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# Multibody Dynamics Simulation - Modelling the Imperfect Perfectly

##### Patrick Morelle - September 14th 2023

Modeling a pair of gears does not seem too complicated a task. Coupling two angles of rotations, describing the geometry of the gears, really, nothing too complicated. It could all be described as a routine job for any and every MBD software in the world.

Now, let us ask ourselves: What could be the role of a “simple” MBD model of a gearbox?

Clearly, the first purpose of such a model is to reproduce the kinematics of such an assembly of gears, making sure the speed of rotation of the shafts is what it is supposed to be, which involves the size and geometry of all the gears, plus the dimensions and positions of the shafts, the geometry of the casings, and so on, which constitute the gearbox.

However, this simple model is very quickly replaced by a more complex one, where the question is to calculate the loads going through the different parts of the gearbox, during the various scenarios that can occur when the user is manipulating the gearstick.

But this more ambitious goal is just a first step. Because as soon as the “perfect” gearbox is designed and its detailed behavior assessed, an interesting question presents itself; what about the “real” “imperfect” gearbox?

Indeed, compared to this ideal perfect design, which is never achieved in reality, a real gearbox measured in real life may exhibit very different and much more complex behavior.

Gear profiles, for example, are the first source of imperfections. Manufacturing tolerances are such that the “perfect” rotation of a pair of gears may be more or less “perturbed” by those imperfections and the way the gears “roll” on top of each other through contact– which indeed is never a purely “rigid-rigid” one, but is, in contrast, influenced by gear deformations.

As a response to this problem, very subtle gear corrections can be imagined by experts to minimize those local perturbations and “smoothen” the motion of those rather complex geometrical entities.

Now comes the real question: Can an MBD model capture such sensitive behavior?

But even before answering this question, we have to realize that it is not only the gear profiles that may not be perfectly manufactured. Other imperfections may appear, for example, shaft misalignments.

Why such misalignments? Manufacturing tolerances may be involved again, but casing deformations are probably a much likelier source of those misalignments.

So, is the solution to move the shaft geometry in a position reflecting some deformed geometry of the casings? … it’s not so simple. Those deformations are, in themselves, a function of the loads running through the different parts of the gearbox, and those loads are, of course, not constant. They vary as a function of time or, we could say, as a function of the different manipulations of the gear stick resulting from the driver’s behavior.

What is apparent here is the need to model a gearbox, not as an assembly of rigid shafts, gears, casings, etc., but, in contrast, to introduce the proper flexible components into the model. Alternatively, or in addition, there is a case to be made for introducing, on top of the behavior of the perfect components, some specific effects in order to monitor the influence of different types of imperfections on the global and local behavior of the gearbox.

Modern MBD software offers many capabilities to do so, allowing users to move from classical kinematic/dynamic simulations of a gearbox to answering “what if” questions and dealing with sensitivity analysis of the gearbox design with respect to real-life imperfections.

If you are interested in the topic, the NAFEMS e-learning course “Next Steps with Multibody Dynamics” may be a source of essential information, discussing this topic in detail as well as many others related to modern trends and tendencies of the MBD discipline. You can also check out the upcoming NAFEMS Multibody Dynamics Conference in Munch, Germany, in November 2023.

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