Tiêu chuẩn iso 01328 1 2013

3.2.2 measurement diameter diameter of the circle concentric with the datum axis 3.2.7 where the probe is in contact with the tooth flanks during the measurement of helix, pitch or toot

Fundamental terms and symbols

For the purposes of this part of ISO 1328, the following terms, definitions and symbols apply.

NOTE 1 For other definitions of geometric terms related to gearing, see ISO 701, ISO 1122-1 and ISO 21771.

NOTE 2 Some of the symbols and terminology contained in this part of ISO 1328 might differ from those used in other documents and International Standards.

ISO 1328 details specific terminology and symbols, systematically organized in alphabetical order in Tables 1 and 2 Table 1 lists terms with definitions formatted into logical groups, while Table 2 presents corresponding symbols alphabetically Tolerance values are denoted with a subscript "T," ensuring clarity in technical specifications.

Table 1 — Terms, listed in alphabetical order, with symbols

Active tip diameter d Na mm

Active tip diameter point on line of action N a –

Adjacent pitch difference tolerance f uT μm

Adjacent pitch difference, individual f ui μm

Contact point tangent at base circle T –

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Cumulative pitch deviation (index deviation), individual F pi μm

Cumulative pitch deviation (index deviation), total F p μm

Cumulative pitch (index) tolerance, total F pT μm

Helix form filter cutoff λβ mm

Length of path of contact g α mm

Maximum length of tip relief L Cαa,max mm

Maximum length of root relief L Cαf,max mm

Minimum length of tip relief L Cαa,min mm

Minimum length of root relief L Cαf,min mm

Number of pitches in a sector k –

Pitch, transverse circular on measurement diameter p tM mm

Profile control diameter d Cf mm

Profile form filter cutoff λ α mm

Radial composite deviation, tooth-to-tooth a f i ” μm

Root form diameter d Ff mm

Single flank composite deviation, total F is μm

Single flank composite tolerance, total F isT μm

Single flank composite deviation, tooth-to-tooth f is μm

Single flank composite tolerance, tooth-to-tooth f isT μm

Single pitch deviation (individual) f pi μm

Start of active profile diameter d Nf mm

Start of active profile point on line of action N f –

Tip form diameter d Fa mm

Working transverse pressure angle αwt deg a Symbols given in ISO 1328-2.

Table 2 — Symbols, listed in alphabetical order, with terms

A Flank tolerance class – b Facewidth (axial) mm

The article discusses key parameters for evaluating contact patterns and profile control in machining, including the reference diameter (mm), tip diameter (d a), base diameter (d b), and measurement diameter (d M) It highlights the significance of understanding the amount of root relief (μm), which impacts tool performance and surface quality The contact pattern evaluation (– d) is crucial for assessing tool contact accuracy, while the profile control diameter (d Cf) ensures precise shape regulation Additionally, the tip form diameter (d Ff) and root form diameter (d Ff) are essential for maintaining optimal cutting geometry, with the profile control diameter (d Cf) serving as a key indicator of profile consistency.

Symbol Term Unit d Na Active tip diameter mm d Nf Start of active profile diameter mm d w Working pitch diameter mm

F is Single flank composite deviation, total μm

F isT Single flank composite tolerance, total μm

F p Cumulative pitch deviation (index deviation), total μm

F pi Cumulative pitch deviation (index deviation), individual μm

F pT Cumulative pitch (index) tolerance, total μm

F βT Helix tolerance, total μm f fα Profile form deviation μm f fαT Profile form tolerance μm f fβ Helix form deviation μm f fβT Helix form tolerance μm f Hα Profile slope deviation μm f HαT Profile slope tolerance μm f Hβ Helix slope deviation μm f HβT Helix slope tolerance μm f i ” Radial composite deviation, tooth-to-tooth a μm f is Single flank composite deviation, tooth-to-tooth μm f isT Single flank composite tolerance, tooth-to-tooth μm f p Single pitch deviation μm f pi Single pitch deviation (individual) μm f pT Single pitch tolerance μm f u Adjacent pitch difference μm f ui Adjacent pitch difference, individual μm f uT Adjacent pitch difference tolerance μm g α Length of path of contact mm h k Tip corner chamfer mm k Number of pitches in a sector –

L cαa,max Maximum length of tip relief mm

L cαa,min Minimum length of tip relief mm

L cαf,max Maximum length of root relief mm

L cαf,min Minimum length of root relief mm

L β Helix evaluation length mm m n Normal module mm

N a Active tip diameter point on line of action –

N f Start of active profile point on line of action – p tM Pitch, transverse circular on measurement diameter mm r i Individual radial measurement μm s Tooth thickness mm

T Contact point at tangent at base circle – z Number of teeth – α wt Working transverse pressure angle deg β Helix angle deg λ α Profile form filter cutoff mm λβ Helix form filter cutoff mm a Symbols given in ISO 1328-2.

General dimensions

3.2.1 reference diameter ddiameter of reference circle

Note 1 to entry: The reference diameter is used to calculate values of tolerances.

Note 2 to entry: See ISO 21771:2007, 4.2.4.

The measurement diameter, denoted as dM, refers to the diameter of the circle concentric with the datum axis (3.2.7) used during gear inspection It is determined when the probe contacts the tooth flanks to accurately measure helix, pitch, or tooth thickness deviations This measurement is essential for ensuring precise gear geometry and maintaining manufacturing quality Proper understanding and application of the measurement diameter are vital for achieving consistent and reliable gear performance.

Note 1 to entry: The measurement diameter is usually near the middle of the flank.

Note 2 to entry: See ISO/TR 10064-3.

The profile form filter cutoff wavelength (λ α) defines the wavelength at which 50% of the amplitude of the involute profile measurement data is transmitted through a Gaussian low-pass filter This cutoff effectively allows only longer wavelength deviations to pass, ensuring that small, high-frequency variations are filtered out to provide a clearer analysis of the profile's overall shape By controlling λ α, engineers can enhance measurement accuracy and better isolate significant surface deviations in the involute profile.

Note 1 to entry: See 4.4.6 and Annex C.

3.2.4 helix form filter cutoff λ β wavelength where 50 % of the amplitude of the helix measurement data is transmitted as a result of the Gaussian low-pass filter, thereby including only longer wavelength deviations

Note 1 to entry: See 4.4.6 and Annex C.

3.2.5 roll path length length of roll linear distance along a base tangent line from its contact with the base circle to the given point on the involute profile in the transverse plane

Note 1 to entry: Roll path length is an alternative to roll angle for specification of selected diameter positions on an involute profile.

Note 2 to entry: See Figure 1 and ISO 21771:2007, 4.3.8.

The length of the contact path, denoted as gα, represents the distance from the start of the active profile, at dNf, to either the tip form diameter, dFa, or the point where contact ceases due to an undercut on the mating part, marking the end of the active profile This measurement is crucial for understanding the engagement length in gear contact analysis Accurate determination of gα ensures proper gear performance and load distribution, making it an essential parameter in gear design and manufacturing.

3.2.7 datum axis axis to which the gear details, and in particular the pitch, profile and helix tolerances, are defined Note 1 to entry: The datum axis of the gear is defined by the datum surfaces.

Note 2 to entry: See ISO/TR 10064-3.

Points on line of action d b base a tip d Cf profile control

Cf profile control d Fa tip form, where tip break starts

Fa tip form d Ff root form, where involute starts

Ff root form d Nf start of active profile

Nf start of active profile

T tangency to base circle line of action NOTE Diameters on mating gear have the same symbols, but different values.

Figure 1 — Diameters and roll path length for an external gear pair

Pitch deviations

3.3.1 individual single pitch deviation f pi algebraic difference between the actual pitch and the corresponding theoretical pitch in the transverse plane on the measurement circle of the gear

Note 1 to entry: It corresponds to the displacement of any tooth flank from its theoretical position relative to the corresponding flank of an adjacent tooth.

Note 2 to entry: For the left flanks, as well as for the right flanks, there are as many values of f pi as there are teeth. Note 3 to entry: See Figure 2.

Key theoretical actual NOTE p tM = π d M /z.

3.3.2 single pitch deviation f p maximum absolute value of all the individual single pitch deviations (3.3.1) observed

Note 1 to entry: f p = max |f pi |.

3.3.3 individual cumulative pitch deviation individual index deviation

F pi algebraic difference, over a sector of n adjacent pitches, between the length and the theoretical length of the relevant arc

Note 1 to entry: n varies from 1 to z ; for the left flanks, as well as the right flanks, there are as many values of F pi as there are teeth.

Note 2 to entry: In theory, it is equal to the algebraic sum of the individual single pitch deviations (3.3.1) of the same n pitches It corresponds to the displacement of any tooth flank from its theoretical position, relative to a datum tooth flank.

Note 3 to entry: See Figure 2 and Annex D.

3.3.4 total cumulative pitch deviation total index deviation

F p largest algebraic difference between the individual cumulative pitch deviation (3.3.3) values for a specified flank obtained for all the teeth of a gear

Note 1 to entry: F p = max F pi – min F pi

Profile deviations

3.4.1.1 profile control diameter start of profile evaluation diameter d Cf specified diameter beyond which the tooth profile is required to conform to the specified design profile (3.4.2.1)

Note 1 to entry: If not specified, the start of active profile diameter, d Nf , is used as the profile control diameter, see the last paragraph of 4.5.

Note 2 to entry: See Figures 1 and 3.

3.4.1.2 tip form diameter d Fa unless otherwise specified, tip diameter minus twice the tip corner radius or chamfer

Note 1 to entry: This is the minimum specified diameter for external gears or maximum specified diameter for internal gears where the tip break (start of tip chamfer or tip corner radius) can occur.

Note 2 to entry: With direct transition between the nominal involute helicoid and the top land of the tooth, the tip corner radius is zero and the tip form diameter is equal to the tip diameter.

Note 3 to entry: See Figures 1 and 3.

The measured profile of the tooth flank should include the portion along which the probe contacts during measurement, encompassing both the profile control diameter (3.4.1.1) and the tip form diameter (3.4.1.2) This ensures accurate assessment of gear tooth geometry and compliance with measurement standards.

Note 1 to entry: See Figure 3. a) External gear b) Internal gear

3.4.1.4 profile evaluation range section of the measured profile (3.4.1.3) starting at the profile control diameter (3.4.1.1), d Cf , and, unless otherwise specified, ending at 95 % of the length to the tip form diameter (3.4.1.2), d Fa

Note 1 to entry: See Figures 4 to 8, 4.4.8 and ISO 21771.

L α roll path length (3.2.5) of the profile evaluation range (3.4.1.4) in a transverse plane

Note 1 to entry: See Figure 1.

3.4.1.6 profile deviation amount by which a measured profile (3.4.1.3) deviates from the design profile (3.4.2.1)

Note 1 to entry: See Figures 4 to 8. a) Total profile deviation b) Profile form deviation c) Profile slope deviation

The key measured profile points along the line of action serve as a facsimile of the designed profile, providing essential data for profile control The mean profile line (Nf) indicates the starting point of the active profile, ensuring precise monitoring of deviations The profile's critical features are highlighted through the mean profile line, aiding in accurate assessment Additionally, the tip form line (Fa), where the tip break initiates, is crucial for evaluating the profile's integrity and ensuring optimal shape and functionality.

Figure 4 — Profile deviations with unmodified involute

``,,`````,,```,,,```,````,`,-`-`,,`,,`,`,,` - a) Total profile deviation b) Profile form deviation c) Profile slope deviation

See the key to Figure 4.

Figure 5 — Profile deviations with pressure angle modified a) Total profile deviation b) Profile form deviation c) Profile slope deviation

Figure 6 — Profile deviations with profile crowning modification a) Total profile deviation b) Profile form deviation c) Profile slope deviation

Figure 7 — Profile deviations with profile modified with tip relief

``,,`````,,```,,,```,````,`,-`-`,,`,,`,`,,` - a) Total profile deviation b) Profile form deviation c) Profile slope deviation

Figure 8 — Profile deviations with profile modified with tip and root relief

3.4.2.1 design profile profile specified by the designer in a diagram where one axis has modifications from a pure involute and the other axis has the roll length along the tangent to the base circle

Note 1 to entry: When the design profile is not specified, it is an unmodified involute and appears as a straight line In Figures 4 to 8, the design profiles are shown as broken-chain (dotted) lines.

Note 2 to entry: See Figures 4 to 8.

3.4.2.2 mean profile line line (or curve) that represents the shape of the design profile (3.4.2.1), but aligned with the measured trace over the profile evaluation range (3.4.1.4)

Note 1 to entry: See 4.4.8.2 for the method to be used.

F α distance between two facsimiles of the design profile (3.4.2.1) which enclose the measured profile (3.4.1.3) over the profile evaluation range (3.4.1.4)

Note 1 to entry: The facsimiles of the design profile are kept parallel to the design profile.

Note 2 to entry: See Figures 4 to 8 and 4.4.8.2.

3.4.2.4 profile form deviation f fα distance between two facsimiles of the mean profile line (3.4.2.2) which enclose the measured profile

(3.4.1.3) over the profile evaluation range (3.4.1.4)

Note 1 to entry: The facsimiles of the mean profile line are kept parallel to the mean profile line.

3.4.2.5 profile slope deviation f Hα distance between two facsimiles of the design profile (3.4.2.1) which intersect the extrapolated mean profile line (3.4.2.2) at the profile control diameter (3.4.1.1), d Cf , and the tip diameter, d a

Note 1 to entry: The facsimiles of the design profile are kept parallel to the design profile.

Helix deviations

The measured helix full flank is determined between the end faces or, if present, the start of end chamfers, rounds, or other modifications designed to exclude that portion of the tooth from engagement During helix measurement, the probe makes contact along this designated full flank, ensuring accurate assessment of the helix angle This method ensures precise evaluation of gear tooth geometry by focusing on the true engaging surface while accounting for any modifications that alter engagement.

3.5.1.2 helix evaluation range flank area between the end faces or, if present, the start of end chamfers, rounds, or other modification intended to exclude that portion of the tooth from engagement, that is, unless otherwise specified, shortened in the axial direction at each end by the smaller of 5 % of the facewidth or the length equal to one module

Note 1 to entry: It is the responsibility of the gear designer to ensure that the helix evaluation range is adequate for the application.

L β axial length of the helix evaluation range (3.5.1.2)

3.5.1.4 helix deviation amount by which a measured helix (3.5.1.1) deviates from the design helix (3.5.2.1)

3.5.2.1 design helix helix specified by the designer in a diagram where one axis has modifications from a pure helix and the other axis has the facewidth

Note 1 to entry: When not specified, it is an unmodified helix.

3.5.2.2 mean helix line line (or curve) that represents the shape of the design helix (3.5.2.1), but aligned with the measured trace Note 1 to entry: See 4.4.8.4 for the method to be used.

``,,`````,,```,,,```,````,`,-`-`,,`,,`,`,,` - a) Total helix deviation b) Helix form deviation c) Helix slope deviation

Key measured helix mean helix line facsimile of design helix facsimile of mean helix line

Figure 9 — Helix deviations with unmodified helix a) Total helix deviation b) Helix form deviation c) Helix slope deviation

Figure 10 — Helix deviations with helix angle modification a) Total helix deviation b) Helix form deviation c) Helix slope deviation

Figure 11 — Helix deviations with helix crowning modification

``,,`````,,```,,,```,````,`,-`-`,,`,,`,`,,` - a) Total helix deviation b) Helix form deviation c) Helix slope deviation

Figure 12 — Helix deviations with helix end relief a) Total helix deviation b) Helix form deviation c) Helix slope deviation

Figure 13 — Helix deviations with modified helix angle with end relief

F β distance between two facsimiles of the design helix (3.5.2.1) which enclose the measured helix (3.5.1.1) over the helix evaluation range (3.5.1.2)

Note 1 to entry: The facsimiles of the design helix are kept parallel to the design helix.

3.5.2.4 helix form deviation f fβ distance between two facsimiles of the mean helix line (3.5.2.2), which enclose the measured helix

(3.5.1.1) over the helix evaluation range (3.5.1.2)

Note 1 to entry: The facsimiles of the mean helix line are kept parallel to the mean helix line.

3.5.2.5 helix slope deviation f Hβ distance between two facsimiles of the design helix (3.5.2.1) which intersect the extrapolated mean helix line (3.5.2.2) at the end points of the facewidth, b

Note 1 to entry: The facsimiles of the design helix are kept parallel to the design helix.

Note 3 to entry: See 4.4.8.4 for the method to be used.

4 Application of the ISO flank tolerance classification system

General

This part of ISO 1328 provides flank classification tolerances and recommends measuring requirements for unassembled gears.

Some design and application considerations can warrant measuring or documentation not normally available in standard manufacturing processes Specific requirements shall be stated in the contractual documents.

Measurement and documentation methods are not mandatory unless explicitly agreed upon by the manufacturer and purchaser For applications requiring measurements beyond the standard recommendations in ISO 1328, it is essential to negotiate special measurement methods before commencing gear manufacturing.

The designation outlined in 4.6.1 should be used when specifying flank tolerance classes according to ISO 1328 This update is important because, in the previous edition, flank tolerance classes had different tolerance values, highlighting the need for consistent referencing Using the current designation ensures compliance with the latest standards and helps maintain precise manufacturing specifications.

Geometrical parameters to be verified

The methods used to measure the geometrical features of gears, as outlined in Table 3, vary based on factors such as tolerance levels, measurement uncertainty, gear size, production volume, available equipment, blank accuracy, and measurement costs Selecting the appropriate measurement method is essential to ensure precision and efficiency For detailed practices related to measuring spur and helical gears, refer to ISO/TR 10064-1, which provides comprehensive guidelines on gear measurement procedures.

Table 3 — Parameters — Locations of definitions and tolerances

Parameter symbol Measurement description Location of tolerance Location of definition Elemental:

Cumulative pitch (index), total Single pitch

Profile, total Profile form Profile slope Helix, total Helix form Helix slope Runout Sector pitch Adjacent pitch difference

Single flank composite, total Single flank composite, tooth-to-tooth Contact pattern (see ISO/TR 10064-4)

Size: s Tooth thickness (see ISO 21771) –

Gears specified to an ISO flank tolerance class must meet all individual tolerance requirements relevant to that specific flank tolerance class and size These requirements are detailed in Tables 4 and 5, ensuring compliance with established standards for precise gear manufacturing.

Table 4 contains lists of the minimum set of parameters that shall be checked for compliance with this part of ISO 1328 With agreement between the manufacturer and purchaser, the alternative list may be used instead of the default list The selection of the default or alternative list may depend on the measuring instruments available The parameter list for a more accurate flank tolerance class may be used when evaluating gears.

Gear tolerances typically apply to both sides of the teeth, ensuring precise operation In certain situations, the loaded flank is specified to require higher accuracy than the non-loaded or minimum-loaded flank If applicable, this information, along with the indication of the loaded flank, must be clearly specified on the gear engineering drawing to ensure proper manufacturing and functionality.

Table 4 — Parameters to be measured

Diameter mm Flank tolerance class Minimum acceptable parameters

Default parameter list Alternative parameter list d ≤ 4 000

This article discusses key parameters such as F β, f β, f Hβ, c pb, and F, emphasizing their roles within gear specifications According to ISO 1328-2 standards, these parameters are applicable when size constraints are not a factor It also highlights that contact pattern acceptance criteria and measurement practices are not defined in this section of ISO 1328, requiring agreement between manufacturer and purchaser.

Table 5 — Minimum number of measurements

Method designator Typical measuring method Minimum number of requirements Elemental:

F p : Cumulative pitch (index), total Two probe

All teeth f p : Single pitch Two probe

F α : Profile, total f fα : Profile form f Hα : Profile slope

F β : Helix, total f fβ : Helix form f Hβ : Helix slope

F is : Single flank composite, total – All teeth f is : Single flank composite, tooth-to-tooth – All teeth c p : Contact pattern – Three places

Sizes: s : Tooth thickness Chordal measurement

Measurement over or between pins Span measurement Composite action test

Three teeth Two places Two places All teeth Unless otherwise specified, the manufacturer shall select:

— the measurement method to be used from among the applicable methods described in ISO/TR 10064-

— the piece of measurement equipment to be used by the selected measurement method, provided it is in proper calibration;

— the individual teeth to be measured, as long as they are approximately equally spaced and meet the minimum number required by the method as summarized in Table 5.

Equipment verification and uncertainty

To ensure accurate gear measurement and traceability, equipment must undergo periodic verification following standard calibration procedures like ISO 18653 Additionally, it is essential to determine the measurement process's uncertainty to maintain precision and reliability in gear calibration.

Considerations for elemental measurements

Before elemental measurement values can be compared with tolerance values, certain operational parameters of the measurement method shall be known These include:

Measurement instruments often meet minimum required standards by default; however, when additional conditions are present, it becomes essential to identify and compensate for the causes of measurement discrepancies to ensure accurate results.

It is important to distinguish between measurement location (the measurement diameter), measurement direction, and tolerance direction.

Specification of design profile, design helix and pitch requires the definition of an appropriate reference axis of rotation, called the datum axis It is defined by specification of datum surfaces See ISO/TR 10064-3.

The tooth geometry is defined relative to the datum axis, which serves as the primary reference for all measurements and associated tolerances The position and orientation of the measurement diameter circle are established based on the datum axis, ensuring precise and consistent evaluation of the gear's dimensions Establishing a clear datum axis is essential for accurate gear manufacturing and quality control.

Surface measurements can be conducted in various ways, including along a direction normal to the surface, at an inclined angle, or following the curvature of a specified circle These methods enable precise assessment of surface shape and position, ensuring accurate results for engineering and manufacturing applications Understanding how to measure in different directions is essential for quality control and surface analysis.

In standard metrology practices, measurements are typically taken in a direction normal to the gear tooth surface At any point on the gear tooth, the normal vector is aligned tangent to the gear’s base cylinder and inclined relative to the transverse plane at the base helix angle This approach ensures accurate and consistent measurements for gear geometry verification.

It is important to understand that gear measuring instruments use different measuring procedures, some measuring in the normal direction, some measuring in other directions.

In ISO 1328, the tolerance direction depends on the specific elemental parameter being measured If the measurement direction differs from the tolerance direction specified for that parameter, original measurement values must be compensated accordingly For sign conventions and proper reporting of these values, refer to sections 4.4.8.2, 4.4.8.4, and 4.4.8.6.

The specified tolerance direction of measurement for all pitch deviations is in the transverse plane along the arc of the measurement diameter, d M , circle.

The specified direction of tolerance for profile and helix deviations is in a transverse plane, on a line tangent to the base circle.

This part of ISO 1328 specifies the measurement diameter, d M , as defined in 3.2.2 as the location for the measurement of helix and pitch parameters (also see 4.4.3 and 4.4.4) The measurement diameter shall be recorded on the inspection record Since the tolerance values are calculated based on the reference diameter, they remain unchanged when the measurement diameter is modified.

When the measurement diameter is not specified, it is given by:

``,,`````,,```,,,```,````,`,-`-`,,`,,`,`,,` - for external gears: d M=d a−2m n (1) for internal gears: d M=d a+2m n (2) where d M is the measurement diameter, mm; d a is the tip diameter, mm; m n is the normal module, mm.

Any tooth surface will exhibit a wide spectrum of deviations from the specified tooth flank form This includes, at one extreme, those of long period, such as a general concavity At the other end of the spectrum are short period irregularities, such as surface roughness.

ISO 1328 specifies that measurement values for involute profile and helix should be modified through low-pass filtering to focus on long-period irregularities before analysis and comparison to tolerances This process reduces or excludes irregularities with wavelengths shorter than the designated filter cutoff wavelength, defined as gear form filter cutoff (λα or λβ) The profile form filter cutoff (λα) should be expressed in terms of roll path length, while the helix form filter cutoff (λβ) must be stated in terms of face width Recommended cutoff wavelengths can be calculated using specific formulas, and wavelengths longer than these recommended values should not be used.

30 (3) but not less than 0,25 mm λ β = b

30 (4) but not less than λα where λα is the profile form filter cutoff, mm; λ β is the helix form filter cutoff, mm.

The actual filter type and form filter cutoffs, λ α and λ β , along with the probe diameter, shall be indicated on the inspection record A Gaussian 50 % type filter is required and defined in accordance with ISO/TS 16610-1 and ISO 16610-21.

Beware that filtering based on the form filter cutoff wavelength values recommended in Formulae (3) and (4) may inadvertently suppress important form deviations that impact gear function These deviations, often called waviness, occur within a wavelength range between the recommended form filter cutoff and the surface roughness filter cutoff To effectively evaluate such form deviations, it is advisable to choose shorter form filter cutoff wavelengths than those specified in the formulas.

See Annex C for additional information.

Measurement data density is essential for accurate surface analysis, as the sampling rate determines the observable wavelength of surface irregularities The inspection record must clearly specify the number of data points within the evaluation length For involute profile measurements, a minimum of 150 evenly spaced data points along the roll length is required Helix measurement datasets should include at least 5 ã b/λβ points to ensure precision When waviness assessment is necessary, the dataset must contain at least 300 points or 5 points per millimeter, whichever is greater, to accurately capture surface variations.

4.4.8 Required measuring and evaluation practices

The measurement probe shall travel the full profile length The probe shall start below the profile control diameter and continue past where the tip break actually starts.

The profile evaluation involves calculating the straight-line gradient of the profile measurement using the least squares method, based on deviations from the designated design profile The assessment always commences at the profile control diameter, d Cf Deviations caused by excess material near the tooth tip within the profile evaluation range are included in both the profile form deviation, f fα, and the total profile deviation, F α Conversely, material removed beyond the profile evaluation range near the tooth tip can generally be disregarded Key aspects of the evaluation include total profile deviation and profile form deviation.

The key measured profile points along the line of action replicate the design profile with high accuracy, ensuring precise control of the mean profile line The starting point of the active profile aligns with the mean profile line to maintain consistency Additionally, the profile features a tip form where the tip break initiates, which is critical for assessing the profile's overall shape and structural integrity These measurements are essential for quality control and ensuring the profile conforms to the specified design parameters.

The mean profile line is created by combining the ordinates of the straight-line gradient of the profile deviation with those of the design profile This line is essential for determining the parameters f fα (see Figures 4b, 5b, 6b, 7b, 8b, and 14b) and f Hα (see Figures 4c, 5c, 6c, 7c, and 8c).

Specification of gear flank tolerance requirements

The information to define the gear flank tolerance requirements on the gear drawing or gear specification should include, but should not be limited to:

— a reference to this part of ISO 1328, i.e ISO 1328-1:2013;

— the flank tolerance class of each tolerance parameter, which may be different for each parameter, and the limits, in micrometres, calculated in accordance with this part of ISO 1328;

— datum axis used for measurement (preferably the functional datum axis; see ISO/TR 10064-3);

— functional datum axis (used for evaluation);

— measurement diameter if different from the recommendation in 4.4.5;

— the minimum number of teeth to be inspected, if different from the minimum recommendation in Table 5;

— the design shape for profile or helix modifications, if they are required;

— the range of evaluation for profile and helix measurement;

— the profile control diameter (defined as a diameter, length of roll or angle of roll);

Additional measurement requirements include tooth thickness measured at the reference diameter, span measurement or dimension over balls, and tip and root diameter It also covers the root fillet profile and surface roughness of the tooth flank, ensuring comprehensive assessment of gear components for optimal performance.

It is usual to define this information as a table of data.

The designer can choose the profile control diameter anywhere between the root form diameter and the start of the active profile diameter The root form diameter is determined based on the closest measurement among the undercut diameter, the point of tangency to the root fillet, or the base circle diameter.

If the profile control diameter is not specified, the start of active profile diameter, d Nf, is used as a substitute When a gear meshes with multiple mating gears, the start of active profile diameter should be considered for each gear to ensure proper profile control diameter selection.

Acceptance and evaluation criteria

4.6.1 Designation of flank tolerance class

Designation/specification of a flank tolerance class in accordance with this part of ISO 1328 shall be as follows:

ISO 1328-1:2013, class A where A designates the design flank tolerance class.

NOTE If the year of publication is not listed, the latest version of ISO 1328-1 applies.

For a given gear, it is permissible to use different flank tolerance classes for each tolerance parameter.

The tolerances for each item that govern the flank tolerance class of gears are calculated by the formulae given in Clause 5.

This section of ISO 1328 outlines the standard tolerances, measurement methods, and definitions, which take precedence unless specific contractual agreements between the manufacturer and purchaser specify otherwise For detailed guidance on measurement uncertainty and its application to specified tolerances, refer to ISO 18653, ISO/TR 10064-5, and ISO 14253-1.

4.6.5 Evaluation of flank tolerance class

The overall flank tolerance class of a gear is determined by the largest flank tolerance class number identified among all the specified tolerance parameters This measurement is based on the criteria outlined in ISO 1328, which ensures proper gear performance and compatibility Understanding this classification is essential for selecting gears that meet precision and transmission requirements.

In specialized applications, additional characteristics such as tooth thickness and surface finish tolerances are essential to ensure optimal performance These critical dimensions and tolerances should be clearly specified on technical drawings or purchase documents ISO/TR 10064-1 and Annexes D to G provide guidance on measurement methods for these important parameters, supporting accurate quality control and reliable functionality.

Presentation of data

ISO 1328 illustrates how the design or measured gear profile deviates from a theoretical pure involute at the specified pressure angle, and how the helix deviates from a theoretical pure helix at the designated helix angle The figures present the profile and helix as horizontal lines to avoid specifying left or right flank or internal/external gear, while most measuring machines display these as vertical lines, with orientation being non-essential.

General

Tolerance values are calculated, in micrometres, by Formulae (5) to (12) given in 5.3.

Use of formulae

The application scope is defined in Clause 1, with specific formulas outlined in Clauses 5.3 (Formulas 5 to 12) These ranges must not be extrapolated beyond their specified limits Any tolerances required for gears outside these ranges should be agreed upon mutually by the manufacturer and the purchaser.

The step factor between two consecutive classes is 2 Values of the next higher (or lower) class are determined by multiplying (or dividing) by 2 The required value for any flank tolerance class may be determined by multiplying the unrounded calculated value for class 5 by 2 ( A − 5 ) where A is the number of the required flank tolerance class.

Values calculated from Formulae (5) to (12) (in 5.3) shall be rounded as follows:

— if greater than 10 àm, round to the nearest integer micrometre;

— if 5,0 àm or greater but less than or equal to 10 àm, round to the nearest 0,5 àm;

— if less than 5,0 àm, round to the nearest 0,1 àm.

When using measuring instruments that read in Imperial inches, values derived from Formulas (5) to (12) in section 5.3 must be converted to ten-thousandths of an inch and rounded following micrometer rounding rules, replacing “micrometre” with “ten-thousandths of an inch.” All parameters in these formulas are originally intended to be entered in millimeters for accuracy and consistency.

Tolerance formulae

Single pitch tolerance, f pT , shall be calculated using Formula (5): f pT=( 0 001 , d+0 4 , m n+5 ) ( ) 2 ( A − 5 ) (5)

5.3.2 Cumulative pitch (index) tolerance, total, F pT

Total cumulative pitch (index) tolerance, F pT , shall be calculated using Formula (6):

Profile slope tolerance, f HαT, shall be calculated using Formula (7) This tolerance shall be applied as a plus/minus (±) value. f H T α =( 0 4 , m n+0 001 , d+4 ) ( ) 2 ( A − 5 ) (7)

Profile form tolerance, f fαT, shall be calculated using Formula (8): f f T α =( 0 55 , m n+5 ) ( ) 2 ( A − 5 ) (8)

Total profile tolerance, F αT, shall be calculated as given by Formula (9) using unrounded tolerance values for profile slope and profile form:

Helix slope tolerance, f HβT , shall be calculated using Formula (10) This tolerance shall be applied as a plus/minus (±) value. f H T β =( 0 05 , d+0 35 , b+4 )( ) 2 ( A − 5 ) (10)

Helix form tolerance, f fβT , shall be calculated using Formula (11): f f T β =( 0 07 , d+0 45 , b+4 )( ) 2 ( A − 5 ) (11)

Total helix tolerance, F βT , shall be calculated as given by Formula (12) using unrounded tolerance values for helix slope and helix form:

This annex presents a strategy using a segmented evaluation or zone evaluation for two or more zones

An example for the gear profile can be a tip zone, middle zone and root zone Adjacent zones are calculated separately, and can have different tolerance classes.

A.2 Zone-based profile tolerance evaluation

Regression analysis is essential for determining slope and form deviations, with each zone—tip and root modifications—considered separately (see Figure A.1) The calculation of regression lines primarily uses zones L αa, L αm, and L αf, while areas between these zones are evaluated for plus material condition and total deviation, with defined lengths that cannot be zero unless a tangential transition occurs Typically, linear regression based on least squares is employed to analyze deviations from the design profile, ensuring accurate assessment of geometric deviations.

C αa amount of tip relief Points on line of action

C αf amount of root relief a tip

L Cαa,max maximum length of tip relief C f profile control

L Cαa,min minimum length of tip relief F a tip form

L Cαf,max maximum length of root relief F f root form

L Cαf,min minimum length of root relief

Figure A.1 — Regression zones for profile with tip and root modification

For the profile slope deviation, f Hα , the regression line of the middle profile zone shall be extrapolated over the area from the profile control point to the tip [see Figure A.2 c)].

The profile form deviation, denoted as fα, measures the distance between two regression line facsimiles that enclose the measured profile within a designated zone This deviation is independently determined for each zone to ensure precise assessment Notably, in the area above the tip break, a plus material condition is incorporated into the adjacent zone, as illustrated in Figure A.2 b), enhancing the accuracy of surface profile evaluation.

NOTE The facsimiles of the regression line are kept parallel to the regression line. a) Total profile deviation b) Profile form deviation c) Profile slope deviation

Key measured profile Points on line of action facsimile of design profile C f profile control mean profile line F a tip form facsimile of mean profile line a tip

Figure A.2 — Zone-based evaluation for profile with tip and root modifications

The total profile deviation, Fα, measures the distance between two facsimiles of the design profile that surround the actual profile, as illustrated in Figure A.2 a) It is essential to consider excess material outside the evaluation range at the tip to ensure accurate assessment of profile conformity.

NOTE 1 The facsimiles of the design profile are kept parallel to the design profile.

NOTE 2 It is common practice to restrict evaluation to the middle zone or to omit F α completely.

A.3 Zone-based helix tolerance evaluation

To determine slope and form deviation accurately, a regression analysis is required When evaluating end relief, each zone is analyzed separately, with areas near the faces designated as Zones I and II (see Figure A.3).

For calculating regression lines, only zones L βI, L βm, and L βII are considered, while areas between these zones are used exclusively for analyzing the plus material condition related to form and total deviation The length of these transitional areas must be defined and cannot be zero, except in cases of tangential transitions Regression analysis is performed based on deviations from the design helix, utilizing the least squares method (Gauss) Typically, a linear regression model is employed for this purpose.

I datum face L CII,max maximum length of end relief

II non-datum face L CII,min minimum length of end relief

C βI amount of end relief L βI end relief zone

C βII amount of end relief L βm middle helix zone

L CI,max maximum length of end relief L βII end relief zone

L CI,min minimum length of end relief

Figure A.3 — Regression zones for a helix with relief at both ends

For the helix slope deviation, f Hβ , the regression line of the middle zone shall be extrapolated to the whole facewidth, b [see Figure A.4 c)].

The helix form deviation, denoted as f fβ, measures the distance between two facsimiles of the regression line that enclose the measured helix within a specific zone This deviation is determined independently for each zone to ensure accurate assessment Additionally, any excess material present between zones and at the helix ends must be included in the analysis to maintain comprehensive and precise results.

NOTE The facsimiles of the regression line are kept parallel to the regression line.

The total helix deviation, Fβ, measures the distance between two instances of the design helix that encompass the actual helix This parameter is essential for assessing the accuracy of helix geometry in manufacturing and design processes When evaluating beyond the specified range, Lβ, particularly at the flank ends, any excess material must be considered to ensure precise measurements and quality control.

NOTE 1 The facsimiles of the design helix are kept parallel to the design helix.

NOTE 2 It is common practice to restrict evaluation to the middle zone or to omit F β completely. a) Total helix deviation b) Helix form deviation c) Helix slope deviation

The key components of the helix include the measured helix L, the βI end relief zone (datum face), and the βII end relief zone (non-datum face) The mean helix line Lβm represents the central component of the helix, serving as a facsimile of the mean helix line Understanding these zones and lines is essential for accurate helix design and analysis, ensuring optimal performance in mechanical and engineering applications Proper measurement and referencing of the helix's end relief zones and the mean helix line are critical for maintaining precision and functionality in complex engineering systems.

Figure A.4 — Zone-based evaluation for a helix with end modifications

Evaluation of profile and helix deviations using the second order analysis method

This annex applies to gears with crowned profiles (also known as barrel-shaped) or crowned helixes, including gears that feature both It utilizes a second-order best fit to analyze deviations from the original profile or helix, ensuring precise measurement and analysis Additionally, the standard flank tolerance classes outlined in Clause 5 can be effectively applied with this method of analysis for comprehensive gear quality assessment.

Clauses 3 and 4 utilize linear analysis to evaluate deviations from the design profile and helix, rather than employing a second-order fit The outcome of this linear analysis is called a mean profile or helix line, which maintains the shape of the original design profile or helix, even if it is curved In contrast, second-order analysis results, as detailed in this annex, are always described as curves, providing a more advanced assessment of deviations.

Profile crowning is a widely used and effective profile modification technique in various applications It involves shaping the profile along a single parabolic curve, as illustrated in Figure B.1 The parabola is calculated within the length L α, and for evaluating parameters such as f Hα and C α, the parabola is extended to the tip diameter for unsegmented designs or to the segment end when analyzed by zones.

B.2.1 Mean second order profile curve

The mean second order profile curve is generated by fitting a second order (quadratic) curve to the measured profile trace within the profile evaluation length, Lα, using the least squares method This curve serves as the foundation for accurately determining key parameters such as f fα (flatness), f Hα (waviness), and Cα (profile roughness) Incorporating the mean second order profile into profile evaluation ensures precise and consistent surface characterization, essential for quality control and surface analysis.

The profile form deviation, f_fα, measures the distance between two replicas of the mean second-order profile curve, positioned at a constant separation from the mean curve to enclose the measured profile over the evaluation length, Lα This parameter is essential for assessing surface texture and quality, with specific reference to monitored conditions such as plus material deviations, as detailed in sections 3.3.10, Figure B.2 a), and 4.4.8.2.

The profile slope deviation, denoted as f Hα, measures the displacement of a line drawn through the intersection points where the extrapolated mean second-order profile curve meets the profile control diameter and the tip diameter This parameter is crucial for assessing surface profile accuracy in machining and manufacturing processes Understanding f Hα helps ensure precision in component dimensions, which is essential for quality control and performance optimization.

The algebraic sign of profile slope deviation, f Hα , using the second order method is determined in the same manner as given in 4.4.8.2.

If there is a design profile slope deviation, C Hα , the initially calculated f HαC is used to determine the profile slope deviation according to Formula (B.1): f H α = f H α C−C H α (B.1)

Profile crowning, denoted as C α, measures the distance along the recorded deviations between the intersection point of the chord with the extrapolated mean second order profile curve (at the profile control diameter and tip diameter) and a parallel tangent line to the mean second order profile curve This parameter is essential for evaluating the crown of the profile, alongside profile form deviation and profile slope deviation, which collectively ensure geometric precision and surface quality.

Tiêu đề	Cylindrical Gears — ISO System Of Flank Tolerance Classification — Part 1: Definitions And Allowable Values Of Deviations Relevant To Flanks Of Gear Teeth
Trường học	University of Alberta
Thể loại	tiêu chuẩn
Năm xuất bản	2013
Thành phố	Switzerland

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