Tolerance analysis of a radio telescope mounting
Sector: Machinery and plant engineeringSpecialist field: Structural mechanicsESO (European Southern Observatory) has commissioned CADFEM to verify the flatness tolerances for mounting the ALMA radio telescope facility in Chile in order to reduce the cost of mounting the 200+ antennas.
Summary
Task
There are high flatness tolerances in all contact areas between the mounting parts. Given the number of foundations to be built (more than 200 antenna stations), these tolerances should be relaxed in order to reduce manufacturing costs.
Solution
Nonlinear contact analyses with very a high resolution of contact stiffness (penetration) were performed.
Customer benefits
The influence of the manufacturing tolerance on the stiffness of the antenna foundation is negligible for the manufacturing tolerances analyzed.
Project Details
Task
The Atacama Large Millimeter Array (ALMA) in the Atacama Desert in northern Chile is an astronomical interferometer comprised of 66 individual radio telescopes ("antennas") of 12 m and 7 m diameter. The base of the antennas is embedded in concrete. The antenna itself is fixed to this base by struts consisting of a flat lower part and a semi-cylindrical upper part. The feet of the antenna have a recess to rest on the ribs. The assembly is held together by M52 bolts. There are high flatness tolerances in all contact areas between the mounting parts. Given the number of foundations to be built (more than 200 antenna stations), these tolerances should be relaxed in order to reduce manufacturing costs. Therefore, the influence of the flatness tolerance on the stiffness of the antenna foundation has to be analyzed. In order to simulate manufacturing-related inaccuracies, convex and concave deformations of these contact surfaces are generated by shifting the x-coordinate of the surface nodes according to a sinusoidal function with respect to the z-coordinate.
Customer Benefit
The deformation of the structure is dominated by the applied bolt prestress. The stiffness during this first loading step is different for all three models. However, once the contact areas are closed, the stiffness of the structure is the same for all three model variants. Therefore, the influence of the manufacturing tolerance on the stiffness of the antenna foundation is negligible for the manufacturing tolerances analyzed.
Solution
Nonlinear contact analyses with very high resolution of the contact stiffness (penetration) were performed. The penetration depth of the contact had to be an order of magnitude less than the flatness tolerance of 20 µm (typical edge length: about 300 mm). Bolt loads and antenna mass were applied to the model. A linear elastic material model with small deformations was assumed for this analysis. Three different solution models had to be compared:
- the unmodified geometry without manufacturing tolerances,
- the model with concave modifications of the contact surfaces
- and the model with convex modifications of the contact surfaces.
Images: © ESO (European Southern Observatory)