Say goodbye to frequent downtime and size! Internal probe closed-loop reverse compensation

🤖 Search Summary：Intelligent manufacturing digital closed-loop——CNCOnline measurement and automatic updating technology for tool repair。This article introduces a complete closed-loop machining solution：After the probe automatically measures the size of the workpiece，Automatically accumulate deviation values into corresponding tool compensation variables through macro programs，Implement”measurement→compensation→Measure again”Automated closed-loop system。core logic：#13001=#13001+#148。

Prepared by: Technical Department of Ningbo Jiangce Technology Co., Ltd.

version：V1.0
Applicable Models：Various brands of CNC machine tool tool alignment systems
Keyword：Closed-loop compensation、Automatic knife repair、#13001、#148、Smart Manufacturing

🚨 Must read for on-site engineers: Safety precautions and disclaimer tips

The numerical control system parameters involved in this article（Like FANUC #3006、#6200）And macro programs（Like O8060 / O9601等）All are standard universal logic。Due to various machine tool factories（Like Mazak、Demage、Muye、Haas and domestic brands Lijia/Horizontal Machining Center/five-axis）PLC ladder diagram control logic、There are differences in the address and coordinate system settings of secondary development variables，Before debugging or running any calibration macro program on the first machine，Please strictly follow the following foolproof measures：

Switch the machine tool to”dry run（Dry Run）”pattern，And quickly move the channel magnification（G00）Restricted to below 5%。

Closely observe the relative movement direction of the measuring needle, tool, and tool setter, and do not leave the Single Block and emergency stop button with your hands.

The technical information provided by our company is for industry experience exchange only, and we do not assume any legal or economic responsibility for physical collisions or workpiece scrapping caused by directly copying the code.

catalogue

Overview and Scope of Application

The basic concept and importance of repeatability
2.1 Definition of repeatability
2.2 Difference between repeatability and accuracy
2.3 Impact of repeatability on processing quality
2.4 Role of repeatability testing in maintenance acceptance

Acceptance criteria for different accuracy levels
3.1 Acceptance criteria for 1.00 μ m accuracy level
3.2 Acceptance criteria for 0.50 μ m accuracy level
3.3 Acceptance criteria for 0.25 μ m accuracy level
3.4 Selection criteria for accuracy level
3.5 Comparison of standards for different levels

Selection of testing methods
4.1 Standard ball testing method
4.2 Gauge block testing method
4.3 Fixed target testing method
4.4 Comparison and selection of three methods
4.5 Testing methods under special working conditions

Testing frequency and statistical methods
5.1 Determination principle of testing frequency
5.2 Minimum testing frequency requirements
5.3 Calculation method of standard deviation
5.4 Meaning and calculation of 2 σ
5.5 Determination and handling of outliers
5.6 Determination of confidence interval

Standardization of testing speed
6.1 Origin of standard testing speed 240mm/min
6.2 Effect of speed on repeatability
6.3 Repeatability testing at different speeds
6.4 Method for setting speed parameters
6.5 Differences between high-speed testing and low-speed testing

Record format and data management
7.1 Standard record form
7.2 Electronic record system
7.3 Data management specifications
7.4 Trend analysis and predictive maintenance

Common testing misconceptions
8.1 Insufficient testing times
8.2 Unstable testing environment
8.3 Improper selection of testing tools
8.4 Data analysis errors
8.5 Neglecting directional differences
8.6 Confusing repeatability and reproducibility
8.7 Misunderstanding the meaning of 2 σ
8.8 Testing speed not meeting standards
8.9 Testing needle status not confirmed
8.10 Temperature influence ignored

The complete process of repetitive testing
9.1 Preparation before testing
9.2 Test execution
9.3 Data recording
9.4 Data analysis
9.5 Result judgment
9.6 Report preparation

Analysis of factors affecting repeatability
10.1 Mechanical factors
10.2 Electrical factors
10.3 Environmental factors
10.4 Operating factors
10.5 Tool factors

Repetitive improvement methods
11.1 Mechanical system optimization
11.2 Electrical system optimization
11.3 Environmental control
11.4 Operating specification optimization

Actual case analysis

Appendix and Standard Reference

📋 Quick search of core instructions

Core logic of closed-loop compensation:

#13001 = #13001 + #148 — Core statement of automatic accumulation knife compensation macro program。#13001Geometric compensation variable for blade 1，#148The deviation value for the current measurement。Automatically accumulate after each measurement，Implement”measurement→compensation→Measure again”Automated closed-loop system

# 10001- # 10099– Geometric bias variables, corresponding to G10 L1 P1-P99. Automatically written through macro programs without the need for manual intervention

1. Overview and Scope of Application

Repetitive testing is the most important, objective, and irreplaceable verification step in the acceptance work after the maintenance of the cutting instrument. Repeatability directly reflects the degree of consistency in the results of multiple measurements of the same target under the same conditions, and is the core evaluation indicator of the comprehensive performance of the cutting instrument.

In the process of serving industries such as automotive parts, aerospace, and precision molds for a long time, Ningbo Jiangce Technology has found that repetitive testing is the most easily overlooked but also the most reflective link of maintenance quality. Our technical team has completed over 5000 repeated acceptance tests, summarized the best practices of three mainstream testing methods: standard ball method, gauge block method, and fixed target method at different accuracy levels, and established a complete test data management standard.

This document comprehensively standardizes the standard process, method selection, data analysis, and acceptance judgment for repetitive testing. The article elaborates on the acceptance criteria for different accuracy levels (1.00 μ m, 0.50 μ m, 0.25 μ m), introduces the advantages, disadvantages, and applicable scenarios of three testing methods: standard sphere, gauge block, and fixed target. Key technical parameters such as testing frequency (at least 10 times), statistical method (2 σ), and standard testing speed (240mm/min) are clarified, and common testing errors are systematically analyzed.

This document is applicable for acceptance testing, regular accuracy calibration, equipment performance evaluation, and quality dispute arbitration after tool maintenance. The main readers are maintenance engineers, quality inspectors, equipment administrators, and process technicians.

2. Basic concepts and importance of repeatability

2.1 Definition of Repeatability

Repeatability refers to the degree of consistency between the results of multiple measurements of the same measurement object under the same measurement conditions. The same measurement conditions usually include:

Same measurement personnel

Same measuring equipment

Same measurement method

Same measurement environment

Same measurement object

Complete within a short time interval

In econometrics, repeatability is typically quantified using the standard deviation (σ) of the measurement results, with a more commonly used metric being 2 times the standard deviation (2 σ). Under the assumption of a normal distribution, 2 σ corresponds to a confidence level of approximately 95%, meaning that 95% of the measurement results fall within the ± 2 σ range.

Mathematical expression:
Repeatability R=2 σ=2 × √ [∑ (x ᵢ – x ̄) ²/(n-1)]

among which

X ᵢ: i-th measurement value

X ̄: The average of n measurements

n: Measurement frequency

2.2 Difference between repeatability and accuracy

Repeatability and accuracy are two different dimensions for measuring the performance of a tool setter, often confused. The difference between the two is as follows:

Accuracy reflects the degree of consistency between the measurement results and the true values. The quantitative indicator of accuracy is bias, which is the difference between the average of multiple measurements and the standard value. The accuracy depends on the calibration quality of the system and the accuracy of the calibration parameters.

Repeatability reflects the degree of consistency between multiple measurement results. The quantitative indicator of repeatability is standard deviation or 2 σ. Repeatability depends on the inherent noise, mechanical stability, electrical stability, and environmental stability of the system.

The relationship between the two:

High repeatability+high accuracy=ideal state (accurate and precise measurement values)

High repeatability+low accuracy=stable measurement value but fixed deviation (can be corrected by recalibration)

Low repeatability+high accuracy=average accurate measurement value with large fluctuations (mechanical or electrical issues need to be investigated)

Low repeatability+low accuracy=worst condition (requiring comprehensive maintenance)

Important conclusion: High repeatability is a prerequisite for high accuracy.. If the repeatability of the tool gauge is poor (measurement results fluctuate greatly), even if the calibration is accurate, the result of a single measurement may deviate from the true value. Therefore, the acceptance test after maintenance should first ensure that the repeatability meets the standard, and then verify the accuracy.

2.3 The impact of repeatability on processing quality

The repeatability of the tool directly affects the stability and consistency of the machining quality:

Effect of tool length repeatability:
Assuming the tool length repeatability of the tool gauge is 2 σ=2 μ m, in 95% of cases, the difference in tool length measured by two tool settings does not exceed 2 μ m. This means:

When replacing the same type of tool during processing, the dimensional change in the Z direction should not exceed 2 μ m

Control the Z-direction consistency of multiple cutting tools within 2 μ m

The starting point error for tool wear compensation shall not exceed 2 μ m

The influence of tool radius repeatability:
Assuming the radius repeatability of the tool gauge is 2 σ=1 μ m, in 95% of cases, the difference in tool radius measured by two tool calibrations does not exceed 1 μ m. This means:

The symmetry deviation of the processed contour shall not exceed 1 μ m

The repeatability of aperture size is controlled within 1 μ m

Control the radius consistency of multiple cutting tools within 1 μ m

Cumulative effect:
In actual machining, tool alignment error will be superimposed with other errors (spindle thermal deformation, tool runout, cutting force deformation, etc.).. Therefore, the repeatability of the tool should be much higher than the requirements for machining tolerances. It is usually required that the repeatability (2 σ) of the tool gauge should not exceed 1/5~1/10 of the machining tolerance.

Example:

Processing tolerance ± 50 μ m → tool setter repeatability should be ≤ 5-10 μ m (2 σ)

Processing tolerance ± 10 μ m → tool setter repeatability should be ≤ 1-2 μ m (2 σ)

Processing tolerance ± 5 μ m → tool setter repeatability should be ≤ 0.5~1 μ m (2 σ)

2.4 The role of repeatability testing in maintenance acceptance

The acceptance testing after maintenance usually includes the following steps:

Appearance inspection: Confirm that there is no damage, no missing installation, and clear labeling

Function testing: Confirm that all functions are normal (motion, communication, triggering, etc.)

Calibration: Perform complete length and radius calibration

Repeatability testing: Verify the consistency of multiple measurements

Accuracy verification: Confirm that the measured value is consistent with the standard value

Among these five stages, repeatability testing is the most objective way to reflect the quality of equipment maintenance. The reason is that:

Visual inspection is a subjective judgment

Functional testing can only make qualitative judgments

The reliability of calibration results depends on repeatability

The premise of accuracy verification is to meet the repeatability standard

Only after passing the repeatability test can the subsequent accuracy verification be meaningful. If the repeatability is not qualified, even if the accuracy appears to be qualified (possibly due to accidental factors), the equipment cannot be put into normal use.

3. Acceptance criteria for different accuracy levels

3.1 Acceptance criteria for accuracy level of 1.00 μ m

Scope of application:

Standard machining center

Universal CNC milling machine

Ordinary turning center

This level of tool gauge is the most common in the market and can meet the needs of the vast majority of mechanical processing

3.2 Acceptance criteria for accuracy level of 0.50 μ m

Scope of application:

High precision machining center

Precision mold processing equipment

Aerospace parts processing equipment

This level of tool setter is suitable for machining scenarios that require high precision

3.3 Acceptance criteria for accuracy level of 0.25 μ m

Scope of application:

Ultra high precision machining center

Optical component processing equipment

Precision mold coordinate grinder

Semiconductor equipment component processing

This level represents the highest level of current tool setting technology

3.4 Basis for selecting accuracy level

The higher the accuracy level, the better. It should be selected reasonably according to actual application needs.

Selection principle:

Matching principle: The repeatability accuracy of the tool setter should be higher than 1/5~1/10 of the machining tolerance

Economic principle: For every level of accuracy improvement, equipment and maintenance costs increase significantly.

Condition principle: Higher precision levels require stricter environmental conditions, and it is necessary to confirm whether the workshop conditions can be met.

Stability principle: The actual repeatability of equipment is affected by multiple factors, and margin should be left when selecting.

Select reference:
| Typical machining types | Machining tolerances | Recommended tool repeatability | Recommended accuracy level |
| ————————————————————————————————————– |
| Rough machining | ± 100 μ m | ≤ 10 μ m (2 σ) | Basic level |
| Semi precision machining | ± 50 μ m | ≤ 5 μ m (2 σ) | General level |
| Precision machining | ± 25 μ m | m | ≤ 1.0 μ m (2 σ) | High precision level (0.5 μ m) |
| Ultra precision machining | ± 5 μ m | ≤ 0.5 μ m (2 σ) | Ultra high precision level (0.25 μ m)|

3.5 Comparison of Standards for Various Levels

comparison items	1.00 μ m level	0.50 μ m level	0.25 μ m level
Length 2 σ requirement	≤1.0μm	≤0.5μm	≤0.25μm
Requirement for radius 2 σ	≤1.0μm	≤0.5μm	≤0.25μm
maximum deviation	≤2.0μm	≤1.0μm	≤0.5μm
Directional uniformity	≤0.3%	≤0.1%	≤0.05%
Test count	≥ 10 times	≥ 10 times	≥ 15 times
test speed	240mm/min	240mm/min	120mm/min
temperature range	20±5℃	20±2℃	20±1℃
warm-up time	≥30min	≥45min	≥60min
Tool accuracy	≤1μm	≤0.5μm	≤0.25μm
Environmental Requirements	Ordinary workshop	Constant temperature workshop	Constant temperature vibration isolation
equipment cost	benchmark	1.5~2 times	3-5 times
Maintenance Difficulty	low	middle	tall

4. Selection of testing methods

4.1 Standard Ball Test Method

The standard ball test method is one of the most commonly used and authoritative repeatability testing methods.

Principle:
Use a precision machined and calibrated standard ball (usually made of ceramic or hard alloy material, with surface roughness Ra ≤ 0.025 μ m and roundness ≤ 0.1 μ m) as the measurement target.. Perform multi-point contact measurements on the surface of a standard sphere using a knife gauge, and evaluate repeatability by analyzing the measurement results.

Testing steps:

Fix the standard ball in the measuring area of the tool setter

Clean the surface of the standard ball

The tool setter approaches the standard ball at a standard speed of 240mm/min

Perform Z-direction contact measurement at the top of the ball head

Record measurement values

Return the measuring needle

Repeat steps 3-6 at least 10 times

analyze data

Advantages:

The standard ball has extremely high roundness and surface quality, and the measurement results are highly reliable

The directional error of the standard sphere is extremely small, making it suitable for evaluating the isotropy of the tool setter

Standard balls have a long service life and are not easily worn out

Internationally recognized reference standards

Disadvantages:

The price of standard balls is relatively high (high-quality ceramic balls)

Special fixing devices are required

High precision requirements for installation location

4.2 Measurement block testing method

The gauge block testing method uses standard gauge blocks as measurement targets and is another commonly used testing method.

Principle:
Use a precision ground standard gauge block (usually with an accuracy level of 0 or 1) as the measurement target.. Perform contact measurement on the working surface of the measuring block using a knife gauge, and evaluate repeatability through multiple measurements.

Testing steps:

Install the measuring block at the measuring position of the tool setter

Clean the working surface of the measuring block

The tool setter approaches the working surface of the gauge block at standard speed

Probe contacts the surface of the gauge block

Record measurement values

Return the measuring needle

Repeat steps 3-6 at least 10 times

analyze data

Advantages:

Gauge blocks are length benchmarks, and data can be directly traced back

The cost of measuring blocks is relatively low

Multiple specifications to choose from, suitable for different measurement ranges

Easy to use and maintain measuring blocks

Disadvantages:

Directionality of the measuring block working surface (must be perpendicular to the direction of movement of the measuring needle)

The measuring block requires good support and fixation

The contact point position of the measuring block needs to be accurately located

The measuring block may wear or deform due to improper use

4.3 Fixed target testing method

The fixed target testing method uses standard workpieces or specialized test pieces fixed on the machine tool worktable as measurement targets.

Principle:
Install a fixed standard component (which can be a standard ring gauge, standard pin, or dedicated test block) on the machine tool worktable, and repeat the measurement of its fixed position with the tool gauge.. The characteristic of this method is that it retains the complete relative motion chain between the machine tool and the tool setter, which can better reflect the actual operating conditions.

Testing steps:

Install the fixed target on the machine tool worktable

Determine the position of a fixed target in the machine coordinate system

Develop measurement program

Execute the measurement program at least 10 times

Record each measurement result

analyze data

Advantages:

Closest to actual operating conditions

Contains the error of the entire motion chain

No additional installation or alignment required

Can be fixed on the machine tool for a long time, facilitating regular testing

Disadvantages:

The accuracy of fixed targets themselves may not be as good as standard balls or measuring blocks

Easy to be affected by workshop pollutants such as cutting fluid and chips

Fixed targets may be damaged or displaced due to accidental collisions

4.4 Comparison and Selection of Three Methods

comparison items	Standard ball method	Measurement block method	Fixed target method
accuracy class	highest	tall	middle
traceability	Excellent	Excellent	good
Implementation Difficulty	middle	low	low
cost	tall	middle	low
environmental adaptability	Excellent	good	middle
Maintenance Requirements	low	low	middle
versatility	internationally accepted	internationally accepted	On site customization

Suggestions for selection:

Acceptance testing: It is recommended to use the standard ball method or gauge block method for data traceability and high reliability.

Daily check: It is recommended to use the fixed target method, which is easy to operate and efficient.

Arbitration test: It is recommended to use the standard ball method, as the results are authoritative and highly acceptable.

Quick diagnosis: It is recommended to use the gauge block method, which has short preparation time and flexible operation.

4.5 Testing methods under special working conditions

Large machine tools:
For large machine tools such as gantry machining centers, standard balls may not be easy to transport and position.. Suggestion:

Use large-sized measuring blocks (200mm or 300mm)

Use fixed targets inside the machine

Using laser interferometer to assist in measurement

Five axis machine tool:
For five axis machine tools, the testing of the tool gauge needs to consider the impact of multi axis linkage.. Suggestion:

Perform basic testing in the vertical state of the spindle (C0 °)

Perform supplementary testing in the tilted state of the spindle

Use the standard ball testing method, as the isotropy of the standard ball can effectively separate the errors of the tool setter and the geometric errors of the machine tool

High speed machining center:
For high-speed machining centers, the tool setter may be affected by the thermal effect of the spindle.. Suggestion:

Test after the spindle reaches thermal equilibrium

Maintain low-speed rotation of the spindle during the testing process (simulate actual machining conditions)

Increase the number of tests to improve statistical reliability

Electric discharge machining machine:
For electric discharge machining machines (especially SODICK and other brands), the testing environment is more special.. Suggestion:

Conduct preliminary testing in the absence of machining fluid

Perform supplementary testing in the machining fluid environment

Strengthen cleaning frequency to prevent machining fluid contamination from affecting test results

5. Test frequency and statistical methods

5.1 Principle for determining the number of tests

The determination of the number of tests requires a balance between statistical reliability and testing efficiency.

Statistical principle:
According to the central limit theorem, as the number of tests n increases, the distribution of sample mean tends to a normal distribution, and the sample standard deviation tends to the population standard deviation.. The more tests conducted, the more reliable the statistical results will be.

Efficiency Principle:
The more tests are conducted, the longer the time and the higher the cost.. Each measurement involves the approach, contact, retraction, and data processing of the tool setter, typically taking 10-30 seconds. 10 tests take about 2-5 minutes, and 30 tests take about 5-15 minutes.

Principle of Experience:

Minimum frequency: 10 times (statistically minimum requirement)

Standard frequency: 10-20 times (recommended range for most maintenance inspections)

Strict verification: 20-30 times (high-precision level acceptance or arbitration testing)

Research analysis: 30~50 times (performance study of tool setter)

5.2 Minimum testing requirements

Why at least 10 times

In statistics, the sample size n has a direct impact on the reliability of standard deviation estimation. When n=3, the confidence interval of standard deviation estimation is extremely wide and has almost no practical value. When n=5, the standard deviation estimation is still not reliable enough. When n ≥ 10, standard deviation estimation begins to have practical value.

The following table shows the reliability of standard deviation estimation under different test times:

Test frequency (n)	Degrees of Freedom (df=n-1)	Coefficient of variation for standard deviation estimation	Practical evaluation
three	two	About 50%	unreliable
five	four	About 35%	Barely usable
ten	nine	About 24%	acceptable
fifteen	fourteen	About 19%	good
twenty	nineteen	About 16%	excellent
thirty	twenty-nine	About 13%	Extremely Excellent

Minimum number of tests for different accuracy levels:

1.00 μ m accuracy level: at least 10 times

Accuracy level of 0.50 μ m: at least 10 times (recommended 15 times)

0.25 μ m accuracy level: at least 15 times (recommended 20 times)

5.3 Calculation method of standard deviation

Sample standard deviation calculation formula:

σ = √[ Σ(xᵢ – x̄)² / (n-1) ]

among which

σ: Sample standard deviation

X ᵢ: i-th measurement value

X ̄: arithmetic mean of n measurements

n: Measurement frequency

(n-1): Degrees of freedom (Bessel correction)

Calculation steps:

Step 1: Record all measured values x ₁, x ₂, x ∝ .., xₙ

Step 2: Calculate the average value x ̄=(x ₁+x ₂+) .. + xₙ) / n

Step 3: Calculate the deviation d ᵢ=x ᵢ – x ̄ between each measurement and the average

Step 4: Calculate the sum of squared deviations S=∑ d ᵢ ²

Step 5: Calculate the variance V=S/(n-1)

Step 6: Calculate the standard deviation σ=√ V

Calculation Example:
Assuming the blade length value (μ m) measured 10 times is:
50.001, 50.002, 49.999, 50.000, 50.001, 49.998, 50.002, 50.000, 49.999, 50.001

The average value x ̄=500.003/10=50.0003 μ m

Deviation d ᵢ: 0.0007, 0.0017, -0.0013, -0.0003, 0.0007, -0.0023, 0.0017, -0.0003, -0.0013, 0.0007

Sum of squared deviations S=(0.0007 ²+0.0017 ²+…+0.0007 ²)=0.0000141

Variance V=0.0000141/9=0.000001567

Standard deviation σ=√ 0.000001567=0.001252 μ m

Repeatability 2 σ=2 × 0.001252=0.002504 μ m ≈ 0.003 μ m

5.4 Meaning and Calculation of 2 σ

The statistical significance of 2 σ:

Under the assumption of normal distribution:

About 68.27% of the measured values fall within the range of μ ± 1 σ

About 95.45% of the measured values fall within the range of μ ± 2 σ

About 99.73% of the measured values fall within the range of μ ± 3 σ

Therefore, 2 σ indicates that at a 95% confidence level, the deviation between a single measurement result and the true value does not exceed 2 σ. That is to say, if the repeatability of the tool gauge is 2 σ=1 μ m, then approximately 95 out of 100 measurements fall within the true value ± 1 μ m.

Why use 2 σ instead of σ

In the field of precision measurement, 2 σ is widely recognized as a repeatability evaluation standard. The reasons are as follows:

International Standard Practice: ISO, ISO/TS, GB/T and other standards all use 2 σ as the repeatability index

Reasonable confidence level: 95% confidence level has sufficient reliability in engineering applications

Easy to understand and compareThe empirical relationship between 2 σ values and maximum error is more intuitive

Easy to fit with tolerances: Processing tolerances are usually given in a ± manner, and 2 σ can be directly compared with tolerances

Calculation of 2 σ:
2 σ=2 × σ

Where σ is the standard deviation calculated according to the method in section 5.3.

5.5 Determination and Handling of Outliers

In repetitive testing, occasional outliers that deviate significantly from other measured values may occur. The handling of outliers requires caution, neither arbitrary removal nor blind retention.

Outlier determination method:

Grubbs’ Test:

Calculate the average value x ̄ and standard deviation σ of all measured values

Calculate the Grubbs statistic G ᵢ=| x ᵢ – x ̄ |/σ for each measurement value

Check the table to determine the critical value G_crit (α=0.05, n=10, G_crit≈2.29)

If G ᵢ>G_crit, then this value is a statistical outlier

La ï da criterion (3 σ criterion):

Calculate the mean x ̄ and standard deviation σ

If | x ᵢ – x ̄ |>; 3σ， Then the value is an outlier

Note: This criterion applies to n<; 10 o'clock is not sensitive enough

Outlier handling methods:

Mark outliers and record specific situations

Analyze the causes of outliers (operational errors, environmental impact, equipment abnormalities?)

If the specific cause of the outlier can be determined, it can be removed

If the cause cannot be determined, keep the outlier and increase the number of tests

After removing outliers, recalculate the statistical indicators

Record outliers and their handling in the test report

Precautions:

The proportion of outlier removal should not exceed 10% of the total number of tests conducted

After removing outliers, the total number of tests should still meet the minimum requirement

If there are multiple abnormal values, it indicates that there is a systematic problem with the tool setter and the fault should be investigated

5.6 Determination of confidence intervals

In addition to point estimation (mean, standard deviation), interval estimation should also be performed on the measurement results.

Confidence interval of mean:
x ̄± t (α/2, n-1) × σ/√ n

Among them, t (α/2, n-1) is the critical value of the t-distribution.

Common t-values:
| n | 95% confidence level (t ₀ ₀₂₅) | 99% confidence level (t ₀) ₀₀₅) |
|—|———————|———————|
| 10 | 2.262 | 3.250 |
| 15 | 2.145 | 2.977 |
| 20 | 2.093 | 2.861 |
| 25 | 2.064 | 2.797 |
| 30 | 2.045 | 2.756 |

Example:
10 measurements, mean 50.0003 μ m, standard deviation 0.001252 μ m
95% confidence interval: 50.0003 ± 2.262 × 0.001252/√ 10=50.0003 ± 0.0009 μ m

This means that at a 95% confidence level, the true measurement value of the tool gauge falls within the range of 50.0003 ± 0.0009 μ m.

Confidence interval of standard deviation：
√[(n-1)σ²/χ²(α/2, n-1)] ≤ σ ≤ √[(n-1)σ²/χ²(1-α/2, n-1)]

Where χ ² is the critical value of the chi square distribution.

6. Standardization of testing speed

6.1 Origin of the standard testing speed of 240mm/min

240mm/min (i.e. 4mm/s) is the internationally recognized standard speed for tool repeatability testing. The establishment of this speed value is based on the following considerations:

Historical Evolution:
In the 1980s and 1990s, the technology of CNC machine tool alignment began to be widely promoted in Europe, especially in Germany and Italy.. At that time, mainstream knife gauge manufacturers (Blum, Marpos, Renishaw, etc.) found that 240mm/min was the optimal balance point between measurement efficiency and measurement accuracy after statistical analysis of a large amount of experimental data.

Technical reasons:

Dynamic error control: At a speed of 240mm/min, the dynamic response (contact force, rebound, vibration attenuation) of the measuring needle when it contacts the tool is in a stable and controllable region

Trigger system response: The trigger sensor (strain gauge or piezoelectric sensor) of the tool gauge has the optimal triggering characteristics at a speed of 240mm/min, and the signal rise time and signal-to-noise ratio reach the optimal balance.

Thermal effect control: The measurement speed of 240mm/min generates the minimum frictional heat and does not introduce significant thermal errors to the measurement results

Mechanical inertia effect: When the axes of the machine tool accelerate and decelerate at a speed of 240mm/min, the mechanical inertia error is within an acceptable range

Standardization process:

In the 1990s, various manufacturers of cutting instruments recommended 240mm/min in their technical manuals

In the 2000s, the ISO standard draft adopted this speed as the standard testing condition

In the 2010s, the default macro program for tool presetters in mainstream CNC systems (Fanuc, Siemens, Heidelberg) was 240mm/min

6.2 The impact of speed on repeatability

The impact of testing speed on repeatability is multifaceted:

Low speed zone (<100mm/min):

Advantages: minimal dynamic effects, stable trigger signal

Disadvantages: Low measurement efficiency and increased susceptibility to environmental temperature drift

Repetitive performance: moderate (susceptible to temperature drift)

Medium speed zone (100~300mm/min):

Advantages: Balancing dynamic effects and temperature drift

Disadvantage: No significant drawbacks

Repetitive performance: optimal (240mm/min is the best point)

High speed area (>300mm/min):

Advantages: High measurement efficiency

Disadvantages: Significant increase in dynamic effects, triggering signal distortion

Repetitive performance: Decrease (worsens with increasing speed)

Speed repeatability relationship curve(qualitative description):

80mm/min: repeatability of approximately 1.0 x reference value

120mm/min: repeatability of approximately 0.9 x reference value

240mm/min: repeatability of 1.0 x reference value (standardized reference point)

480mm/min: repeatability of approximately 1.5-2.0 times the reference value

960mm/min: repeatability of approximately 3.0~5.0 x reference value

6.3 Repeatability testing at different speeds

To comprehensively evaluate the performance of the tool setter, it is recommended to conduct comparative tests at different speeds.

Standard Testing(Acceptance Testing):

Speed: 240mm/min

Number of times: at least 10 times

Purpose: To obtain repeatability data under standard operating conditions

Low speed test(diagnostic test):

Speed: 120mm/min

Number of times: at least 10 times

Purpose: To evaluate repeatability at low speeds and diagnose the reasons for poor repeatability in high-speed measurements

High speed test(Performance cap test):

Speed: 480mm/min or 720mm/min

Number of times: at least 10 times

Purpose: To evaluate repeatability at high speeds and determine the optimal operating speed range for the equipment

Comparative analysis of test results:

If the repeatability of low-speed testing is significantly better than that of standard speed testing, it indicates that:

Insufficient dynamic performance of the system (mechanical system damping is too small or electrical system response is too slow)

The pre tension force of the measuring needle, the friction characteristics of the guide rail, and the electrical filtering parameters should be checked

If the repeatability of high-speed testing is comparable or similar to that of standard speed testing, it indicates that:

The system has excellent dynamic performance

Can improve measurement efficiency while ensuring accuracy

6.4 Method for Setting Speed Parameters

Set measurement speed in CNC system:

Fanuc System:

Set the measurement feed rate through parameter No. XXXXX

Or specify the speed through the F-word when calling macro programs

G65 P9801 X100.0 Y0.0 Z-200.0 T1 F240.0

Among them, F240.0 represents a measurement speed of 240mm/min.

Bloom system:

By setting parameters in the O9700 macro program

Or set through the system maintenance interface

Marposs system:

Set measurement speed through parameter # 501

Setup method：Input in MDI mode#501=240

Precautions for speed setting:

After setting the speed, the consistency between the actual speed and the set speed should be verified

The measurement speeds of different axes (X/Y/Z) should be set separately

The fast approach speed (usually 2000mm/min) and measurement speed (240mm/min) should be distinguished and set accordingly

The speed setting should be maintained after the system is powered off

6.5 Differences between High Speed Testing and Low Speed Testing

comparison items	Low speed test (120mm/min)	Standard speed (240mm/min)	High speed test (480mm/min)
Single measurement time	About 8-12 seconds	About 5-8 seconds	About 3-5 seconds
10 times total time consumption	About 1.5-2 minutes	About 1-1.5 minutes	About 0.5~1 minute
Repeatability (2 σ)	Usually optimal	standard value	Usually decreases by 30~100%
Applicable scenarios	High precision acceptance and diagnostic testing	Standard Acceptance	Efficiency priority scenario
dynamic effect	Small	moderate	big
Temperature sensitivity	High (long duration)	moderate	Low (short duration)

Suggestion:

Initial acceptance: Obtain comparable standardized data using standard speed of 240mm/min

Daily inspection: The speed can be appropriately increased (360mm/min) to improve efficiency

Precision acceptance: Reduce speed (120mm/min) to achieve better repeatability

7. Record format and data management

7.1 Standard Record Form

The records of repetitive testing should be standardized, complete, and traceable. The following is the recommended standard record table format.

Test Basic Information Table:

project	Record content
Device Information
Equipment Number
Device Model
Manufacturing Number
Installation Location
Test information
Test Date
Test time
tester
Test purpose	□ Acceptance after maintenance □ Regular verification □ Fault diagnosis □ Other____
Test standard
Acceptance accuracy level	□1.00μm □0.50μm □0.25μm
Test Method	□ Standard ball method □ Gauge block method □ Fixed target method
Standard speed	240mm/min
environmental conditions
Environmental temperature (℃)
Temperature change rate (℃/h)
Relative humidity (%)
Vibration state	□ Normal □ Abnormal
Tool information
Type of testing tool	□ Standard ball □ Gauge block □ Fixed target
Tool Number
Tool standard value (mm)
calibration validity period

Repeatability Test Data Record Table:

Measurement number	Measurement value (mm)	Deviation (μ m)	Remark
one
two
three
four
five
six
seven
eight
nine
ten
11 (optional)
12 (optional)
13 (optional)
14 (optional)
15 (optional)
statistical results
average
standard error
Repeatability 2 σ
maximum deviation
Minimum deviation
range

Test Conclusion Table:

project	required value	measured value	judgment
Length repeatability (2 σ)	≤____μm	____μm	□ Qualified □ Unqualified
Maximum deviation in a single measurement	≤____μm	____μm	□ Qualified □ Unqualified
comprehensive evaluation			□ Qualified □ Unqualified
Remark
Signature of testing personnel
Signature of reviewer
Date

7.2 Electronic Recording System

It is recommended to use electronic recording systems to manage repetitive test data, in order to improve the efficiency and reliability of data management.

Functional requirements for electronic record systems:

Automatically collect test data (communicate with CNC system or tool alignment controller)

Automatically calculate statistical indicators (mean, standard deviation, 2 σ, etc.)

Automatically generate test reports

Data storage and traceability

Trend analysis function

User permission management

Recommended data format:

CSV format (easy to import into Excel or other data analysis software):
Test date, test time, equipment number, test times, measurement values (mm)
2026-06-27,10:00:00, TS-001,1,50.001
2026-06-27,10:00:15, TS-001,2,50.002

JSON format (for easy data exchange between systems):
{
“test_date”: “2026-06-27”,
“device_id”: “TS-001”,
“test_type”: “repeatability”,
“measurements”: [
{“seq”: 1, “value”: 50.001},
{“seq”: 2, “value”: 50.002},
…
],
“statistics”: {
“mean”: 50.0003,
“std_dev”: 0.00125,
“repeatability_2sigma”: 0.0025
}
}

7.3 Data Management Standards

Data saving:

All test data should be kept for at least 2 years

Electronic data should be backed up regularly (at least once a week)

The test data of important equipment should be permanently saved

Data Traceability:

Each test data should be traceable to specific equipment, testing personnel, and testing conditions

Data modification should be recorded in the audit log

Paper and electronic records should be consistent

Data Security:

Access permissions should be set for test data

The modification of data should be approved

The deletion of data should be approved and recorded

7.4 Trend analysis and predictive maintenance

Repetitive testing data can not only be used for acceptance judgment, but also for trend analysis and predictive maintenance.

Trend analysis:
By conducting periodic (weekly or monthly) repetitive tests, plot the 2 σ values for each time as a trend chart.. By observing the trend chart, it can be observed that:

Repetitive slow deterioration trend (indicating mechanical component wear or electrical component aging)

Repetitive sudden changes (indicating collision or component damage)

The pattern of seasonal variation in repeatability (indicating the influence of temperature or other environmental factors)

Predictive maintenance:
When repetitive data shows the following trends, preventive maintenance should be arranged:

2σThe value continues to rise and approaches 80% of the allowable upper limit

2σValue in the short term（1Within a month）Rising by more than 50%

Sudden increase or significant instability of standard deviation

Regular periodic fluctuations occur

Maintenance Decision Reference:

Trend characteristics	Possible reasons	Recommended measures
2 σ slowly increases	Mechanical wear	Arrange regular maintenance
2 σ rapidly increases	Component damage or collision	Immediate maintenance
2 σ periodic fluctuation	Temperature influence or electrical interference	Check environmental control and electrical systems
2 σ suddenly decreases and stabilizes	Possible measurement error	Retest and verify again
Increase in standard deviation	System instability	Search for unstable sources

8. Common Testing Misconceptions

8.1 Insufficient number of tests

Misconception Description:
Testers calculate repeatability after only 3-5 measurements in order to save time.. This is very common in practice, but it is one of the most serious testing misconceptions.

Problem analysis:
When n=3, the coefficient of variation of standard deviation estimation is as high as about 50%.. This means that the calculated repeatability value may differ from the true value by more than 50%. From a statistical perspective, three measurements cannot provide reliable repeatability evaluation.

Correct practice:
Strictly implement the requirement of at least 10 measurements.. For high-precision level (0.25 μ m) tool presetters, the measurement frequency should reach 15-20 times.

Case: In a certain test, only 5 measurements were taken, and 2 σ=0.8 μ m was calculated, which is considered qualified.. But after increasing to 10 measurements, 2 σ=1.3 μ m was calculated, and it was judged as unqualified. This is a typical example of misjudgment caused by insufficient sample size.

8.2 Unstable testing environment

Misconception Description:
Testers ignore the influence of environmental factors on repeatability and conduct tests under conditions of large temperature fluctuations, vibration, or airflow interference..

Problem Analysis:

For every 1 ℃ change in temperature, the mechanical structure of the tool gauge (taking steel parts as an example) undergoes a thermal deformation of approximately 11.5 μ m/m

Vibration will directly affect the triggering stability of the measuring needle

Airflow may cause local temperature fluctuations

The correct approach:

Check if the ambient temperature is within the allowable range before testing

Confirm that the temperature change rate does not exceed the requirement

Close the nearby air conditioning vents and equipment exhaust fans

Suspend nearby large vibration sources (stamping machines, forging presses, etc.)

8.3 Improper selection of testing tools

Misconception Description:
Use standard balls or measuring blocks with insufficient accuracy levels for testing.. For example, using a gauge block with an accuracy of ± 2 μ m to test requires a tool setter with a profile of 2 σ ≤ 1.0 μ m.

Problem analysis:
The error of the testing tool will be superimposed on the measurement results of the tool setter.. If the accuracy of the testing tool is on the same level as that of the tool setter, the test results will not truly reflect the performance of the tool setter.

The correct approach:

The accuracy of the testing tool should be at least three times higher than the accuracy level of the tool setter

The testing tool should be within the effective calibration cycle

The surface of the testing tool should be clean and undamaged

Record the calibration values and calibration numbers of the testing tools

8.4 Data analysis errors

Misconception Description:
Common analysis errors include:

Mistakenly mistaking the range (maximum minimum) for repeatability

Use the overall standard deviation formula (divided by n instead of n-1)

Ignore the impact of outliers

Unit conversion error

Problem Analysis:

The range is greatly affected by the sample size and cannot be used as a stable repeatability indicator

Dividing the overall standard deviation by n will underestimate the standard deviation (biased estimation)

Not handling outliers can distort statistical results

The correct approach:

Using the sample standard deviation formula σ=√ [∑ (x ᵢ – x ̄) ²/(n-1)]

Using 2 σ as the repeatability index

Handle outliers according to prescribed methods

Check and confirm unit conversion

8.5 Neglecting directional differences

Misconception Description:
Only conduct repeatability testing in the Z direction (length), ignoring repeatability testing in the X/Y direction (radius).. Or conduct radius testing in only one direction.

Problem Analysis:

The repeatability in the X/Y direction is usually worse than in the Z direction (because it involves the linkage of two axes)

The pre travel of the measuring needle varies in different directions

There are differences in the servo performance and mechanical characteristics of each axis of the machine tool

The correct approach:

Perform repeatability tests in the Z direction (length) and X/Y direction (radius) separately

The radius test should be conducted in multiple directions (at least 4 directions)

Record repetitive data in all directions

8.6 Confusion between repeatability and reproducibility

Misconception description:
Confuse repeatability and reproducibility, or replace repeatability requirements with reproducibility data..

Concept differentiation:

term	English	definition	Change conditions
repetitiveness	Repeatability	Consistency under the same conditions	No change
reproducibility	Reproducibility	Stability under different conditions	Personnel/equipment/environmental changes

The correct approach:

The repeatability index should be used for acceptance testing after maintenance

Reproducibility testing is applicable to GR& R analysis and supplier evaluation

Do not replace repetitive acceptance with reproducible data

8.7 Misunderstanding the meaning of 2 σ

Misconception Description:
Misunderstanding 2 σ as “all measured values must be within ± 2 σ range” or “2 σ is the maximum measurement error”.

Correct understanding:
The meaning of 2 σ is that, under the assumption of normal distribution, about 95% of measurement results fall within the range of ± 2 σ.. This means that out of 20 measurements, it is expected that one measurement result will exceed the ± 2 σ range. This is a normal statistical phenomenon and does not represent a malfunction of the tool setter.

The correct approach:

When a single measurement value exceeds the range of 2 σ, there is no need to immediately determine it as unqualified

Statistical methods should be used to evaluate the overall data

If there are multiple instances of out of range data, consider equipment issues

8.8 Test speed does not meet the standard

Misconception Description:
Testers arbitrarily set the testing speed, did not use the standard speed of 240mm/min, or had unstable speed during the testing process..

Problem Analysis:

Different speeds result in different repeatability results (as described in Section 6.2)

The test results at different speeds cannot be directly compared

Unstable speed can introduce additional errors

The correct approach:

Acceptance testing uses a standard speed of 240mm/min

Confirm if the actual speed is stable

Indicate the testing speed in the test record

8.9 Needle status not confirmed

Misconception Description:
Failure to check the condition of the measuring needle before testing, using a bent, worn, or loose measuring needle for testing..

Problem Analysis:

Curved measuring needles can cause directional deviation

Worn measuring needle ball head can cause unstable contact points

Loose measuring needles will introduce additional mechanical clearances

The correct approach:

Before testing, check if the measuring needle is straight and if the ball head is intact

Confirm that the measuring needle is securely installed

Replace the measuring needle if necessary

8.10 Temperature effect ignored

Misconception Description:
Testers do not record the ambient temperature in the records, nor do they consider the impact of temperature on the measurement results..

Problem analysis:
The thermal expansion coefficient of the steel tool setter is about 11.5 × 10 ⁻⁶/℃.. For measuring a blade length of 100mm, a temperature change of 1 ℃ will result in a measurement error of approximately 1.15 μ m. If the temperature effect is not considered, this error will be classified as repeatability, resulting in a biased evaluation of repeatability.

The correct approach:

Record the ambient temperature before testing

Ensure that the tool setter and testing tools reach thermal equilibrium

Use temperature compensation function (if available)

Record temperature data in the test report

9. Complete process of repetitive testing

9.1 Preparation before testing

Step 1: Confirm device status

The tool setter has been repaired and is functioning properly

Calibration completed (calibration is a prerequisite for repetitive testing)

The system has no alarm information

Step 2: Confirm environmental conditions

The ambient temperature is within the allowable range

The temperature change rate meets the requirements

No obvious vibration or airflow interference

Stable power supply

Step 3: Prepare testing tools

Choose appropriate testing tools (standard balls, measuring blocks, or fixed targets)

Confirm that the calibration certificate of the testing tool is within its validity period

Cleaning testing tools

Install and fix testing tools

Step 4: Set Test Parameters

Set test speed (standard speed 240mm/min)

Set the number of tests (at least 10 times)

Set data recording method (automatic or manual)

Step 5: Preheat the equipment

Preheat for at least 30 minutes upon startup

Perform several predictions to confirm that the system is working properly

9.2 Test Execution

Step 1: Establish Reference

Determine the position of the test target in the machine coordinate system

Develop or call measurement programs

Execute a prediction once to confirm that the program is functioning properly

Step 2: Perform repeated measurements

Perform at least 10 measurements under constant conditions

Each measurement should be evenly spaced (recommended interval of 10-15 seconds)

Observe each measurement and pay attention to any abnormal fluctuations

If any obvious abnormalities are found, investigate the cause and record it

Step 3: Record test data

Record each measurement value in order

Record testing time and environmental conditions

Record any abnormal situations during the testing process

9.3 Data Recording

Use the standard record table in section 7.1 to record the following data:

Test basic information (equipment, environment, tools, personnel, etc.)

Raw data for each measurement

Abnormal situations during the measurement process

9.4 Data Analysis

Step 1: Data organization

Check data integrity

Confirm measurement units and accuracy

Step 2: Calculate statistical indicators

Calculate the average value x ̄

Calculate the standard deviation σ

Calculate repeatability 2 σ

Calculate the maximum deviation Δ _max

Step 3: Outlier Detection

Use Grubbs test or 3 σ criterion to detect outliers

Handle outliers according to the method in section 5.5

Step 4: Draw a Chart

Draw a line graph of the distribution of measurement values (observe the trend of changes)

Draw a histogram of the measured values (observe the distribution pattern)

Draw a normal probability plot (to test the normality hypothesis)

9.5 Result judgment

Step 1: Compare acceptance criteria

Compare the calculated 2 σ value with the required value of the corresponding accuracy level

Compare the maximum deviation value with the required value

Confirm whether the directional uniformity meets the requirements

Step 2: Comprehensive judgment

If all indicators are qualified, it is judged as qualified

If any indicator fails, it is judged as unqualified

Analyze the reasons for non-compliance and take corrective measures

Step 3: Issue a test report

Prepare a formal test report

Includes all test data and statistical results

Include judgment conclusions

Signature of testers and auditors

9.6 Report Preparation

The test report should include the following content:

Basic information: Equipment number, model, testing date, testing personnel

Testing conditions: Environmental temperature, humidity, testing speed, testing tool information

Test Data: Raw data measured each time

Statistical analysis: mean, standard deviation, 2 σ, maximum deviation

Judgment result: Qualified/Unqualified

Remarks: Abnormal situations and handling instructions

Signature: Signature of tester and reviewer

10. Analysis of factors affecting repeatability

10.1 Mechanical factors

influencing factors	influence mechanism	impact level	improvement method
Rail clearance	The gap between the guide rails leads to inconsistent movement direction	big	Adjust the pre tightening force of the guide rail
Bearing wear	Bearing wear leads to unstable movement	big	replace the bearing
Measuring needle status	Bending of measuring needle or wear of ball head	big	Replace the measuring needle
Contact surface status	There are burrs or dirt on the contact surface	middle	Cleaning and deburring
Tightening and loosening	Loose fastening of components	big	Check and tighten
Lubrication state	Poor lubrication leads to unstable movement	middle	Check and replace lubricant
Mechanical alignment	Poor installation alignment	middle	Re centering

10.2 Electrical Factors

influencing factors	influence mechanism	impact level	improvement method
Power stability	Voltage fluctuations affect sensor output	middle	Install a voltage regulator power supply
electromagnetic interference	EMI affects signal quality	middle	Improve shielding and grounding
Cable status	Cable damage or poor contact	big	Replace the cable
Sensor aging	Sensor sensitivity decreases	big	Replace the sensor
Filter settings	Unreasonable filtering parameters	middle	Optimize filtering settings
Accuracy of analog-to-digital conversion	Insufficient ADC resolution	Small	Upgrade hardware

10.3 Environmental Factors

influencing factors	influence mechanism	impact level	improvement method
temperature change	Mechanical deformation caused by thermal expansion and contraction	big	Temperature Control
vibration	Vibration interference measurement process	big	Vibration isolation measures
Humidity	Humidity affects electrical performance	Small	Dehumidification
airflow	Temperature fluctuations caused by airflow	middle	Isolation airflow
Lighting changes	The influence of light intensity on optical measurement	middle	Hengguang Control

10.4 Operational factors

influencing factors	influence mechanism	impact level	improvement method
Unstable measurement speed	Speed fluctuations affect triggering characteristics	middle	Standardized speed setting
Non-standard operation	The measurement program is not standardized	middle	Develop operational standards
log errors	Data recording error	big	automatic collection
Insufficient preheating	Not reaching thermal equilibrium	big	Ensure preheating time

10.5 Tool Factors

influencing factors	influence mechanism	impact level	improvement method
Surface roughness of cutting tools	Surface roughness affects contact points	middle	Use cutting tools with good surface quality
Tool jumping	Tool jumping affects radius measurement	big	Improve tool installation
Tool Material	Different materials have different elasticity	Small	Unified tool materials
Tool shape	Complex shapes affect edge detection	middle	Use simple shaped cutting tools

11. Repetitive improvement methods

11.1 Optimization of Mechanical Systems

Guide rail adjustment:

Check the straightness of the guide rail and re scratch if necessary
Adjust the pre tensioning force of the guide rail to eliminate gaps
Replace the worn guide rail slider

Needle maintenance:

Regularly check the straightness of the measuring needle and the roundness of the ball head
Use high-precision measuring needles (ball roundness ≤ 0.5 μ m)
Install the measuring needle using a standard torque wrench

Lubrication optimization:

Use high-quality lubricants
Develop a reasonable lubrication cycle
Keep the lubrication system clean

Structural rigidity improvement:

Check the torque of all fasteners
Add supporting structures (if necessary)
Reduce cantilever length

11.2 Electrical System Optimization

Power optimization:

Use an independent power supply to power the tool setter
Install power filter and voltage regulator
Check the grounding system

Signal processing optimization:

Adjust filtering parameters (increase filtering time constant)
Use shielded cables
Optimize signal transmission path

Sensor maintenance:

Regularly check sensor sensitivity
Clean the surface of the sensor
Replace sensors periodically

11.3 Environmental Control

Temperature control:

Install a constant temperature air conditioning system
Control the temperature at 20 ± 1 ℃
Reduce temperature gradient

Vibration Control:

Install vibration damping pad
Stay away from vibration sources
Use vibration isolation foundation (high-precision equipment)

Airflow control:

Avoid direct air conditioning blowing on the tool setter
Using a windshield cover
Control workshop airflow

11.4 Optimization of Operating Standards

Standardized operations:

Develop detailed operating procedures
Using an automatic measurement program
Reduce manual intervention

Data Management:

Establish a testing database
Regularly analyze data trends
Discover problems in a timely manner

Personnel training:

Regularly conduct operational training
Enhance quality awareness
Establish an assessment system

12. Actual case analysis

Case 1: Failure to meet repeatability standards – loose measuring needle

Background: After repairing the tool gauge on a machining center, the repeatability test result was 2 σ=1.8 μ m, exceeding the acceptance standard of 1.0 μ m.

Troubleshooting process:

Check environmental conditions: temperature 21 ℃, rate of change 0.5 ℃/h, normal
Check the appearance of the measuring needle: no bending, no wear
Check the installation of the measuring needle: It was found that there is a small gap between the measuring needle and the mounting seat (not visible visually, but can be felt by gently pushing with your hand)
Reinstall the measuring needle using a torque wrench

Result: After reinstallation, the repeatability test result is 2 σ=0.6 μ m, which is qualified.

Conclusion: Loose installation of the measuring needle leads to non-compliance with repeatability standards..

Case 2: Repetitive directional deviation – poor lubrication of the guide rail

Background: During the acceptance test of a tool setter for a certain machine tool, the Z-direction repeatability of 2 σ=0.5 μ m was qualified, but the X-direction repeatability of 2 σ=1.5 μ m exceeded the standard..

Troubleshooting process:

Check the X-axis guide rail: uneven lubrication film and dry marks were found on the surface of the guide rail
Check the lubricating oil circuit: Partial blockage in the lubricating oil circuit
Clean the lubricating oil circuit and replace the lubricating grease
retest

Result: The repeatability in the X direction has been improved to 2 σ=0.7 μ m, which is qualified..

Conclusion: Poor lubrication of the X-axis guide rail leads to unstable movement and poor repeatability in that direction..

Case Three: Temperature induced Repetitive Drift

Background: During winter acceptance testing, a high-precision tool setter passed the 2 σ=0.3 μ m test in the morning and exceeded the 2 σ=0.7 μ m test in the afternoon.

Troubleshooting process:

Check the difference between two tests: During the afternoon test, the workshop heating was turned on and the ambient temperature increased from 18 ℃ to 24 ℃
The temperature change rate is 1.5 ℃/h, exceeding the requirement of 0.5 ℃/h
Analysis suggests that temperature changes cause thermal deformation of the tool setter, introducing measurement errors

Result: After the temperature stabilized, retesting restored 2 σ to 0.3 μ m.

Conclusion: Excessive temperature change rate leads to deterioration of repeatability..

Case 4: Test speed setting error

Background: After maintenance and acceptance of a certain tool setter, the testing personnel used a measurement speed of 600mm/min for repetitive testing, and the result was 2 σ=2.5 μ m.

Troubleshooting process:

Check test parameters: Found measurement speed set to 600mm/min
Reason for understanding: Testers believe that testing speed does not affect repeatability
Adjust the speed to 240mm/min and retest

Result: At standard speed, the repeatability of 2 σ=1.2 μ m still exceeds the standard. Further investigation revealed that the measuring needle was worn. After replacing the measuring needle, 2 σ=0.8 μ m at 240mm/min is qualified.

Conclusion: The combination of testing speed and probe wear leads to excessive repeatability..

13. Appendix and Standard Reference

Appendix A: List of Relevant Standards

Standard Number	Standard Name	Correlation with Repetitive Testing
ISO 230-2	Machine Tool Test Procedures – Part 2: Determination of Position Accuracy and Repeatability	General standard for precision testing of machine tools
ISO 230-9	Machine Tool Test Procedures – Part 9: Evaluation of Measurement Systems	Evaluation criteria for measuring systems such as cutting instruments
ISO 5725-1~6	Accuracy of measurement methods and results	Basic standards for repeatability and reproducibility
GB/T 17421.2	General rules for machine tool inspection – Part 2: Determination of positional accuracy and repeatability	National Standard
GB/T 6379	Accuracy of measurement methods and results	National standards for repeatability and reproducibility
VDI/DGQ 3441	Statistical inspection of machine tool position accuracy	German Standard
JIS B 6191	Machine Tool Test Procedure – Determination of Position Accuracy	Japanese standards

Appendix B: Recommended Statistical Tools

Tool Type	Recommended tools	Purpose
spreadsheet	Microsoft Excel	Basic data recording and statistical analysis
statistical software	Minitab	Professional statistical analysis (GR&R, SPC, etc.)
Specialized software	Provided by the knife instrument manufacturer	Automatic data collection and analysis
online tool	Various statistical analysis websites	Quick calculation and verification
Custom Program	Python/R Script	Automated data analysis and report generation

Appendix C: Table of critical values for t-distribution (commonly used values)

Degrees of freedom (n-1)	α=0.10(t₀. ₀₅)	α=0.05(t₀. ₀₂₅)	α=0.01(t₀. ₀₀₅)
nine	one point eight three three	two point two six two	three point two five zero
fourteen	one point seven six one	two point one four five	two point nine seven seven
nineteen	one point seven two nine	two point zero nine three	two point eight six one
twenty-four	one point seven one one	two point zero six four	two point seven nine seven
twenty-nine	one point six nine nine	two point zero four five	two point seven five six

Appendix D: Grubbs Test Critical Values Table

n	α=0.05	α=0.01
ten	two point two nine zero	two point four eight two
eleven	two point three five five	two point five six four
twelve	two point four one two	two point six three six
thirteen	two point four six two	two point six nine nine
fourteen	two point five zero seven	two point seven five five
fifteen	two point five four nine	two point eight zero six
sixteen	two point five eight five	two point eight five two
seventeen	two point six two zero	two point eight nine four
eighteen	two point six five one	two point nine three two
nineteen	two point six eight one	two point nine six eight
twenty	two point seven zero nine	three point zero zero one

Appendix E: Repetitive Testing Checklist

Pre test check:

The tool setter has completed maintenance and basic functional testing
Calibration completed
The measuring needle is in good condition (no bending, no wear, firmly installed)
The accuracy of the testing tool is qualified and within its validity period
The testing tool has been cleaned
The ambient temperature is within the allowable range
The temperature change rate meets the requirements
No obvious vibration interference
Test speed set to 240mm/min
Set the test frequency to at least 10 times
The equipment has been fully preheated (≥ 30 minutes)

During testing, check:

Every measurement interval is uniform
Observing the measured values, there are no abnormal fluctuations
Record changes in environmental conditions
Record any abnormal situations

After testing, check:

The data is complete and there are no omissions
Statistical calculation is correct
Outliers have been handled according to regulations
The judgment result is based on evidence
Complete test report
The test report has been archived

Document Revision Record

version	Date	Revision Content	Reviser
V1.0	2026-06-27	Initial version	Ningbo Craftsmanship and Testing Technology Department

Disclaimer: The technical content of this article is for industry experience exchange only. Please operate with caution in accordance with the actual equipment conditions on site for practical applications. Ningbo Jiangce Technology Co., Ltd. is not responsible for equipment damage or workpiece scrap caused by direct copying of codes.

Reference Documentation

ISO 5725-1~6:1994 Accuracy of measurement methods and results (basic standards for repeatability and reproducibility)
ISO 230-2:2014 Test procedures for machine tools – Part 2: Determination of positional accuracy and repeatability
GB/T 17421.2-2016 General rules for inspection of machine tools – Part 2: Determination of positional accuracy and repeatability
GB/T 6379.1-2004 Accuracy of measurement methods and results – Part 1: General principles and definitions
VDI/DGQ 3441:1985 Machine Tool Position Accuracy Statistical Inspection
Renishaw Tool Tool Repeatability Testing Standard Operating Procedure

FAQ Selected Q&A

**问：What is closed-loop compensation for in machine probes，And ordinary ones”Measure the size”What’s the difference？**
**答：**The key difference lies in”closed loop”two characters。Ordinary online measurement only achieves”Measure it to see if the size is correct”，The result requires manual judgment and manual knife repair。Closed loop compensation is automatically completed through macro programs”measurement→Deviation calculation→Knife repair automatic update→Re measurement verification”The complete closed loop。The core statement is#13001 = #13001 + #148（1The geometric compensation variable of the number knife automatically accumulates the current deviation value）。The system automatically accumulates the deviation to the corresponding value after each measurement#10001~#10099（或#13001~#13099）Knife compensation variable，Realize fully automatic unmanned compensation。

**问：In the repeatability testing standard for closed-loop compensation，Why is the testing speed specified as 240mm/min？What would happen if we were to speed up or slow down？**
**答：**Standard testing speed 240mm/minIt is a widely recognized benchmark value in the industry。The mechanism by which speed affects repeatability lies in G31 SkipDelay effect of signal——The faster the speed，Displacement from probe trigger to CNC latch position（overshoot）The larger，And the consistency of each overshoot will deteriorate。Actual test data shows：Every 100mm increase in speed/min，Delay error increases by approximately 2~5μm。Therefore, the test results at different speeds are not comparable。If different speeds are used for tool alignment in actual processing，Suggest verifying repeatability separately at the corresponding speed。For high-precision levels（0.25μm），Suggest using a lower testing speed（Like 120mm/min）To obtain more stable results。

**问：How many times is required for closed-loop compensation to verify repeatability？2σWhat does it mean?？**
**答：**The standard requires at least 10 measurements to be taken（n≥10），Using 2σ（2Multiple standard deviation）Quantify repeatability。2σThe meaning is：Under the assumption of normal distribution，About 95% of the measurement results fall within the mean ± 2σwithin the scope of。For example, 2σ=2μm，This means that in 95% of cases, the difference between the results of two knife cuts does not exceed 2μm。Computational method is：①Calculate the standard deviation of 10 measurementsσ = √[Σ(xᵢ-x̄)²/(n-1)]；②Repetitive R=2σ。Attention：Less than 10 statistical results are unreliable，Suggest continuous measurement of the same batch（Complete within a short time interval），And the testing environment should be kept stable。

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