TIGERFASTENERS
How badly your tightening method controls preload
Preload is what the joint needs, and the way you tighten decides how precisely you can deliver it. VDI 2230 puts a number on that imprecision and then multiplies it straight into the design, which is why the tool on the bench ends up deciding how big the bolt has to be.
The quantity
VDI calls it the Anziehfaktor, tightening factor, symbol αA, and also describes it as the assembly uncertainty factor. It is a ratio:
αA = FM max / FM min
FM min is the minimum assembly preload you need; FM max is the largest that could actually turn up once the tightening procedure, the tool and the friction scatter have had their say.
Where it sits in the procedure is worth getting right, because it is easy to look in the wrong place. αA is selected at calculation step R1, “Determining the tightening factor”, which points to §5.4.3, with the table in Annex A as Table A8. R5 computes FM min, and R6/1 is where the multiplication happens: FM max = αA FM min.
The table, with the numbers people usually quote wrong
Table A8 states the scatter relative to the mean assembly preload, and the two columns are related by
ΔFM / 2FMm = (αA − 1) / (αA + 1)
| Method | αA | Scatter |
|---|---|---|
| Ultrasonic elongation control | 1.1–1.2 | ±5–9% |
| Mechanical tensioning at the bolt or nut | 1.1–1.3 | ±5–13% |
| Mechanical elongation measurement | 1.1–1.5 | ±5–20% |
| Hydraulic, friction- and torsion-free tensioning | 1.1–1.4 | ±5–17% |
| Yield-point control, powered or manual | 1.2–1.4 | ±9–17% |
| Angle control, powered or manual | 1.2–1.4 | ±9–17% |
| Torque control, calibrated on the original joint | 1.4–1.6 | ±17–23% |
| Torque control set from estimated friction, class B | 1.6–2.0 | ±23–33% |
| Torque control set from estimated friction, class A | 1.7–2.5 | ±26–43% |
| Impact wrench, pulse tool, or by operator feel | 2.5–4.0 | ±43–60% |
Three things get misquoted from this table often enough to be worth naming.
- True hydraulic tensioning is 1.1–1.4, not the 1.3–1.4 that circulates in web summaries.
- The 1.4–1.6 “hydraulic tool” row is torque control applied with a hydraulic tool, which is a different thing from a hydraulic tensioner.
- A manual torque wrench has no single value. It lands at 1.4–1.6, 1.6–2.0, 1.7–2.5 or 2.5–4.0 depending entirely on how the torque was set, and by feel it is in the worst row on the table.
Angle and yield control follow a different route
Table A8 lists αA = 1.2–1.4 for angle and yield-point control, and R1 then instructs you to use αA = 1 in the calculation for those two methods.
The reason is in Table A8's own note: bolts tightened this way are sized against FM min and are not sized by forming FM max = αAFM min. The upper end of the preload is governed instead by the yield scatter of the actual bolt batch, and R10/3 handles it with pmax = 1.4 FMTab / Ap min.
So the 1.2–1.4 remains a guide value for achievable scatter, and dropping it into every angle or yield design equation is a mistake.
That route is worked through in torque plus angle, including why Table A8 does not say 1.0.
NASA uses a different framework, with its own numbers
NASA-STD-5020B does not use αA. It uses a preload variation Γ, with separate cmax and cmin for the tolerance on the installation control parameter itself:
Ppi-max = cmax(1 + Γ)Ppi-nom
Ppi-min = cmin(1 − Γ)Ppi-nom
| Installation method | Γ |
|---|---|
| Torque control | 25% |
| Torque control, unlubricated or as-received | 35% |
| Turn-of-nut / turn-angle | 25% |
| Bolt stretch | 10% |
For separation-critical joints those defaults are not available. You have to establish Γ from testing that meets the configuration requirements in its Table 2, at 90% probability and 95% confidence, two-sided.
Where the familiar ±25% comes from
We were going to attribute it to VDI. It is not a VDI number. VDI's torque row, for torque calibrated on the original joint, is ±17–23%.
The ±25% traces to NASA RP-1228 Table VII, which reproduces the Industrial Fasteners Institute's torque-measuring table citing IFI Fastener Standards, 5th edition, 1970:
| Method | Accuracy |
|---|---|
| Torque wrench | ±25% |
| Turn-of-nut | ±15% |
| Fastener elongation | ±3–5% |
| Strain gauges | ±1% |
The “up to about ±30%” version traces to RP-1228's Table VIII, after a 1987 Machine Design reference issue, which gives torque control as ±15–30%. Machinery's Handbook, 31st edition, carries the same ±25% for a torque wrench alongside ±8% for yield-point sensing and ±1% for ultrasonic.
These numbers are not interchangeable with each other. VDI's are guide values converted from αA; NASA-STD's 10% is a design substitute value for Γ; a published experiment comparing methods on M10 and M14 phosphated bolts reported torque control at about 18% scatter (3s) and ultrasonic clamp-force control at about 2.9%, which is a result for that equipment and those specimens rather than a design allowance.
Why the tool ends up sizing the bolt
The chain runs through VDI's calculation steps in order.
- R2 establishes the required minimum clamp load FK erf. It covers transmitting transverse load by friction, and it may also have to cover sealing and preventing the joint from opening.
- R3–R4 account for how the external load is shared, and for preload lost to embedding and to temperature.
- R5 gives FM min = FK erf + (1 − Φ*en)FA max + FZ + ΔF′Vth.
- R6 multiplies: FM max = αA FM min.
- R7 onward checks that FM max passes the assembly stress and surface pressure limits.
So at a fixed FM min, a larger αA raises the maximum assembly preload the design has to survive, and that maximum has to clear yield and bearing-face limits. Choosing a worse tightening method makes the bolt bigger, or forces a better method.
None of this is the tool's tolerance. A setting wrench above 10 N·m is permitted ±4% under ISO 6789, which is a different quantity measured on a test rig rather than on your joint. What that standard does and does not require of the tool, including the calibration interval and the storage rule it never contains, is the torque wrench standard has no storage rule.
One qualification on how we first put this. Saying the scatter is a design input rather than a precision problem draws the line too hard: VDI lists tool error, setting error, operating error and reading error among αA's sources, so it is partly a precision matter. The accurate version is that preload scatter is more than a process metric — in this calculation it has to become a design input.
Temperature moves the preload again after assembly, and VDI feeds that into the same equation: temperature moves preload.
Where this connects
Scatter at installation is only half the story — preload also falls in service without the nut turning, and a torque audit cannot see it.
Why preload matters at all, and what it does and does not buy, is in the bolt is a spring, and so is the joint. What the torque itself is buying is in torque and clamp force, and the friction it silently assumed is in the friction the torque assumed.
References
- VDI 2230 Blatt 1:2015-11 — R1 and §5.4.3 (determining αA), Eq. (R1/1) and Eq. (130), Table A8 in Annex A (guide values and the special rule for angle and yield control), R2 (FK erf), R5 (FM min), R6/1 (FM max), R7/3, R10/3 (pmax for angle and yield methods)
- NASA-STD-5020B — §4.3.1 Eq. (3)–(5) (Γ, cmax, cmin), §4.3.3 and TFSR 7 and Table 3 (values, and the 90/95 requirement for separation-critical joints), Appendix A.2 Eq. (25) and (26a)–(26b)
- NASA RP-1228, Fastener Design Manual (1990) — Table VII after IFI Fastener Standards 5th ed. (1970); Table VIII after Machine Design (1987)
- Machinery's Handbook, 31st edition — torque wrench ±25%, turn-of-nut ±15%, yield-point sensing ±8%, bolt elongation ±3–5%, ultrasonic ±1%
- Persson and Roloff, 2016, DOI 10.1177/0954406215619648 — measured scatter by control method on M10 and M14
- Preload Control Method of Threaded Fasteners: A Review, 2024, DOI 10.1186/s10033-024-01082-w
Acceptance for any particular joint is governed by your drawing and the standards it invokes.
This page covers step 2, the thread. The whole order is substrate, thread, head, drive, finish, documentation, and why doing it out of order is rework rather than a tweak is in specifying a screw.
Common questions
What is the tightening factor in VDI 2230?
It is the Anziehfaktor, symbol alpha A, also described as the assembly uncertainty factor. It is the ratio of the maximum assembly preload that could turn up to the minimum assembly preload you need. It is selected at calculation step R1, which points to clause 5.4.3, with guide values in Table A8 of Annex A, and it is multiplied into the design at R6 where maximum assembly preload equals alpha A times minimum assembly preload.
How much preload scatter does a torque wrench give?
It depends entirely on how the torque was set. VDI 2230 Table A8 gives plus or minus 17 to 23 per cent where the torque was calibrated by testing on the original joint, 23 to 33 per cent where it was set from an estimated friction coefficient in class B, 26 to 43 per cent for class A, and 43 to 60 per cent for tightening by operator feel or with an impact wrench. There is no single value for a manual torque wrench independent of those conditions.
Where does the familiar plus or minus 25 per cent come from?
Not from VDI. It traces to NASA RP-1228 Table VII, which reproduces the Industrial Fasteners Institute table citing IFI Fastener Standards, fifth edition, 1970, giving a torque wrench at 25 per cent, turn-of-nut at 15 per cent, fastener elongation at 3 to 5 per cent and strain gauges at 1 per cent. The version quoted as up to 30 per cent traces to the same document’s Table VIII, after a 1987 Machine Design reference issue.
Can I use Table A8 values for angle-controlled tightening?
Not directly in the sizing equations. Table A8 lists 1.2 to 1.4 for angle and yield-point control, but calculation step R1 instructs you to use a tightening factor of 1 for those two methods. Bolts tightened that way are sized against the minimum assembly preload rather than by forming a maximum from it, and the upper end of preload is governed by the yield scatter of the actual bolt batch, which R10/3 handles separately.
How does the tightening method affect bolt size?
Through the calculation order. R2 establishes the required minimum clamp load, R3 and R4 account for load sharing and for preload lost to embedding and temperature, R5 gives the minimum assembly preload, and R6 multiplies it by the tightening factor to get the maximum assembly preload. That maximum then has to pass the assembly stress and surface pressure checks, so at a fixed minimum a worse tightening method raises the maximum the design must survive.
Enquiries
If a torque figure on a drawing has to survive assembly by hand, say what the tightening method is. The same required clamp load asks for a different bolt depending on how precisely it can be delivered.