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Modes of a rotating disc - Error in solver

Dear Comsol Community/Team,

I am currently beginning to study the rotational effects on the vibrational modes of a spinning wheel. I started looking at a simpler structure like a disc that is spinning with constant angular velocity, at a rate due to the translational speed/radius, to familarize myself with effects of the centrifugal force (stiffening/softening) as well as the coriolis force.

I took your rotatinal_blade.mph from the Application library that makes use of 'Rotating Frame' to adapt my model. However, I often get the Error: "Failed to find a solution. Maximum number of Newton iterations reached. There was an error message from the linear solver. The relative residual (0.0065) is greater than the relative tolerance. Returned solution is not converged. Not all parameter steps returned." The convergence plot of the nonlinear solver is added below. I was figuring out I can avoid the error if I either turn off the centrifugal force, or if I model an annulus with a hole at the disc centre. So far, an annulus with fixed boundary at the hole is sufficient as a starting point and since I am excluding the axle. But in a later study, I might want to include an axle and hence it would be important to have a model that works without the hole.

In the accompanying PDF file of the rotating_blade.mph model I found the statement: "Note that the spin-softening affects not only the modal solution but also adds a positive feedback to the stationary nonlinear solution. If the structure has a natural mode for which spin-softening dominates over the stress-stiffening effect, the natural frequency of this mode becomes zero for some rotational frequency. This means that the structure looses all stiffness, and that no stable solution exists for higher angular velocities. So if the nonlinear solver does not converge for a very fast rotation, it should come as no surprise." I could, however, not clearly relate this to my model, since the convergence error occurs even if I turn off the spin-softening or use very low rotational speed (1 km/h), but the solutions does converge at any speed if I put in the hole in the disc centre.

Is there any reason why this is occuring or is it a know problem I am not aware of? I added my model in the appendix and hope, from it, it might become clear what I am doing wrong. I am also happy to provide more information about the model in a second post below this.

Any help is very much appreciated and thank you very much for considering my request.

With the best wishes,

Christopher Knuth

2 Replies Last Post Feb 25, 2021, 7:56 AM EST

Posted: 3 months ago
Updated: 3 months ago

Since there are no constraints, the stiffness matrix for the stationary study step will be singular. You must constrain the disk at the center.

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Henrik Sönnerlind
COMSOL

Posted: 2 months ago

Dear Henrik,

thank you very much for your quick response, makes very much sense. I did not pay much attention on the stationary study, when thinking about the problem. I now added a constraint at the disc center in the stationary study only, not in the Eigenfrequency study. Works perfectly fine now, thanks for the help.

With best wishes,

Christopher Knuth