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True Position Tolerance: How We Interpret, Machine and Measure It真位置公差:我们如何解读、加工与测量

A Bavarian automation builder came to us with a 260 x 160 x 20 mm aluminum manifold plate that two shops had already tried and one had already failed. It carried eight Ø6.5 clearance holes that had to drop over M6 shoulder pins on the mating valve block. Every plate they received passed their incoming check: each hole centre sat inside ±0.10 mm of nominal on both X and Y, measured from the two datum edges. Roughly one plate in six still would not drop onto the pins.

We did not touch the program, the fixture or the machine. With the customer's agreement, we replaced the coordinate dimensions with a Ø0.25 position tolerance at MMC against a three-plane datum reference frame, and the plates started assembling at 100%. The parts did not get more accurate. The drawing stopped accepting the parts that never should have passed.

*(Composite example; details changed.)*

That is what a position tolerance does. The trade still calls it GD&T true position, which is what ASME Y14.5 named it before the 2009 edition, and it is the single most misunderstood line on a machine drawing. It is not a tighter version of ±0.10. It is a different shape of tolerance zone, a different question about the part, and when you add the material condition modifier it becomes a tolerance that grows as the part gets easier to assemble. We are going to walk through the whole thing the way we actually use it on the floor: what the zone is, what MMC and bonus tolerance really hand you, how virtual condition decides whether your assembly fits, why most position arguments are really datum arguments, and how we measure the number on a CMM so that two shops stop reporting two different answers.

Manifold plate being inspected on a CMM
A manifold plate on the CMM table: every hole is measured against one datum reference frame, never against the neighbouring hole.三坐标测量机上的歧管板:每个孔都相对同一基准体系测量,而不是相对相邻的孔。

What true position actually controls

True position is a geometric tolerance that defines a zone around the theoretically exact location of a feature. That exact location comes from basic dimensions: the numbers in boxes on the drawing, which carry no tolerance of their own. The tolerance lives entirely in the feature control frame.

For a hole, the zone is a cylinder of diameter *t*, centred on true position, perpendicular to the datum reference frame. The axis of the produced hole has to fall entirely inside that cylinder. Not the centre point at the top face, not the centre point at the bottom. The whole axis.

Three things follow from that, and each one matters more than it looks:

A complete position callout carries the geometric characteristic symbol (a crosshair in a circle), a tolerance value with a diameter symbol in front of it, and then whatever the function actually needs: a material condition modifier, and datum references in order of precedence. "Ø0.25 (M) A B C" reads as: the axis must sit inside a cylinder of 0.25 mm diameter, at maximum material condition, located from A then B then C. The modifier and the datums are optional in the sense that a legal callout can omit them, and both get omitted wrongly far more often than they get applied. Drop the diameter symbol and you have specified a 0.25 mm wide zone between two parallel planes rather than a cylinder, which is a genuine error we see on incoming drawings roughly once a month.

Coordinate tolerancing versus true position: the square zone nobody budgets for

Here is the comparison that converts most engineers.

A coordinate dimension of ±0.10 in X and ±0.10 in Y produces a square tolerance zone, 0.20 mm on a side. Its area is 0.20 x 0.20 = 0.040 mm². Now consider the corner of that square: dx = 0.10, dy = 0.10. The radial displacement from the true position is sqrt(0.10² + 0.10²) = 0.141 mm. Both coordinates are in tolerance, so the part passes, but the hole centre is 0.141 mm away from where the pin is waiting, which is 41% further out than the ±0.10 the designer had in mind.

The smallest round zone that contains that square has a diameter of 2 x 0.1414 = 0.283 mm, and its area is π x 0.1414² = 0.0628 mm². That is 57% more area than the square, for the same worst-case corner. This is the origin of the number everyone quotes, and it is real.

Coordinate ±0.10True position Ø0.283True position Ø0.25
Zone shapeSquare, 0.20 x 0.20Round, Ø0.283Round, Ø0.25
Zone area0.0400 mm²0.0628 mm²0.0491 mm²
Max radial displacement accepted0.141 mm (corner only)0.141 mm (any direction)0.125 mm (any direction)
Accepts a 0.141 mm displaced holeYesYesNo
Constant allowance in every directionNoYesYes

Two conclusions, and they are not in conflict. If you convert a coordinate callout to position and want to reject nothing that used to pass, use the circumscribed diameter (0.283 in this example) and you gain 57% of area for free. If instead your assembly was failing, the corner of that square is exactly where the failures were, and a round zone smaller than the circumscribed circle removes them without touching the parts that were genuinely fine. We recommended Ø0.25 on the manifold plate for the second reason, and it cost the customer nothing in scrap, for a reason explained in the next section.

Material condition: MMC, LMC and the bonus tolerance you are giving away

The modifier in the feature control frame decides whether the position tolerance is fixed or whether it grows as the feature is produced away from its worst case.

ModifierNameWhat it meansPosition tolerance behaviour
(M)Maximum material conditionFeature at its heaviest: smallest hole, largest pinGrows by the departure from MMC
(L)Least material conditionFeature at its lightest: largest hole, smallest pinGrows by the departure from LMC
noneRegardless of feature size, or material size (RFS before Y14.5-2018, RMS in the current edition)Applies at every produced sizeFixed, no bonus

For a hole of Ø6.5 ±0.10, the size range is 6.40 to 6.60 mm. One note for anyone reading ISO drawings alongside ASME ones: what this guide calls virtual condition, the ISO GPS system calls maximum material virtual size. MMC is the smallest hole, 6.40 mm, because that is where the wall has the most material left. Specify position Ø0.25 at MMC and you get this:

Produced hole sizeDeparture from MMC (6.40)BonusEffective position tolerance
6.40 mm (MMC)0.000.00Ø0.25
6.45 mm0.050.05Ø0.30
6.50 mm0.100.10Ø0.35
6.55 mm0.150.15Ø0.40
6.60 mm (LMC)0.200.20Ø0.45

Bonus tolerance is not a loophole. It is physically correct, and this is the part that finally made sense to that Bavarian customer. A bolt-through hole that comes out 0.15 mm larger than its minimum already gives the fastener 0.15 mm more clearance, so allowing it 0.15 mm more location error costs the assembly nothing. The two are the same slack. Coordinate tolerancing, by contrast, applies the same ±0.10 to a 6.40 hole and a 6.60 hole, which means it is simultaneously too loose on the tight hole and too tight on the loose one.

That is why our scrap fell after we tightened the number to Ø0.25. Take a hole produced at 6.50 with 0.12 mm of radial offset: the position deviation is 2 x 0.12 = Ø0.24, and the old ±0.10 rule rejected it on X. Its Ø0.10 of bonus lifts the allowance to Ø0.35, so it ships. Now take a hole at 6.40 with the same 0.141 mm radial offset, or Ø0.283 of position: the old rule passed it, the assembly jammed on it, and under Ø0.25 it fails, which is correct, because the smallest hole sitting at the largest offset is exactly the combination that does not fit.

When do we argue against the modifier? On features where fit rather than clearance governs the function, and therefore often on press fits. A threaded hole is not automatically RFS either, despite what most guides repeat: we choose from the assembly rather than from the feature type, and when the fastener envelope and the required assembly clearance justify it, a tapped hole can legitimately carry MMC together with a projected tolerance zone. LMC has its place too, mainly where minimum wall thickness is the governing risk, but it turns up on perhaps one drawing in fifty that crosses our desk.

CNC milling a bolt hole pattern in one set-up
Milling a bolt-hole pattern in one clamping: the datums and the holes share a single set-up, which is what makes a Ø0.03 true position realistic.一次装夹铣出螺栓孔组:基准与孔共用同一装夹,这才是 Ø0.03 真位置能够成立的前提。

Virtual condition: the one number that decides whether it assembles

Bonus tolerance is the reason you cannot read a position callout without computing the virtual condition. Virtual condition is the worst-case boundary the feature can never violate, and for an internal feature such as a hole it is:

VC = MMC of the hole - the position tolerance = 6.40 - 0.25 = Ø6.15 mm

That Ø6.15 is the diameter of the largest pin that is guaranteed to pass through the hole when the hole sits at its worst permitted position. It is the number a functional go gauge is built to, and it is the number that tells you whether the assembly works, because it combines size error and location error into one boundary. The position tolerance alone does not tell you that. The size tolerance alone does not tell you that.

On the manifold plate: shoulder pins at Ø6.0. VC of Ø6.15 guarantees 0.15 mm of diametral clearance at the worst possible combination of a small hole and an off-position hole. That is the whole design question, answered in one number, before anyone cuts metal, and on prototype runs it is the difference between one iteration and three. If the customer had needed Ø6.2 pins, the Ø0.25 at MMC callout would have been impossible at 6.40 MMC and we would have had the conversation at the quote stage, which is where it belongs.

Zero positional tolerance at MMC, and when we recommend it

There is a version of the same callout that surprises people the first time they see it: position Ø0 at MMC.

CalloutHole at 6.40 (MMC)Hole at 6.55Hole at 6.60 (LMC)Virtual condition
Ø0.25 at MMCØ0.25 allowedØ0.40 allowedØ0.45 allowedØ6.15
Ø0 at MMCØ0.00 allowedØ0.15 allowedØ0.20 allowedØ6.40

Read that carefully. The second row lifts the guaranteed clearance, raising the virtual condition from Ø6.15 to Ø6.40. It pays for that by being stricter everywhere else: at a produced size of 6.60 mm it permits Ø0.20 of position, against Ø0.45 in the first row. Nothing here is free. That trade is exactly right for bolt-through clearance holes on a fixed fastener size, because what you want to maximise is the guaranteed hole, and what you can afford to give up is location precision on the holes that already came out oversized.

We recommend it when the fastener envelope and the required assembly clearance justify moving all of the available location tolerance into bonus tolerance, and we flag it in the DFM review because it looks like a typo to anyone who has not met it before. We do not recommend it when the hole also has to seal, locate a dowel, or carry a thread.

Datums: why most position disputes are really datum disputes

If you take one operational point away from this guide, take this one. When two shops report different true position numbers for the same part, it is almost never the measurement. It is the datum reference frame.

A datum reference frame is a coordinate system built from the actual part, in a fixed order of precedence:

Change the order and you change every number on the report. Choose a datum the part does not actually locate on in service and you have measured something irrelevant. We see drawings where the primary datum is a face that is machined in a later operation than the holes it controls, which means the tolerance is being applied to a relationship that the process cannot see.

There is a second trap: datum feature shift. If a datum reference carries the MMB modifier (maximum material boundary, the datum equivalent of MMC) and the datum feature is produced away from that boundary, the datum simulator no longer fills it and the part is free to move. A datum hole of Ø10 ±0.05 has an MMB of 9.95. Produce it at 10.02 and the simulator leaves 0.07 mm of diametral clearance, so the part is free to move by up to 0.035 mm in any one radial direction, which can surface as up to Ø0.07 in a diametral position result. That is a real, legal, intended effect, and it is also why a report generated with a hard gauge can disagree with a report generated by a CMM that mathematically best-fits the datum.

Engineering review of datum scheme on a drawing
Datum review at the quoting stage: the datum order on the drawing has to match the order the part is actually located in the machine and in service.报价阶段的基准评审:图纸上的基准顺序必须与零件在机床上和在使用中的实际定位顺序一致。

Projected tolerance zones: the tapped-hole trap

A position tolerance applies to the axis of the feature over its own length. For a tapped hole in a 20 mm plate, that is 20 mm of thread. The screw that goes into it, however, sticks out 35 mm and then has to find a clearance hole in the next part up the stack. Nothing in a standard position callout controls where the screw tip ends up.

The fix is the projected tolerance zone modifier, a P in a circle placed after the tolerance value, followed by the projection height. Specify Ø0.25 projected 25 mm and the tolerance zone extends 25 mm above the surface, which is where the fastener actually lives.

The arithmetic is unkind if you skip it. A tapped hole whose axis leans by 0.5° is perfectly in tolerance over its own 20 mm of thread, but 25 mm above the surface that lean has added 25 x tan(0.5°) = 0.22 mm of lateral offset, on top of whatever the position error already was. Assemblies bind, and nobody can find the out-of-tolerance feature, because no feature is out of tolerance.

We recommend a projected tolerance zone on every drawing where a threaded hole receives a stud, a long screw or a dowel pin. It is one symbol and it prevents a class of failure that looks like a mystery from the assembly line.

Composite position: pattern location versus feature-to-feature

A single-segment position callout does two jobs at once and is often too strict at one of them. It controls where the whole pattern sits relative to the datums, and it controls how the holes sit relative to each other. Composite position splits them into two segments in one frame:

For the manifold plate: Ø0.5 to A B C in the upper segment, Ø0.2 in the lower. The eight holes have to sit within 0.5 mm of nominal as a group, and within 0.2 mm of each other. That is the functional requirement stated honestly. The single-segment version would have had to use Ø0.2 for both, and would have rejected plates that assembled perfectly.

One caution worth writing on the drawing: ASME Y14.5 and the ISO GPS system encode multi-level position control differently, and ISO 5458 is the document that actually governs positional tolerancing of hole patterns on the ISO side. They also differ on composite rules, including whether the lower segment may repeat datum references and which edition permits what. Cite the governing standard and its edition in the title block, because the symbol alone does not settle it. Our shop works to whichever standard the drawing block names, and we ask when the block is silent.

How we measure true position, and why two shops report two numbers

Here is our actual procedure on a CMM, and the four places where the number can legitimately move.

  1. Establish the datum reference frame from the real part. Measure datum A as a plane, B as a plane or line, C as a plane or point, in that order of precedence. We use the high-point (tangent) convention unless the drawing or the customer's own report specifies least squares. On a 260 mm plate with 0.04 mm of flatness, the difference between a tangent-plane datum and a least-squares datum shifts every hole by up to 0.04 mm before anyone measures a hole. That alone explains most "your report disagrees with ours" conversations.
  2. Measure the feature as an axis, not a point. At least two circles at different depths, constructed into an axis. On a shallow feature this is where uncertainty creeps in: on a 1.5 mm thick sheet-metal hole, a 2° ambiguity in axis direction is 1.5 x tan(2°) = 0.052 mm of reported position that nobody asked for and no gauge would find.
  3. Apply the material condition. With an MMC modifier, the reported tolerance is the specified value plus the measured departure from MMC of that specific hole. Each hole gets its own bonus. A report that shows one flat tolerance for all eight holes has not applied the modifier.
  4. Report the actual deviation as a diameter. True position deviation is twice the radial displacement: 2 x sqrt(dx² + dy²). A hole 0.06 off in X and 0.05 off in Y is 0.156 mm of true position, not 0.078. We have seen incoming inspectors compare a radial number against a diametral tolerance and reject good parts, and the reverse.

For the full comparison of the equipment behind those numbers, and what each method is honestly good for, see our CNC inspection methods guide. Whether that equipment can repeat the reading at all is its own question, answered by our gage repeatability and reproducibility study. The tolerance vocabulary itself, including how position interacts with size limits, is covered in the CNC machining tolerance guide.

Verifying assembled parts against the position callout
Final assembly check: a true position callout is only as good as the assembly it is protecting, and that is what we verify against.最终装配核对:真位置标注的价值只体现在它所保护的装配上,而我们正是按装配来验证的。

What true position we can actually hold, by process

The table below is what we commit to in a quotation, not what a machine brochure claims. Everything assumes datums and features produced in the same clamping unless noted.

ProcessRealistic true position (diameter)What sets the limit
CNC milling, bored or reamed, datums in the same set-upØ0.02 to Ø0.05 mmMachine volumetric accuracy, tool deflection
CNC milling, drilled and reamed across two set-upsØ0.05 to Ø0.10 mmRe-fixturing error, not the machine
CNC milling, drilled only, no reamØ0.10 to Ø0.20 mmDrill walk on entry
CNC turning, cross features in one chuckingØ0.03 to Ø0.06 mmSpindle repeatability, live-tool alignment
5-axis, features on different faces, one clampingØ0.02 to Ø0.05 mmRotary axis accuracy; our 5-axis envelope reaches 750 x 650 x 500 mm
Sheet metal, pierced in a progressive dieØ0.08 to Ø0.15 mmStrip pitch accuracy, pilot wear
Sheet metal, laser-cut hole, see the sheet metal tolerance guideØ0.10 to Ø0.20 mmKerf and thermal drift on the contour
Casting, as-castØ0.5 to Ø1.5 mmPattern and mould variation; use position on as-cast holes and bosses only where the assembly needs it, and profile where the requirement sits on an as-cast surface

Two rules of thumb follow. Anything under Ø0.05 needs the datums and the holes in one clamping, and above roughly Ø0.15 mm you should ask whether position is the right control at all, or whether a clearance slot would serve the assembly better and cost less. Holding the number once and holding it across a run are different claims, and our control plan and capability study guide covers the part a single report cannot show. Our general capability sits at ±0.01 mm on critical features across 200+ CNC machines, and the five-axis guide explains why one clamping buys you most of this. Material choice moves these bands too: the materials guide shows why 6061-T6 and 17-4PH do not land in the same row.

What buyers actually ask us

Can you just hold ±0.05 on everything? We can, and it will cost you roughly 30 to 60% more per part, because blanket tight tolerances force extra operations and full inspection on features that do not need either. Surface callouts are the same story, and the surface roughness guide covers where Ra earns its cost. Tell us which features mate and which ones only have to look right. We will put the tight number where it pays. The supplier selection guide lists the questions that separate shops that can hold the number from shops that merely say they can.

The last shop said our position tolerance was impossible. Usually the number is fine and the datum scheme is the problem, or the datums are machined after the holes. We rewrite the frame, keep your number, and it becomes machinable. The same review catches datum schemes that fight the milling service or the turning service you actually need. Roughly three times in five, that is the whole fix.

Do you need the 3D model or is the 2D drawing enough? For a position callout, the drawing is the governing document and the model is a convenience. What we do need is the datum scheme marked on the drawing, because the model rarely carries it. Our DFM analysis review is free and returns within 24 hours, and the datum conversation is the first thing in it.

What if our drawing has no datums at all? Then a position callout cannot be evaluated, and two suppliers will each invent one. We will propose a frame based on how the part locates in your assembly, send it back for approval, and quote against it. That is a five-minute conversation compared with a five-week argument later.

On programmes running to IATF 16949 or ISO 13485, the datum scheme and the measurement convention also have to be documented in the first article inspection package, because that is where the two reports get reconciled, and the serial-level record is described in the traceability marking guide. The metrology behind it is summarised by NIST and the National Physical Laboratory in plain language, and Zeiss documents the CMM side.

Automotive manifold plate with machined hole pattern
Automotive and automation plates are where a wrong datum scheme costs the most: high hole counts, fixed fasteners, no room for a corner-case failure.汽车与自动化板类零件是基准方案出错代价最高的地方:孔数多、紧固件固定、容不下角落里的失效。

Frequently asked questions

What is the difference between true position and coordinate tolerancing?

Coordinate tolerancing gives a square zone, true position gives a round one. A square zone of ±0.10 accepts a hole sitting 0.141 mm away from true position at its corner, which is 41% further out than the designer intended, and that is usually where assembly failures live. A round zone gives the same allowance in every direction, and with a material condition modifier it grows as the hole gets larger.

How do you calculate true position from a CMM report?

Take the deviations in X and Y from basic dimensions, compute the radial displacement as sqrt(dx² + dy²), then double it. A hole 0.06 off in X and 0.05 off in Y is 0.156 mm of true position, not 0.078. Compare that doubled number against the tolerance in the feature control frame, plus any bonus from the material condition modifier.

What does MMC mean on a position callout, and should I use it?

MMC is maximum material condition: the smallest hole or the largest pin. With it, the position tolerance grows by however far the produced feature departs from MMC, which is physically correct for bolt-through clearance holes because a bigger hole gives the fastener more room. Use it on clearance features. Avoid it on press-fit and threaded features, where RFS is the honest choice.

Can you hold a 0.05 mm true position on a machined part?

Yes, when the datums and the holes are produced in one clamping and the holes are bored or reamed. Ø0.02 to Ø0.05 mm is our routine band for that case. Across two set-ups the realistic band opens to Ø0.05 to Ø0.10 mm, and drilled-only holes sit at Ø0.10 to Ø0.20 mm because drill walk dominates.

Why does my supplier's CMM report show a different position than my gauge?

In most cases it is the datum convention, not the measurement. A tangent-plane datum and a least-squares datum on a part with 0.04 mm of flatness can differ by that much before a single hole is measured. The second most common cause is comparing a radial deviation against a diametral tolerance. Align the datum convention and the reporting convention first, then compare numbers.

Do I need GD&T on every drawing?

No, and using it everywhere is a cost you pay twice. Apply position where a feature has to mate with something at a known location: hole patterns, dowels, threaded holes. Leave plain size tolerances on features that only have to fit or look right. The return on GD&T is highest exactly where two parts have to come together without hand fitting.

References

  1. ASME Y14.5, Dimensioning and Tolerancing. ASME
  2. ISO 1101, Geometrical product specifications (GPS): Geometrical tolerancing, tolerances of orientation, location and run-out.
  3. ISO 5458, Geometrical product specifications (GPS): Positional tolerancing, and ISO 2692 for the maximum material virtual size convention.
  4. Metrology and measurement uncertainty. NIST
  5. Dimensional metrology guidance. National Physical Laboratory
  6. Coordinate measuring machine technology. Zeiss Metrology

Conclusion

Twenty-three years of machining has convinced us that true position arguments are rarely about accuracy. They are about a drawing that describes a part in one language and an assembly that needs it in another. The round zone, the material condition modifier, the datum order and the virtual condition are the four places where those two languages get reconciled, and all four are far cheaper to settle during the quoting stage than they are after metal has been cut.

Across 23+ years of machining, we have learned to settle the datum scheme and the reporting convention before anyone writes a tool path, because our 200+ CNC machines hold ±0.01 mm on critical features only when the drawing and the inspection method agree about where the measurement starts. Send us the drawing, the mating part if you have one, and the volume. We will come back within 24 hours with a datum proposal, a machinability verdict, a virtual condition calculation and a price, with DFM free, working to IATF 16949, ISO 9001 and ISO 13485. If the honest answer is that your callout is looser than it needs to be, we will say that too. Get in touch with our team.

一位巴伐利亚的自动化设备厂找到我们,带来一块 260 x 160 x 20 mm 的铝制歧管板。这块板已经有两家工厂做过,其中一家做砸了。板上有八个 Ø6.5 的过孔,必须能套进配对面阀块上的 M6 带肩销。他们收到的每块板都通过了来料检验:以两条基准边为起点测量,每个孔的中心在 X 和 Y 两个方向上都落在名义值 ±0.10 mm 以内。但仍有大约六分之一的板套不进销子。

我们没有改程序、没有改夹具、也没有换机床。在客户同意的前提下,我们把坐标尺寸换成了 Ø0.25 的位置度,标注 MMC,并配上一个三平面基准体系。之后这批板的装配通过率达到 100%。零件并没有变得更精密,是图纸不再放行那些本来就不该合格的零件。

*(合成案例,细节已改动。)*

这就是位置度的作用。行业里至今仍叫它 GD&T 真位置,这是 ASME Y14.5 在 2009 版之前的叫法,也是机械图纸上被误解最深的一行标注。它不是被收紧过的 ±0.10。它是一种形状不同的公差带,问的是关于零件的一个不同的问题;再配上材料状态修饰符之后,它还会随着零件变得更容易装配而自动变大。下面我们按车间里真实的使用顺序把它讲完:公差带是什么形状,MMC 和补偿公差到底给了你什么,虚拟条件如何决定总成能不能装上,为什么大多数位置度的争执其实是基准的争执,以及我们在三坐标上怎样测这个数,好让两家工厂不再报出两个答案。

Manifold plate being inspected on a CMM
A manifold plate on the CMM table: every hole is measured against one datum reference frame, never against the neighbouring hole.三坐标测量机上的歧管板:每个孔都相对同一基准体系测量,而不是相对相邻的孔。

真位置到底控制的是什么

真位置是一项几何公差,它围绕某个要素的理论正确位置定义一个公差带。这个理论正确位置来自基本尺寸,也就是图纸上打方框的那些数字,它们自身不带公差。公差完全写在形位公差框里。

对于一个孔,公差带是一个直径为 *t* 的圆柱,以理论正确位置为中心,垂直于基准体系。加工出来的孔的轴线必须整体落在这个圆柱之内。不是上表面那个中心点在里面,也不是下表面那个中心点在里面,而是整条轴线。

由此可以推出三件事,每一件都比看上去更要紧:

一个完整的位置标注包含形位特征符号(圆圈里的十字线)、前面带直径符号的公差值,以及根据功能真正需要的其余内容:材料状态修饰符,以及按优先顺序排列的基准参照。"Ø0.25 (M) A B C" 读作:轴线必须落在一个直径 0.25 mm 的圆柱之内,处于最大实体状态,基准顺序为先 A 再 B 再 C。修饰符和基准在「不写也合法」这个意义上是可选的,而这两样被漏写的次数远远多于被正确使用的次数。漏掉直径符号,你规定的就是两平行平面之间 0.25 mm 宽的区域而不是圆柱,这是我们在来料图纸上大约每月都会遇到一次的真实错误。

坐标公差对比真位置:那块没人算过的方形区域

下面这个对比说服过大多数工程师。

X 方向 ±0.10、Y 方向 ±0.10 的坐标尺寸,产生的是一个方形公差带,边长 0.20 mm,面积是 0.20 x 0.20 = 0.040 mm²。现在看这个方形的角点:dx = 0.10,dy = 0.10。相对理论正确位置的径向偏移量是 sqrt(0.10² + 0.10²) = 0.141 mm。两个坐标都在公差之内,零件判定合格,但孔中心距离销子在等的位置有 0.141 mm,比设计师心里想的 ±0.10 远出了 41%。

能包住这个方形的最小圆形公差带,直径是 2 x 0.1414 = 0.283 mm,面积是 π x 0.1414² = 0.0628 mm²。在最坏情况的角点上,这比方形多出 57% 的面积。这就是大家引用的那个 57% 的来处,它是真实的。

坐标公差 ±0.10真位置 Ø0.283真位置 Ø0.25
公差带形状方形,0.20 x 0.20圆形,Ø0.283圆形,Ø0.25
公差带面积0.0400 mm²0.0628 mm²0.0491 mm²
可接受的最大径向偏移0.141 mm(仅角点)0.141 mm(任意方向)0.125 mm(任意方向)
是否接受偏移 0.141 mm 的孔是是否
各方向余量是否恒定否是是

由此得到两个结论,两者并不矛盾。如果你要把坐标标注换算成位置度,并且不想判废任何一个原本合格的零件,就用外接圆直径(本例中为 0.283),这样你白白多拿到 57% 的面积。反过来,如果你的总成正装不上,那么恰恰是这个方形的角点位置在出废品,用一个比外接圆更小的圆形公差带就能把废品剔掉,而不会误伤那些本来确实没问题的零件。我们在歧管板上推荐 Ø0.25 属于第二种情况,而且客户在报废上没有多花一分钱,原因在下一节。

材料状态:MMC、LMC,以及你正在白白送掉的补偿公差

形位公差框里的修饰符决定的是:位置公差是固定的,还是随着要素偏离其最坏情况而变大。

修饰符名称含义位置公差行为
(M)最大实体状态要素最重时:最小的孔、最大的销按偏离 MMC 的量增大
(L)最小实体状态要素最轻时:最大的孔、最小的销按偏离 LMC 的量增大
无与要素尺寸无关/与材料尺寸无关(Y14.5-2018 之前称 RFS,现行版本称 RMS)适用于每一个加工尺寸固定,无补偿

对于一个 Ø6.5 ±0.10 的孔,尺寸范围是 6.40 至 6.60 mm。给同时要读 ISO 图纸和 ASME 图纸的同行一句提醒:本指南所说的虚拟条件,在 ISO GPS 体系里叫最大实体虚拟尺寸。MMC 是孔最小的状态,即 6.40 mm,因为此时壁上剩下的材料最多。如果把位置度规定为 Ø0.25 并标 MMC,你会得到:

加工后孔径偏离 MMC(6.40)补偿公差实际位置公差
6.40 mm(MMC)0.000.00Ø0.25
6.45 mm0.050.05Ø0.30
6.50 mm0.100.10Ø0.35
6.55 mm0.150.15Ø0.40
6.60 mm(LMC)0.200.20Ø0.45

补偿公差不是钻空子,它在物理上是正确的,这也是那位巴伐利亚客户最终听懂的部分。一个比最小尺寸大了 0.15 mm 的螺栓过孔,本身就已经给紧固件多让出了 0.15 mm 的间隙,因此允许它再多 0.15 mm 的位置误差,对总成没有任何代价。两者是同一份余量。相比之下,坐标公差对 6.40 的孔和 6.60 的孔施加同样的 ±0.10,这意味着它同时对小孔太松、对大孔太紧。

这也解释了为什么我们把数值收紧到 Ø0.25 之后,废品反而下降了。以一个加工成 6.50、径向偏移 0.12 mm 的孔为例:其位置偏差为 2 x 0.12 = Ø0.24,旧规则会因为 X 方向超差而判废;它的 Ø0.10 补偿量把容许值抬到 Ø0.35,于是它出货。再看一个加工成 6.40、径向偏移同为 0.141 mm 的孔,即 Ø0.283 的位置度:旧规则放行了它,总成套不进去,而在 Ø0.25 之下它会判废,这是正确的,因为最小的孔叠上最大的偏移,恰恰就是装不进去的那一种组合。

那我们什么时候会反对使用修饰符?在功能由配合而非间隙决定的要素上,因此往往是过盈配合。另外,螺纹孔也并不像多数指南反复强调的那样「自动就该用 RFS」:我们是从总成出发做选择,而不是从要素类型出发;当紧固件包络面和所需的装配间隙支持时,一个螺纹孔完全可以合法地带 MMC,并同时配投影公差带。LMC 也有它的位置,主要用于最小壁厚才是主要风险的时候,但在交到我们手上的图纸里,大概五十张里才会出现一张。

CNC milling a bolt hole pattern in one set-up
Milling a bolt-hole pattern in one clamping: the datums and the holes share a single set-up, which is what makes a Ø0.03 true position realistic.一次装夹铣出螺栓孔组:基准与孔共用同一装夹,这才是 Ø0.03 真位置能够成立的前提。

虚拟条件:唯一一个决定总成能否装上的数字

正是因为存在补偿公差,你才无法在不计算虚拟条件的情况下读懂一个位置标注。虚拟条件是这个要素永远不得逾越的最坏情况边界,对一个孔这类内尺寸要素而言:

VC = 孔的 MMC - 位置公差 = 6.40 - 0.25 = Ø6.15 mm

这个 Ø6.15 指的是:当孔位于其允许的最差位置时,仍能保证通过的销子的最大直径。功能性通规就是按这个数值制造的,它也是告诉你总成能不能工作的那个数字,因为它把尺寸误差和位置误差合并成了一个边界。只看位置公差回答不了这个问题,只看尺寸公差也回答不了。

回到那块歧管板:带肩销为 Ø6.0。Ø6.15 的虚拟条件保证了在最坏的「小孔+偏移孔」组合下仍有 0.15 mm 的直径间隙。整个设计问题在动刀之前就被一个数字回答了;放在 打样件 上,这就是打一轮和打三轮的区别。如果客户需要的是 Ø6.2 的销子,那么在 MMC 为 6.40 的前提下,Ø0.25 标 MMC 的方案根本不可能成立,而这番对话我们会在报价阶段就谈掉——它本来就该在那个阶段谈。

MMC 下的零位置公差,以及我们何时推荐它

同一标注还有一种版本,第一次看到的人都会愣一下:位置度 Ø0,标 MMC。

标注孔径 6.40(MMC)孔径 6.55孔径 6.60(LMC)虚拟条件
Ø0.25 标 MMC允许 Ø0.25允许 Ø0.40允许 Ø0.45Ø6.15
Ø0 标 MMC允许 Ø0.00允许 Ø0.15允许 Ø0.20Ø6.40

请仔细读一下。第二行抬高了保证间隙,把虚拟条件从 Ø6.15 提升到 Ø6.40。代价是它在其他所有位置都更严:当加工尺寸为 6.60 mm 时,它只允许 Ø0.20 的位置度,而第一行允许 Ø0.45。这里没有白得的东西。对于配合固定规格紧固件的螺栓过孔,这笔交换恰好是对的,因为你想最大化的是那个「保证能通过的孔」,而你可以放弃的,是那些本来就偏大、位置精度并不重要的孔。

我们会在紧固件包络面和所需装配间隙支持「把全部可用位置公差都转成补偿公差」时推荐它,并且会在 DFM 评审里专门标出来,因为在没见过的人眼里它就像一个笔误。当这个孔还要兼做密封、定位销或攻螺纹时,我们不推荐它。

基准:为什么大多数位置度争执其实是基准争执

如果你从本指南里只带走一条实操经验,请带走这一条。当两家工厂对同一个零件报出不同的真位置数值时,问题几乎从来不在测量本身,而在基准体系。

基准体系是用真实零件按固定优先顺序建立起来的坐标系:

顺序一变,报告上的每一个数字都变。选了一个零件在使用中并不靠它定位的基准,你测出来的就是一件无关的事。我们见过这样的图纸:主基准是一个比它所控制的孔更晚加工出来的面,这意味着公差被施加在一个工艺上根本看不到的关系上。

还有第二个陷阱:基准要素偏移。如果基准参照带 MMB 修饰符(最大实体边界,即基准侧对应的 MMC),而基准要素加工后偏离了该边界,那么基准模拟件就不再填满它,零件便可以自由移动。一个 Ø10 ±0.05 的基准孔,其 MMB 为 9.95。若加工成 10.02,模拟件之间留下 0.07 mm 的直径间隙,零件因此可以在任意一个径向上移动最多 0.035 mm,而这在一个直径制的位置度结果里最高会表现为 Ø0.07。这是一个真实、合法、符合设计意图的效应,也是为什么用量规做出的报告会与用三坐标数学最佳拟合基准做出的报告不一致。

Engineering review of datum scheme on a drawing
Datum review at the quoting stage: the datum order on the drawing has to match the order the part is actually located in the machine and in service.报价阶段的基准评审:图纸上的基准顺序必须与零件在机床上和在使用中的实际定位顺序一致。

投影公差带:螺纹孔的陷阱

位置公差只对要素自身长度范围内的那条轴线生效。对一块 20 mm 厚板上的螺纹孔来说,那就是 20 mm 的螺纹。可是拧进去的那颗螺钉伸出 35 mm,然后还要在上一层的零件里找到一个过孔。标准的位置标注里没有任何东西控制螺钉尖端最终落在哪里。

解决办法是投影公差带修饰符:写在公差值之后的一个带圆圈的 P,后面跟着投影高度。规定 Ø0.25、投影 25 mm,公差带就向上延伸到表面之上 25 mm,而这正是紧固件真正所在的位置。

如果省掉它,算术会很不客气。一个轴线倾斜 0.5° 的螺纹孔,在它自己那 20 mm 螺纹长度内完全合格,但在表面之上 25 mm 处,这个倾斜已经额外带来 25 x tan(0.5°) = 0.22 mm 的横向偏移,叠加在本来就存在的位置误差之上。总成卡死,而所有人都找不到超差的要素,因为没有哪个要素超差。

我们建议:凡是有螺纹孔要装螺柱、长螺钉或定位销的图纸,都加投影公差带。只是一个符号,却能挡掉一整类从总装线上看像玄学一样的失效。

复合位置度:孔组定位与要素之间

单段位置标注同时干两件事,而其中一件事往往过严。它既控制整个孔组相对基准的位置,又控制各个孔之间的相对位置。复合位置度用一个框把它们拆成两段:

还是那块歧管板:上段 Ø0.5 相对 A B C,下段 Ø0.2。八个孔作为一组要落在名义值 0.5 mm 之内,彼此之间要落在 0.2 mm 之内。这才是诚实地把功能需求说了出来。单段的写法只能两个数都用 Ø0.2,那样会把本来装配得很好的板一起判废。

有一点值得写在图纸上:ASME Y14.5 与 ISO GPS 体系对多级位置控制的规定是不同的,而 ISO 体系里真正管辖孔组位置度的是 ISO 5458。两者在复合规则上也有分歧,包括下段是否可以重复标注基准参照、以及具体哪一版允许什么。请在标题栏里写明所依据的标准及其版本,因为单靠符号裁决不了这类分歧。我们车间按图纸标题栏所写的标准执行,标题栏沉默时我们会主动问一句。

我们如何测量真位置,以及为什么两家工厂会报出两个数

下面是我们在三坐标上的实际做法,以及这个数值可以合法地发生变化的四个地方。

  1. 用真实零件建立基准体系。 依次测量基准 A 为平面、B 为平面或直线、C 为平面或点,遵循规定的优先顺序。除图纸或客户自己的报告指定用最小二乘法外,我们默认采用高点(相切)约定。在一块有 0.04 mm 平面度的 260 mm 板上,相切平面基准与最小二乘基准之间的差异,会在任何人开始测孔之前就把每个孔挪动最多 0.04 mm。仅此一项就解释了大多数「你们的报告和我们的对不上」的对话。
  2. 把要素当轴线测,而不是当一个点。 至少在不同深度测两个圆,再构造成一条轴线。在浅要素上,正是不确定度溜进来的地方:在一个 1.5 mm 厚的钣金孔上,轴线方向 2° 的歧义就是 1.5 x tan(2°) = 0.052 mm 的报出位置误差,没人要这个数,任何量规也找不到它。
  3. 施加材料状态。 带 MMC 修饰符时,报出的容许值是规定值加上该孔实测偏离 MMC 的量。每个孔有自己的补偿量。一份报告如果给八个孔都显示同一个平坦的公差,那它就没有施加修饰符。
  4. 以直径形式报出实际偏差。 真位置偏差是径向位移的两倍:2 x sqrt(dx² + dy²)。一个 X 偏 0.06、Y 偏 0.05 的孔,其真位置是 0.156 mm,而不是 0.078。我们见过来料检验员拿径向数值去比对直径制公差,把好件判废,反过来也一样。

关于这些数字背后的设备,以及各种方法各自真正擅长的领域,请看我们的 请看我们的CNC 检验方法指南。而这套设备到底能不能复现同一个读数,本身又是一道题,答案在我们的量具重复性与再现性研究指南里。至于公差术语本身,包括位置如何与尺寸极限相互作用,则在 CNC 加工公差指南 中有说明。

Verifying assembled parts against the position callout
Final assembly check: a true position callout is only as good as the assembly it is protecting, and that is what we verify against.最终装配核对:真位置标注的价值只体现在它所保护的装配上,而我们正是按装配来验证的。

我们能真正稳定做到的真位置,按工艺分

下面这张表是我们在报价中真正承诺的数字,不是机床样本上的宣传值。除另有说明外,全部假定基准与要素在同一次装夹中加工。

工艺现实可达的真位置(直径)限制来自哪里
CNC 铣削,镗或铰,基准同一次装夹Ø0.02 至 Ø0.05 mm机床空间精度、刀具挠曲
CNC 铣削,两次装夹钻孔后铰孔Ø0.05 至 Ø0.10 mm重新装夹误差,而不是机床
CNC 铣削,只钻孔不铰Ø0.10 至 Ø0.20 mm入钻时的钻尖漂移
CNC 车削,一次装夹加工横向特征Ø0.03 至 Ø0.06 mm主轴重复性、动力刀座对中
五轴,不同面上的特征,一次装夹Ø0.02 至 Ø0.05 mm回转轴精度;我们的五轴行程达 750 x 650 x 500 mm
钣金,在 级进模 中冲孔Ø0.08 至 Ø0.15 mm料带步距精度、导正销磨损
钣金,激光切割孔,参见 钣金公差指南Ø0.10 至 Ø0.20 mm切缝宽度与轮廓上的热漂移
铸造,铸态Ø0.5 至 Ø1.5 mm模样与铸型波动;只有总成需要时才在铸态孔和凸台上用位置度,要求落在铸态表面上时应改用面轮廓度

由此得到两条经验法则。凡是低于 Ø0.05 的要求,都需要基准与孔在同一次装夹中加工;而一旦超过大约 Ø0.15 mm,你就该反问:位置度到底是不是正确的控制手段,还是说开一个让位长圆孔反而对总成更好、成本更低。把这个数值做到一次容易,做到整批稳定是另一回事,我们的控制计划与过程能力研究指南讲的就是单份报告看不出来的那一半。我们在 200 多台 CNC 机床上的通用能力是关键特征 ±0.01 mm,而 五轴指南 解释了为什么一次装夹能买来这里的大半成果。材料选择也会挪动这些区间:材料指南 说明了为什么 6061-T6 和 17-4PH 不会落在同一行里。

买家真正会问我们的问题

你们能不能全图统一按 ±0.05 做? 能,但单件成本大约要多出 30% 到 60%,因为全面的紧公差会逼出额外工序,并让本来两者都不需要的特征走上全检。表面粗糙度标注也是同样的道理,表面粗糙度指南 讲了 Ra 在哪里才配得上它的成本。请告诉我们哪些特征要配合、哪些只要看上去没问题就够了。我们会把紧的数值花在刀刃上。想判断一家工厂究竟守得住这个数,还是只会嘴上说守得住,可以看看 供应商选择指南 里列的那些问题。

上一家工厂说我们的位置公差做不到。 通常情况下数字本身没问题,问题出在基准方案上,或者基准是在孔之后才加工的。我们把坐标系重写一遍,保留你原来的数字,它就变得可加工了。同一轮评审还能揪出与你真正需要的 铣削服务 或 车削服务 打架的基准方案。大约五次里有三次,这就是全部的修法。

你们需要 3D 模型,还是 2D 图纸就够了? 对位置标注而言,图纸是受控文件,模型只是方便工具。我们真正需要的是图纸上标明的基准方案,因为模型里通常没有它。我们的 DFM 分析 评审免费、24 小时内回复,而基准这件事是其中的第一项内容。

如果我们的图纸一个基准都没有怎么办? 那么位置标注就无法评定,两家供应商会各自发明一套。我们会按零件在你总成中的定位方式提出一个坐标系,发回给你确认,再据此报价。这是一次五分钟的沟通,换来的是不用在五周后再吵一场。

在按 IATF 16949 或 ISO 13485 运行的项目上,基准方案和测量约定还必须写进 首件检验 文件包,因为两份报告正是在那里完成对齐的;序列化记录的做法则在 追溯打标指南 里有说明。背后的计量学部分,NIST 与 英国国家物理实验室 都用通俗语言做了概述,三坐标一侧则由 蔡司 做了文档化。

Automotive manifold plate with machined hole pattern
Automotive and automation plates are where a wrong datum scheme costs the most: high hole counts, fixed fasteners, no room for a corner-case failure.汽车与自动化板类零件是基准方案出错代价最高的地方:孔数多、紧固件固定、容不下角落里的失效。

常见问题

真位置和坐标公差的区别是什么?

坐标公差给出的是方形公差带,真位置给出的是圆形公差带。±0.10 的方形公差带会接受一个在角点处距离理论正确位置 0.141 mm 的孔,比设计师本意远出 41%,而装配失效通常就藏在那里。圆形公差带在各个方向上给出相同的余量,并且配上材料状态修饰符后,会随着孔径变大而变大。

怎么从三坐标报告算出真位置?

取 X 和 Y 相对基本尺寸的偏差,按 sqrt(dx² + dy²) 算出径向位移,再乘两倍。X 偏 0.06、Y 偏 0.05 的孔,其真位置是 0.156 mm,而不是 0.078。把这个加倍后的数字去和形位公差框里的公差值比对,再加上材料状态修饰符带来的补偿量。

位置标注上的 MMC 是什么意思,我该用吗?

MMC 是最大实体状态:孔最小或销最大的时候。带 MMC 时,位置公差会按加工要素偏离 MMC 的量增大,这对螺栓过孔在物理上是正确的,因为孔越大给紧固件的余量越多。请把它用在间隙类要素上,在过盈配合与螺纹特征上避免使用,那里 RFS 才是诚实的写法。

你们能在机加工零件上做到 0.05 mm 的真位置吗?

能,前提是基准与孔在同一次装夹中加工、且孔经过镗或铰。这种情况下我们的常规区间是 Ø0.02 至 Ø0.05 mm。分两次装夹时,现实区间放大到 Ø0.05 至 Ø0.10 mm;只钻孔不铰的孔落在 Ø0.10 至 Ø0.20 mm,因为此时主导因素是钻尖漂移。

为什么供应商的三坐标报告和我的量规结果不一样?

多数情况下这是基准约定的问题,而不是测量的问题。在一个有 0.04 mm 平面度的零件上,相切平面基准与最小二乘基准之间的差异,可以在还没测任何一个孔之前就达到 0.04 mm。第二常见的原因,是拿径向偏差去比对直径制公差。先把基准约定和报数约定统一起来,再去比数字。

每张图纸上都必须用 GD&T 吗?

不必,而且到处都用意味着你要付两次钱。请把位置度用在那些需要与某个已知位置的零件配合的要素上:孔组、定位销孔、螺纹孔。只需要能装上或者看着顺眼的特征,留普通尺寸公差就够了。GD&T 的回报最高的地方,恰恰是两个零件必须无需手工修配就能装在一起的地方。

参考

  1. ASME Y14.5,尺寸与公差标注。ASME
  2. ISO 1101,产品几何技术规范(GPS):几何公差,方向、位置与跳动公差。
  3. ISO 5458,产品几何技术规范(GPS):位置公差标注,以及 ISO 2692 关于最大实体虚拟尺寸的约定。
  4. 计量学与测量不确定度。NIST
  5. 几何量计量指南。英国国家物理实验室
  6. 三坐标测量机技术。蔡司计量

结语

二十三年的加工经历让我们确信:真位置的争执很少真的是关于精度的。它们源于一份用一种语言描述零件的图纸,和一个用另一种语言要求零件的总成。圆形公差带、材料状态修饰符、基准顺序和虚拟条件,就是这两种语言得以对齐的四个位置,而这四件事在报价阶段谈定,都比动刀之后再去谈要便宜得多。

在 23 年以上的加工经历中,我们学会了在有人编写刀路之前就把基准方案和报数约定谈定,因为我们那 200 多台 CNC 机床只有在图纸和检验方法对「从哪里开始测量」达成一致时,才能在关键特征上守住 ±0.01 mm。把图纸发给我们,有配合件就一并发来,再告诉我们年用量。我们会在 24 小时内给出基准提案、可加工性结论、虚拟条件计算和报价,DFM 免费,并按 IATF 16949、ISO 9001 和 ISO 13485 执行。如果诚实的答案是你的标注其实可以更松,我们也会照说。联系我们的团队。

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