FV-5 Phase Model (Clamping Force Curve)

The goal of the model is to fully capture the physical mechanisms—from design through to potential loosening—in causal order and to make them controllable through design.

The five phases are:

1. Design
2. Tightening and Assembly Phase
3. Settling Phase
4. Creeping and Relaxation Phase
5. Loosening Phase

During the design phase, the functional and economic constraints are defined. More than 80% of the subsequent costs and functional reliability are determined during this phase.

Basic Mechanical Principle
The bolted joint is modeled as an elastic two-spring system in accordance with VDI 2230 Sheet 1:2015-11:

• Screw spring stiffness cS
• Clamping part stiffness cK

The force distribution factor is:

Φ = c S c S + c K

Additional elastic resilience reduces cS or increases the total compliance. This reduces the force transfer factor Φ.

Consequence: The additional bolt load during operation is reduced.

Consideration of spring-like fasteners

Effective spring-like elements with reproducible residual spring force according to DIN 267-26:2005-12 are often not explicitly taken into account in conventional calculations.

If these elements are incorporated into the calculations, the following results occur:

• lower additional bolt load
• more stable preload force
• increased slip resistance
• a delayed transition to the loose rotation phase
• robustness against settlement losses

Design potential

The increased system flexibility allows for:

• Cross-section and weight optimization
• Reduction in bolt size while maintaining the same functional reliability
• Cost advantages at the assembly level

The design thus proactively ensures stability over the entire life cycle.

The assembly defines the actual initial preload force FV0

During tightening, a defined torque is applied, which is converted into a preload force (Fv) through friction at the thread and between the head and nut. The preload force curve shows a rapid increase until the target value (torque or angle limit) is reached.

Physical focus: Relationship between tightening torque, friction coefficients, and resulting clamping force.

Characteristic: Ideally, an approximately linear, or possibly slightly nonlinear, rise in the Fv curve.

This phase defines the initial state for all subsequent changes in the preload force.

The following factors are crucial:

• uniform surface pressure in the compression cone
• reproducible coefficient of friction window
• controlled tightening procedure (torque, angle of rotation, or a combination)

The preload force is calculated as follows:

F V = M A d 2 ⋅ μ thread + μ head

Variations in the coefficient of friction dominate the variation in preload force.
Elastic elements play a supporting role here:

• more uniform force distribution
• reduction of local stress peaks
• stabilization of the initial preload force

The elastic operating phase begins upon completion of assembly.

The settling phase begins as soon as the fasteners are tightened. During this phase, plastic adaptation processes occur in all zones responsible for force distribution in the bolted joint. The goal is to form contact surfaces capable of bearing the actual load—accompanied by an unavoidable initial decrease in preload.

Physical Causes of Embedding

Embedding is not a prolonged process, but rather a predominantly short-term plastic adaptation process. It results from:

• plastic leveling of microscopic roughness peaks,
• microdeformations in the head and nut seating areas as well as in the interface surfaces,
• local material flow due to high contact pressures in the compression cone,
• microscopic relative slip under tangential loading.

These mechanisms lead to an effective shortening of the clamping length. Since the screw is elastically stretched, any shortening immediately results in a reduction of the loss of preload.

Factors influencing loss of preload

The magnitude of the settlement-induced loss of preload Δ F Z depends significantly on:

• the surface properties (roughness, coating, hardness),
• the material pairing of the contacting surfaces,
• the magnitude of the assembly preload (contact pressure),
• the geometry and stiffness of the interface surfaces,
• the number and location of the joints in the force path.

Particularly critical factors include short clamping lengths, soft materials, or multiple interface surfaces, as the relative influence of a given settlement displacement is greater in these cases.

Characteristics of the Settlement Phase

The settlement phase is characterized by:

• a brief, often abrupt loss of preload immediately after assembly,
• the dominance of plastic processes (clearly distinct from time-dependent creeping or relaxation),
• high safety relevance for slip resistance, sealing function, and long-term durability.

Mechanically, the loss of preload can be described in simplified terms as follows:

ΔF Z = c total ⋅ Δs

where
Cges = total spring stiffness of the system
ΔS = resulting settlement

The greater the total elastic compliance, the smaller the relative loss of preload for the same settlement.

Significance for functional safety

The settling phase often determines whether the connection remains permanently slip-resistant. If the minimum clamping force is not maintained even in this early phase, a latent risk of loosening arises under dynamic loading.

The design countermeasure therefore does not consist of “over-tightening,” but rather in specifically increasing the system compliance so that settlement can be elastically compensated.

The settling phase is thus not a side effect of assembly—it is the first test of the design.

Mathematical treatment (VDI 2230, in brief):

• Settling travel reserve: Increase in elastic elongation through an adapted tightening procedure.
• Increase in resilience: Application of various countermeasures, including the use of spring-loaded fasteners to reduce relative Fv loss.

This phase is time-dependent and material-specific.

Relaxation

Stress reduction at constant elongation due to:

• Microplasticity
• Viscoelastic flow
• Contact stress redistribution

Occurs over weeks to months.

Creeping

Slow plastic elongation under constant stress due to dislocation motion in the crystal lattice. Occurs over years.

Both effects continuously reduce the prestress.

Spring elements slow this decline:

• Residual spring force has a compensating effect
• The minimum clamping force remains above the yield point for a longer period
• The transition to Phase 5 is delayed

Objective: Stabilization of the preload force through the system’s elastic resilience

Elastic resilience describes the sum of all reversible elastic deformations in the direction of force flow and is decisive for the joint’s ability to compensate for changes in preload resulting from embedding, relaxation, or temperature.

Contributions to the total yield (δges):

• Longitudinal elongation of the screw,
• elastic compression of the clamping parts,
• spring effect of additional fasteners (tension washers, residual spring force washers, NSK® washers),
• elastic deformation in the area where the head and nut contact the surface.

δges = δ screw + δ components + δ spring element

The larger δges is, the more elastic energy can be stored, and the smaller the effect a given embedding or relaxation displacement has on the remaining preload force. In this context, spring elements act as mechanical energy reservoirs.

Effects on the preload force curve (abridged):

• lower preload force drop under embedding, relaxation, and temperature loads,
• more stable clamping force under dynamic and thermal stress,
• improved slip resistance and increased resistance to loosening,
• extended lifetime of the joint.

For electrical screw connections, increased resilience also leads to more stable contact pressure and reduced fluctuations in contact resistance.

Normative integration (compact):
VDI 2230 as well as standards such as DIN 267-26, DIN EN 16984, and DIN EN 17976 enable the computational and experimental determination of the spring effect and thus the targeted design of the overall compliance.