CAEFatigue: Calculating the minimum clearance between two components under load

What is The Minimum Clearance Between Two Components Under Load?

It’s an easy enough question to answer if the load is static, a little harder for a transient, but when the loading is in the frequency domain or even defined as a PSD it’s a much harder thing to calculate.

Why? Well, let’s look at an example.

Imagine you have two circuit boards (blue and red) installed in a housing (cyan).

There is an electromagnetic requirement that they be kept a certain distance apart so that sensitive circuitry on one is not interfered with by the magnetic field around power electronics on the other.

But is that maintained when the boards are subject to a random loading spectrum such as seen during launch to orbit?

If we do some rough calculations and add a big factor of safety we separate the boards more than is probably needed, making the housing larger and increasing the mass. And putting needless mass into space is expensive.

How to Calculate Minimum Clearances

Looking at the two boards situation. If their responses to excitation are in phase across the spectrum then the clearance is a simple calculation from the displacement and original spacing.

If the boards always oscillate in antiphase it’s a worse case, but still comparatively easy to calculate.

These scenarios are possible but extremely unlikely. In practice the boards will have very different modal behaviour and the phase angle between their responses at different frequencies of excitation will be different across the range of excitation.

Based on the phase angle for each response you can do a small calculation to work out what the worst case phase angle is and what the clearance is.

But you have potentially hundreds of frequency steps to examine, and it’s not always the simple first bending mode you are looking at, at higher frequencies the modes are more complex so you need to consider the clearance across the boards, or at least across the area where the power electronics are located. These values then need combining with the PSD input to arrive at a value for RMS minimum clearance for the random loading environment. It’s a lot of crunching of numbers, which is why the tendency is to work out the worst case value.

What does CAEFatigue Bring To The Table?

Luckily CAEFatigue has a tool to do this for us. CAEFatigue was developed originally to a predict fatigue life for structures under random loading. It’s used in a number of defence, aero and auto companies where processing rainflow cycle counting for a time history of load is computationally inefficient, but processing the loading to a PSD and predicting life from that can be done in a few short hours or minutes.

With that computational structure in place it was relatively easy to add a module to perform random response too. This module has an option that was developed for an exhaust manufacturer to predict the probability of collision between their exhaust and the car underbody. We can use this capability to predict the minimum clearance between our circuit boards.

How Does The Analysis Process Work?

CAEFatigue needs the input file (Nastran, Marc, Abaqus, LS-Dyna or Ansys) plus the results from a unit frequency response analysis in the same code. It has a process-flow style interface that leads us through setting up our simulation.

We work through the building blocks populating the necessary inputs until we get to the ‘Run’ option, from which the solver is launched and the results are displayed in the lower set of blocks.

Our simplest option for clearance is to look at the minimum distance between two points.

This solve takes a couple of seconds to run, so we could interactively explore across the board to find the worst case. This plot shows the minimum clearance between the two nodes is 3.26mm, using 5xRMS for the maximum displacement. A zero or negative value would indicate a collision.

If we are looking at an area rather than a pair of nodes the algorithm optimises the solution by throwing away detected pairs that have no chance of a collision (since it was developed as a collision detection process). This means we wouldn’t get a full picture of the clearance conditions, but we can cheat that with a workaround.

The methodology is as follows:

1. Take the area we wish to study from one of the boards.
2. Create a set of nodes offset from this towards the other board. The distance used is such that any movement nearer the other board that would violate the clearance requirements is manifest as a collision between these nodes and the other board.

    

   These additional stand-off nodes have no mass and do not affect the stiffness of the component so the modal solution remains unchanged.
3. We can now run our RMS calculation between two lists of nodes rather than a simple pair, in this case the nodes on our artificial stand-offs and the nodes on the other board.
4. We get results for each node in terms of the minimum clearance seen and to which node.
5. These results are also available in csv spreadsheet form to allow more rapid identification of the worst case.

CAEFatigue is a very powerful tool set with capabilities, such as this example, beyond simply calculating the lifespan of a component. If you are interested in this specific solution, or have other fatigue needs and want to know if we can help, please get in touch.