four retained form profiles at both conditions.Alternating systems would therefore produce different direct labels for cylindricity, flatness, perpendicularity, and sphericity.
- Uncertainty and capability: Tolerance mapping complements full-covariance and task-specific uncertainty analyses, calibration and error compensation, and capability studies rather than replacing them.These established methods support conformity decisions, improve result streams, and assess task suitability.
- Substitution planning: A tolerance inside the interval marks a decision-sensitive task requiring matched measurands, probing, software settings, uncertainty budgets, and an allowable difference before substitution.A tolerance outside the interval preserves the same arithmetic label but does not prove equivalence.
- Data limitations: Repeated workbook values made the unique profile the analytical unit, because counting repeated rows as independent observations would create pseudoreplication.Missing native reports and measurement-procedure details limit interpretation of the comparison.
- Recommended validation: A controlled comparison should use traceable features, common measurand definitions and software settings, randomized order, independent repositioning, and a pre-specified equivalence margin.It should also log temperatures, select replication for precision or power, and report task-specific uncertainty.
5. Conclusions
The tolerance map converts inter-system measurement differences into tolerance-specific label disagreement. In the retained data, the fixed CMM was about 11.2 μm higher, and disagreement occurred for all four form characteristics and overlapping dimensional intervals.
- Tolerance-specific disagreement: The disagreement interval for a dimensional characteristic is defined by the two system means’ distances from nominal.Its width is no greater than the raw inter-system difference and equals that difference only when both readings lie on the same side of nominal.
- Retained-data results: 11.2 μm higher were the fixed-CMM values than the articulated-arm values at both condition labels.This numerical separation alone does not determine whether instrument choice changes the inspection label.
- Retained-data results: All four form characteristics fell on opposite sides of the recorded 10 μm limit.Thus, the recorded form labels disagreed across the two systems.
- Retained-data results: 6.573 μm at 20 °C and 4.995 μm at 30 °C were the mean widths of the strongly overlapping dimensional disagreement intervals.These results identify where instrument choice can alter the recorded inspection decision, but they do not identify the correct instrument or certify interchangeability.
Declaration of generative AI and AI-assisted technologies in the manuscript preparation process
The authors used AI-assisted technologies during manuscript preparation for language editing, organization, and consistency checking, while retaining responsibility for the content.
- AI assisted with language editing, organization, and consistency checking during preparation of the work.
- The authors reviewed and edited the manuscript after using AI assistance.
- The authors take full responsibility for the manuscript’s content.