## General Mechanical

Topics relate to Mechanical Enterprise, Motion, Additive Print and more

#### How to understand y axis under cylindrical coordinate system ？

• biao.zhou
Subscriber

I know that in ANSYS, if I select the current coordinate system as the cylindrical coordinate system (csys,1), then x represents r, y represents r*Δθ, which is the distance along the circumference, and z is consistent with the Cartesian coordinate system. However, when I process my modal shape results in the post-processor (/post1), I still encounter difficulties in understanding.

I tried to perform a modal analysis on a compressor's bladed disk and extract its mode shapes. The modal analysis is based on a single-sector model with cyclic symmetry settings.

As shown in the figure below, when I predefine the global coordinate system as the global cylindrical coordinate system (csys,1) and specify the result coordinate system in /post1 to also use the solution coordinate system (rsys,solu), I extract the modal shape data of a single sector. The value of y (which is rθ) is very large. When I divide y by x to obtain the θ value in the cylindrical coordinate system, it still exceeds the range of (-π,π), which confuses me.

When I extract the mode shapes of the entire disk, the value of y is still very large, indicating that the error is not caused by extracting the mode shapes of a single sector.

I would like to know what such a large y value represents, whether the θ it reflects is truly usable, or if I need to do some processing to make it usable. (Please note that I used the PRNSOL command to display the mode shapes, and GPT-4 told me that the mode shapes extracted using this command have not been scaled, i.e., they are the original mode shape data.)

• Chandra Sekaran
Ansys Employee

I know that in ANSYS, if I select the current coordinate system as the cylindrical coordinate system (csys,1), then x represents r, y represents r*Δθ, which is the distance along the circumference, and z is consistent with the Cartesian coordinate system.

In a cylindrical coordinate system the X represents radius, Y represents angle in degrees (not distance), and Z represents axial location.

• biao.zhou
Subscriber

You believe that the Y in the cylindrical coordinate system does not represent the circumferential displacement but the angle. However, I found this statement in the ANSYS help documentation, which states that when specifying the result coordinate system as a cylindrical coordinate system using RSYS,1, UY represents the tangential displacement.

• mjmiddle
Ansys Employee

Using cylindrical coordinate systems can be confusing, or any CS that has an angular axis, for that matter. The main reason is that all elements and nodes in APDL have Cartesian CS. So while you can specify preprocessing values (CSYS) using a cylindrical CS, you can never really retrieve results (RSYS) in a cylindrical coordinate system. In either case it is using pseudo cylindrical CS. It rotates element or nodal coordinate systems (Cartesian CSs) to be aligned with local cylindrical directions at every element centroid or node. In the case or preprocessing (loads/constraints), those directions may only agree at the start of the analysis if any angular loading or deformation occurs throughout the analysis. Refer to the Ansys help section (https://ansyshelp.ansys.com/): //Mechanical APDL// Basic Analysis Guide // 7. The General Postprocessor (POST1) // 7.3. Additional POST1 Postprocessing

Radial or Z displacements alone will not cause a problem with results in cylindrical CS and are easy to interpret. When angular displacements occur (by loading or deformation), then both cylindrical X and Y will be hard to interpret and my not be very useful to report in cylindrical CS.

For reporting results in a true cylindrical CS, I find it best to use a a Cartesian RSYS where x,y coordinates are in the plane of r,theta. Then convert for each node. Assuming UPCOORD was not done:

UR = sqrt((NX(Id)+UX(Id))**2 + (NY(Id)+UY(Id))**2) – sqrt(NX(Id)**2 + NY(Id)**2)

Use atan2(y,x) to get cylindrical angle (same as tan(y/x), except it accounts for angle quadrants due to signs of x and y).

UTheta = atan2(NY(Id)+UY(Id), NX(Id)+UX(Id)) - atan2(NY(Id), NX(Id))

• biao.zhou
Subscriber

In my analysis, I specified the global cylindrical coordinate system as my solution coordinate system and nodal coordinate system from the beginning. In post-processing, I also used this coordinate system. Even so, are the results I extracted still not the real global cylindrical coordinate system?

I am very interested in your idea that the cylindrical coordinate system specified by RSYS is actually the local cylindrical coordinate system of each node. Can you provide the source of this statement? I didn't find this statement in the help documentation.

You finally shared how to obtain data in the real cylindrical coordinate system. You think I should extract data in the Cartesian coordinate system through RSYS,1 and finally convert it through formulas. I will give it a try.

If you can tell me more about the inherent problems of the cylindrical coordinate system in ANSYS and how to extract data, it would be of great help to me.