• English
  • 中文
  • Français
  • Deutsch
  • Español
  • Português
  • 日本語
  • 한국어
  • Nederlands
  • Türkçe
  • Bahasa Indonesia
  • ไทย

Tolerance Stack-Up Analysis: Worst Case, RSS, and Why Neither Number Saved the Part公差叠加分析:最坏情况法、RSS,以及为什么两种算法都救不了那个零件

A customer sent us a five-part audio chassis for quoting, and the drawing looked fine. Front panel 12 mm thick. PCB 1.6 mm. Four standoffs at 18 mm. A rear panel with a 3 mm pocket. An extruded aluminum body cut to 186 mm. Every dimension carried a tolerance somebody could defend, and the gap between the PCB edge and the rear pocket was called out at 0.20 mm nominal. The assembly did not close. Not sometimes, not at the tail of the distribution. It failed twice in the first fifty units, and always in the same place, which is the signature of arithmetic rather than of a machine. (Composite example; details changed.)

The arithmetic is not hard. Add the plus and minus on those five links and you get 0.40 mm of possible movement against a 0.20 mm gap. Before a single chip was cut, that assembly had a negative clearance of 0.20 mm at worst case. The customer's engineer had done a stack-up, but he had done it on his own three machined parts and left the PCB and the extrusion out, because those came from other suppliers and, in his words, were somebody else's tolerance.

They are nobody else's tolerance. They are in the same chain, so they are in the same sum. That is the whole discipline, and it is where most of the arguments we have about drawings actually start.

We machine in Dongguan. The floor runs more than 200 CNC machines, the shop has been at this for more than 23 years, IATF 16949 and ISO 9001 and ISO 13485 are in the quality system, and quotations come back inside 24 hours with a free DFM review. We run stack-ups on customer assemblies every week, because a stack-up is the only document that tells you whether "±0.01 mm" on your print buys anything. Below is how we do it, with the numbers from that chassis, including the part of the story where the correct engineering answer was not a tighter tolerance at all.

Machined aluminum audio front panel with tight tolerance features
A machined front panel like this one is the link most engineers tighten first. In the chassis above it was the smallest contributor in the chain.像这样的机加工前面板,往往是工程师第一个想收紧的环节。在上面的机箱案例里,它却是整条链上贡献最小的一项。

What a Stack-Up Answers, and What It Does Not

A tolerance stack-up is a calculation of how the tolerances on individual dimensions combine at one feature that matters. That feature has a name in the analysis: the gap, the clearance, the flush condition, the critical dimension. You pick it before you do any arithmetic, and if you cannot name it in one sentence, you are not ready to calculate anything.

There are two questions a stack-up can answer and one it cannot. The first is whether the parts assemble at all: is the minimum gap positive, is the maximum interference acceptable, does the connector line up with the cutout. The second is whether the assembly functions: does the seal still compress, does the optical axis stay within its budget, does the bearing preload land in the range the bearing maker asked for. What a stack-up cannot tell you is whether the design is good. A part can assemble perfectly and still be a bad design.

Most of the stack-ups we see from customers are one-dimensional and hand-written on a printout, and most of them are correct as far as they go. The failures are almost never in the addition. They are in the link list: a missing supplier part, a position tolerance entered as a linear one, an angular callout treated as if it had no lever arm, or a thermal term that never made it onto the page.

It is also worth separating a stack-up from a tolerance specification, because the two get confused. A specification says what one feature may measure, and our CNC machining tolerance guide is about that question. A stack-up says what happens when several specified features meet, which is a different and usually more expensive question.

The Five Links That Broke the Chassis

Here is the chain as it should have been written. The critical dimension is the clearance between the PCB edge and the inside face of the rear pocket. Everything between the front panel's outer face and that pocket is a link.

LinkNominalToleranceSupplier of that tolerance
Front panel thickness12.00 mm±0.02 mmUs, machined
PCB thickness1.60 mm±0.15 mmBoard house, IPC class 2
Standoff height, four off18.00 mm±0.05 mmUs, turned
Rear panel pocket depth3.00 mm±0.03 mmUs, machined
Extrusion length, cut to size186.00 mm±0.15 mmExtruder, cut off saw
Gap, the critical dimension0.20 mmresultnobody, it is the output

Sum the absolute tolerances and you get 0.40 mm. That is the worst-case total variation, and it is symmetric around nominal, so the gap can run from minus 0.20 mm to plus 0.60 mm. Negative clearance means the parts interfere. There is no assembly in which the PCB is 0.20 mm inside the rear pocket and everything else is nominal.

Look at who owns what. Of that 0.40 mm, the three machined parts contribute 0.10 mm between them. The PCB contributes 0.15 and the extrusion 0.15. We could hold our three parts to ±0.005 mm, at roughly three times the machining cost and with a grinder in the route, and the gap would still be negative at worst case. This is the single most common misallocation in precision hardware: the buyer negotiates hardest with the supplier who is already the smallest contributor.

The three machined bands sit near ISO 286 grades, and the same arithmetic that makes IT7 21 micrometers at Ø30 makes it 46 micrometers at 186 mm, which is why nobody writes grades on saw-cut stock. The PCB and the extrusion bands come from their own processes, not from the standard. If the grade system is unfamiliar, our ISO tolerance grades guide works it out from the standard tolerance unit.

The PCB number surprises people, so it is worth stating plainly. A 1.6 mm FR4 board is commonly toleranced at about ten percent of finished thickness, which is 0.16 mm, and IPC class 2 work sits in that neighborhood. Add press-fit connectors, a stiffener or a heavy copper layer and the finished thickness moves further. That tolerance is a real physical property of laminated glass fabric and resin, not a lack of care by the board house. It belongs in the chain exactly as written.

Worst Case: Add Them Up

Worst case is the arithmetic you can do on paper, and it is the only method that needs no data about the processes.

For a simple chain where each link contributes directly to the gap, the total variation is the sum of the individual half-bands:

WC = ± (a1 + a2 + a3 + ... + an)

where each a is the half-band of that link, so ±0.02 mm for a 0.04 mm band, and so on. The gap's minimum value is the nominal gap minus that sum. With our five links, WC = ±0.40 mm against a 0.20 mm nominal gap, so the minimum gap is minus 0.20 mm and the assembly is not buildable to print.

Worst case is the correct tool in three situations, and we use it in all three. Safety-critical features, where a single non-conforming assembly is unacceptable and no statistical argument will be accepted by the customer or the auditor. Small production quantities, where the distribution never gets a chance to average out and the first unit may well be the bad one. And any chain that contains a link you cannot characterize, which in practice means a supplier part with no capability data, because you cannot assume a distribution you have never measured.

It is also the only defensible answer when the customer has no process capability data, and that is most of the time. If a stack-up says the assembly cannot close at worst case, the honest reply is not "it will probably be fine". It is to change the design, the chain, or the gap.

RSS: Square Them, Take the Root

Root sum square assumes the links vary independently and each sits near the middle of its band, and then the combined variation is:

RSS = ± sqrt(a1² + a2² + a3² + ... + an²)

Same five links: the square root of 0.0004 + 0.0225 + 0.0025 + 0.0009 + 0.0225, which is the square root of 0.0488, which is 0.221 mm. Against the same 0.20 mm gap, the minimum gap is minus 0.021 mm. Still negative, still not buildable, but roughly ten times closer to zero than the worst-case answer.

That is the seduction of RSS and also its danger. It gives you a number you like, and the number is only valid under conditions nobody verified: independent links, centered processes, known distributions, no single link parked at its limit. In our chassis, the extrusion is cut on a saw that drifts as the blade wears, so its length distribution is not centered on nominal; it is offset by whatever the operator last set. That single fact invalidates the RSS result for the whole chain, no matter how good the other four links are.

Two practical guards. First, apply a statistical inflation factor when the process capability is not excellent. Bender's rule of thumb, an empirical correction rather than a standard, multiplies the RSS result by about 1.5 when processes run at a Cpk near 1 and by less as capability improves. Our 0.221 becomes 0.33, which is close enough to the worst-case 0.40 to make the point: with ordinary capability, RSS buys you much less than the formula promises.

Second, never mix methods inside one chain. We see worksheets where three links are added linearly and two are root-sum-squared, usually because the author had capability data for two suppliers. That hybrid has no theoretical basis and produces a number that is neither an upper bound nor a statistical estimate.

Why Neither Number Saved the Part

Both calculations agreed the assembly could not close, so the next question was what to change. The reflex answer is to tighten tolerances, and on this chassis it would have cost real money for no result, because the two largest links were not ours to tighten. The board house would have quoted a sorted lot at a premium and a four-week lead time. The extruder would have smiled.

The actual fix was to stop treating the interface as a fit. We deepened the rear pocket by 1.40 mm, so the gap now runs from 1.20 mm to 2.00 mm across the full 0.80 mm spread of the chain, and dropped in a 2.4 mm closed-cell polyethylene pad that compresses to whatever it finds. At the tight end the pad is compressed 50 percent, at the loose end about 17 percent, and both still hold the board against its standoffs. The gap stopped being a precision dimension and became a compression range, and a compression range is satisfied by every combination the five links can produce. The pad costs 0.04 dollars die cut. The extra pocket depth costs one more roughing pass, a few cents on a feature that was already being machined.

The number that justified it was not the tolerance, it was the rework. Before the change, 4.1 percent of units came back from final assembly with the PCB sitting proud of the rear pocket, which meant disassembling the unit, re-machining or scrapping a 12 mm front panel, and rebuilding. At 11.50 dollars per event including labor and the scrapped panel, that is 0.47 dollars per unit shipped. The compliant pad is 0.04. No tolerance tightening we could have bought came within a factor of ten of that trade.

This is the part of stack-up work that does not get written down often enough. The output of the analysis is not a tighter drawing. It is a decision about where variation is allowed to live, and the cheapest place is usually a compliant element, an oversized pocket, a slotted hole, a shim, a spring, or a fastener with a washer face. Precision is expensive. Compliance is cheap. Use precision where the function demands it and compliance everywhere else.

Quality engineer measuring a machined part during first article inspection
First article inspection tells you whether the process is centered. A stack-up tells you whether it matters. The two documents only work as a pair.首件检验告诉你过程是否居中;公差叠加分析告诉你这件事到底重不重要。这两份文件必须成对使用。

Sensitivity: Not Every Link Moves the Gap Equally

In a simple series chain every link has a sensitivity of 1, which is why the five links above could simply be added. Real assemblies are rarely that tidy. Sensitivity is the partial derivative of the gap with respect to the link, and it can be less than one, more than one, or negative.

Three cases we meet constantly:

Sensitivity is also the answer to "which tolerance should I tighten". Rank the links by their contribution to the total, not by how tight they look. In our chassis the front panel at ±0.02 mm looked like the precision part and contributed 5 percent of the chain. The PCB at ±0.15 mm was the loose part and contributed 37 percent. If you have budget for exactly one change, spend it on the link with the largest sensitivity times tolerance, and if that link belongs to another supplier, treat the interface rather than the part.

When the Link Is a Position Tolerance

This is where most hand-written stack-ups go wrong, and it goes wrong in a predictable direction: the number gets entered at twice its real value.

A position tolerance of Ø0.2 mm describes a cylindrical zone 0.2 mm in diameter. Its contribution to a linear gap in any one direction is the radius, 0.1 mm, not 0.2. Enter it as 0.2 and you have doubled that link. Enter it as 0.1 mm and you have correctly treated a diameter as a bilateral band, but only if the zone is centered on the true position, which is the assumption the whole analysis rests on.

The second error is forgetting bonus tolerance. If the position callout carries a maximum material condition modifier and the feature departs from MMC, the allowable position error grows by exactly the amount of that departure. A Ø6.6 mm hole toleranced plus 0.2 over zero has 0.2 mm of bonus available at its largest size, which is often more than the position tolerance itself. Ignoring bonus makes the analysis conservative, which is safe but expensive: it can push a buyer into a tighter hole tolerance than the joint actually needs.

A worked joint, because this is easier with numbers. A cover plate bolts to a housing with four M6 screws. The housing has tapped holes, the cover has clearance holes Ø6.6 +0.2 over 0, the screw shank is Ø6.0 maximum.

For a fixed fastener joint, where one side is threaded, the standard relationship in ASME Y14.5 is:

T1 + T2 = H_min − F_max

With H_min 6.6 and F_max 6.0, the right side is 0.60 mm. Split evenly, each part gets Ø0.30 mm of position tolerance. That is generous, and it means a shop can hold the pattern on a machining center without a special fixture. A floating joint, where both parts carry clearance holes, is allowed twice that total, 1.20 mm or Ø0.60 mm per part, because the fastener is free to move in both holes rather than being anchored by one of them. That factor of two is the whole reason threaded joints need tighter patterns than bolted-through joints.

The practical use of that formula in a quoting conversation is the reverse direction. When a drawing asks for Ø0.05 mm position on a clearance-hole pattern, we compute the available clearance and often find the requirement is five times tighter than the joint needs. We say so in the DFM note, the customer usually relaxes it, and the price drops. That is free money and it comes directly out of doing the stack-up.

Our true position inspection guide covers how those zones are actually verified on a CMM, including the difference between a position result and a concentricity result, which is another place where a factor of two appears without warning.

Angular and Two-Dimensional Stacks

One-dimensional stacks assume every link acts along the same line. That is true for a stack of plates and false for almost everything else: a bracket with two bends, a housing with a bore at an angle, a mechanism with a linkage. In two dimensions the links combine as vectors, and the gap is the resultant rather than the sum. A bent bracket brings its own arithmetic as well, because the flat pattern, the bend deduction and the tolerance on each leg all enter the chain, which is the subject of our sheet metal tolerance guide.

We handle this in three levels of effort, chosen by what the decision is worth.

  1. Vector sum by hand for a two-link or three-link chain with one or two angles. Draw the chain, resolve each link into X and Y, add, and take the resultant. Fifteen minutes with a calculator and a sketch.
  2. A spreadsheet with explicit X and Y columns when the chain has five to ten links. Each link gets a nominal, a half-band and an angle. The spreadsheet computes worst-case corners by trying all combinations of extremes, which for ten links is 1,024 combinations and takes a computer no time at all.
  3. Monte Carlo sampling when the geometry is non-linear, when there are rotational joints, or when the number of links makes the corner enumeration explode. More on that below.

The failure mode in 2D is dropping the angle. A link that is 40 mm long at 30 degrees contributes 34.6 mm in X and 20 mm in Y, and its tolerance ellipse is not the same as its tolerance band. Engineers who copy a 1D worksheet into a 2D problem usually keep the band and lose the projection, and the result is wrong by the cosine of an angle nobody wrote down.

Monte Carlo, in Plain Language

Monte Carlo simulation replaces arithmetic with sampling. You give each link a distribution instead of a tolerance band, then draw one random value from each link, add them up, and record the result. Do that ten thousand times and you have a distribution of the gap, from which you can read the fraction of assemblies that fall outside the requirement.

It earns its keep in four situations. Non-linear geometry, where a rotation turns into a displacement and no closed-form sum exists. Chains long enough that worst case is absurdly pessimistic, which is the normal state of a 30-part assembly. Mixed distributions, where one link is normal because it comes off a controlled machine and another is uniform because it is a saw cut. And any case where the customer asks a probability question, such as what percentage of units will need a shim.

It is also easy to misuse. Feeding it tolerances disguised as distributions, treating a rectangular band as a normal curve, or assuming independence between two features machined in the same set-up, will all produce a confident number that means nothing. Two bores machined in one operation share their location error; they are correlated, and a Monte Carlo run that samples them independently will understate the risk.

For most of the parts we quote, the honest hierarchy is: worst case by default, RSS when the customer supplies capability data and the chain is simple, Monte Carlo when the geometry is not linear or the question is explicitly probabilistic. A Monte Carlo result on a chain of unknown distributions is a more precise guess, not a better answer.

The Tolerance You Lose Before You Measure

Every stack-up ends in a measurement, and the measurement has its own uncertainty. ISO 14253-1 handles this with a guard band: conformance to an upper limit is only established when the measured value plus the expanded uncertainty still sits inside the limit. In plain terms, you lose part of your tolerance band to the act of proving you met it.

Take a ±0.02 mm callout, which is a 0.04 mm band, measured with an expanded uncertainty of 0.006 mm at 95 percent confidence. The guard band eats 0.006 mm at each end, so the acceptance zone is 0.028 mm, which is 70 percent of the band the designer specified. Thirty percent of that tolerance is spent on measurement, not on manufacturing. On a ±0.10 mm callout the same uncertainty costs 6 percent, which is why loose tolerances are cheap to verify and tight ones are not.

The old rule of thumb is ten to one, the gauge ten times finer than the tolerance. Modern practice accepts four to one, applied to the expanded uncertainty of the whole measurement rather than to the resolution of the instrument. The CMMs we inspect on are typically specified at 2.5 micrometers plus 1 micrometer per 300 mm of measured length, which on a 186 mm extrusion is 3.1 micrometers. Against the extrusion's ±0.15 mm that is trivial. Against the front panel's 0.04 mm band it is 8 percent, which is why we measure those panels in a temperature-controlled room rather than on the bench next to the machine.

If your stack-up leaves less than 10 percent margin between the calculated worst case and the requirement, the measurement system is part of the chain whether you put it there or not. We treat that margin as a link with its own tolerance, and the gage R&R study is how we prove the link is small enough to ignore. Where the measurement is a CMM program rather than a hand tool, probe strategy and point count enter the uncertainty budget too, which our CNC inspection methods guide covers in detail.

Temperature: A Link Nobody Puts in the Chain

The chassis in the opening example is 6063 aluminum, 186 mm long, with a coefficient of thermal expansion around 23 micrometers per meter per degree Celsius. Between a 20 degree inspection room and a 25 degree assembly line, that body grows 0.021 mm. Between a 20 degree inspection room and a 30 degree August afternoon on a loading dock in Dongguan, it grows 0.043 mm.

That is a single link, larger than the front panel's entire tolerance band, and it appears on no drawing. Steel at 11.5 micrometers per meter per degree gives about half the movement for the same length, which is why a mixed aluminum and steel assembly drifts in one direction as it warms rather than growing symmetrically. On a shaft in a housing the same coefficient difference changes the fit itself, and our shaft and hole fits guide works through an aluminum housing with a steel shaft for exactly that reason.

Three rules we apply. Measure at 20 degrees Celsius, or record the temperature and correct for it, because a part measured at 28 degrees is not the part you will ship. Design stacks with a thermal term whenever the assembly spans more than about 100 mm or mixes materials with coefficients that differ by more than a factor of two. And when a customer reports that a part "fits in the morning and not in the afternoon", ask about temperature before asking about the machine, because the machine is usually innocent.

The 20 degree reference is not arbitrary: it is the temperature at which the standard is realized and at which gauge blocks are calibrated, and the BIPM publishes the definitions that national labs work from. For the shop-floor side of the same subject, NIST's metrology portal is a better starting point than most textbooks.

Surface grinding a hardened steel component to a tight tolerance
When a stack-up genuinely demands a tight link, grinding is often the process that delivers it. Choosing that link deliberately is the difference between a cost premium and a cost disaster.当叠加分析确实要求某个环节收紧时,磨削往往是能实现它的工艺。有意识地选择收紧哪一个环节,是「合理溢价」与「成本灾难」之间的区别。

How This Shows Up in a Quote

A stack-up reaches us in one of three states, and each gets a different reply.

The first is a complete worksheet with a named critical dimension, all links listed including supplier parts, and a stated method. We check the arithmetic, check the tolerance ownership, and quote. Sometimes we find one link entered at twice its value, we say so, and the quote comes down.

The second is a drawing with tight tolerances and no analysis. We pick the three or four features that dominate the cost, run the chain ourselves from the drawing's own dimensions, and send back a short note: these two features drive 70 percent of the price, this one appears to be tighter than the joint requires, and here is what the part would cost with that one relaxed. This is the free DFM review, and it is the most valuable thing we send before an order. Where the feature is a milled pocket or a bore pattern, the milling capability page lists the envelope and the accuracy we can hold on it, so the note stays anchored to machines rather than to adjectives.

The first production run is where the analysis meets the machine, and the first article inspection guide is how we confirm on real parts that the chain behaves the way the worksheet predicted, before the batch is released.

The third is a complaint that an assembly does not close, with a photo of a gap and a drawing that looks fine. In that case we ask for the four numbers that settle it: the actual measured values of the links on the failing units, the assembly sequence, the temperature at assembly, and the name of the critical dimension. Nine times out of ten the answer is in the link nobody listed.

Our position on tightening is simple and sometimes unpopular. We will not sell you a tighter tolerance that does not change the function, because you will pay for it on every unit and it will not fix anything. If the chain says the problem is a PCB thickness, the answer is a compliant interface or a selective assembly step, not a grinder.

A Worksheet You Can Copy

Seven steps, in the order that avoids rework.

  1. Name the critical dimension in one sentence. If you cannot, stop and find it.
  2. List every link between the two references, including purchased parts, finishes, adhesives and thermal expansion. The finish is a link: anodizing adds 0.005 to 0.015 mm per surface on aluminum, and hard anodizing adds more.
  3. Write the nominal and the half-band for each link, and write down who supplies that tolerance. Ownership is what makes the next conversation possible.
  4. Set the sensitivity of each link: 1 for a series linear chain, the projection for an angled one, the radius for a position tolerance, the lever arm for an angular one.
  5. Compute worst case. If the minimum gap is positive and the maximum is acceptable, you are done and you should stop analyzing.
  6. If worst case fails, compute RSS only if you have centered, capable processes and independent links. Apply a statistical factor and see whether the answer survives.
  7. If both fail, change the design before you change a tolerance: a compliant element, a slot, a shim, a deeper pocket, or a selective assembly step. Then re-run the two calculations to confirm the change worked.

The one thing not to do is tighten every link by the same percentage, which is what happens when a project is late and somebody applies a blanket note. A blanket note does not allocate anything; it just makes all five suppliers unhappy and moves the cost without moving the risk.

What Buyers Actually Ask Us

Can you tell me if my drawing will assemble, without me sending the whole assembly? Often, yes, if you send the critical dimension and the links around it. We will not guess the parts we cannot see. Send the section view that contains the gap and the purchased components in that chain, and we can do useful work in an hour.

Is RSS acceptable to use in a PPAP submission? Only if the customer approves the method and you have capability data to support it. Most automotive customers accept statistical tolerance analysis when it is documented, but the default expectation in a PFMEA-driven quality plan is worst case, and our control plan and capability study guide covers the evidence you need before the argument is worth having.

Why does my stack-up pass on paper and fail on the line? Usually one of four things: a link that was left out, a position tolerance entered as a linear band, a process that is not centered so the distribution is offset, or an assembly that is forced rather than located. The fourth is the most common in our experience, and it is a fixture problem rather than a tolerance problem.

Does a tighter tolerance always cost more? Not per feature, but almost always per part. One tight feature on an otherwise ordinary part can often be held in the same set-up for no extra money. Five tight features usually means a second operation, a controlled environment, or a grinder, and that is where the price step appears.

How do you handle a stack-up on a part you only machine, not assemble? We work to the interface you define and we tell you what we can hold. If the assembly's critical dimension depends on a purchased component, that component's tolerance belongs in the chain, and it is your chain, not ours. We will still run the numbers with you because it costs us an hour and saves a rework.

FAQ: tolerance stack-up

What is the difference between worst case and RSS in a tolerance stack-up?

Worst case adds every tolerance in the chain, so it is an absolute upper bound on variation and needs no process data. RSS takes the square root of the sum of squares, which is smaller because it assumes the links vary independently and sit near the middle of their bands. Worst case answers "can this ever fail", RSS answers "how often will it fail", and only the second question needs capability data to be meaningful.

When is RSS not allowed?

When a link has no known distribution, when the process is not centered, when two links are correlated because they were machined in the same set-up, or when the customer or the standard governing the part requires worst case. In safety-critical work, worst case is normally mandatory regardless of capability, and no statistical argument substitutes for it.

How do I convert a position tolerance into a linear tolerance for a stack?

Divide the diameter of the position zone by two. A Ø0.2 mm position tolerance contributes 0.1 mm in any single direction, assuming the zone is centered on true position. Do not add the full diameter to a chain of bilateral tolerances, and do not forget the bonus tolerance available when the feature departs from maximum material condition.

Does the surface finish count as a link?

Yes. Anodizing, plating and coating all change the dimension of the surface they are applied to, and the change is not always symmetric. Anodizing on aluminum typically adds 0.005 to 0.015 mm per surface depending on the process, and hard anodizing adds more. On a stack that has 0.05 mm of margin, a coating on two faces can consume half of it.

What is Bender's factor and should I use it?

Bender's factor is a statistical inflation applied to RSS results, commonly around 1.5 when processes run at a capability index near 1.0 and lower as capability improves. It exists because RSS assumes perfect centering and independence, which real processes rarely deliver. We apply it whenever a customer wants to use RSS on production parts, and it usually brings the answer back close to worst case.

Can you do the stack-up for us?

For the features we machine, yes, and we do it as part of the free DFM review before quoting. For a full assembly we need the links we do not make, including their tolerances and their suppliers. We will run the arithmetic and tell you which link dominates. What we will not do is sign off on a stack-up that depends on a supplier part we have never measured and a process we have never seen.

Let's Talk About Your Assembly

If you have a drawing with a gap that keeps closing in the wrong direction, send it over. We will run the chain, tell you which link is actually driving it, and say plainly whether the answer is a tighter tolerance, a different interface, or a design change that costs three cents. Sometimes the answer is that your print is fine and your assembly fixture is not, and we will tell you that too.

Free DFM on the drawing, a quotation inside 24 hours, ±0.01 mm on the features we commit to, and a shop in Dongguan with more than 200 CNC machines behind it. Send us the drawing and the critical dimension, or reach us on WhatsApp at +86 17620300785 and by email at gongtianbao@xhlmarketing.com.

一位客户把一台由五个零件组成的音频机箱送过来报价,图纸看上去没有问题。前面板厚 12 mm,PCB 厚 1.6 mm,四根 18 mm 的支撑柱,后盖板带一个 3 mm 深的凹槽,挤压铝型材机壳按 186 mm 下料。每一个尺寸上的公差,单独拿出来都有人能为之辩护;PCB 边缘到后盖凹槽之间的间隙,图纸标注名义值 0.20 mm。结果这台机箱装不上。不是偶发,也不是分布尾部才出问题,而是在前五十台里就出现了两次,而且每次都在同一个位置——这是"算术问题"而非"机床问题"的典型特征。(合成案例,细节已改动。)

算术本身并不复杂。把这五个环节的正负公差加起来,得到 0.40 mm 的可能变动量,而留给它的间隙只有 0.20 mm。于是在切下第一刀之前,这个装配在最坏情况下就已经有 0.20 mm 的负间隙。客户的工程师其实做过叠加分析,但他只算了自家三个机加工零件,把 PCB 和型材排除在外,理由是这两样来自别的供应商,"那是别人的公差"。

可它们并不是"别人的公差"。它们在同一条链上,所以就在同一个总和里。整个公差叠加这门手艺的核心就在这里,而我们对图纸的绝大多数争论,也正是从这句话开始的。

我们在东莞做机加工,车间有 200+ 台 CNC,这行干了 23+ 年,质量体系通过 IATF 16949、ISO 9001 和 ISO 13485 认证,24 小时内返回报价,并附免费 DFM 评审。客户装配体的叠加分析我们每周都在算,因为只有这张表能回答:你图纸上那个"±0.01 mm",到底买到了什么。下面就是我们的算法,用的正是那台机箱的真实数字,也包括故事里那一段——正确的工程答案根本不是收紧公差。

Machined aluminum audio front panel with tight tolerance features
A machined front panel like this one is the link most engineers tighten first. In the chassis above it was the smallest contributor in the chain.像这样的机加工前面板,往往是工程师第一个想收紧的环节。在上面的机箱案例里,它却是整条链上贡献最小的一项。

叠加分析能回答什么,不能回答什么

公差叠加分析,是计算各个尺寸上的公差在某个关键特征处如何合成的过程。这个关键特征在分析里有个名字:间隙、配合、齐平条件或关键尺寸。你必须先把它点出来,再做任何运算;如果你没法用一句话说清它是谁,那就还没到可以开始算的时候。

叠加分析能回答两个问题,另有一个问题它回答不了。第一是零件能不能装起来:最小间隙是否为正、最大过盈是否可接受、连接器能否对准开孔。第二是装起来之后能不能用:密封圈是否仍有压缩量、光轴是否仍在预算内、轴承预紧是否落在轴承厂给的区间。它回答不了的是"这个设计好不好"——一个零件可以装得严丝合缝,同时仍然是个糟糕的设计。

把叠加分析和公差标注分开看也有必要,这两件事经常被混为一谈。标注说的是"单个特征允许测出多少",我们的 CNC 加工公差指南讲的是这个问题。叠加分析说的是"几个已标注的特征碰在一起会发生什么",这是另一个问题,而且通常是更贵的那个问题。

我们收到的客户叠加表,绝大多数是一维的、手写在打印件上的,而且就其所及基本都算对了。出错的地方几乎从来不在加法,而在环节清单:漏了一个外购件、把一个位置度当成线性公差填进去、忽略了角度标注的力臂、或者一项热膨胀从来没有被写进表里。

把机箱压垮的五个环节

这是这条链本该被写出来的样子。关键尺寸是 PCB 边缘与后盖凹槽内侧面之间的间隙,从前面板外表面到这个凹槽之间的一切,都是链上的环节。

环节名义值公差这个公差由谁提供
前面板厚度12.00 mm±0.02 mm我们,机加工
PCB 厚度1.60 mm±0.15 mm板厂,IPC 二级
支撑柱高度,四根18.00 mm±0.05 mm我们,车削
后盖板凹槽深度3.00 mm±0.03 mm我们,机加工
型材长度,下料186.00 mm±0.15 mm挤压厂,切割锯
间隙,即关键尺寸0.20 mm结果没有人,它是输出值

把各环节的公差绝对值相加,得到 0.40 mm,这就是最坏情况下的总变动量。它以名义值为中心对称,所以间隙的取值可以是负 0.20 mm 到正 0.60 mm。负间隙意味着干涉:不存在这样一种装配,PCB 比后盖凹槽深进去 0.20 mm,而其余环节还都停在名义值上。

看看这些公差分别归谁。这 0.40 mm 里,三个机加工零件加起来只占 0.10 mm,PCB 占 0.15 mm,型材占 0.15 mm。我们完全可以把自家三个零件做到 ±0.005 mm,成本约为原来的三倍,工艺路线里还要加一道磨削,但最坏情况下的间隙依然是负数。这是精密硬件里最常见的错配:采购花最大力气去压的那个供应商,本来就是贡献最小的那一个。

PCB 这一项常让人意外,值得说清楚。1.6 mm 的 FR4 板,成品厚度公差通常在厚度的百分之十上下,也就是 0.16 mm,IPC 二级大致就在这个范围。加上压接连接器、加强板或者厚铜层,成品厚度还会继续跑。这个公差是玻纤布与树脂层压出来的真实物理属性,不是板厂不上心,它在链里就该按原样写进去。

三个机加工的公差带大体落在 ISO 286 的等级附近——同一条算术在 Ø30 处让 IT7 等于 21 微米,在 186 mm 处让它变成 46 微米,所以没人会在锯切下料件上写等级。PCB 和型材的公差则来自它们各自的工艺,不来自这个标准。如果对等级体系不熟,我们的 ISO 公差等级指南从标准公差单位开始一步步算了出来。

最坏情况法:直接相加

最坏情况是你能在纸上算完的方法,也是唯一不需要任何过程数据的方法。

对于每个环节都直接作用于间隙的简单链,总变动量等于各环节半公差带之和:

WC = ± (a1 + a2 + a3 + ... + an)

其中每个 a 是该环节的半公差带,比如公差带 0.04 mm 就对应 ±0.02 mm。间隙的最小值,等于名义间隙减去这个和。我们这五个环节算下来是 ±0.40 mm,而名义间隙只有 0.20 mm,于是最小间隙是负 0.20 mm,这个装配按图做不出来。

有三种场合必须用最坏情况,我们三种都用。涉及安全的关键特征,一个不合格品都不可接受,客户和审核员也不会接受任何统计学论证。小批量生产,分布根本没有机会相互抵消,第一台很可能就是最差的那一台。以及链上包含你无法表征的环节——实践中就是没有任何能力数据的外购件,因为你不能假设一个你从未测量过的分布。

当客户拿不出过程能力数据时,最坏情况也是唯一站得住的答案,而多数时候就是这种情况。如果最坏情况显示装不上,诚实的回复不是"大概没事",而是改设计、改链、改间隙,三选一。

RSS:先平方,再开根

均方根法(RSS)假设各环节相互独立地变动、且各自都落在公差带中部,那么合成变动量为:

RSS = ± sqrt(a1² + a2² + a3² + ... + an²)

同样五个环节:0.0004 + 0.0225 + 0.0025 + 0.0009 + 0.0225 之和是 0.0488,开根得 0.221 mm。对着同一个 0.20 mm 的间隙,最小间隙是负 0.021 mm。仍然是负数,仍然做不出来,但比起最坏情况的那个负 0.20 mm,已经靠近零将近十倍。

RSS 的诱惑就在这里,危险也在这里。它给出一个你喜欢的数字,而这个数字只在没人验证过的条件下成立:环节相互独立、过程居中、分布已知、没有任何单一环节停在极限上。在那台机箱里,型材是锯床下料的,锯片一磨损长度就漂,所以它的分布并不以名义值为中心,而是偏在操作工上一次设定的位置上。就这一条,足以让整条链的 RSS 结论失效,其他四个环节再好也没用。

两条实用的护栏。第一,过程能力不够好时,加一个统计放大系数。Bender 经验系数(这是经验修正,不是标准条文)在 Cpk 接近 1 时把 RSS 结果乘以约 1.5,能力越好乘得越少。我们的 0.221 变成 0.33,已经接近最坏情况的 0.40,足以说明问题:在普通能力水平下,RSS 给你的好处远没有公式承诺的那么多。

第二,绝不在同一条链里混用方法。我们见过这样的表格:三个环节线性相加,两个环节开根相加,通常是因为作者只拿到两家供应商的能力数据。这种混合算法没有理论基础,算出来的数既不是上界,也不是统计估计。

为什么两种算法都救不了这个零件

两种算法都判定装不上,于是下一个问题就是改什么。条件反射式的答案是收紧公差,而在这台机箱上,那会花钱且没有结果,因为贡献最大的两个环节根本不归我们管。板厂会报一个筛选批的价格和四周交期,挤压厂只会笑一笑。

真正的解法,是停止把这个界面当成"配合"。我们把后盖凹槽加深了 1.40 mm,于是间隙在整个 0.80 mm 的链跨度上变成 1.20 mm 到 2.00 mm,再放一片 2.4 mm 厚的闭孔聚乙烯泡棉,让它压到哪儿算哪儿。最紧的一端泡棉被压掉 50%,最松的一端大约 17%,两种情况都还能把 PCB 压实在支撑柱上。间隙不再是精密尺寸,而是一个压缩区间,而压缩区间能被这五个环节的所有组合满足。泡棉模切成本 0.04 美元,凹槽加深只是多一道粗加工,几美分的事,而且那个特征本来就要加工。

真正让这个决定成立的不是公差,是返工。改动之前,4.1% 的产品在总装阶段被退回来,PCB 高出后盖凹槽,处理方式是拆机、重做或报废一块 12 mm 的前面板、再装回去。按每起 11.50 美元(含人工与报废面板)算,摊到每台出货就是 0.47 美元。泡棉是 0.04 美元。我们能买到的任何一种收紧方案,代价都比这笔账高出十倍以上。

这一段是叠加分析里最少被写下来的部分:分析的产出不是一张更严的图纸,而是一个关于"变动量允许待在哪里"的决定,而最便宜的落脚点通常是柔性件、加深的凹槽、腰形孔、垫片、弹簧,或者带垫圈面的紧固件。精密很贵,柔性很便宜。功能需要的地方用精密,其余所有地方用柔性。

Quality engineer measuring a machined part during first article inspection
First article inspection tells you whether the process is centered. A stack-up tells you whether it matters. The two documents only work as a pair.首件检验告诉你过程是否居中;公差叠加分析告诉你这件事到底重不重要。这两份文件必须成对使用。

敏感度:不是每个环节都等量地推动间隙

在简单的串联链里,每个环节的敏感度都是 1,所以上面五个环节可以直接相加。真实装配很少这么整齐。敏感度是间隙对某个环节的偏导数,它可以小于 1、大于 1,也可以是负数。

我们最常遇到三种情况:

敏感度也是"该收紧哪个公差"的答案。按各环节对总量的贡献排序,而不是按它看起来有多紧排序。在那台机箱里,±0.02 mm 的前面板看起来像是精密件,却只占整条链的 5%;±0.15 mm 的 PCB 看起来松,却占了 37%。如果预算只够改一处,就改"敏感度乘公差"最大的那个环节;如果那个环节属于别的供应商,那就去处理界面,而不是处理零件。

当环节是一个位置度

这是手写叠加表最容易错的地方,而且错的方向很固定:填进去的数字是真值的两倍。

位置度 Ø0.2 mm 描述的是一个直径 0.2 mm 的圆柱形公差带。它在任意一个方向上对线性间隙的贡献是半径 0.1 mm,不是 0.2。填 0.2,你就把这个环节放大了一倍。填 0.1 mm,才是把直径带正确地当成对称公差带处理——前提是公差带以理论位置为中心,而这正是整个分析赖以成立的那个假设。

第二个错误是忘了补偿公差。如果位置度带最大实体要求,而特征偏离了最大实体,允许的位置误差就会按偏离量等量增大。一个 Ø6.6 mm、公差 +0.2/0 的孔,在最大尺寸时可用补偿量是 0.2 mm,往往比位置度本身还大。忽略补偿会让分析偏保守,安全但费钱:它可能把采购逼到比接头实际需要更紧的孔径公差上。

用一个接头把这件事算清楚。一块盖板用四颗 M6 螺钉锁在壳体上,壳体是螺纹孔,盖板是 Ø6.6 +0.2/0 的通孔,螺钉杆径最大 Ø6.0。

对于固定紧固件接头(一侧是螺纹),ASME Y14.5 给出的标准关系是:

T1 + T2 = H_min − F_max

H_min 取 6.6、F_max 取 6.0,右边是 0.60 mm。平均分配,每个零件拿到 Ø0.30 mm 的位置度,这已经相当宽松,意味着车间在加工中心上不需要专用工装就能保证孔组位置。如果换成浮动接头,两侧都是通孔,允许的总量翻倍到 1.20 mm,即每件 Ø0.60 mm,因为紧固件在两个孔里都能浮动,而不是被其中一个锚住。这个"两倍"就是螺纹接头比通孔接头更需要收紧孔组的全部原因。

这条公式在报价沟通里是反着用的。当图纸要求通孔孔组做到 Ø0.05 mm 位置度,我们算一下可用间隙,经常发现要求比接头实际需要紧五倍。我们在 DFM 备注里说明,客户通常会放宽,价格随之下降。这是白捡的钱,而且它直接来自叠加分析。

这些公差带在 CMM 上到底怎么验,包括位置度结果与同轴度结果的区别(又一个会突然冒出来的"两倍"),见我们的 真实位置度检测指南。

角度叠加与二维叠加

一维叠加假设所有环节都作用在同一条线上。对一叠板件成立,对其余几乎所有东西都不成立:带两道折弯的支架、轴线带角度的壳体、带连杆的机构。二维里各环节按矢量合成,间隙是合矢量而不是代数和。折弯件还自带一套算术,因为展开料、折弯扣除以及每条边的公差都会进入链里,这部分见我们的 钣金公差指南。

我们按"这个决定值多少钱"分三档处理。

  1. 两个或三个环节、只含一两个角度时,手算矢量合成。画出链条,把每个环节分解到 X 和 Y,相加,取合矢量。一张草图和计算器,十五分钟。
  2. 五到十个环节时,用带 X、Y 列的表格。每个环节给名义值、半公差带和角度,表格穷举各环节取极值的所有组合来算最坏情况的角点。十个环节是 1,024 种组合,计算机眨眼就算完。
  3. 几何非线性、含转动关节、或者环节多到穷举爆炸时,用蒙特卡洛抽样。下面再说。

二维里最常见的失误是把角度弄丢。一个 40 mm 长、与轴线成 30 度的环节,在 X 方向贡献 34.6 mm,在 Y 方向贡献 20 mm,它的公差椭圆和它的公差带不是一回事。把一维表格照抄进二维问题的人,通常保住了公差带却丢掉了投影,结果就差了那个没人写下来的角度的余弦。

用大白话说蒙特卡洛

蒙特卡洛仿真用抽样代替算术。你给每个环节一个分布而不是一个公差带,然后从每个环节随机取一个值、相加、记录结果。做一万次,你就得到间隙的分布,从中可以读出有多少比例的装配落在要求之外。

它在四种情况下值得用。几何非线性,旋转会变成位移、不存在闭式求和的时候。链条长到最坏情况荒谬地悲观的时候,三十个零件的装配基本都这样。分布混杂,一个环节因为来自受控机床是正态的,另一个因为锯切是均匀的。以及客户问的是一个概率问题,比如"有多少比例需要加垫片"。

它也很容易被用错。把公差伪装成分布喂进去、把矩形带当成正态曲线、或者假设同一装夹加工出来的两个特征相互独立,都会产出一个很自信但毫无意义的数字。一次装夹加工的两个孔共享定位误差,它们是相关的;独立抽样的蒙特卡洛会低估风险。

对我们报价的多数零件,诚实的层级是:默认用最坏情况;客户提供了能力数据且链条简单时用 RSS;几何非线性、或者问题本身是概率问题的时候用蒙特卡洛。在一串分布未知的链上跑蒙特卡洛,得到的是更精确的猜测,而不是更好的答案。

你在测量之前就已经损失掉的那部分公差

每一次叠加分析最后都要落到测量上,而测量本身有不确定度。ISO 14253-1 用保护带处理这件事:只有当测得值加上扩展不确定度仍然落在限值以内,才算确立了符合性。说白了,为了证明你达标,你要让出一部分公差带。

取一个 ±0.02 mm 的标注,公差带 0.04 mm,测量扩展不确定度在 95% 置信度下为 0.006 mm。保护带在两端各吃掉 0.006 mm,可接受区变成 0.028 mm,只有设计所给公差带的 70%。那 30% 不是花在制造上,是花在测量上。同样 0.006 mm 的不确定度,放在 ±0.10 mm 的标注上只占 6%,这就是为什么松公差便宜好验、紧公差又贵又难验。

老经验是十倍法则:量具要比被检公差精细十倍。现代做法接受四比一,而且比的是整个测量的扩展不确定度,不是仪器的分辨率。我们检验用的 CMM 通常标称 2.5 微米加每 300 mm 测量长度 1 微米,在 186 mm 的型材上是 3.1 微米。对着型材的 ±0.15 mm,它可以忽略;对着前面板的 0.04 mm 公差带,它占 8%,这就是那些面板必须在恒温室里测、而不能在机床旁边的台面上测的原因。

如果你的叠加结果与要求之间的余量不足 10%,那么测量系统就已经在链上了,不管你写没写它。我们把这个余量当成一个自带公差的环节,而 重复性与再现性(GR&R)研究就是用来证明这个环节小到可以忽略的方法。当测量靠的是 CMM 程序而不是手持量具时,测点策略与采点数也会进入不确定度预算,这部分我们在 CNC 检测方法指南里展开。

温度:没人写进链里的一个环节

开头那台机箱是 6063 铝,长 186 mm,热膨胀系数约每米每摄氏度 23 微米。从 20 度的检验室到 25 度的装配线,机身长 0.021 mm;从 20 度的检验室到东莞八月装货月台上的 30 度,它长 0.043 mm。

这是一个环节,比前面板整个公差带还大,而且它在任何一张图纸上都不存在。钢的系数是每米每摄氏度 11.5 微米,同样长度只有一半的变形量,这就是为什么铝钢混装的组件升温时是朝一个方向漂,而不是对称地长大。轴装进壳体时,同一个系数差还会直接改变配合本身,我们的 轴孔配合指南里那个"铝壳配钢轴"的例子就是为这件事写的。

我们守三条规矩。在 20 摄氏度下测量,或者记录温度并做补偿,因为在 28 度下测过的零件不是你将要发货的那个零件。装配跨度超过约 100 mm,或者材料系数相差两倍以上时,链里必须带热项。以及,当客户说"上午装得进、下午装不进",先问温度再问机床,因为机床通常是无辜的。

20 度这个基准并非随意选定:它既是标准被复现、也是量块被校准的温度,国际计量局(BIPM)发布各国计量院工作的定义基础。至于车间现场的那一面,NIST 的计量门户比多数教科书更适合当起点。

Surface grinding a hardened steel component to a tight tolerance
When a stack-up genuinely demands a tight link, grinding is often the process that delivers it. Choosing that link deliberately is the difference between a cost premium and a cost disaster.当叠加分析确实要求某个环节收紧时,磨削往往是能实现它的工艺。有意识地选择收紧哪一个环节,是「合理溢价」与「成本灾难」之间的区别。

这些在报价里长什么样

叠加分析送到我们手上时通常是三种状态,每种对应一种回复。

第一种,是一份完整的表格:点明了关键尺寸,列全了包括外购件在内的所有环节,写清了所用方法。我们核对算术、核对公差归属,然后报价。有时会发现某个环节被填成了真值的两倍,我们说出来,报价跟着降下来。

第二种,是一张公差很紧但没有分析的图纸。我们挑出决定成本的三四个特征,用图纸自己的尺寸把链跑一遍,回一份简短的说明:这两个特征占了价格的 70%,这一个看起来比接头实际需要更紧,如果把它放宽,零件是这个价。这就是免费 DFM 评审,也是下单前我们给出的最有价值的东西。当特征是铣削凹槽或孔组时,铣削能力页列出了我们能覆盖的行程与精度,说明因此落在机床上,而不是落在形容词上。

第一批生产是分析和机床碰面的地方,首件检验指南讲的就是我们如何在真实零件上确认这条链的行为与表格预测一致,然后才放行批量。

第三种,是"装不上"的投诉:一张有缝隙的照片,一张看起来没问题的图纸。这种情况我们只要四个数:失效那几台上各环节的实测值、装配顺序、装配时的温度、以及关键尺寸的名字。十次里有九次,答案就在没人列出来的那个环节上。

我们对"收紧公差"的立场很简单,有时也不讨喜:我们不会卖给你一个不改变功能的更紧公差,因为你会在每一台上为它付钱,而它什么也修不好。如果链子告诉你问题出在 PCB 厚度上,答案是一个柔性界面或者一道选配工序,不是一台磨床。

一张可以直接抄走的表格

七步,按这个顺序做可以少返工。

  1. 用一句话点出关键尺寸。说不出来,就停下来先找到它。
  2. 列出两个基准之间的每一个环节,包括外购件、表面处理、胶粘剂和热膨胀。表面处理也是环节:阳极氧化在铝上每面增加 0.005 到 0.015 mm,硬质氧化更多。
  3. 写下每个环节的名义值和半公差带,并写清这个公差由谁提供。归属决定了下一步的对话能不能进行。
  4. 给每个环节定敏感度:串联线性链取 1,带角度的取投影,位置度取半径,角度取力臂。
  5. 算最坏情况。如果最小间隙为正、最大值也可接受,就到此为止,别再往下算。
  6. 最坏情况不过关,才去算 RSS,而且要满足过程居中、有能力、环节独立。加上统计放大系数,看结论还站不站得住。
  7. 两种都不过关,先改设计再改公差:柔性件、腰形孔、垫片、加深的凹槽,或者一道选配工序。改完把两个算法重跑一遍,确认改动生效。

唯一不要做的,是把所有环节按同一个百分比收紧——项目延期时总会有人甩出一条统一要求。统一要求不分配任何东西,它只是让五个供应商都不高兴,把成本挪了个位置,风险一动不动。

买家实际会问我们的问题

我只发关键尺寸和周围的几个零件,不发整套装配图,你能判断装得上吗? 很多时候可以。看不见的零件我们不猜。把包含那个间隙的剖视图、以及链上的外购件发过来,一小时之内我们就能给出有用的结论。

PPAP 里可以用 RSS 吗? 只有在客户批准该方法、且你有能力数据支撑时才行。多数汽车客户在文件齐全时接受统计公差分析,但在 PFMEA 驱动的质量计划里,默认期望是最坏情况;要让这场讨论值得进行,需要哪些证据,见我们的 控制计划与能力研究指南。

为什么我的叠加在纸上过关、在线上失败? 通常是四件事之一:漏了一个环节;把位置度当成线性带填进去;过程不居中导致分布偏移;或者装配是靠"硬压"而不是靠"定位"。第四条在我们经验里最常见,而它是工装问题,不是公差问题。

公差越紧一定越贵吗? 按特征算不一定,按零件算几乎一定。一个普通零件上只有一个紧特征,常常能在同一装夹里做出来,不加钱。五个紧特征通常意味着二次装夹、受控环境或者磨床,价格台阶就出现在这里。

如果你们只做加工、不做装配,叠加分析怎么处理? 我们按你定义的界面加工,并告诉你我们能守住什么。如果装配的关键尺寸取决于一个外购件,那个零件的公差就在链上,而那条链是你的链,不是我们的。我们仍然会陪你算,因为花我们一小时,能省你一次返工。

常见问题:公差叠加

公差叠加里,最坏情况法和 RSS 有什么区别?

最坏情况把链上每个公差都加起来,因此是变动量的绝对上界,不需要任何过程数据。RSS 取平方和再开根,结果更小,因为它假设各环节独立变动、且都落在公差带中部。最坏情况回答"这件事有没有可能失败",RSS 回答"多久失败一次",而只有第二个问题需要能力数据才有意义。

什么情况下不能用 RSS?

当某个环节没有已知分布、当过程不居中、当两个环节因为在同一装夹中加工而相关、或者当客户或适用标准要求最坏情况时。安全关键的工作通常强制要求最坏情况,任何统计学论证都不能替代它。

位置度怎么换算成线性公差放进链里?

把位置度公差带的直径除以二。Ø0.2 mm 的位置度在任意单一方向上贡献 0.1 mm,前提是公差带以理论位置为中心。不要把这个直径整个加进一串对称公差里,也不要忘记特征偏离最大实体时产生的补偿公差。

表面处理也算一个环节吗?

算。阳极氧化、电镀和涂层都会改变它们所附着表面的尺寸,而且变化不总是对称的。铝件阳极氧化按工艺不同,每面通常增加 0.005 到 0.015 mm,硬质氧化更多。在一个只剩 0.05 mm 余量的链上,两个面做涂层就能吃掉一半。

Bender 系数是什么,我该用吗?

Bender 系数是加在 RSS 结果上的统计放大系数,过程能力指数接近 1.0 时常用 1.5,能力越高用得越小。它存在的原因是 RSS 假设了完美居中和相互独立,而真实过程很少做到。客户想在量产件上用 RSS 时我们都会加上它,加了之后结果通常又回到接近最坏情况的位置。

你们能帮我们做叠加分析吗?

我们自己加工的那些特征可以,而且是免费 DFM 评审的一部分,在报价之前就做。整套装配的话,我们需要那些不由我们制造的环节,包括它们各自的公差和供应商。我们会把算术跑完,告诉你是哪个环节在主导。我们不会做的,是在一个既没有实测过外购件、也没有见过其过程的基础上,替一份叠加分析签字。

聊聊你那套装配

如果你有一张图纸,上面的间隙总是往错误的方向闭合,发过来。我们把链跑一遍,告诉你到底是哪个环节在推动它,并且直说答案是收紧一个公差、换一种界面,还是一个只值三美分的结构改动。有时候答案是:你的图纸没问题,你的装配工装有;这种话我们也会照直说。

免费 DFM 评审、24 小时内报价、在我们承诺的特征上做到 ±0.01 mm,背后是东莞一家拥有 200+ 台 CNC 的工厂。把图纸和关键尺寸发给我们,或者通过 WhatsApp +86 17620300785、邮箱 gongtianbao@xhlmarketing.com 联系我们。

Get a QuoteFree DFM · 24h