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Geometrical Tolerances

Geometrical Tolerancing

Introduction..... Reference Standards..... Notation..... Maximum Material Requirement.....
Least Material Requirement..... Theoretically exact dimensions..... Projected Tolerance Zonee..... Envelope Requirement.....
Common zone..... Datum targets..... Free State tolerances.....


These notes attept to clarify the meanings of the supplimentary symbols used for geometric tolerancing.    The notes are outline in nature.    Detailed notes are found in the identified standards and it is suggested that these standards are consulted for clearest understanding of the requirements.

Reference Standards

BS ISO 1101:1983 Technical Drawings - Geometrical tolerancing - Tolerancing of form, orientation, location and run-out - Generalities, definitions, symbols, indications on drawings

BS ISO 5459:1981 Technical Drawings - Geometrical tolerancing - Datums and datum-systems for geometrical tolerances

BS EN ISO 2692:2006 Geometrical product specifications (GPS) � Geometrical tolerancing �Maximum material requirement (MMR), least material requirement (LMR)and reciprocity requirement (RPR)

BS ISO 8015:1985,Technical drawings � Fundamental tolerancing principle
BS ISO 10579:1985,Technical drawings -Dimensioning and tolerancing Non-rigid parts


Note: The following descriptions are very much shortened versions of those found in the standards and are not considered to be definitive.

CM: Common zone, Applying single set of geometrical tolerances to a number of separate features
DTI:Datum target indication. Used when defining a reference surface using one or more daturm target features
LMC: Least material condition of a component at that limit of size where the material of the feature is at its minimum everywhere, e.g. maximum hole diameter and minimum shaft diameter

LMS: The dimension defining the least material condition of a feature.

LMVS :The size generated by the collective effect of the least material size, LMS, of a feature and the geometrical tolerance (form, orientation or location).

LMVC: Least material virtual condition.  The condition of a component of least material virtual size.

LMR: Least material requirement, defining a geometrical feature of the same type and of perfect form, with a given dimension equal to LMVS, which limits a a feature on the inside of the material e.g wall thickness.

MMS :Maximum material size; The size of the maximum material condition.

MMVC:Maximum material virtual condition, is a perfect form condition of the feature.

MMVS:Maximum material virtual size, is the size generated by the collective effect of the maximum material size, MMS, of a feature of size and the geometrical tolerance (form, orientation or location) given for the derived feature of the same feature of size NOTE 1 Maximum material virtual size, MMVS, is a parameter for size used as a numerical value connected to MMVC.

PJ: Projected tolerance zone. A geometric tolerance zone which projects from an actual design features such as a hole
MMR,Maximum material requirement; The identified requirement for a feature of size, defining a geometrical feature of the same type and of perfect form, with a given value for the intrinsic characteristic (dimension) equal to MMVS, which limits the non-ideal feature on the outside of the material. This parameter is used to control the assembleability of the components.

Maximum Material Requirement

The minimum assembly clearance occurs when each of the mating componentsis at its maximum material size (e.g. the largest pin size and the smallest hole size) it additionally occurs when the geometrical deviations e.g. the form, orientation and location deviations of the components size and their derived features centre line surface form are also at their maximum.     Assembly clearance are maximised when the sizes of the assembled features of size are at least material size e.g. the smallest shaft size together with the largest hole size and when the geometrical variations e.g. the form, orientation and location deviation and their derived features are at zero.    If the size of one mating part is less than its maximum material size, the indicated geometrical tolerance of the feature may be increased without endangering the assembly to the other part.     This assembly function is controlled by the maximum material requirement.

The maximum metal requirement is that the component boundaries should not violate the maximum metal virtual condition of the perfect form at the size meeting the maximum metal requirement e.g largest external or smalles hole dia of fullest external form.    When the maximum metal condition symbol (M) (in circle) when used in the tolerance frame, it is indicated by a symbol placed after

- the tolerance value
- the datum letter
- or both

With maximum material requirement, the two requirements (size and geometrical tolerance) are transformed into one collective requirement.    In the figure below the shaft is required to be perfectly straight at maximum metal condition.   If the shaft was at its lower limit of size then it is acceptable that the shaft is allowed to be 0,5mm out in straightness.

In the figure below maximum metal requirement is with a 0,5mm allowance.   If the shaft was at its lower limit of size then it is acceptable that the shaft is allowed to be 1,0mm out in straightness.    At the upper limit of size the shaft is allowed to be 0,5mm out in straighness.

In the figure below maximum metal virtual condition is with a 0 mm allowance.  A cylinder of 10mm dimeter must be at 90o to the basplate with no angular allowance. A cylinder of 9,5mm diameter may be out of vertical be 0,5mm over its length.   Also a cylinder of variable diameter (within its tolerance) can be out of vertical only such that it does not violate MMVC with a MMVS = 10mm dia at 90o to the plate.

If the intended function of the a part a shown below is an assembly with a plate with two holes 50 mm apart.     The holes are required to be perpendicular to the contact surface of the plate then the pins are dimensioned as follows.

The maximimum metal requirement is applied to holes in a similar way as shown below.

An example of the application of maximum material requirement to coaxiality is illustrated in the figure below

Least Material Requirement

The least material requirement shall be indicated by the specification modifier symbol    .    When the least metal requirement symbol is used in the tolerance frame, it is indicated by a symbol placed after

- the tolerance value
- the datum letter
- or both

This requirement is generally used to limit the least material situation e.g. when it is necessary to limit the minimum wall thickness between a hole and the side or the outside diameter of a component.    An example of dimensioning which includes least metal requirements is provided in the figure below.

Theoretically exact dimensions

The dimension determining the theoretically exact form, orientation or position respectively must not be toleranced.     The corresponding actual dimensions may only vary by the tolerances of form, orientation or position specified within the tolerance frame.This is illustrated in the figure below

Projected tolerance zones

In some cases, the tolerance of orientation and position shall apply not to the feature itself but to the external projection of it. Such projected tolerance zones shall be indicated by the symbol P (in circle)

Envelope requirement (ref BS ISO 8015 clause 6,1

For a component feature e.g a cyliderical surface or a feature based on two parallel plane surfaces, the envelope requirement may be used.    This means the the envelope form at maximum material condition shall not be violated.    This is indicated by a symbol .

This requirement is illustrated by the following simple example

Common zone

it is possible to apply a single tolerance zone to several separate features.  An example of this is if a machine tool has separate surfaces which have all to be made with a common flatness tolerance.  This example is shown below.  In the tolerance frame the symbol CZ is added as the standard abbreviation for "common zone".

Datum Targets

When surfaces are identified as datum faces there is the problem that real surfaces vary significantly from ideally flat surfaces.    Using a real surface as datum face can result in poor repeatability of measurements.    For these situations datum targets may be used.     A daturm target may be a point, a line or a defined local surface.    If one datum surface is to be identified then three surface identifiers are require.    For two adjacent normal surfaces then three datum targets are required on the primary surface and two are required on the secondary surface.    If three adjacent normal surfaces are to be identified then three datum targets are required on the primary surface and two are required on the secondary surface and one is required on the tertiary surface.   

The figure below provides a crude example of a block with three datum faces to be identified and a hole which is provided with geometrical tolerances relative to the three datum faces

The figure illustrates the representative drawing . The datum face A is identified with the three datum points A1,A2,A3,. The datum face B is positioned using the two datum circular areas B1 and B2. The datum surface C is positioned using the datum circular daturm surface C1

Free State

In BS ISO 10579 a non-rigid part is defined as a part which deforms to an extent that in the free state is beyond the dimensional and/or geometrical tolerances on the drawing.    This condition applies to parts made of elastic or plastic materials or of thin flexible materials.

The free state condition of a part is when it is not restrained and subject only to the force of gravity.

The distortion of such a part should be such that if will be brought within the specified tolerances for verification at assembly or by assembly using forces expected under the normal assembly conditions.

Drawings of non-rigid parts should include ;

An identification of the standard BS ISO 10579 in the notes section
A note identifying the conditions providing the restraint in the assembled conditions when the drawing requirements apply
Geometrical variations allowed in the free state with a modifying in the tolerance frame.   
A note identifying the condition of the free state e.g orientation

A crude example of how a free state geometrical tolerance is applied is provided in the figure below.    The interpretation of this figure is that the tolerances followed by shall apply in the free state. The other tolerances apply in the assembled condition


Links Providing information on Geometrical Tolerancing
  1. Volvo Drawing Standards......For access to document 5023,501 on European-Standard-based drawing procedures
  2. Volvo Geometrical Tolerancing...For access to document 5062,2e on European-Standard-based geometrical tolerancing
  3. Baseline Uncertainty in Geometric Tolerance Inspection...... Interesting downloadable paper
  4. Drawing Standards... Downloadable Notes from Dartmouth U. (USA Not ISO)

Geometrical Tolerances