Exploring the ISO System of Limits and Fits - Part II: Calculation of Tolerance Grade

In the previous blog, we introduced the fundamental concepts of the ISO system of limits and fits, which provides a framework for designing parts with specific fits, such as holes and shafts. In this second part of the series, we will focus on the calculation of tolerance grades, a key element in the system that helps determine the accuracy and precision of manufactured parts.

Calculation of Tolerance Grades

In the ISO system of limits and fits, the values for tolerance grades remain consistent over a range of basic sizes. This range is defined by diameter steps, which represent the minimum and maximum sizes within that range. These diameter steps are crucial in ensuring that the tolerance grades, such as IT 1 to IT 16, can be applied uniformly across various sizes of parts. The values of tolerance grades for a given diameter range are typically multiples of the tolerance unit ‘i’, which is calculated using the R5 series of preferred numbers. For sizes up to and including 500 mm, the tolerance unit ‘i’ can be determined by the formula:

Experience has shown that in manufacturing processes, dimensional inaccuracies tend to be proportional to the cube root of the absolute size. This relationship is reflected in the ISO system, where the tolerance unit ‘i’ is calculated in units of 10⁻³ mm or µm from above equation.

In the ISO system of limits and fits, the tolerance unit 'i' is calculated in units of 0.001 mm (or 10⁻³ mm). The basic size D is the geometric mean of the diameter steps between which a particular basic size lies. This means that for a given size, the tolerance values are based on the average of the minimum and maximum size within the diameter step range, rather than the exact size.

The geometric mean is calculated as follows:

Diameter Steps in 'mm'
To and Inc	1-3
Over To and Inc	3-6
Over To and Inc	6-10
Over To and Inc	10-18
Over To and Inc	18-30
Over To and Inc	30-50
Over To and Inc	50-80
Over To and Inc	80-120
Over To and Inc	120-180
Over To and Inc	180-250
Over To and Inc	250-315
Over To and Inc	315-400
Over To and Inc	400-500

For tolerance grades IT01 to IT1, the tolerances are calculated as follows : 

For IT01, tolerance = 0.3 + 0.008 D 

For IT0, tolerance = 0.5 + 0.012 D  

For IT1, tolerance = 0.8 + 0.02 D

For IT2 to IT4 the values of tolerance grades are placed geometrically between the tolerance grades of IT1 and IT5

The values of the tolerances for tolerance grades IT5 to IT16 are given below :

Tolerance Grade

IT5

IT6

IT7

IT8

IT9

IT10

IT11

IT12

IT13

IT14

IT15

IT16

Magnitude

7i

10i

16i

25i

40i

64i

100i

160i

250i

400i

640i

1000i

The values of fundamental tolerances are given

The following list will demonstrate where these grades are applied according to their tolerance range in a particular application.

IT01 to IT4 – For the production of gauges, plug gauges, measuring instruments

IT5 to IT 7 – For fits in precision engineering applications

IT8 to IT11 – For General Engineering

IT12 to IT14 – For Sheet metal working or press working

IT15 to IT16 – For processes like casting, general cutting work

Supplements:

✔ Exploring the ISO System of Limits and Fits : Part-I

Quiz on ISO Tolerance Grades

Exploring the ISO System of Limits and Fits Part-I

The core purpose of any limit system is to offer guidance on factors that are inherently complex and difficult to analyze. In situations involving mating parts with relative motion, variables such as load conditions, rotational speed, lubrication methods, and environmental factors present challenges that are not easily quantified. A detailed analysis for every scenario would rarely be practical or cost-effective.

Therefore, the designer must rely heavily on experience or seek guidance from others. The main objectives of any general system of standard fits and limits are to assist the user in

✔ Choosing appropriate functional clearances and interferences for a specific application or type of fit.

✔ Defining tolerances that strike a practical and cost-effective balance between fit precision and manufacturing costs.

ISO (International Organization for Standardization) System of Limits and Fits.

The ISO system applies to holes and shafts ranging from the smallest sizes up to 3150 mm. For sizes beyond this range, a wide variety of fits are available, with tolerance grades spanning from very fine to broad tolerances. The standard provides the option to use either a hole-based or shaft-based system, depending on the application requirements.

For any given basic size, there are 28 different hole sizes. These are created by progressively increasing the size (oversized holes) and progressively decreasing the size (undersized holes) relative to the basic size. The variation from the basic size for each hole is determined by the fundamental deviation. These size differences define the required fit between mating parts.

The "28 holes" are designated by the capital letters: A, B, C, CD, D, E, EF, F, FG, G, H, J, JS, K, M, N, P, R, S, T, U, V, X, Y, Z, ZA, ZB, and ZC. Each of these 28 holes is associated with a selection of 18 tolerance grades, labeled from IT0 1, IT0, and IT1 to IT16. The chosen tolerance grade determines the level of manufacturing accuracy required for the part.

Similarly, for shafts, there are 28 designated sizes for a given basic size, represented by lowercase letters from 'a' to 'zc'. Each of these shafts is also associated with 18 tolerance grades, which are designated in the same manner as for the holes.

The general arrangement of holes and shafts is shown in the figure below.

For shafts designated from 'a' to 'g', the upper deviation lies below the zero line, indicating that these shafts are undersized relative to the basic size. For shafts from 'j' to 'zc', the upper deviation is above the zero line, meaning these shafts are oversized relative to the basic size. This arrangement ensures that the corresponding fits between holes and shafts are accurately defined according to the required tolerances.

Similarly, the lower deviations for holes designated from 'A' to 'G' are above the zero line, indicating that these holes are oversized relative to the basic size. For holes from 'J' to 'ZC', the lower deviations are below the zero line, meaning these holes are undersized relative to the basic size. This variation in deviations helps define the specific fits between the holes and shafts based on the tolerance grades.

The shaft designated as 'h', where the upper deviation is zero, is referred to as the Basic Shaft. Similarly, the hole designated as 'H', where the lower deviation is zero, is known as the Basic Hole. These serve as reference points, with all other holes and shafts being specified in relation to these basic sizes.

The general trend for the shafts is that for shafts 'a' to 'g', both the upper and lower limits fall below the zero line. As a result, these shafts are undersized relative to the basic size and typically result in clearance fits when paired with corresponding holes. In these fits, there is always a gap or clearance between the shaft and the hole, ensuring easy assembly and movement.

For the 'h' shaft, the upper limit coincides with the basic size, meaning this shaft is manufactured to the exact nominal size. When assembled with the 'H' hole, which has a lower deviation of zero, this shaft will provide close running fits. These fits offer minimal clearance, ensuring a precise and smooth connection between the shaft and the hole, suitable for applications where accuracy and tight tolerances are essential.

For 'j' shafts, the tolerance zone is spread both above and below the zero line, resulting in transition fits when assembled with corresponding holes. This means the fit can either provide a slight clearance or a slight interference, depending on the actual size of the shaft and hole, allowing for a range of fitting conditions.

For 'k' to 'zc' shafts, the entire tolerance zone lies above the zero line (the basic size), meaning these shafts are oversized relative to the basic size. As a result, these shafts will always provide interference fits when paired with holes. In these fits, the shaft is larger than the hole, creating a tight, press-fit connection that ensures a firm and secure assembly, often used for applications requiring high strength and rigidity.

In conclusion, the limit system helps designers navigate complex factors like load, speed, and lubrication by providing standardized guidance. The ISO System of Limits and Fits defines 28 hole and 28 shaft sizes with 18 tolerance grades, balancing precision and cost. These tolerances create clearance, transition, or interference fits, ensuring the right fit for each application. Designers use this system to select the best fit for efficient and reliable assembly.

Supplements:

✔ Essential Terminology for Understanding Limit Systems in Mechanical Engineering

Quiz on ISO System of Limits and Fits

Essential Terminology for Understanding Limit Systems in Mechanical Engineering

In mechanical engineering, a Limit System is essential for controlling the dimensions of machine components during manufacturing. Achieving exact dimensions is ideal, but in practice, tolerances must be established to accommodate deviations. This framework allows engineers to define acceptable variations in size, ensuring that parts fit together correctly.

To successfully apply the Limit System, it’s crucial to establish the fit between mating components. This involves selecting one part as a reference (the constant member) while allowing the other to deviate based on the chosen fit type. The two primary systems are:

✔ Hole Basis System: Here, the hole dimensions are fixed, and the shaft dimensions vary.

✔ Shaft Basis System: In this system, the shaft dimensions are constant, while the hole dimensions vary.

Understanding the essential terminology in Limit Systems is crucial for professionals in mechanical design. Here’s a detailed overview of the important terms:

1. Nominal Size: The theoretical size specified in engineering drawings. For instance, a "30mm shaft" refers to a nominal size of 30mm.
2. Basic Size: Often synonymous with nominal size, it is the dimension to which tolerances are applied. Example: 30.000 ± 0.015.
3. Actual Size: The size measured using instruments, which must fall within the specified tolerance limits. Example: A shaft measured at 30.010mm.
4. Limits of Sizes: The maximum (Upper Limit) and minimum (Lower Limit) sizes allowed for a part. For example, for a shaft of 30.000 ± 0.015, the limits are 30.015mm and 29.985mm.
5. Allowance: The difference between the basic sizes of a hole and a shaft, indicating whether a fit is clearance (positive allowance) or interference (negative allowance). Example: For a hole of 29.990/29.980 and a shaft of 30.000, the allowance is -0.020mm.
6. Tolerance: The range of acceptable size variation, defined as the difference between the upper and lower limits. Tolerance can be unilateral (one-sided) or bilateral (both sides). 
   
7. Tolerance Zone: The range between the upper and lower limits where the actual size can fall.
   
   
   
8. Zero Line: An imaginary line representing the basic size, used as a reference for measuring deviations.
9. Upper Deviation: The difference between the basic size and the maximum size. Example: For a shaft of 30.000 ± 0.015, the upper deviation is 0.015mm.
10. Lower Deviation: The difference between the basic size and the minimum size. Example: For a shaft of 30.000 ± 0.015, the lower deviation is also 0.015mm.
11. Actual Deviation: The difference between the basic size and the actual size of a manufactured part. Example: If a shaft measures 30.010mm, the actual deviation is 0.010mm.
12. Mean Deviation: The average of the upper and lower deviations, providing an overall indication of size variation.
13. Fundamental Deviation: Represents the form of allowance, with upper deviation for shafts and lower deviation for holes.

The terminology used in Limit Systems is crucial for precision in mechanical design. Understanding these terms allows engineers to effectively manage the fit and function of machine elements, ensuring reliable performance. The next steps involve exploring types of fits and systems for further insight into effective engineering practices.

Supplements:

✔ Exploring Tolerances in Engineering: Part I – What is a Tolerance?

✔ Exploring Tolerances in Engineering: Part II – Why use Tolerances?

✔ Exploring Tolerances in Engineering: Part III - How Are Tolerances Determined?

Exploring Tolerances in Engineering: Part III - How Are Tolerances Determined?

In this concluding article of our "Exploring Tolerances in Engineering" series, we’ll explore how tolerance limits are determined and the various types of tolerances that exist. Understanding these concepts is vital for ensuring parts function correctly and are manufactured efficiently.

When designing a part, it's essential to keep tolerances as large as possible while ensuring the part works properly. This balance helps avoid unnecessary costs, as tight tolerances can lead to higher manufacturing expenses and wasted resources.

Here are some key methods for determining tolerance limits:

1. Existing Parts

Leveraging historical data is a key strategy in design and manufacturing, especially when working with established components. By referencing the proven production processes of a component, you can set new tolerances that are both practical and achievable. For instance, consider a valve that has been produced successfully for years. When introducing a new feature to this valve, you can establish tolerances for the new design based on the successful parameters used previously. This approach minimizes the risk of manufacturing complications and builds on a foundation of past successes.

2. Engineering Knowledge References

Consulting authoritative texts, such as Machinery’s Handbook, is crucial for selecting the appropriate tolerances in engineering design. These resources compile industry standards and best practices, making them invaluable for engineers seeking reliable guidance. For example, if you're designing a hole for a close fit around an M12 bolt, the "Clearance Holes for Metric Fasteners" table can provide precise diameter limits for different fits. This allows you to quickly determine the necessary tolerances, ensuring that your design meets both functional and manufacturing requirements.

3. Scientific Principles

Conducting tests, such as prototyping and cycle tests, is essential for determining tolerances effectively. These scientific tests validate whether a part performs as expected under real-world conditions. Through this process, you can make iterative adjustments based on the insights gained from testing. For instance, if a prototype consistently fails under stress, you can modify the design before moving to full-scale production. This approach ensures that the final part functions correctly and meets performance expectations, ultimately enhancing reliability and reducing the risk of costly manufacturing issues.

Example: Imagine a team developing a new smartphone model. During prototype testing, they discover that the screen cracks easily when dropped from a height. Rather than proceeding to mass production with this design flaw, the team decides to strengthen the screen material and redesign the corners to absorb shock better. By making these adjustments based on the prototype's performance, they ensure that the final product is more durable and meets customer expectations for reliability. This proactive approach not only improves the phone's reputation but also prevents potential recalls and costly repairs down the line.

4. Professional Experience

Gaining insights over time is vital for engineers and machinists, as their practical experience allows them to understand which tolerances work best for specific applications. This accumulated knowledge helps in setting realistic tolerances that can be effectively achieved in a manufacturing environment. Additionally, understanding the limits of tools and machines is crucial when establishing tolerances. For example, a machinist may know that a particular CNC machine can reliably achieve tolerances of ±0.01 mm, which directly informs the design process and ensures that the final product meets performance requirements without exceeding the machine's capabilities.

Types of Tolerances

While dimensional tolerances are the most recognized, several other types of tolerances are crucial:

1. Dimensional Tolerances

Tolerances define acceptable limits for physical measurements, including diameter, thickness, and length. For instance, if a part’s diameter is specified as 10 mm with a tolerance of ±0.2 mm, the acceptable range becomes 9.8 mm to 10.2 mm. This flexibility is crucial as it helps streamline the manufacturing process by minimizing the need for rework, allowing for smoother production and ensuring that parts can fit together properly even with slight variations.

2. Geometric Tolerances

Geometric tolerances specify allowable variations in the shape, orientation, and location of a part. These tolerances are crucial for assembly, as they ensure that components fit together correctly. For example, a tolerance requiring that two surfaces be perpendicular within ±0.1 mm is vital for maintaining proper alignment during assembly. This precision directly impacts the performance of the final product, highlighting the importance of geometric tolerances in achieving reliable and functional designs.

3. Force or Load Tolerances

Load tolerances define the maximum forces or loads that a part can safely handle. Understanding these tolerances is crucial for safety and performance, especially in applications subjected to dynamic loads. For instance, a spring may have a tolerance on its spring rate, indicating how much it can compress or extend under specified loads without failing. By knowing these limits, engineers can ensure that components perform reliably and safely within their intended applications, preventing potential failures that could lead to safety hazards.

4. Test Criteria Tolerances

Test criteria tolerances establish the conditions for evaluating a part to ensure it meets quality and performance standards. For example, a component might need to pass a fatigue test at a specified load for a defined number of cycles—such as 10,000 cycles—without failure. These criteria are essential for verifying that a part functions correctly before it is approved for use, ensuring reliability in real-world applications and helping to prevent potential issues during operation.

In summary, setting tolerance limits is vital for effective manufacturing. By using existing parts, referring to engineering books, testing designs, and drawing on experience, designers can determine the right tolerances to ensure parts work well. Different types of tolerances—like size, shape, strength, and testing conditions—help define acceptable variations, leading to better quality products and smoother production. Understanding and applying these principles can greatly improve both the design and manufacturing processes, resulting in successful engineering results.

Supplements:

✔ Exploring Tolerances in Engineering: Part I – What is a Tolerance?

✔ Exploring Tolerances in Engineering: Part II – Why use Tolerances?

Reference:

✔ Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook. 30th edition.  Industrial Press Inc.

✔ Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook. 29th edition.  Industrial Press Inc.

✔ ASME B18.2.8-1999, Clearance holes for bolts, screws and studs

METRIC CLEARANCE HOLE CHART

Metric clearance hole chart for metric bolts and screws according to ASME B18.2.8

M2 Clearance Hole :

Close fit: 2.2 mm, Normal fit: 2.4 mm , Loose fit: 2.6 mm

M3 Clearance Hole :

Close fit: 3.2 mm, Normal fit: 3.4 mm , Loose fit: 3.6 mm

M4 Clearance Hole :

Close fit: 4.3 mm, Normal fit: 4.5 mm , Loose fit: 4.8 mm

M5 Clearance Hole :

Close fit: 5.3 mm, Normal fit: 5.5 mm , Loose fit: 5.8 mm

M6 Clearance Hole :

Close fit: 6.4 mm, Normal fit: 6.6 mm , Loose fit: 7 mm

M8 Clearance Hole :

Close fit: 8.4 mm, Normal fit: 9 mm , Loose fit: 10 mm

M10 Clearance Hole :

Close fit: 10.5 mm, Normal fit: 11 mm , Loose fit: 12 mm

M12 Clearance Hole :

Close fit: 13 mm, Normal fit: 13.5 mm , Loose fit: 14.5 mm

Metric Clearance Holes Chart
Nominal Screw Size	Fit Class - Normal			Fit Class - Close			Fit Class - Loose
	Nominal Drill Size	Hole Diameter		Nominal Drill Size	Hole Diameter		Nominal Drill Size	Hole Diameter
		Min.	Max.		Min.	Max.		Min.	Max.
M1.6	1.8	1.8	1.94	1.7	1.7	1.8	2	2	2.25
M2	2.4	2.4	2.54	2.2	2.2	2.3	2.6	2.6	2.85
M2.5	2.9	2.9	3.04	2.7	2.7	2.8	3.1	3.1	3.4
M3	3.4	3.4	3.58	3.2	3.2	3.32	3.6	3.6	3.9
M4	4.5	4.5	4.68	4.3	4.3	4.42	4.8	4.8	5.1
M5	5.5	5.5	5.68	5.3	5.3	5.42	5.8	5.8	6.1
M6	6.6	6.6	6.82	6.4	6.4	6.55	7	7	7.36
M8	9	9	9.22	8.4	8.4	8.55	10	10	10.36
M10	11	11	11.27	10.5	10.5	10.68	12	12	12.43
Nominal Screw Size	Fit Class - Normal			Fit Class - Close			Fit Class - Loose
	Nominal Drill Size	Hole Diameter		Nominal Drill Size	Hole Diameter		Nominal Drill Size	Hole Diameter
		Min.	Max.		Min.	Max.		Min.	Max.
M12	13.5	13.5	13.77	13	13	13.18	14.5	14.5	14.93
M14	15.5	15.5	15.77	15	15	15.18	16.5	16.5	16.93
M16	17.5	17.5	17.77	17	17	17.18	18.5	18.5	19.02
M20	22	22	22.33	21	21	21.21	24	24	24.52
M24	26	26	26.33	25	25	25.21	28	28	28.52
M30	33	33	33.39	31	31	31.25	35	35	35.62
M36	39	39	39.39	37	37	37.25	42	42	42.62
M42	45	45	45.39	43	43	43.25	48	48	48.62
M48	52	52	52.46	50	50	50.25	56	56	56.74
Nominal Screw Size	Fit Class - Normal			Fit Class - Close			Fit Class - Loose
	Nominal Drill Size	Hole Diameter		Nominal Drill Size	Hole Diameter		Nominal Drill Size	Hole Diameter
		Min.	Max.		Min.	Max.		Min.	Max.
M56	62	62	62.46	58	58	58.3	66	66	66.74
M64	70	70	70.46	66	66	66.3	74	74	74.74
M72	78	78	78.46	74	74	74.3	82	82	82.87
M80	86	86	86.54	82	82	82.35	91	91	91.87
M90	96	96	96.54	93	93	93.35	101	101	101.87
M100	107	107	107.54	104	104	104.35	112	112	112.87