Torque-Method Tightening: The Relationship Among Torque, Preload and the K Factor
Executive Summary
Tightening a bolt essentially stretches it with wrench torque to generate axial preload. But torque and preload are not a one-to-one linear relationship—per GB/T 16823.2, tightening torque T = K·F·d, where K is the troublesome torque coefficient. This article explains where the torque actually goes, why K fluctuates, and why the torque method can only "give an approximate preload".
Table of Contents
What Tightening Does: Turning Torque into Axial Preload
What makes a bolted joint reliable is not the subjective feel of "how tight", but establishing a stable axial preload (clamp force F). Preload clamps the connected parts together, so the joint does not slip, separate or loosen under working load. The problem is that wrenches and torque guns can directly measure only torque T, while the designer really wants preload F. Torque-method tightening builds a conversion bridge between the two.
Per GB/T 16823.2 "General rules for tightening of threaded fasteners", engineering uses the classic linear formula to describe this relationship:
T = K · F · d
where T is the applied tightening torque (N·m), F is the expected axial preload (N), d is the nominal thread diameter (m), and K is the torque coefficient. That is, once you know the target preload F and bolt diameter d, just look up K and back-calculate how much torque to apply. This is exactly the source of the shop-floor torque-gun setpoint.
T = K·F·d: Where the Torque Goes
The torque applied by the wrench is mostly "eaten" by friction; only a small part actually converts into bolt axial tension. The classic torque split is:
| Where Torque Goes | Rough Share | Action |
|---|---|---|
| Bearing-face friction (under head / nut face) | ~50% | Overcomes friction at the nut-to-connected-part contact |
| Thread-pair friction (flanks) | ~40% | Overcomes friction between internal and external thread meshing faces |
| Converted into bolt axial preload | ~10% | Elastically stretches the bolt, generating clamp force |
In other words, of the 100 N·m you apply, the part actually clamping the joint may correspond to only 10 N·m worth of preload. This is why K is essentially "a function of friction": the larger the friction, the smaller the preload produced by the same torque. Expanded, K is jointly determined by thread friction coefficient, bearing-face friction coefficient, thread lead angle and thread form angle; engineering usually folds these into one measurable coefficient.
Why the K Value Fluctuates: Friction Coefficient Is Key
K is not a constant; it swings widely with surface condition. Below are typical K ranges under different lubrication/surface treatments (per GB/T 16823.2 and common torque-clamp-force test results):
| Surface Condition | Typical K | Notes |
|---|---|---|
| Steel, unlubricated, clean and dry | ~0.20–0.24 | High friction; high and scattered K |
| Zinc-plated passivated, conventional oil film | ~0.18–0.20 | The most common field default |
| Fully lubricated with engine oil / grease | ~0.14–0.16 | Low friction; markedly more preload at the same torque |
| Zinc-flake coating (Dacromet-type) / PTFE coating | ~0.10–0.13 | Low friction; good consistency |
| Stainless, unlubricated | ~0.25 and up | Galling-prone; must be measured |
Factors affecting K include: surface-treatment type and thickness, presence and type of lubricant, roughness of threads and bearing faces, coating thickness, part temperature, and even the number of repeated tighten/break cycles. Precisely because these factors are hard to keep strictly identical on site, K carries inherent scatter.
The Inherent Limit of the Torque Method: Preload Scatter
The torque method is the simplest and most widespread tightening method, but it has a ceiling: preload accuracy is governed by friction, with large scatter. Under normal production conditions, the actual preload obtained by torque control alone typically fluctuates ±25%–±40% relative to the target. To avoid over-yield, design has to set the target preload low—usually only 60%–70% of the elastic preload corresponding to bolt yield strength (Rp0.2)—leaving safety margin for friction scatter.
This creates a contradiction: set preload high, and the low-friction batch will tighten past yield, plastically stretching or even breaking the bolts; set it low, and the high-friction batch will be under-preloaded, and the joint loosens easily. The torque method's limit is essentially "using a friction-sensitive quantity to control an elastic quantity".
To put numbers on it: a typical dry zinc-plated 10.9 bolt at K = 0.20 on M12 delivers a target preload around 25 kN, but the real spread across a batch is easily 18–32 kN. If you design the joint to need 30 kN minimum clamp and tighten by a torque set for a nominal 25 kN, the low-friction tail already exceeds yield while the high-friction tail delivers barely half the required clamp—both tails are failures, for opposite reasons. This is precisely why safety-critical joints moved away from pure torque control decades ago, and why torque-angle and yield-point methods exist as the upgrade path.
Engineering Countermeasures: Using the Torque Method Correctly
The torque method has limits, but once you understand its temperament, you can still make reliable joints:
- Measure K, do not copy empirical values: per GB/T 16823.3 "Fasteners—Torque-clamp force test", measure K on the actual bolt batch, then set torque from the real value.
- Unify surface condition and lubrication: use same-batch, same-surface bolts for one joint; specify whether and with what oil to minimize friction scatter.
- Control speed and tools: use calibrated torque guns / torque wrenches; avoid too-fast spinning that heats and changes friction; calibrate tool accuracy regularly.
- Leave preload safety margin: set target preload at 60%–70% of Rp0.2, absorbing K scatter with margin.
- Upgrade the method for critical joints: for engine cylinder heads, connecting rods, chassis and other high-precision joints, switch to torque-angle or yield-point control, reducing dependence on friction at the root.
Conclusion: The Torque Method Is "Adequate but Not Precise"
Torque-method tightening follows T = K·F·d; about 90% of the torque is consumed in thread and bearing-face friction, with only about 10% converted into axial preload; K is set by surface condition and lubrication, and its swing directly yields ±25%–±40% preload scatter. The key to using the torque method correctly is to measure K, unify surface condition, and leave ample safety margin; for critical joints demanding high precision, turn to the angle method and yield-point method.
YF Zhichengjia, founded in Shenzhen in 2005, is a fastener manufacturer and can provide torque-clamp-force test data and joint-tightening consulting per the GB/T 16823 series. For more material, see the technical documentation library, or contact our technical engineers.
