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GD&T F U N D A M E N T A L   &   B E N E F I T S

Geometric Dimensioning and Tolerancing (GD&T) is a system for defining and communicating engineering tolerances. It uses a symbolic language on engineering drawings and computer-generated three-dimensional solid models that explicitly describes nominal (danh nghĩa) geometry and its allowable variation (sự thay đổi, sự khác nhau). There are many benefits implementing GD&T, most noticeably —» Product Reliabilty Improvement —» Errors, Re-work, Rejections and Scrap Elimination —» Easy to Identify Deviating Processes That Affect Quality and Restore Them for Maximizing Yield.

How GD&T Enable Drawings for Higher Product Quality and Lower Cost? Below are steps towards a correct and complete G D & T Drawing:

W H A T   A R E   R U L E S   O F   G D & T   ?

To help conform to this standard of measurement, a system for defining tolerances known as Geometric Dimensioning and Tolerancing (GD&T) was developed. Below are the rules of GD&T.

N O N R I G I D   P A R T S

A nonrigid part is a part that can have different dimensions while restrained (kiềm chế) in assembly than while relaxed (thanh thản) in its "free state." Rubber, plastic, or thin-wall parts may be obviously nonrigid. Other parts might reveal themselves as nonrigid only after assembly or functioning forces are applied. That's why the exemption of "nonrigid parts" from Fundamental Rule is meaningless. Instead, the rule must be interpreted as applying to all parts and meaning. "Unless otherwise specified, all dimensions and tolerances apply in it free state condition." Thus, a designer must take extra care to assure that a suspected nonrigid part will have proper dimensions while assembled and functioning. To do so, one or more tolerances may be designated to apply while the part's assembly and/or functioning.

N O N R I G I D   P A R T S — S P E C I F Y I N G   R E S T R A I N T

Specifying Restraint: A nonrigid part might conform (thích nghi với) to all tolerances only in the free state, only in the restrained state, in both states, or in neither state. Where a part, such as a rubber grommet, may or may not need the help of restraint for conformance (sự phù hợp, sự thích hợp), the designer may specify optional restraint. This allows all samples to be inspected in their free states. Parts that pass are accepted. Those that fail may be reinspected — this time, while restrained. Where there is a risk that restraint could introduce unacceptable distortion, the designer should specify mandatory (có tính cách bắt buộc) restraint instead.

Restraint may be specified by a note such as UNLESS OTHERWISE SPECIFIED, ALL DIMENSIONS AND TOLERANCES MAY (or SHALL) APPLY IN A RESTRAINED CONDITION. Alternatively, the note may be directed only to certain dimensions with flags and modified accordingly (phù hợp với điều đã được nhắc đến hoặc biết đến). The note shall always include (or reference a document that includes) detailed instructions for restraining the part. A typical note (example: THIS TOLERANCE APPLIES WHEN DATUM FEATURE A IS MOUNTED AGAINST A FLAT SURFACE USING FOUR .250-28 BOLTS TORQUED TO 10 FOOT POUNDS.) identifies one or two functional datum features (themselves nonrigid) to be clamped into some type of gage or fixture. The note should spell out any specific clamps, fasteners, torques, and other forces deemed necessay to simulate expected assembly conditions.

R U L E   N U M B E R   1

Rule #1 at MMC (Only): Y14.5 decrees (quy định) that, unless otherwise specified or overridden by another rule, a feature's MMC size limit spine shall be perfectly formed (straight or flat, depending on its type). Ex: A diameter .997–1.000 shaft then its MMC is 1.000. It's in perfect form that it's should have perfect straightness, circularity and cylindricity. This invokes (viện dẫn chứng) a boundary of perfect form at MMC (also called an envelope). The form tolerance increases as the actual size of the feature departs from MMC toward LMC. Rule #1 doesn't require the LMC boundary to have perfect form.

R U L E   N U M B E R  2

Rule #2: RFS automatically applies. (ex: diameter 1.000 / .900 / .800 steeped shaft). The bigger diameter is asigned as (datum B) and the smaller diameter .800 is controlled by a concentric geometric tolerance and this tolerance is applied without any dimensional size constraints ie regardless of feature size (RFS).


Size Limits (Level 1 Control): For every feature of size, the designer shall specify the largest and the smallest the feature can be. Size Limit Bounday The standards provide three options for specifying size limits on the drawing: symbols for limit and fits, limit dimensioning (Ø.250/.245 or Ø.245/.250) or (25.45/25.00 not 25.45/25 or 32 +0.25/–0.10 not 32 +0.25/–0.1), and plus and minus tolerancing (.247 +.003/-.002 or .250 +/–.005) or (32 0/–.02 or 32 +0.02/0). Where tolerances directly accompany a dimension, it's important to coordinate the number of decimal places expressd for each value to prevent confusion. The rules depend on whether the dimension and tolerance values are expressed in inches (.500 +.005/–.000 not .500 +.005 /0) or millimeters (0.7 not .7 or 25.1 not 25.10 or 12 not 12.0).

Size Limit Boundaries: For every feature of size, the designer shall specify the largest and the smallest the feature can be (see Size Limits). With size limit boundary, we're concerned with the exact requirements these size limits impose (áp đặt) on a feature. It starts with a geometric element called a spine. The spine for a cylindrical feature is a simple (nonself-intersecting) curve in space that nay be straight or wavy, and we take an imaginary solid ball whose diameter equals the small size limit of the cylinde feature, and sweep its center along the spine. This generates a "wormlike" 3-dimensional bounday for the feature's smallest size. Then, we may create a secon spine, and sweep another ball whose diameter equals the large size limit of the cylindrical feature. This generates a second 3-D boundary, this time for the feature's largest size. Wwhether it's an internal or external feature, both feature surfaces shall contain the smaller boundary and be contained within the larger boundary.


Level 2 – Overall Feature Form: For feature of size that must achieve a clearance fit in assembly, such as the right image (Cylindrical features of size that must fit in assembly), Cylindrical features of size that must fit in assembly we calculate the size tolerances based on the assumption that each feature, internal and external, is straight. Ex: The designer knows that a Ø.501 maximum pin will fit in a Ø.502 minimum hole if both are straight. If one is out of shape, they usually won't go together. Because Level 1's size limit boundaries can be curved, they can't not assure assemblability. Leve 2 adds control of the overall geometric shape of form of a feature of size by establishing a perfectly formed boundary beyond which the feature's surface(s) shall not encroach (xâm lấn, xâm phạm).

  1. At LMC (Only): Figure 1a illustrates a case where a geometric tolerance is necessary to assure an adequate (tương xứng, xứng đáng; thích hợp, thích đáng, thoả đáng) "skin" of part material in or on a feature of size, rather than a clearance fit. In such an application, the feature of size at LMC represents the worst case. An LMC modifier applied to the geometric tolerance overrides Rule #1 for the controlled feature of size. Instead, the feature's LMC spine shall be perfectly formed (straight or flat, depending on its type). This invokes a boundary of perfect form at LMC. The MMC boundary need not have perfect form. The same true for a datum feature of size referenced at LMC.
  2. Feature of size associated with an MMC modifier and an LMC modifier
  3. At both MMC and LMC: There are cases where a feature of size is associated with an MMC modifier in one context, and an LMC modifier in another context. Figure 1b illustrate the datum B bore is controlled with a perpendicularity tolerance at MMC, then referenced as a datum feature at LMC. Each modifier for this feature, MMC and LMC, invokes perfect form for the feature's corresponding size limit boundary.
  4. At neither MMC nor LMC – the Independency Principle: Y14.5 exempts (miễn, được miễn) the follwing from Rule #1.
    — Stock, such as bars, sheets, tubing, structural shapes, and other items produced to established industry or government standards that prescribe limits for straightness, flatness, and other geometric characteristics. Unless geometric tolerances are specified on the drawing of a part made from these items, standards for these items govern (ảnh hưởng) the surfaces that remain in the as-furnished condition on the part.
    — Dimensions for which restrained verification is specified in accordance with (see Specifying Restraint).
    — A cylindrical feature of size having a straightness tolerance associated with its diameter dimensions as described in (see Straightness Tolerance for a Cylindrical Feature).
    — A width-type feature of size having a straightness or (by extension of principle) flatness tolerance associated with its width dimensions as described in (Flatness Tolerance for a Width-Type Feature).
Perfect Form at MMC Not Required

In these cases, feature form is either noncritical or controlled by a straightness or flatness tolerance separate from the size limit. Since Rule #1 doesn't apply, the size limits by themselves impose neither an MMC nor an LMC boundary of perfect form. Example of an electrical bus bar In Fig. 1c, the cross-sectional dimensions have relatively close tolerances, not because the bar fits closely inside anything, but rather because of a need to assure a minimumcurrent-carrying capacity without squandering expensive copper. Neither the MMC nor the LMC boundary need be perfectly straight. However, if the bus bar is custom rolled, sliced from a plate, or machined at all, it won't automatically be exempted from Rule #1. In such a case, Rule #1 shall be explicitly nullified by adding the note PERFECT FORM AT MMC NOT REQD adjacent to each of the bus bar's size dimensions.

Level 2 Adjustment – Actual Local Sizes: Since Level 3 qnd 4 tolerances impose (page 5-45)

Level 2 Tolerances: It is intended to control feature form. Thus, the tolerance zone must interact with actual feature size independently at each cross section of the feature. Though the effective control is reduced from 3D down to 2D, inspection is more complicated.


Level 3 – Virtual Condition Boundary for Orientation: For two mating feature of size, Level 2's perfect form boundaries can only assure assemblability in the absence of any orientation or location restraint between the two features–that is, the features are free-floating relative to each other. In this figure is an example of a pin fitting into a hole, and added a large flange around each part. The two flanges shall bolt together and make full contact. This introduces an orientation restraint between the two mating features. When the flanges faces are bolted together tightly, the pin and the hole must each be very square to their respective flange faces. Despite (dù, mặc dù, không kể, bất chấp) the fact that the pin and the hole might each respect thier MMC boundaries or perfect form, nothing prevents those boundaries from being badly skewed (nghiêng, xiên, lệch) to each other. In this example, we've restrained the virtual condition boundary perpendicular to the flange face. The part portion illustrates how matability is assured for any part having a pin that can fit inside it Ø1.298 MMC virtual condition boundary and any part having a hole that can contain its Ø1.298 MMC virtual condition boundary.

An orientation tolerance applied to a feature of size, modified to MMC or LMC, establishes a virtual condition boundary beyond which the feature's surface(s) shall not encroach (xâm lấn, xâm phạm). For details on how to apply an orientation tolerance, see (Level 3 Control – Orientation Tolerance) below. In addition to perfect form, this new boundary has perfect orientation in all applicable degrees of freedom relative to any datum feature(s) we select (see Degrees of Freedom). The shape and size of the virtual condition boundary for orientation are governed by the same rules as for form at Level 2. A single feature of size can be subject to multiple virtual condition boundaries.

Level 3 – Orientation Tolerance: (page 5-103)...


Level 4 – Positional Tolerance: How does it work? A positional tolerance may be specified in an RFS, MMC or LMC context.

Level 4 – Virtual Condition Boundary for Location: For two mating features of size, Level 3's virtual condition boundary for orientation can only assure asemblability in the absence of any location restraints between the two features. , for example, where no other mating features impede optimal location alignment between pin and hole. In this figure, we've moved the pin and hole close to the edges of the flanges and added a larger bore and boss mating interface at the center of the flanges. When the flange faces are bolted together tightly and the boss and bore are fitted together, the pin and the hole must each still be very square to their respective flange faces. However, the parts can no longer slide freely to optimize the location alignment between the pin and the hole. Thus, the pin and the hole must each additionally be accurately located relative to its respective boss or bore.

A position tolerance applied to a feature of size, modified to MMC or LMC, takes the virtual condition boundary one step further to Level 4. How to apply it?. In addition to perfect form and perfect orientation, the new boundary shall have perfect location in all applicable degrees of freedom relative to any datum features we select (see Degrees of Freedom). The shape and size of the virtual condition boundary for location are governed by the same rules as for form at Level 2 and orientation at Level 3, with one addition. For a spherical feature, the tolerance is preceded (đến hoặc đi trước) by the "SØ" symbol and specifies a virtual condition boundary that is a sphere. A single feature of size can be subject to multiple virtual condition boundaries – one boundary for each form, orientation, and location tolerance applied. In this figure, four datums are identified with dimensions and tolerances added. The central boss has an MMC size limit of Ø1.297 and a perpendicularity tolerance of Ø.002 at MMC. Since it's an external feature of size, its virtual condition is Ø1.297 + Ø.002 = Ø.1299. The bore has an MMC size limit of Ø.1303 and a perpendicularity tolerance of Ø.004 at MMC. Since it's an internal feature of size, its virtual condition is Ø.1303 – Ø.004 = Ø.1299. It's important to observe that for each perpendicularity tolerance, the datum feature is the flange face. Each virtual condition boundary for orientation is restrained perfectly perpendicular to its referenced datum, derived from the flange face as shown, the boss and bore will mate every time. The same method applied for Ø.500 boss and Ø.514 bore. Any pin contained within its Ø.506 boundary can assemble with any hole containing its Ø.506 boundary.

Level 3 or 4 – Virtual Condition Equal to Size Limit (Zero tolerance): In the same example, the boss's functional extremes are at Ø1.291 and Ø1.299. Between them, the total tolerance is Ø.008. Based on this assumptions (điều được chấp nhận là đúng hoặc chắc sẽ xảy ra, giả định) about process variation, we arbitrarily (tùy tiện) divided this into Ø.006 for size and Ø.002 for orientation. Thus (do đó, theo đó, vì thế, vì vậy), the Ø1.297 MMC size limit has no functional significant (quan trọng, đáng kể). We might just divided the Ø.008 total into Ø.004 + Ø.004, Ø.006 + Ø.002, or even Ø.008 + Ø.000. In this case, where the only MMC design consideration is a clearance fit, it's not necessary for the designer to apportion (chia ra từng phần) the fit tolerance. This is accomplished (thực hiện, hoàn thành) by stretching the MMC size limit to equal the MMC virtual condition size and reducing the orientation or positional tolerance to zero. In this assembly, the central boss has an MMC size limit of Ø1.297 and a perpendicularity tolerance of Ø.000 at MMC. Since it's an external feature of size, its virtual condition is Ø1.297 + Ø.000 = Ø1.297. Compare to the part portion of (Using virtual condition boundaries to restrain location and orientation between mating features and Zero orientation tolerance at MMC and zero positional tolerance at MMC). The conversion to zero orientation and positional tolerances made no change to any of the virtual condition boundaries, and therefore, no change in assemblability and functionality. However, manufacturability improved significantly for both parts. Allowing the process to apportion tolerances opens up more tooling choices. In addition, a perfectly usable part having a boss measuring Ø.1.299 with perpendicularity measuring Ø.0005 will no longer be rejected.

The same rationale (lý do căn bản) may be applied where a Level 3 or 4 LMC virtual condition exits. Unless there's a functional reason for the feature's LMC size limit to differ from its LMC virtual condition, make them equal by specifying a zero orientaion or positional tolerance at LMC, as appropriate (thích hợp; thích đáng). A zero tolerance doesn't require perfection; it simply allows parity (sự bình đẳng; tình trạng bằng nhau) between two different levels of control. The feature shall be manufactured with size and orientation adequate (tương xứng, xứng đáng; thích hợp, thích đáng, thoả đáng) to clear the virtual condition boundary. In addition, the feature shall nowhere encroach beyond its opposite size limit boundary.

Resultant Condition Boundary

Resultant Condition Boundary: For the Ø.514 in this example, there is primary and secondary design requirements. Since the hole must clear for the Ø.500 pin in the mating part, the hole's orientation and location can be controled with a positional tolerance modified to MMC. This creates an MMC virtual condition boundary that guarantees air space for the mating pin. But now, the wall might get too thin between the hole and the part's edge. To address this concern, we need to determine the farthest any point around the hole from true position (the ideal center). That distance constitutes a wors-case perimeter for the hole show in the right image called the resultant (tổng hợp, kết quả) condition boundary. We can then compare the resultant condition boundary with that for the flange diameter and calculate the worst-case thin wall, then adjust the positional tolerance and/or the size limits for the hole and/or the flange.

Resultant condition is defined as a variable value obtained by adding/subtracting the total allowable geometric tolerance to the feature's actual mating size. Table in Y14.5 show resultant condition values for feature sizes between the size limits. However, the only resultant condition value that anyone cares about is the single worst-case value defined as determined by three factors: 1. The feature's type (internal or external), 2. The feature's size limits and 3. The specified geometric tolerance value.


Regardless of Feature Ssize (RFS): It's the default condition of all geometric tolerances by rule #3 of GD&T and requires no callout. Regardless of feature size simply means that whatever GD&T callout you make, is controlled independently of the size dimension of the part.

Method for RFS: (page 5-38)...


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