Learning Forum

[ami2020]

I have what is essentially a cylindrical tube with two disk-shaped plates at the ends, supported at four points on the side of the cylinder (meant to represent an optical cavity). I am trying to measure the change in distance along the cylinder axis between the centers of the inner faces of the plates due to vibrations in each of the 3 directions of the system. In Harmonic Response, I tried applying a harmonic nodal displacement at the 4 support points and measuring the frequency response at the center of the plates over a range of frequencies. I also tried using Static Structural as a low-frequency limit, inserting a fixed support at the 4 support points and applying a gravity-like acceleration to the whole system.

[peteroznewman]

nI am interested in small structural deformations in optical systems. nIs there a way to measure just the relative displacement of the two points in the z-axis instead of their absolute displacement?nThe difference in the absolute displacements of the two points is the relative displacement.nOptical systems are sometimes connected to a frame using kinematic mounts. The benefit of a kinematic mount is that deformation in the frame does not induce deformation in the optical elements. There may be rigid body motion of the optical elements, but no stress. Four fixed points is not a kinematic mount. That means deformation in the frame (that you have not shown) can have an effect on the distance between the two points.n

[ami2020]

, nThank you very much for your answer. nTaking the difference of the two absolute displacements is what I am currently trying to do, but that doesn't seem to work well for the case where the harmonic displacement is in the same direction as the deformation I am trying to measure. If I shake the support in the longitudinal direction with an amplitude of, for instance, 1mm, I get displacements of 1mm at both the points of interest. Basically, the deformation of the cavity is completely hidden by its rigid motion, which is many orders of magnitude bigger.n

[peteroznewman]

nIt's possible to measure nanometers of difference under a rigid body motion of 1 mm.n

[ami2020]

I should also mention that the problem is not just that the results do not reflect the symmetry of the model, but also the mesh does not converge. In the picture below the mesh size is set at 1.5mm (the total length of the cylinder is 34cm), with refinements at the supports and at the ends, but I went down to 0.5mm and the results were still mesh dependent (and all over the place). If the mesh is the cause, I am not sure how to make it better.nRegarding the boundary conditions, it is true that, depending on the exact nature of the support, fixed boundary conditions are probably too restrictive. I would rather not add too much complexity to the support before I am at least able to solve this simpler problem, but, as an alternative, I tried fixing the top surface of the supports in the vertical direction only and leaving the body free in the horizontal directions, so that the cavity is simply supported, rather than fixed. However, in this case the simulation fails due to the model being insufficiently constrained, despite there being no horizontal forces.

[peteroznewman]

nCan you describe the optical system in more detail. Are the ends of the cylinder lenses or mirrors? What happens when the distance between the faces changes? Is it just the distance? What about tilt? Have you considered the effect static forces like gravity or thermal changes will have on the optical system? n

[ami2020]

The optical system consists of two mirrors at the ends of a rigid spacer forming a standing wave cavity resonator. The stability of the resonator depends on the stability of both the distance between the mirrors and their relative tilt. I am trying to compare different spacer geometries and optimize the shape and position of the supports in order to make both the change in length and tilt due to external vibrations as small as possible (although so far I only focused on the change in length). nSo far I have been trying to look at the effect of static/low-frequency forces by applying a gravity-like acceleration in each of the three directions in turn in Static Structural. I also included gravity in the Harmonic Response analysis by using the Pre-stress option.nThermal changes are a matter of concern, too, but I did not consider them here. They should be kept under control by using a material with very low coefficient of thermal expansion and a temperature-controlled environment.nn

[peteroznewman]

Array nThank you for those details. I read the Wikipedia entry for Optical cavity https://en.wikipedia.org/wiki/Optical_cavity and it has this gem: Flat mirrors are not often used because of the difficulty of aligning them to the needed precision. There is a lot more detail later on that page such as the mirrors must be aligned parallel within a few seconds of arc,  and Simple cavities are often aligned with an alignment laser—a well-collimated visible laser that can be directed along the axis of the cavity. Observation of the path of the beam and its reflections from various optical elements allows the elements' positions and tilts to be adjusted. More complex cavities may be aligned using devices such as electronic autocollimators and laser beam profilers.nAfter reading this, I wonder how the two flat mirrors are connected to the rigid tube. Are the two flat faces on the rigid tube able to be made parallel to a few seconds of arc? If so, what holds the mirror surface against this face? Excessive retaining forces can distort the mirror or the tube. nI can imagine an assembly where one mirror is fixed to the tube, while the other mirror is on a frame that has two axes of rotation to allow the tilt to be adjusted. In that way the tilt of one mirror can be adjusted while an alignment autocollimator or laser is measuring the tilt of the mirror while the alignment is adjusted.nAnother consideration is how the tube/mirror assembly connects to a support frame. A kinematic mount is preferred. What that means is that deformations in the support frame will not induce stress in the tube/mirror assembly. nHolding the tube fixed at four points is not a kinematic mount. Hold the tube at three points to have a kinematic mount, but not three fixed points, three points with a spherical joint. There are many ways to connect three points to ground, and we can talk more about that if you want.n

[ami2020]

After reading this, I wonder how the two flat mirrors are connected to the rigid tube. Are the two flat faces on the rigid tube able to be made parallel to a few seconds of arc? If so, what holds the mirror surface against this face? Excessive retaining forces can distort the mirror or the tube.nThe mirrors are going to be attached to the rigid tube by optical contact bonding. It's a process in which parts with conformal (and extremely smooth) surfaces brought into contact adhere to each other due to the formation of intermolecular bonds. I think this type of bonding should prevent excessive forces.nHolding the tube fixed at four points is not a kinematic mount. Hold the tube at three points to have a kinematic mount, but not three fixed points, three points with a spherical joint. There are many ways to connect three points to ground, and we can talk more about that if you want.nThank you very much for your suggestions, I looked into spherical joints and will try to implement it and I'll come back if I have questions. n

[peteroznewman]

One design of a spherical joint is to use a bipod arrangement. Three of them make a kinematic mount. Image from https://aip.scitation.org/doi/10.1063/1.4902151n