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Cylindrical Coordinate Systems

10/30/2008 7:47 AM

I hope someone can refresh my memory here.

I am working on some FEA and am using a cylindrical coordinate system for loading and constraining. I know how to apply to loads and constraints using a standard x,y,z system but I am struggling with the cylindrical system as its been over 5 years since using one.

I have attached a diagram (I hope!) of a basic cylinder with the cylindrical coordinate system at the top.

Translation in the Z-axis is an obvious one and the rotation about the Z-axis is the cylinder revolving. I have a feeling that radial (R) translation is simply that the cylinder is moving away from its original axis (ie in the X or Z direction of the standard WCS in the diagram).

Can anyone explain to me the translation in Theta, rotation in Theta and rotation in R please? Simple diagrams would be great as I have read explanations on the internet but at times its like trying to learn a foreign language. If I am incorrect with any of my assumptions above can you also please point me in the right direction.

Cheers everyone

Kev B

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#1

Re: Cylindrical Coordinate Systems

10/30/2008 10:04 AM

coordinates transform usually use normal system. if you use polar coodinates implement translation, its very complex. you have to know rotation angle and radia scale, rotation is simple, R= constant, you can only set thita. the total theta= origianl theta + new angle. but in nornal system its simple, like we all know X=x+x1; Y=y+y1, then rotatio.

We can use polar (cylindrical) coordiante calculate gyrator (rigid body of revolution).

why dont you use normal system transform at first and then transform to cylindrical system to calculate object coordinates?

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#2
In reply to #1

Re: Cylindrical Coordinate Systems

10/30/2008 10:18 AM

Mainly because he analyses bolting and in cartesian coordinates it is difficult to introduce a torque load.

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#3

Re: Cylindrical Coordinate Systems

10/30/2008 10:26 AM

Nick Name is right.

I am wanting to put a rotational force on one of our products (which is more complex than a cylinder but obviously I cant post it up here).

Say for example I wanted to apply a rotational force to a nut and restricted it from moving by constraining another face. This is the type of application I am trying to analyse. Therefore I am using a cylindrical coordinate system.

The problem arises when I have to decide whether or not to make a certain condition 'free' or 'fixed'. I am not sure what each condition is.

Kev B

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#4
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Re: Cylindrical Coordinate Systems

10/30/2008 1:23 PM

Think what happens if you introduce the load and what would happen if you block a movement. All models for simulations have to be correct from a physics point of view.

A nut must have a rotational freedom and as well an axial one which will generate the deformation of the contact area and due to it the resistant force and following friction torque.

Better you already used my PM do it once more and I can help you since it depends of the FEA programme you use.

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#5

Re: Cylindrical Coordinate Systems

10/30/2008 7:42 PM

A point P can be located by cylindrical coordinates (r, Θ, z) as well as rectangular coordinates (x, y, z). The transformation between these coordinates is

x = r cosΘ

y = r sinΘ

z = z

or

r = (x2 + y2) 1/2

Θ = tan-1(y/x)

z = z

The z axis is the same for each system of coordinates.

Do you still need a diagram?

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#6
In reply to #5

Re: Cylindrical Coordinate Systems

10/30/2008 10:12 PM

the formula you list is two coordiantes systems exchange. Look at the inverse transform, you will see how complex for polar coordinates to translation. that why I suggest he use cardesian coordinates transform at first, [from his wcs translation to cs2 point and rotate around x anxial +90 then change to polar coordiantes ( cylindric) to calucate body of revoluton. all these transform are simple under aid of computer programm. There are force system equatin for him to deal with the object(belt, tangent direction and normal force applied to the wheel).a virtue work principle may be used for FEA. nick name can obviously help him with this fea. this is out of my depth.

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#7
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Re: Cylindrical Coordinate Systems

10/31/2008 5:46 AM

Thanks for that - I see how they relate to each other.

I am using Pro/E with Pro/Mechanica.

When constraining the model using a cylindrical coordinate system I need to fix it transationally and rotationally in the directions of the cylindrical system.

How does something translate in Θ and rotate in Θ?? Would this not be the same movement?

Obviously 'r' is the movement away from the central axis but how would you rotate in 'r'?

Sorry for all the questions.

Kind Regards

Kev Brown

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#8
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Re: Cylindrical Coordinate Systems

10/31/2008 12:15 PM

I am more than a little rusty on this, so please bear with me. As I recall, working on a structural frame program in Cartesian coordinates, there was a global system and a local system. For any given member, the equilibrium equations could easily be written in the local system. Before it could be assembled into a global stiffness factor, the coordinates had to be transformed from the local to the global system.

If the local origin is different than the global origin, a transformation must be made to express the member position in terms of global coordinates.

If the orientation of the local member is not the same as the global orientation, a transformation involving pure rotation must be made to express the member position in terms of global coordinates.

In general, neither the member origin nor its orientation will be the same as the chosen global reference system, so a transformation of coordinates involving both translation and rotation is necessary in order to create a global stiffness matrix.

A transformation is simply a way of expressing local coordinates in terms of global coordinates. If the origin and orientation are the same for both systems, no transformation is necessary.

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#9
In reply to #7

Re: Cylindrical Coordinate Systems

10/31/2008 2:42 PM

Pretend you have a mounting lug on the OD. A tangential force through the lug will try to rotate the lug around the Z-axis through an angle theta. A radial force will try to translate the lug radially.

Similarly, a nut on one end will try to twist the cylinder, producing a rotation around the Z-axis, but, depending on the other constraints/loads, may not produce a radial movement.

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#10

Re: Cylindrical Coordinate Systems

10/31/2008 9:36 PM

I have no idea what your model looks like. Assuming you are dealing with only prismatic members, you may use any system of coordinates you wish. My preference would be the Cartesian system, but other systems may be employed if there is some benefit in so doing.

Each node in the structure has six degrees of freedom, three translational and three rotational. Using Cartesian coordinates, the translational degrees are usually called x, y and z. The rotational degrees of freedom could be called Θx, Θy and Θz.

In the Cartesian coordinate system, the right hand rule (RHR) is usually employed, although it is totally arbitrary and a left hand rule could be used equally well (for all you southpaws). With the RHR, the fingers point in the direction of rotation and the thumb points in the direction of the next axis. The X axis rotates into the Y axis such that the thumb points in the positive direction of the Z axis. Similarly for Y-Z-X and Z-X-Y.

An applied torque at a node is a vector quantity, often designated by an arrow with a double head. If a member is parallel to the Z axis and you wish to indicate a positive torque at the right end, point your thumb in the direction of the Z axis and let your fingers tell you which way the torque is turning.

In the case of a cylindrical coordinate system, the situation is similar. An applied torque or moment in the Z direction signifies a moment about the Z axis. An applied moment in the R direction, using the RHR is a moment about the radius from the Z axis to the point P. An applied moment in the Θ direction is not quite so intuitive but, given the meaning of the other two, it has to be a vector in the positive sense of the angle Θ at right angles to R (or parallel to the tangent of the circle).

After solving the stiffness matrix for the applied loading, rotations will follow the same right hand rules as applied torques. Moments will be in radians if all other dimensions are kept consistent.

From the standpoint of simplicity, unless someone can show me a different point of view, I would have to agree with cnpower. The Cartesian coordinate system is the easiest and most logical system to use.

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#11
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Re: Cylindrical Coordinate Systems

11/01/2008 6:29 AM

Dear Bruce,

Moments are in Nm or foot-pounds never in "radians". The radian is an angle unit. Sorry but engineering is a precise profession.

From an other point of view the constrains are in the case of Kev contact constrains. And for a comment made by some one before a radial displacement can occur even if it no radial force. You have to look not any more as macro mechanic but as an effect ot the Poisson transverse deformation and a nut which is stressed axially will increase its transversal dimensions either due to the radial forces generated by the threads flancs angle or only due the transverse deformations.

It is a bit more complex to build a FEA model.

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#12
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Re: Cylindrical Coordinate Systems

11/01/2008 11:10 AM

Moments are in Nm or foot-pounds never in "radians". The radian is an angle unit. Sorry but engineering is a precise profession.

My error! I meant to say that rotations are in radians if all other inputs are in consistent units.

Your other comment is not clear to me.

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#13
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Re: Cylindrical Coordinate Systems

11/01/2008 1:05 PM

Let us assume you have two bodies in contact which ever reference system is used.

If a compressive force appears the bodies will have the trend to shorten and increase their transverse dimensions. this transverse effect is governed by Poisson's coefficient which in most cases is around 0.3. Exception being rubber with a value near to 0.5.

On the contact surface the elements of the 2 bodies will move in transverse direction (for a cylindrical reference in radial direction) although the load is only axial. To allow this radial sliding the displacement in radial direction has to stay free. If a constrain of this movement is introduced the stress level will grow up since the material cannot deform in a free way.Of course in advanced programmes friction can also be considered.

In a nut the axial force generates a radial pressure ,variable along the threads which has as well an effect in "opening" the nut. In some designs this effect is used to make the thread load more uniform.

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#14
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Re: Cylindrical Coordinate Systems

11/01/2008 7:22 PM

Hello nick name,

Well I agree that compression in an axial direction results in expansion in a radial direction, but I would assume the Pro/Mechanica program could take that into account for each finite element if it was considered important. I assume that Poisson's Ratio is one of the properties entered into the program for the material of the structure under study as well as modulus of elasticity, shear modulus and so on.

I do not know the shape of the finite elements Kev is using, so it is difficult to comment on details of the analysis.

What I thought Kev was asking is the meaning of translations and rotations, particularly with respect to R and Θ when using a cylindrical coordinate system. That is what I was attempting to address.

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#15
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Re: Cylindrical Coordinate Systems

11/02/2008 3:07 AM

The programme for FEA (which ever kind) takes into consideration the effect but if the constrains are not correct the programme will respect them and will give wrong results. It has nothing to do with the kind of element used by the programme.

I wanted to stress the importance of physically correct constrains since the question was (look at the by Kev joined screen) connected with the kind of constrains.

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#16
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Re: Cylindrical Coordinate Systems

11/02/2008 11:43 AM

Hellow nick name,

I found the following quote in Chapter 1 of the Pro/Mechanica Tutorial.

FEA User Beware!

Users of this (or any other FEA) software should be cautioned that, as in other areas of computer applications, the GIGO ("Garbage In = Garbage Out") principle applies. Users can easily be misled into blind acceptance of the answers produced by the programs. Do not confuse pretty graphs and pictures with correct modeling practice and accurate results.

A skilled practitioner of FEA must have a considerable amount of knowledge and experience. The current state of sophistication of CAD and FEA software may lead non-wary users to dangerous and/or disastrous conclusions. Users might take note of the fine print that accompanies all FEA software licenses, which usually contains some text along these lines: "The supplier of the software will take no responsibility for the results obtained . . ." and so on. Clearly, the onus is on the user to bear the burden of responsibility for any conclusions that might be reached from the FEA.

Having never used this program and perhaps having a misconception as to what is meant by "constraints" and how to apply them, I think it best for me to leave this where it is.

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#17
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Re: Cylindrical Coordinate Systems

11/02/2008 5:28 PM

Hi,

As for all simulations without a good knowledge and a lot of experience there is a high risk especially if the user "believes" in the results even if qualitatively they seem wrong. i met such situations when young engineers learned perfectly the programmes (FEA especially) and were surprised when after building the protos the results were soooo different from their computed ones. I practice FEA since more than 20 years and I came to the result that the biggest error is to believe that the programme is "intelligent". Unfortunately many do it.

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