How to Write Geometric Tolerances｜Explanation of geometric tolerances from basics to applications

 

Here.mechanical drawing　and ... andTolerance design　mentioned in the articleGeometric tolerances.　Here is a note about the

 

Have you ever experienced drawings with geometric tolerances in which "the intent of the drawing was not correctly communicated to the manufacturing department" or "rework occurred due to discrepancies in recognition with the supplier?　Many of these problems are caused by ambiguous shape and positional instructions that cannot be expressed by dimensions alone.

 

There are many drawings in which geometric tolerances are regarded as mere shape limitation instructions and "simple expressions" are used to give such instructions.　However, I believe that this is inevitable.Frankly, it is too complicated.　　This is complicated because it limits the errors that can occur in the actual part reproduced from the drawing.

 

When we try to learn geometric tolerancing, we tend to miss the essence of the subject because of the numerous symbols and ways of expressing tolerance values, etc. that are on the table.　Therefore, this article aims to touch on the essence of geometric tolerancing, and to answer some of the questions you may have about geometric tolerancing, what geometric tolerancing is and how it can solve your design problems, and how it can be used to solve your design problems.Need to know how to write correctly　The following is a detailed explanation of the following information.　Please refer to it.

What are Geometric Tolerances? The Basics and Importance Explained

Differences and advantages with dimensional tolerances

Tolerances in mechanical drawings can be broadly classified into "dimensional tolerances" and "geometric tolerances.　The first is the "design".　　The two are fundamentally different in purpose and scope of regulation and complement each other to fully express the designer's intent.

 

Dimensional tolerances mainly regulate the "size" of parts.　For example, for dimensions such as length and diameter, the tolerance from the standard value is indicated as "±0.1".Measurement is based on two-point measurement using calipers or micrometersand check if the distance between those two points is within the specified range.　However, dimensional tolerances alone cannot guarantee the geometry of a part.　Even if the diameter of the hole meets the dimensional tolerance, the possibility that the entire hole is distorted into an oval or barrel shape cannot be eliminated.

 

On the other hand,Geometric tolerances regulate "distortion of the shape itself" and "relationship (posture and position)" of multiple parts, which cannot be regulated by dimensional tolerances.　The "Flatness" indicates the waviness of the surface. Flatness clearly indicates the undulation of the surface, squareness indicates the tilt of the surface relative to the reference plane, and positionality indicates the deviation of the hole from its correct position.

 

The greatest advantage of introducing geometric tolerancing is the ability to accurately communicate design intent without ambiguity.　The "discovery" culture is in the　　Especially in today's globalized manufacturing world, the culture of "discovery," in which the intention of the customer is not written on the drawings, is no longer acceptable.　By using the universal language of geometric tolerancing, the same interpretation is possible no matter who reads the drawings, thereby preventing defects and rework caused by communication errors.

 

 

Shape tolerances regulate the shape of individual parts

Shape tolerance regulates the correctness of the "shape itself" that a part should have, and is applied to a "single shape" that does not require a relationship with other parts.　The datum is then used as the reference datum for the measurement.　The key feature is that no datum is needed as a reference for measurement. Form tolerances include straightness, flatness, circularity, cylindricity, and line and surface contours.

 

For example, "flatness" regulates how much "undulation" or "unevenness" is allowed in areas that should be flat.　Valve mounting surfaces of hydraulic equipment and cylinder heads of enginesmating face　Such as,Extremely important where parts adhere to each other to ensure sealing　The result will be a　Poor flatness can lead directly to leakage of fluid or combustion gases, resulting in poor product performance and failure.

 

Roundness" and "cylindricity" also determine the performance of rotating parts. If the shaft or housing hole that the bearing fits into is not an exact circle, stress will be concentrated in a specific area, causing vibration, abnormal noise, and premature failure.　Cylindricity, in particular, regulates the three-dimensional shape, including not only the roundness of the cross section (roundness) but also the straightness in the axial direction (straightness), and thus can meet more demanding specifications.　Thus.Shape tolerances are the first step in assuring the basic quality that a part should have on its own.　It can be said that

 

 

List of shape tolerance types and symbols

 

Application Examples of Shape Tolerance

Shape tolerances guarantee the correctness of the "shape itself" of a single part　I will do so.

• Straightness: Applied to rails of linear guides and screw shafts of ball screws, which require precise linear motion. It is the cornerstone of smooth linear motion, since any bends in rails or shafts directly lead to increased running resistance, deteriorated positioning accuracy, and reduced service life.
• Flatness: This is essential for surfaces that maintain airtightness through gaskets, such as valve mounting surfaces of hydraulic equipment and cylinder heads of engines. Undulation of surfaces directly leads to fluid and gas leakage and significantly impairs product performance.
• Roundness and cylindricity: Applies to the shaft (journal section) where the bearing fits and the cylinder bore where the piston reciprocates. If the shape is not round or cylindrical, it may cause early breakage due to stress concentration and output loss due to poor airtightness.
• Contour: Applied to components whose performance is determined by their geometry, such as camshafts in engines (line contouring) and turbine blades in aircraft engines (surface contouring). It is used to maximize performance by accurately achieving complex curves and surfaces as designed.

 

 

Posture tolerance regulates part tilt

Attitude tolerance regulates the "orientation" of a form (surface, axis, etc.) with respect to a reference datum　It is.　Unlike shape tolerances, which regulate the shape of individual parts,There must always be a relationship to the criteria.　There are three types of posture tolerances: parallelism, squareness, and inclination.

 

Parallelism" regulates how far two surfaces or lines maintain the same distance from each other.　For example, if the two shafts supporting the gears inside a reduction gear (gearbox) are not parallel to each other, tooth contact between the gears will deteriorate (one-sided contact), causing abnormal noise, abnormal wear, and reduced power transmission efficiency.

 

Squareness" assures that a surface or axis is exactly 90 degrees to a reference.　If the spindle axis of a machine tool is not perpendicular to the table surface on which the workpiece is placed, the accuracy of the part being machined cannot be guaranteed. This is a fundamental element that determines the machining accuracy of the entire machine.

 

And "inclination" regulates the tilt of a surface that should be at a specific angle to a reference.　By properly dictating these posture tolerances, we can assure that multiple parts will fit together exactly in the angular relationship as designed.

 

 

List of posture tolerance types and symbols

 

Examples of Posture Tolerance Applications

Attitude tolerance regulates the "orientation" with respect to a reference (datum), and is used to determine the assembly accuracy of a part.　It is directly related to the

• Parallelism: Applies to two parallel shafts supporting gears in a reduction gear (gearbox). If the shafts are not parallel to each other, the gears will hit one another, leading to abnormal noise, abnormal wear, and reduced power transmission efficiency.
• Squareness: Used to guarantee the perpendicularity of the machine tool spindle to the table surface. If the spindle is tilted with respect to the table, the accuracy of the parts to be machined cannot be guaranteed, and this is a fundamental factor that determines the overall performance of the machine.
• Inclination: (assumed use case) Applies to fixtures that combine parts at a specific angle, or to nozzle mounting surfaces that are positioned at an angle. Ensures that the fixture is mounted at a theoretically accurate angle with respect to the reference plane and meets functional requirements.

 

 

Positional tolerances regulate the positioning of parts

Positional tolerances regulate how accurately a point, line, plane, etc. should be positioned relative to a reference datumIt is　It is essential to guarantee assembly and interchangeability, especially when multiple components are combined.

 

The typical "position degree" mainly regulates how much a hole, boss, or other form can deviate from its theoretically exact position.　When multiple bolts are used to fasten a part, it is more functional and reasonable to regulate the entire hole pattern as a single group by position degree than to regulate the position of individual holes by dimensional tolerance.

 

Other positional tolerances include "coaxiality," which aligns the centers of two axes, and "symmetry," which indicates that a groove or other feature is symmetrical with respect to the center.　Proper use of these tolerances ensures that the part will function exactly as designed and in position.

 

List of Position Tolerance Types and Symbols

 

Positional Tolerance Application Examples

Positional tolerances regulate "positional accuracy" relative to a reference (datum) and ensure interchangeability and ease of assembly of parts.　I will do so.

• Position degree: Applies to multiple bolt hole patterns drilled in flanges and plates of any mechanical device. Since assembly cannot be performed unless the holes align with those of mating parts, a single tolerance controls the positioning of multiple holes to ensure compatibility.
• Coaxiality/concentricity: Applies to cases where the center axes of two or more cylindrical objects need to be aligned, such as the input shaft of a reduction gear coupled to the output shaft of a motor. If the shaft centers are misaligned, the coupling will be subjected to undue force, which may cause vibration and premature bearing failure.
• Symmetry: (Intended use) Applies to keyways and mounting holes of symmetrically positioned parts. Ensures symmetrical placement of shapes with respect to the center of the part, ensuring rotational balance and assembly uniformity.

 

 

Runout tolerance regulates runout of rotating parts

Runout tolerance regulates the amount of surface "runout" when the part is rotated around a reference axis (datum)　and is mainly applied to rotating parts such as motor shafts, pulleys, and brake discs.

 

Circumferential Runout regulates the magnitude of runout at any one cross-section of a surface when the part is rotated. It evaluates the combined effects of circularity and concentricity at that cross section.

 

On the other hand,Total runout" is a tighter tolerance that regulates the magnitude of runout across the entire surface.　The following is a list of the most common types of runout.　　In addition to circumferential runout, it also includes the effects of cylindricity, squareness, and parallelism, and is therefore used for parts that require particularly high rotational accuracy, such as turbine shafts that rotate at high speeds.　Properly setting these tolerances ensures smooth machine operation, suppression of vibration and noise, and safety.

 

 

List of runout tolerance types and symbols

The "circumferential runout" symbol cannot be displayed as a text symbol, so it is described in text that shows its shape.

 

Application examples of runout tolerance

Runout tolerance regulates the "runout" of rotating parts and is essential for performance and reliability, especially for parts rotating at high speeds.　It is.

• Circumferential runout: This applies to brake discs and pulleys in automobiles. Large runout during rotation can cause unpleasant vibration (judder) during braking and shorten the life of the belt.
• Total runout: Applied to parts rotating at very high speeds, such as precision spindles on machine tools and turbine shafts on turbochargers. By strictly regulating runout over the entire surface, fatal vibrations caused by unbalance are prevented and high machining accuracy, performance, and safety are guaranteed.

 

 

How to write geometric tolerances

Role of the datum as a design basis

The concept of "datum" is essential to correctly understand and indicate geometric tolerances, especially posture and position tolerancesIt is.　　In a nutshell, a datum is a theoretically accurate point, line, or plane that serves as a "reference" for regulating geometric tolerances.

 

Because of machining errors in actual parts, perfectly straight lines and flat surfaces do not exist.　Therefore,On the drawing, a specific face or hole (datum shape) of the part is specified, from which the ideal reference is established.　For example, if the bottom surface of a part is designated as the datum, the surface is brought into contact with a very flat surface, such as a surface plate, during measurement.　The surface of the surface plate then serves as a theoretically accurate "datum plane" from which the parallelism, squareness, etc. of the rest of the part can be uniquely evaluated.

 

The selection of a datum should not be arbitrary, but should faithfully reflect how the component will be installed and function within the product.　Generally, the main mounting surfaces in the assembly are set as the first datum, and the surfaces and holes related to positioning are set as the second and third datums, in order of priority.　The first priority is to be determined.　This order of priority should be determined by taking into account the assembly sequence of parts and machining setup.

 

 

Correct rules for the tolerance entry frame

Geometric tolerance instructions are given using a rectangular box called a "tolerance entry box.　By correctly applying the structure and entry rules of this box, design intent can be communicated without ambiguity.

 

The tolerance entry frame is divided into two or more compartments according to function.

• Compartment 1: Enter the "geometric characteristic symbol" indicating the type of geometric tolerance to be regulated.　For example, "⟂" for squareness, "⌖" for positional degrees, and so on.
• Compartment 2: Enter the allowable tolerance values in numerical values.　If the tolerance range is a cylinder or circle, add the diameter symbol "φ" before the numerical value. To be described later.When the maximum entity tolerance method is applied　will also append a symbol such as "Ⓜ" to this parcel.
• Compartment 3 and beyond: For when a reference datum is required, such as posture tolerance, position tolerance, runout tolerance, etc,In order of priority, from left to rightFill in the datum indicator letters (e.g., A, B, C).

 

This tolerance entry frame is tied to the form to be regulated using an indication line (leader line).　At this time,It is necessary to clearly distinguish and indicate whether the object to be regulated is the "surface itself" or the "axis line or center plane" defined by its dimensions by placing the arrow of the indication line on the outline line of the form or on the extension line of the dimension line.　There are

 

 

Drawing instructions in accordance with JIS standards

The rules for mechanical drawing are defined by the Japanese Industrial Standards (JIS).　In recent years, this JIS standard has undergone major revisions to conform to International Organization for Standardization (ISO) standards, and the active use of geometric tolerancing is now mandatory or strongly recommended.

 

In the past, in Japanese manufacturing, even if it was not specified in the drawings, the manufacturer would take into account the intentions of the designer to create a high-quality product.Discovery."The culture called "the culture of the world" existed.　However, today, with the globalization of manufacturing bases, such tacit understanding is no longer valid with overseas suppliers who have different cultures and customs.　　This is because overseas partners take only the information on the drawings as absolute contractual instructions.

 

For this reason,In the revised JIS standard, the standard is to use geometric tolerances (especially positional tolerances) rather than conventional dimensional tolerances, especially for indicating the positional relationship between shapes.This is the first step in the design process.　This makes it possible to accurately convey the design intent to anyone in the world, even though the drawings contain many symbols.　As a designer, it is important to always be aware of the latest JIS standards and create drawings that comply with them,Essential for ensuring quality and managing business risk in the global supply chain　It is.

 

 

Concept and illustration of tolerance range

Central to understanding geometric tolerancing is the concept of "tolerance zone.A tolerance zone is a geometric space or area into which a regulated form (surface, axis, etc.) is defined as having to fit.

 

For example, if "flatness 0.08" is indicated, the tolerance range is "the space between two perfectly parallel planes separated by 0.08 mm.　It means that the actual surface of the part must fit perfectly within this space.

 

This concept of tolerance range clarifies the difference in rationale between dimensional and geometric tolerances.　shown in the following table.　For example, if the position of a hole is indicated by dimensional tolerances in the x- and y-directions, the tolerance range is "square".　On the other hand,If the same function is indicated by a geometric tolerance positional degree, the tolerance range is defined by a "circle (cylinder)" centered at a theoretically exact position　The following is a summary of the results of the project.

 

From a functional standpoint, a circular tolerance zone is more reasonable because the distance from the center determines whether a bolt will pass through or not.　And a circular tolerance zone inscribed in a square tolerance zone fulfills the same function but has a wider allowable area of about 57%.　This means more freedom of machining for the manufacturer, which directly leads to lower defect rates and, ultimately, cost reductions.　Thus,Understanding the concept of tolerance range is very important for functional and economical design　It is.

 

 

Advanced Use of Geometric Tolerances

What is the maximum material tolerance method (MMC)?

The Maximum Material Condition method, or MMC for short, is one of the applied principles of geometric tolerancing and is a very powerful method to reduce manufacturing costs while guaranteeing the assemblability of parts.　On the drawing, the tolerance value is indicated by the symbol "Ⓜ" after the tolerance value.

 

The "maximum entity state," which is the basis of this method, is the state in which the volume (entity) of the part is the largest.　Specifically, it is the maximum allowable diameter for a shaft and the minimum allowable diameter for a hole.

 

The main purpose of the MMC is to guarantee 100% assembly of parts that have a "clearance fit" relationship, such as bolts and holes.　The designer sets the tolerances so that the tightest combination, i.e., the largest shaft fits the smallest hole without problems.

 

When this method is applied, the "size" and "position and orientation" tolerances of the part are linked. In other words, the further away the actual finished dimensions of the part are from the maximum entity state (less material), the more additional tolerance is given to the geometric tolerance value. This concept leads to the next bonus tolerance.

 

 

Bonus Tolerance Reduces Costs

The greatest benefit created when applying the maximum entity tolerance method (MMC) is "bonus tolerance."It is.　The idea is that the further the actual finished dimensions of a form are from its maximum material dimension (MMC), the additional geometric tolerance value is allowed for the difference.

 

Let us consider a concrete example.　 Suppose that the dimensions of a certain hole are specified as "φ10 ±0.1" and the positional tolerance is "φ0.2Ⓜ".

• The maximum material material dimension (MMC) of this hole is "φ9.9", which is the smallest diameter, since it has the most material.
• If this hole is machined with MMC's φ9.9, the allowable position tolerance is φ0.2 as indicated in the drawing.
• However, if the hole is machined at the maximum allowable diameter of "ø10.1", it is only "10.1 - 9.9 = 0.2 mm" away from the MMC.
• This 0.2 mm is added to the original positional tolerance as a bonus tolerance.
• Therefore, the total positional tolerance in this case is "φ0.2 (original tolerance) + φ0.2 (bonus tolerance) = φ0.4", which is a wider tolerance.

This concept makes reasonable allowances on drawings for the functional fact that "if a hole is slightly out of alignment, but the hole is made larger, the mating bolt will pass through with no problem." Bonus tolerances allow the manufacturing department to work within wider tolerances, which directly leads to higher yields and lower disposal costs.

 

 

Efficient assembly inspection with functional gauges

Another major advantage of applying the maximum material tolerance method (MMC) is that it greatly simplifies inspection methods.　The MMC is located at　Forms to which MMC is applied can be judged pass/fail with a simple street/stop gauge called a "functional gauge" without the use of expensive and time-consuming CMMs.

 

This functional gauge is an inspection tool that physically simulates the case where the mating part exists in its most severe state (maximum entity state). For example, when inspecting the positional degree of a hole, a gauge is prepared with a pin that imitates a bolt of the mating part and stands in a theoretically accurate position. If the gauge passes smoothly through the hole to be inspected (Go), the part is instantly determined to be functionally acceptable for actual assembly.

 

If the gauge does not pass (No-Go), the part is rejected. This method is very efficient because it verifies combined dimensional and positional (or orientation) tolerances at once. Especially for mass-produced items, it enables quick and low-cost 100% inspection, which has the effect of dramatically reducing the man-hours and costs of the inspection process. Thus, applying MMC at the design stage leads to optimization of the inspection process as well as manufacturing.

 

 

Realization and verification of geometric tolerances

Relationship between processing method and achieved accuracy

The tolerance values that designers enter in their drawings are more than just numbers.　It is an economic metric that directly determines the manufacturing method, the number of processes, and the final product cost.The tighter the tolerance, the more the cost tends to increase exponentially　The following is located in the

 

For example, the flatness that can be achieved by general milling is about 0.02 mm, but to reduce it to 0.005 mm would require grinding with an expensive grinder, which would increase costs many times over.Achieving tighter tolerances incurs additional costs such as more precise machine tools, more machining time, higher defect rates, and more sophisticated inspections.　It is.

 

Therefore,The designer's key responsibility is to set tolerances that are appropriate, but not unnecessarily tight, to the extent that product functionality is assured.　Overdesign" that requires excessive precision "just to be safe" not only does not contribute to improved product performance, but is the biggest factor in unnecessarily increasing manufacturing costs.　The first two are the following.

 

 

Measuring methods and selection of appropriate measuring instruments

It is essential to have a process to objectively "verify" that the indicated geometric tolerances meet the required specifications.　It is.　　Selecting the best measurement method for the required accuracy, type of tolerance to be measured, and production volume is the key to efficient and reliable quality assurance.

 

Although CMMs are highly versatile and can measure almost all geometric tolerances with a single machine, they are also very expensive to install, time-consuming to measure, and not suitable for ultra-high-precision measurements in the micron range.

 

On the other hand, "roundness and cylindrical profile measuring machines" are suitable for measuring tolerances related to rotating parts such as roundness, cylindricity, and runout at the submicron level. Contour Measuring Machines" are specialized for measuring complex two-dimensional contours.

 

Even without expensive measuring machines, many geometric tolerances can be measured simply by combining basic measuring tools such as surface plates, dial gauges, and V-blocks.The designer must be aware of how the indicated tolerances will be measured and keep in mind that the design must be verifiable.

 

 

summary

Optimal geometric tolerances improve quality

As we have seen, geometric tolerancing is more than just a drafting rule; it is a strategic tool for designers that determines product quality, cost, and international competitiveness.　In order to dictate optimal geometric tolerances and inherently improve product quality, one must always be aware of the following points

• Start design from functional requirements
• Datum reflects the way it is assembled.
• Actively utilize MMC to reduce costs
• Consider manufacturing and inspection processes
• Distinguish between dimensional and geometric tolerances
• Correctly understand the concept of tolerance range
• Comply with the latest JIS and ISO standards
• Guarantee the quality of individual parts with shape tolerances
• Define angular relationships between parts with posture tolerances
• Positional tolerances ensure assembly compatibility
• Runout tolerances guarantee performance of rotating parts
• Take advantage of bonus tolerance
• Assume inspection by a functional gauge
• Avoid excessive precision requirements (overdesign)
• Close coordination between design, manufacturing, and quality assurance

 

That's it.

 

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