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Fits That Work
Tolerance budgets, measurement decisions and evidence for assembly release
Follow a mechanical assembly from functional limits to tolerance budgets, temperature checks, measurement uncertainty and a defensible release decision.
Start readingAbout this book
A component can satisfy its drawing and still contribute to an assembly that binds, rattles or cannot be accepted with confidence. The missing connection is often between the function, the dimensional model, the manufacturing process and the evidence used to release the result.
This book develops that connection through ten chapters. It follows a fictional stop-cartridge assembly: a housing contains a cartridge and a spacer, leaving a controlled axial gap. The model starts with three dimensions, then encounters temperature, geometry, imperfect measurement, production variation and a proposed design change. Each complication changes what the original calculation can legitimately claim.
Every case value, dataset, cost and exercise is invented for education. None describes a BIZOMAT customer, product or result. Dimensions are in millimetres unless another unit is stated. The cases are deliberately simple enough to reproduce by hand or with the included Python examples. They are not instructions to release a particular real assembly.
The reader should be comfortable with basic algebra and engineering drawings. Read sequentially to develop a complete decision record; use individual chapters when reviewing a specific assumption. Exercises include a worked answer or a review criterion so the reasoning can be checked independently.
Scope and source use
The existing Engineering Design Practice collection introduces tolerances, fits and drawing practice. This authored book adds a continuous numerical investigation and an explicit acceptance decision. It does not replace a fit standard, a geometric product specification, a component manufacturer’s requirements or a qualified design review.
The supplied Machinery’s Handbook helped frame the dimensional questions. Its 2012 edition is treated as historical technical background. Current source pages were checked for the methods actually cited; no claim is made that an old handbook establishes a current contractual standard. The chapter sequence, assembly, tables, exercises, code and release records are original. Source authors and organisations do not endorse this publication.
Select the applicable drawing standard and edition with the customer and supplier. Resolve safety, regulatory and specialised material requirements within the actual project. The book’s most useful habit is simple: keep the calculation and its limits together, so a correct number cannot quietly become an unsupported promise.
Who this book is for
Mechanical designers, manufacturing engineers, quality practitioners and technical leads who can read a drawing and need to connect dimensional decisions with assembly performance.
What you will learn
- Translate an assembly function into a signed dimensional model with explicit operating conditions.
- Distinguish guaranteed dimensional bounds from statistical predictions and measurement uncertainty.
- Evaluate temperature, geometry, process shifts and measurement decisions before tightening tolerances.
- Prepare a traceable release record and identify changes that invalidate its evidence.
Inside this book
Chapters
- 01Define the function before the toleranceTurn an assembly requirement into a measurable quantity, an operating envelope and an explicit model before allocating dimensional tolerances.
- 02Calculate the dimensional boundsBuild and check a signed worst-case tolerance stack, distinguish half-widths from total tolerances and test asymmetric limits without hidden assumptions.
- 03Use statistics without losing the limitsCompare worst-case and statistical stacks, test distribution and correlation assumptions, and recognise why a drawing tolerance is not a standard deviation.
- 04Carry the stack through temperatureCalculate differential thermal expansion, evaluate dimensional limits at operating temperature and identify the conditions that invalidate a uniform-temperature model.
- 05Connect size to datums and geometryIdentify the geometric assumptions hidden in a linear stack, relate measurements to functional references and calculate simple angular and radial effects.
- 06Make measurement and acceptance agreeBuild a transparent uncertainty budget, apply an explicit guard-band decision rule and distinguish a measured result from a manufacturing tolerance.
- 07Spend the tolerance budget deliberatelyCompare nominal shifts, tighter features, adjustment and selective assembly using functional margin, manufacturing effort and inspection consequences.
- 08Make a pilot answer the right questionPlan a dimensional pilot, retain sequence and context, distinguish process shifts from measurement effects and report capability claims with their limits.
- 09Preserve the evidence when the design changesEvaluate coating, material, supplier and drawing changes against the assembly model, and maintain revision and effectivity records that protect interchangeability.
- 10Assemble a defensible release decisionComplete the stop-cartridge case, reconcile calculation and inspection evidence, and state exactly what can be released and what remains outside the approved envelope.
Apply This in Practice
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References and source notes
The manuscript and worked examples are original BIZOMAT writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 20 October 2026.
- Erik Oberg, Franklin D. Jones, Holbrook L. Horton and Henry H. Ryffel; Christopher J. McCauley, senior editor. Machinery's Handbook, 29th edition (2012). Industrial Press. Supplied reference examined selectively: contents, thermal-property context, allowances and tolerances, and measuring instruments. Printed pages 376, 629 and 675 are examples of the material consulted. Historical background only; no tables, artwork, fit values or prose reproduced.
- National Physical Laboratory. Fundamental Good Practice in Dimensional Metrology, Good Practice Guide 80 (2005; online edition consulted). Reference for temperature effects and practical dimensional measurement. Chapter 4 uses independently chosen dimensions and explicitly assumed expansion coefficients.
- Barry N. Taylor and Chris E. Kuyatt, NIST. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, Technical Note 1297 (1994). Sections 5 and 6 support the distinction between combined standard uncertainty and expanded uncertainty in Chapter 6. The numerical budget is original.
- Joint Committee for Guides in Metrology. Evaluation of measurement data: The role of measurement uncertainty in conformity assessment, JCGM 106 (2012). Background for agreeing a conformity decision rule and understanding guard bands. The book's interval-containment rule is an explicitly chosen teaching rule, not a claim of mandatory compliance.
- NIST/SEMATECH. What is Process Capability? NIST/SEMATECH e-Handbook, section 6.1.6 (online handbook). Supports the limited capability discussion in Chapter 8, including the need for process stability and appropriate distribution assumptions.
- NIST/SEMATECH. Gauge R & R studies, NIST/SEMATECH e-Handbook, section 2.4 (online handbook). Further study on separating measurement effects, operators and time. The small pilot in this book is deliberately not presented as a complete gauge R&R study.