Metrology, Machine Accuracy, and Quality Control

Introduction and Context

Metrology is the science of measurement. In machine technology, it provides the evidence needed to determine whether a manufactured part conforms to its drawing, specification, functional requirement, and process capability. Measurement is not limited to checking dimensions after production. It supports process planning, machine acceptance, tool compensation, maintenance, capability studies, supplier control, and continuous improvement.

A modern machining system contains several sources of variation: machine geometry, spindle and guideway errors, thermal distortion, tool wear, fixture inaccuracy, material behaviour, programming errors, environmental changes, and measurement uncertainty. Quality control therefore requires more than a highly accurate instrument. It requires a measurement system that is suitable for the tolerance, correctly calibrated, properly used, and interpreted with knowledge of the manufacturing process.

The central relationship is:

The true value is generally unknown. Systematic error produces bias, while random error causes scatter. Metrology attempts to estimate, reduce, and control both.

Learning Objectives

After studying this chapter, you should be able to:

1. Explain dimensional, geometric, and surface measurement systems used in machine technology.
2. Distinguish accuracy, precision, resolution, repeatability, reproducibility, and uncertainty.
3. Interpret tolerances, fits, limits, and geometric dimensioning and tolerancing (GD&T).
4. Select appropriate instruments and inspection methods for a specified requirement.
5. Evaluate process capability and interpret inspection data.
6. Explain calibration, traceability, measurement-system analysis, and machine acceptance testing.
7. Analyse error sources and describe compensation methods used in conventional and CNC machines.
8. Apply quality-control principles to a realistic machining problem.

1. Fundamental Measurement Concepts

1.1 Measurement, standards, and traceability

A measurement is an experimental process that assigns a value to a quantity. A measurement result should include the numerical value, unit, method, instrument, environmental conditions, and—where significant—measurement uncertainty.

The International System of Units (SI) provides the principal dimensional units. In machining, millimetres and micrometres are common. One micrometre is 1 μm = 0.001 mm. The instrument must be appropriate to the size and tolerance of the feature; a micrometer with a 1 μm resolution is not automatically capable of verifying a 1 μm tolerance.

Metrological traceability is an unbroken chain of calibrations linking a measurement result to a recognized reference, normally through national or international standards. Traceability does not mean that a result is error-free. It means that the calibration history and uncertainty are documented.

1.2 Accuracy and precision

Accuracy describes closeness to the accepted reference value. Precision describes the closeness of repeated results to one another. A system can be precise but inaccurate if it has a substantial bias. It can be approximately accurate on average but imprecise if repeated results are widely scattered.

Important terms include:

• Resolution: the smallest readable or detectable increment.
• Sensitivity: change in indication per change in measurand.
• Bias: systematic difference between the average measured value and the reference value.
• Repeatability: variation when the same operator uses the same instrument and method under nearly identical conditions.
• Reproducibility: variation caused by changes such as operators, instruments, laboratories, or conditions.
• Stability: ability of a measurement system to maintain its statistical properties over time.
• Uncertainty: quantified doubt associated with a measurement result.

A useful conceptual model for a measured result is:

where y is the observed result, x is the measurand value, b is systematic bias, and ε is random error. The model assumes that the errors are additive and that the operating range is sufficiently small for this approximation to be valid.

1.3 Sources of measurement error

Measurement errors may arise from:

• Instrument error: scale error, zero error, hysteresis, wear, or poor calibration.
• Environmental error: temperature gradients, vibration, humidity, and airborne contamination.
• Method error: incorrect datum selection, excessive contact force, cosine error, or poor alignment.
• Workpiece error: burrs, distortion, residual stress, roughness, and thermal expansion.
• Operator error: inconsistent handling, parallax, inadequate cleaning, or incorrect interpretation.

For a linear dimension affected by thermal expansion, the approximate change is:

where ∆L is dimensional change, α is the coefficient of linear expansion in 1/°C, L is the original length, and ∆T is temperature change in °C. The relation assumes uniform temperature, unconstrained expansion, and a temperature range over which α is effectively constant.

For example, a 200 mm steel component with α = 11.5 × 10^-6/°C changing by 5 °C changes by:

∆L = 11.5 × 10^-6 × 200 × 5 = 0.0115 mm

This change is 11.5 μm, which can be significant when the tolerance is only 20 μm. Precision inspection therefore commonly uses temperature control near the reference temperature specified by the applicable standard, often 20 °C.

2. Dimensional Measurement Systems

2.1 Direct measurement instruments

Direct instruments indicate the dimension being measured.

A caliper is suitable for general inspection, but it should not be selected merely because its display shows more decimal places. Instrument capability depends on accuracy, repeatability, resolution, contact geometry, environment, and operator technique.

2.2 Comparative measurement

A comparator measures deviation from a known reference rather than determining the complete dimension directly. Examples include dial indicators, lever-type indicators, electronic probes, air gauges, and optical comparators. Comparative measurement is especially effective for high-volume production because a master or setting standard can be used to check many parts rapidly.

A comparator reading is interpreted as:

The reference must itself be suitable, stable, and traceable. Comparative methods reduce some systematic effects but do not eliminate errors in the reference, alignment, temperature, or contact condition.

2.3 Coordinate measuring machines

A coordinate measuring machine (CMM) determines points in a three-dimensional coordinate system. A probe may be tactile, scanning, optical, or multisensor. Software fits geometric elements such as planes, circles, cylinders, and cones to measured points and evaluates dimensions and GD&T characteristics.

CMM advantages include flexibility, data storage, automated reporting, and the ability to evaluate complex geometry. Limitations include high cost, sensitivity to temperature and vibration, dependence on fixturing and probing strategy, and the possibility of obtaining a mathematically precise result from an inappropriate datum scheme.

A CMM program must define:

1. The coordinate system and datum reference frame.
2. Feature sampling strategy and number of points.
3. Probe qualification and stylus configuration.
4. Filtering or outlier rules, if permitted by the specification.
5. Geometric fitting method.
6. Reporting conventions and decision rules.

2.4 Optical and surface measurement

Optical comparators project a magnified profile for visual or digital comparison. Vision systems use cameras and image processing to measure edges, holes, profiles, and printed marks. Laser scanners and structured-light systems capture dense point clouds, although their accuracy depends on calibration, surface reflectivity, resolution, and software processing.

Surface texture is commonly described using parameters such as R_a, the arithmetic mean roughness. In a simplified profile over evaluation length L,

where y(x) is the deviation of the measured profile from the mean line. In practical instruments, the profile is filtered according to specified cut-off and evaluation lengths. R_a alone does not describe waviness, lay direction, isolated scratches, or functional peaks and valleys; the measurement standard and filtering conditions must therefore be reported.

3. Tolerances, Limits, and Fits

3.1 Size tolerances

A tolerance defines the permitted variation in a dimension. For a nominal dimension D_N with upper and lower limits D_U and D_L,

For a symmetric tolerance written as D_N ± t, the total tolerance width is 2t. For example, 50.00 ± 0.02 mm has limits of 49.98 mm and 50.02 mm and a total tolerance width of 0.04 mm.

Limits are more useful for inspection than nominal size. A component is conforming only when the measured characteristic satisfies the stated specification and the measurement decision accounts for the applicable decision rule and uncertainty.

3.2 Allowance and fits

An allowance is the intentional difference between mating features at maximum material conditions. For a hole and shaft:

• Minimum clearance = smallest hole − largest shaft.
• Maximum clearance = largest hole − smallest shaft.
• Interference exists when the shaft is larger than the hole.

A clearance fit always has positive clearance; an interference fit always has negative clearance when expressed as hole minus shaft; a transition fit may produce either clearance or interference depending on actual sizes. Standard fit systems, such as hole-basis systems, organize tolerances so that practical combinations can be selected consistently.

3.3 Tolerance stack-up

When dimensions contribute to an assembly result, their variations accumulate. Worst-case stack-up assumes all dimensions simultaneously occur at their limiting values:

where Tᵢ is the tolerance contribution of dimension i. This is conservative and appropriate when functional failure cannot be accepted.

If independent, centred variations are reasonably represented by statistical distributions, a root-sum-square estimate is often used:

Here Tᵢ represents a standard-deviation-based contribution, not necessarily a full bilateral tolerance. The RSS method assumes independence and suitable statistical control; it must not be used to justify nonconforming parts or uncontrolled processes.

4. Geometric Dimensioning and Tolerancing

Size tolerances control individual dimensions. GD&T controls form, orientation, location, and profile in relation to datums and functional requirements.

4.1 Main geometric-control groups

A datum is a theoretically exact reference established from a physical feature. A datum reference frame commonly uses a primary, secondary, and tertiary datum to constrain six degrees of freedom: three translations and three rotations. The datum scheme should reproduce how the part functions or is assembled, not merely how it is convenient to inspect.

4.2 Position tolerance

A position tolerance zone for a cylindrical feature is commonly cylindrical. If the positional tolerance diameter is ⌀t, the axis of the actual feature must lie within a cylindrical zone of diameter t located at the theoretically exact position. Position is not equivalent to two independent plus-or-minus coordinate tolerances.

Material condition modifiers affect functional clearance. Maximum material condition (MMC) is the condition containing the greatest amount of material: smallest hole or largest shaft. Least material condition is the opposite. Bonus tolerance may become available as a feature departs from MMC, when the specification permits it.

Correct GD&T interpretation requires attention to the feature control frame, datum order, tolerance zone shape, material condition modifiers, projected zones, and applicable standard. A drawing should not be evaluated by reading isolated symbols without considering the complete datum structure.

5. Uncertainty and Measurement-System Analysis

5.1 Uncertainty budget

Uncertainty is evaluated by identifying significant input quantities, estimating their standard uncertainties, and combining them according to a valid model. For independent components, a common approximation is:

where u_c is combined standard uncertainty and uᵢ are standard uncertainty components. If sensitivity coefficients are required because the output is not a direct sum, the general form is:

Here cᵢ = ∂f/∂xᵢ is the sensitivity coefficient, uᵢⱼ is covariance, and f is the measurement model. The simplified form assumes independent inputs and unit sensitivity coefficients.

An expanded uncertainty is often reported as:

where k is a coverage factor selected according to the desired coverage probability and statistical assumptions. k ≈ 2 is commonly associated with approximately 95% coverage under suitable conditions, but it is not universally valid.

5.2 Gauge capability and MSA

Measurement-system analysis evaluates whether a measurement process is adequate for its intended use. A gauge repeatability and reproducibility (GR&R) study separates variation associated with equipment repeatability and appraiser reproducibility from part-to-part variation. The study design should use representative parts spanning the actual process range, trained operators, repeated trials, and a documented measurement method.

A frequently used percentage is:

where σ_GRR is the estimated standard deviation due to the measurement system and σ_total is the total observed standard deviation under the selected study model. Acceptance guidelines vary by industry and risk. A low percentage is desirable, but numerical thresholds must not replace engineering judgment, especially for safety-critical features or narrow specifications.

6. Statistical Process Control and Capability

6.1 Control versus capability

Statistical process control (SPC) asks whether a process is stable and predictable over time. Capability asks whether a stable process can meet specification limits. A process may be capable on average but unstable, or stable but incapable because its variation is too large or its mean is poorly centred.

For measurements approximately normally distributed with process mean μ and standard deviation σ, capability indices are:

USL and LSL are upper and lower specification limits. C_p measures potential capability if centred; C_pk also accounts for off-centre operation. These formulas assume a stable process, meaningful estimates of μ and σ, and a distribution for which the normal approximation is appropriate.

Worked Example: Capability of a Turned Diameter

A stable turning process produces a diameter with mean 25.006 mm and standard deviation 0.004 mm. The specification is 25.000 ± 0.015 mm. Therefore, USL = 25.015 mm and LSL = 24.985 mm.

The process spread has potential capability of 1.25, but the mean is too close to the upper limit, so actual capability is only 0.75. Tool-offset adjustment or process centring is required before relying on the process for production. The organization must define its acceptance criterion; commonly used targets such as 1.33 are not universal regulatory requirements.

6.2 Control charts

For individual measurements, an Individuals–Moving Range chart may be used when subgrouping is impractical. For subgroup means, an X̄ chart monitors process location, while an R or S chart monitors within-subgroup variation. Control limits are calculated from process data and should not be confused with specification limits. Control limits describe expected process behaviour; specification limits describe customer or design requirements.

Signals such as a point beyond a control limit, sustained trends, or nonrandom runs require investigation. The correct response is to search for assignable causes rather than repeatedly adjusting the machine after every small fluctuation. Excessive adjustment can increase variation, a condition sometimes called tampering.

7. Calibration, Verification, and Acceptance Testing

7.1 Calibration practice

Calibration compares an instrument or standard with a reference of known value under specified conditions. A calibration certificate should identify the equipment, serial number, measurement results, uncertainty, reference standards, environmental conditions, date, and traceability.

Calibration is different from adjustment. Calibration determines error; adjustment changes the instrument to reduce error. After adjustment, the instrument should be recalibrated. Verification is confirmation, supported by objective evidence, that specified requirements have been fulfilled.

A sound calibration system includes:

1. Identification and status labelling of equipment.
2. Defined calibration intervals based on risk, history, use, and manufacturer information.
3. Protection against damage and unauthorized adjustment.
4. Records of failures, out-of-tolerance conditions, and impact assessment.
5. Personnel competence and documented procedures.
6. Control of reference standards and environmental conditions.

If an instrument is found out of tolerance, previously inspected product may require a risk-based review. The organization should determine when the error began, which products were affected, and whether reinspection or containment is necessary.

7.2 Machine-tool accuracy and acceptance testing

Machine acceptance testing establishes whether a new, relocated, repaired, or rebuilt machine meets specified performance requirements. Tests may include:

• Positioning accuracy and repeatability of linear axes.
• Straightness, squareness, parallelism, and angular accuracy.
• Spindle radial and axial runout.
• Spindle speed accuracy and thermal stability.
• Table, fixture, and rotary-axis performance.
• Circular interpolation or contouring tests.
• Surface finish and machining tests using representative conditions.

Tests should be based on the applicable machine-tool standard, manufacturer specification, or contract requirement. A laser interferometer may measure positioning errors, while ball-bar testing can reveal servo mismatch, backlash, scale errors, squareness, and reversal effects. Acceptance criteria must be agreed before testing; otherwise, a technically correct test may still produce a disputed decision.

Machine accuracy is not the same as part accuracy. A highly accurate machine can produce poor parts because of incorrect workholding, tool wear, thermal drift, programming, or material distortion. Acceptance testing should therefore combine geometric verification with functional machining tests where appropriate.

8. Error Compensation in CNC Manufacturing

Errors can be reduced by improving machine construction, controlling the environment, maintaining tooling, and applying compensation.

8.1 Geometric and volumetric compensation

CNC controllers may store pitch-error, backlash, straightness, squareness, and tool-length or tool-radius compensation values. A simplified one-axis compensated position can be represented as:

where e(x) is the measured positional error at location x. The sign depends on the controller convention and the definition of error; compensation values must therefore be validated experimentally.

Volumetric compensation models the combined effect of errors in multiple axes. It can improve positioning throughout the workspace, but it cannot correct a poorly defined coordinate system or compensate reliably for changing thermal conditions unless thermal behaviour is included in the model.

8.2 Thermal compensation and tool wear

Temperature changes alter machine structure, spindle assemblies, fixtures, and workpieces. Sensors may estimate thermal growth and update compensation values. Tool-wear compensation uses inspection data or in-process monitoring to modify tool offsets. Compensation should be based on a controlled relationship between measured deviation and the relevant cause. Blind offset changes can hide process deterioration and create unstable production.

Modern systems may combine probing, spindle-load monitoring, force sensing, acoustic emission, and machine-learning models. Artificial intelligence can help detect drift or classify tool condition, but the model requires representative data, validation, change monitoring, and human oversight. It should not be treated as a substitute for calibration, engineering controls, or traceable measurement.

9. Quality-Control Planning and Decision Rules

Inspection planning begins with product function and risk, not with the instruments already available. For each characteristic, specify:

• Feature and drawing requirement.
• Datum or reference system.
• Tolerance and applicable standard.
• Measurement method and instrument.
• Resolution, accuracy, and uncertainty requirements.
• Sampling frequency and reaction plan.
• Record, retention, and traceability requirements.

A decision rule defines how measurement uncertainty is considered when accepting or rejecting a part. If a measured value lies very close to a specification limit, a simple comparison may create a high risk of false acceptance or false rejection. Guard bands, additional measurement, or customer-approved rules may be used. The chosen rule must be documented and applied consistently.

Quality control also has ethical and governance dimensions. Inspectors must not alter data, omit failed results, or report capability indices without confirming process stability and measurement adequacy. Safety-critical characteristics require stronger controls, independent review where appropriate, and complete records. Digital inspection data should have access control, audit trails, backups, and protection against unauthorized modification.

10. Illustrative Case: Bore Size Drift in a CNC Production Cell

Background

An illustrative automotive-machining cell produces aluminium housings containing a precision bearing bore specified as 60.000 ± 0.010 mm. The bore is finish-machined on a CNC machining centre and checked with a calibrated air gauge.

Problem

The first-shift inspection records show a gradual increase in bore size. The process remains within specification for several hours, but late-shift parts approach the upper limit. Operators respond by changing the tool offset whenever a reading appears high. Scrap and rework increase, and inspection records from two gauges disagree by approximately 4 μm.

Analysis

The quality engineer first verifies the gauges using traceable master rings. One air gauge is within calibration requirements, but its zero setting is unstable because the air supply regulator is fluctuating. The second gauge is satisfactory. A GR&R study using representative bores shows that the unstable gauge contributes excessive measurement variation.

After replacing the regulator and allowing the gauges and masters to reach the controlled inspection temperature, the study is repeated. Measurement variation is reduced to an acceptable level for the production tolerance. A time plot of reliable measurements shows two effects: gradual thermal growth of the spindle and tool wear near the end of tool life.

Approach and solution

The team takes five actions:

1. Stabilizes air pressure and introduces a start-of-shift gauge verification.
2. Establishes a 20 °C-controlled inspection area and a defined part-soak time.
3. Uses spindle warm-up and records machine temperature.
4. Replaces reactive offset changes with a validated tool-wear compensation schedule.
5. Adds a control chart with a documented reaction plan and periodic master checks.

A capability study is conducted only after the process is stable and the measurement system is acceptable. The mean is centred near 60.000 mm, and the resulting C_pk exceeds the organization’s approved criterion.

Outcome

False alarms caused by the unstable gauge are eliminated. Tool changes are made according to evidence rather than isolated readings. Late-shift drift is reduced, inspection records become consistent, and the cell produces fewer nonconforming bores.

Learning points

The case demonstrates that measurement-system problems can imitate process problems. Capability indices are meaningless when the gauge is inadequate or the process is unstable. Thermal control, calibration, measurement-system analysis, and a disciplined reaction plan must operate together.

11. Best Practices and Limitations

Best practice is to measure at the point of use, control temperature and cleanliness, use the shortest reliable measurement chain, align instruments correctly, minimize contact-force variation, and verify instruments before critical work. Measurement methods should be validated on representative parts, including burrs, roughness, geometry, and operator access.

No measurement system is universally superior. A CMM may be unsuitable for rapid shop-floor feedback; a caliper may be entirely appropriate for a noncritical rough dimension; an optical system may struggle with reflective surfaces; and an air gauge may be excellent for a bore but useless for a complex profile. Selection must be based on function, tolerance, production rate, uncertainty, risk, and cost.

The most important limitation is that inspection detects or estimates conformance; it does not automatically create quality. Quality is produced by a capable, controlled process supported by suitable design, equipment, people, methods, and information.

Chapter Summary

Metrology provides the foundation for reliable decisions about manufactured parts and machine performance. Dimensional instruments, comparators, CMMs, optical systems, and surface-measurement equipment each have appropriate applications and limitations. Accuracy, precision, resolution, repeatability, reproducibility, bias, and uncertainty must be distinguished.

Tolerances define permissible variation, while fits describe the functional relationship between mating features. GD&T communicates form, orientation, location, profile, runout, and datum relationships more effectively than isolated size tolerances. Measurement uncertainty and measurement-system analysis are essential before inspection data are used for acceptance or capability studies.

SPC separates stable process behaviour from specification compliance. C_p indicates potential spread capability, whereas C_pk also considers centring. Calibration establishes traceability and evidence of performance; machine acceptance testing verifies geometric and functional requirements. CNC compensation can reduce known geometric, thermal, and tool-wear errors, but it must be validated and cannot replace sound process control.

Effective quality control integrates design requirements, measurement planning, calibration, environmental control, statistical analysis, ethical data practices, and documented reaction plans. The professional objective is not simply to find defective parts, but to understand and control the causes of variation.

Key Terms

Metrology: Science of measurement and its application.

Traceability: Unbroken calibration relationship to a recognized reference.

Accuracy: Closeness of a result to an accepted reference value.

Precision: Closeness of repeated results to one another.

Resolution: Smallest readable or detectable increment.

Bias: Systematic difference between an average result and a reference.

Repeatability: Variation under essentially identical measurement conditions.

Reproducibility: Variation caused by changed operators, equipment, or conditions.

Uncertainty: Quantified doubt associated with a measurement result.

Tolerance: Permitted variation in a specified characteristic.

Allowance: Intentional difference between mating features at a material condition.

Fit: Relationship between the sizes of mating features.

Datum: Theoretical reference established from a physical feature.

GD&T: System for specifying geometric requirements and datum relationships.

Calibration: Comparison with a traceable reference under specified conditions.

Verification: Confirmation that specified requirements have been fulfilled.

Capability: Ability of a stable process to meet specification limits.

Control chart: Time-ordered chart used to assess process stability.

Compensation: Deliberate correction applied for a known or estimated error.

Measurement-system analysis: Evaluation of variation and suitability of a measurement process.

Review Questions

Short Answer Questions

1. Distinguish accuracy from precision and give one example of a system that is precise but inaccurate.
2. Why can thermal expansion be important when measuring a precision component?
3. What is the difference between calibration and adjustment?
4. Distinguish specification limits from control limits.
5. Why is a datum reference frame important in GD&T inspection?

Long Answer Questions

1. Explain the operating principles, strengths, and limitations of calipers, micrometers, comparators, and CMMs.
2. Describe how uncertainty is evaluated and explain the meaning of combined and expanded uncertainty.
3. Explain size tolerances, fits, allowance, and worst-case versus statistical tolerance stack-up.
4. Describe the difference between process stability and process capability, including the interpretation of C_p and C_pk.
5. Explain how machine-tool acceptance testing and CNC error compensation contribute to manufacturing accuracy.

Analytical / Application Questions

1. A shaft is specified as 20.000 ± 0.010 mm. A measurement system has an estimated expanded uncertainty of ±0.006 mm near the upper limit. Analyse the risk of accepting a measured value of 20.009 mm and recommend an appropriate decision approach.
2. A bore process has USL = 40.020 mm, LSL = 39.980 mm, μ = 40.012 mm, and σ = 0.004 mm. Calculate C_p and C_pk, then determine whether centring or variation reduction should receive priority.
3. Design an inspection and reaction plan for a CNC-machined housing that includes a critical bore, a perpendicularity requirement, and a surface-roughness requirement. Justify the instruments, calibration checks, sampling strategy, and treatment of uncertainty.

Multiple Choice Questions with Answers

Question 1

Which term describes closeness of repeated measurement results to one another?

A. Accuracy

B. Precision

C. Traceability

D. Sensitivity

Correct Answer: B. Precision

Question 2

A 200 mm steel part with α = 11.5 × 10^-6/°C changes temperature by 5 °C. What is its approximate dimensional change?

A. 0.00115 mm

B. 0.0115 mm

C. 0.115 mm

D. 1.15 mm

Correct Answer: B. 0.0115 mm

Question 3

Which GD&T group controls parallelism and perpendicularity?

A. Form

B. Orientation

C. Location

D. Profile

Correct Answer: B. Orientation

Question 4

What is the principal purpose of calibration?

A. To increase instrument resolution automatically

B. To compare an instrument with a traceable reference under specified conditions

C. To eliminate all measurement uncertainty

D. To replace inspection procedures

Correct Answer: B. To compare an instrument with a traceable reference under specified conditions

Question 5

A process has USL = 10.10, LSL = 9.90, and σ = 0.02. What is C_p?

A. 0.83

B. 1.00

C. 1.67

D. 3.33

Correct Answer: C. 1.67

Question 6

What does C_pk account for that C_p does not?

A. Instrument resolution only

B. Process-centre location relative to specification limits

C. The nominal machine travel

D. The number of inspection operators

Correct Answer: B. Process-centre location relative to specification limits

Question 7

Which statement about control limits is correct?

A. They are always identical to specification limits

B. They describe expected process behaviour based on process data

C. They are selected only from the drawing tolerance

D. They indicate the measurement instrument’s resolution

Correct Answer: B. They describe expected process behaviour based on process data

Question 8

Which condition is most directly associated with reproducibility?

A. Repeated readings by one operator with one instrument

B. Variation caused by different operators using the measurement method

C. The smallest scale division of an instrument

D. Expansion of a workpiece caused by temperature

Correct Answer: B. Variation caused by different operators using the measurement method

Question 9

For a shaft and hole, which condition represents a clearance fit?

A. The shaft is always larger than the hole

B. The hole is always larger than the shaft

C. The shaft and hole must have identical limits

D. The fit necessarily produces interference

Correct Answer: B. The hole is always larger than the shaft

Question 10

What is a major risk of changing CNC offsets after every small measurement fluctuation?

A. It can increase process variation through inappropriate adjustment

B. It always improves centring

C. It eliminates tool wear

D. It makes calibration unnecessary

Correct Answer: A. It can increase process variation through inappropriate adjustment