This project was sponsored by Rolls-Royce PLC as part of my PhD work.


When assembling an aircraft engine, its contact behaviour (such as rigidity, damping, etc.) can be determined by measuring its vibration modes. Since the contact behaviour dictates dynamic parameters, it is essential in controlling unwanted effects, such as blade flutter and undesirable aeroelastic phenomena.

An interesting observation occurs when an engine is disassembled and reassembled during maintenance. Even if the same components were used when reassembling, one observes that the vibration modes and, consequently, the contact behaviour of the engine changes.

There is still no clear answer as to why this happens. Since it is observed even when using the same components as before, empirical evidence from maintenance suggests that more than the components, the assembly order might have an effect here.


This project sought to lay down the foundations to investigate this phenomenon. Our hypothesis is that the tightening sequence of the bolt arrays affects the system's behaviour.

Bolted joints are one of the most used types of fixture in industry and when the contact area is small compared with the joint’s thickness, they represent an example of receding contacts, which are characterised by the reduction of the contact area when a loading is applied. Despite their ubiquity, axisymmetric receding contacts are not fully understand, and the current literature on the problem is limited either to plane problems or to frictionless cases.

This work presented an analysis of the frictional behaviour of fundamental axisymmetric receding contacts. The geometry of the problem is represented in an idealised format, through the contact of a semi-infinite thin layer of material and an elastic half-space. This allows for a precise solution to be found.

Results and conclusions

An idealised model of a frictional axisymmetric bolted joint was developed. It was shown that the receding contacts modelled present the basic properties that the contact snaps upon the application of any load, the interfacial tractions are proportional to the applied load, the extent of the contact size and slip zone are independent of the load, and the tractions are independent of the material parameters (namely the Poisson’s ratio).

The results from the models were verified against FE data.

The proposed model only accounts for an external normal load applied to the joint. Improvements can be made to the load by considering a torque loading. Also, the substrate is represented by a semi-infinite half-space when in reality both sides of the joint are often of the same thickness.

Questions still remain about the interaction between receding contacts, i.e. if the tightening sequence influences the contact behaviour of bolted joints. An investigation of this effect can be done by looking at the interaction between a pair of solutions from the proposed model.


The axisymmetric frictional receding contact of a layer pressed against a half-space by pressure outside a disk

The axisymmetric frictional receding contact of a layer pressed against a half-space by a point force

An idealised description of the frictional receding contact behaviour of a bolted joint

An analysis of axisymmetric receding contacts