Axial force
What is an axial force? (Definition)
Axial force is a load that acts parallel to the longitudinal axis of a component. It can be either tensile (stretching the component) or compressive (compressing it). Axial forces are one of the three primary internal loads in mechanical engineering – alongside shear and bending moments – and they directly determine the strength, stability and service life of shafts, bolts and structural members.
Axial force formula and calculation
The axial force F in a straight member with uniform cross-section is calculated from the normal stress σ acting on the cross-sectional area A:
F=P⋅A
P stands for the pressure or stress and A for the cross-sectional area of the component. Further calculations may be required depending on the application and the forces acting, such as in bolted connections or when analyzing structural elements under axial loads.
Worked example: preload in a bolted connection
Consider an M16 property-class 8.8 bolt tightened to 90 % of its yield strength. A typical assembly preload according to VDI 2230.
- Yield strength of class 8.8: σ_y = 640 N/mm²
- Stress cross-section of M16: A_s = 157 mm²
- Target stress: 0.9 · σ_y = 576 N/mm²
F = 576 N/mm² · 157 mm² ≈ 90 400 N ≈ 90 kN
This 90 kN preload is the axial force the bolt must sustain over its entire service life including superimposed working loads and any thermal expansion in the joint.
Compressive vs. tensile axial force
Although tensile and compressive axial forces share the same formula, the failure mechanisms are fundamentally different.
Tensile loading is governed by the material’s yield strength and ultimate tensile strength. The component fails when the applied stress exceeds the yield limit, leading to permanent plastic deformation, or – under cyclic loading – by fatigue crack growth.
Compressive loading introduces a second, often more critical failure mode: buckling. For slender members, the critical buckling load is given by Euler’s formula
F_cr = π² · E · I / (K · L)²
where E is the modulus of elasticity, I the smallest area moment of inertia of the cross-section, L the length and K an end-condition factor. Buckling failure can occur at axial stresses well below the material’s yield point – making slenderness a more decisive design parameter than strength alone.
Where axial forces occur in mechanical engineering
Axial forces can be found in numerous applications in mechanical engineering:
Bolted connections:
In a bolted joint, the assembly preload is itself an axial force – typically 60–90 % of the bolt’s yield strength. This preload generates the clamping force that holds the joint together. External working loads superimpose additional tensile or compressive components, and the joint must be designed so the bolt never loses its preload and never exceeds its endurance limit. VDI 2230 is the standard reference for preload calculation in Europe.
For applications that require high torque transmission without the parasitic axial loads of keyed shafts, TAS Schäfer locking assemblies provide a purely friction-based shaft–hub connection.
Bearings:
Bearings transfer axial loads between rotating and stationary parts. The bearing type must match the axial-load profile:
- Tapered roller bearings and angular contact ball bearings handle combined radial and axial loads in one direction.
- Thrust ball and cylindrical roller thrust bearings are designed for pure axial loads.
- Standard deep-groove ball bearings can absorb only modest axial forces.
Choosing the wrong bearing type for the actual axial load is one of the most common causes of premature bearing failure.
Shafts and axles:
Shafts are loaded axially whenever helical or bevel gears are mounted on them. The axial component of the gear tooth force is F_a = F_t · tan β for a helical gear, where F_t is the tangential force and β the helix angle. In pump and turbine shafts, the pressure differential across the impeller or rotor produces a continuous axial thrust that has to be reacted by a thrust bearing or balancing piston. Locking assemblies and shrink discs are designed to transmit torque between shaft and hub without introducing additional axial loads.
Locking assemblies and hydraulic shrink discs are designed to transmit torque between shaft and hub without introducing additional axial loads which makes them the preferred coupling for gearboxes, wind turbines and rolling mills.
Piston machines:
In internal combustion engines, hydraulic cylinders and reciprocating compressors, the gas or fluid pressure on the piston creates an axial force F = p · A that drives the connecting rod. For an automotive engine with a peak combustion pressure of 9 MPa and a piston diameter of 80 mm, the peak axial force on the connecting rod is roughly 45 kN applied tens of times per second.
Effects of excessive axial forces on components
Axial forces can have a significant impact on mechanical systems. Excessive axial forces can lead to deformation, fatigue or even failure of components. It is therefore important to take these forces into account when designing and analyzing mechanical systems. Engineers use various methods to monitor and control axial forces to ensure the reliability and service life of machines and systems.
How to reduce or control axial forces
There are several methods to reduce or control axial forces in mechanical systems:
Bearings designed for axial loads
Special bearings can help to absorb and distribute axial forces.
Component geometry optimization
The effect of axial forces can be reduced by adapting the shape and size of components.
Damping elements (e.g., friction springs)
Damping elements can help to reduce the effects of axial forces on mechanical systems.
Cyclic and impact axial loads can be absorbed by friction springs, which dissipate energy through internal friction between conical inner and outer rings.
Material selection:
The choice of materials with suitable mechanical properties can increase the resistance to axial forces.
Related TAS Schäfer products
TAS Schäfer designs and manufactures shaft–hub components engineered to transmit high torque while keeping axial loads predictable and controllable:
- Locking assemblies frictional shaft–hub connections that transmit torque without keying or welding.
- Shrink discs external clamping elements for solid and hollow shafts, ideal where axial loads must be kept off the key.
- Hydraulic shrink discs for fast assembly and dismantling on large gear and turbine shafts.
- Friction springs high-damping spring elements that reduce peak axial loads.
- Flange couplings and shaft couplings rigid couplings designed for predictable axial-load transfer.