mechanische simulation an werkzeugmaschinen · ansys conference & 30. cadfem users‘ meeting...

ANSYS Conference & 30. CADFEM Users‘ Meeting 2012 www.usersmeeting.com

Mechanische Simulation an Werkzeugmaschinen


Content

• Stiffness Analysis of a milling machine

• Linear Dynamics: Modal and harmonic Analysis

• Guideways idealisation

• Weight influence on accuracy (as a function of position)

• Outlook: System simulation

09.11.2012 U. Bänninger 2


Stiffness Analysis of a milling machine

Goal: – Get the global stiffness matrix and

the influence coefficient matrix

– Get the coupling terms (off diagonal terms / crosstalk)

– Stress concentration regions (qualitative for better understanding)



Global stiffness matrix

The static structural analysis counts 3 steps : Each step corresponds to a load case. Each load case applies a unit force in one of the 3 directions of the global coordinate system. A contact point between tool and workpiece is defined (TCP). From the contact point, a remote force to a surface of “tool side” and an opposite remote force to a surface of “workpiece side” are applied.


tool side

workpiece side


Global stiffness matrix


Rigidity matrix

Influence coefficient matrix [m/N ] : (unknown)

Displacement vector [m] : (measured at the

remote point)

Force vector [N ] : (known)

Influence coefficient matrix ?

3 load cases :

fA

A

f

,

0

0

1

00

00

00

1

1

1

1

1

1

1

1

1

1

1

1

z

y

x

z

y

x

,

0

1

0

00

00

00

1

2

1

2

1

2

1

2

1

2

1

2

z

y

x

z

y

x

1

0

0

00

00

00

1

3

1

3

1

3

1

3

1

3

1

3

z

y

x

z

y

x

111

fA

1

3

1

2

1

1

1

3

1

2

1

1

1

3

1

2

1

1

1

zzz

yyy

xxx

A

(1) stands for workpiece

ANSYS Conference & 30. CADFEM Users‘ Meeting 2012 www.usersmeeting.com 09.11.2012 U. Bänninger 6

For any force applied to the machine-tool:

The total deformation of the machine-tool is:

The global influence coefficient matrix is given by:

The global stiffness matrix is given by

2

3

1

3

2

2

1

2

2

1

1

1

2

3

1

3

2

2

1

2

2

1

1

1

2

3

1

3

2

2

1

2

2

1

1

1

zzzzzz

yyyyyy

xxxxxx

totA

21 ff

21

tot

12112112211 )( fAAfAfAfAfAtot

)( 21 AAAtot

1 tottot AK

Kf


• An APDL-Snippet evaluate and printout the influence coefficient matrix and the global stiffness matrix:



Stiffness Analysis

• Example



Linear Dynamics: Modal

Find the first eigenfrequencies and eigenmodes of the machine tool.

Generally speaking, for a given energy, the higher the eigenfrequency, the lower the amplitude.

Goal is to:

– Identify the eigenmodes that might influence the machining process

– Find constructive modifications that will change these modes and / or increase the corresponding frequency.



Considerations about point masses In a modal analysis, the total weight of all bodies is important. Consequently, the weight of eliminated elements must be represented in the model.

Each body which does not contribute to the global stiffness is a candidate for a replacement by a point mass.

Each eliminated body should be replaced by a “point mass”. But this would take too long.

Thus, each body which is heavier than 5% of the body to which it is fixed will be replaced by a point mass. The others which are less than 5% will be regrouped in one “point mass” or added to an existing “point mass”.

This method will not be applied to the whole geometry but applied separately for each region (logically defined by yourself).

The mass of bodies which are not present in the original CAD file or which are not drawn in details should be estimated and added to the model as “point mass” => think about cooling medium and so on...

09.11.2012 U. Bänninger 10


Results in a modal analysis I

• Total deformations are useful to understand the mode shapes and to identify the eigenfrequencies which could cause problems during operation. But a harmonic analysis is necessary to determine which modes really influence the cutting process for a given excitation.

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23 Hz 48 Hz


Results in a modal analysis II

• Von-Mises stress distributions are useful to identify which areas are responsible for the deformation of the structure. (weak regions = stress concentration) The values given in the scale are normalized values but the distribution is correct.

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Flexible vs. Rigid Bodies

It could be interesting to consider all bodies as rigid. The modes obtained that way show how the bushings influence them :

The more the modal frequency and the mode shape are similar for the rigid and the flexible model, the more the mode is influenced by the bushings/machine elements.

09.11.2012 U. Bänninger 13

23 Hz

28 Hz

35 Hz

50 Hz

48 Hz

58 Hz

68 Hz

96 Hz

flexible behavior

rigid behavior

62 Hz

77 Hz


Linear Dynamics: Harmonic

Concept

The machine is excited over a frequency range by a given force. Amplitudes and phases are computed

Results accuracy depend greatly on the accuracy of the input force and on the damping used

Very useful to determine how much an eigenmode will influence the machining process and to get amplitudes between modes.

09.11.2012 U. Bänninger 14


Harmonic Analysis

• Example

09.11.2012 U. Bänninger 15


Idealisation of guides

Bearings, guideways , ball screws, “feet”

Kinematic connections like bearings or guideways are too complex to be modelled efficiently using finite element analysis. This would need a very large number of nodes and would end up with convergence issues. Thus, it is best practice to model them with idealized joints (bushing, discret springs).

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Example: Shaft bearings

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000000

000000

000000

00000

00000

00000

axial

radial

radial

K

K

K

K


Idealisation of guideways

Idealisation study at the ETH Zurich

• Was is the best way to idealise guideways with FEM?

09.11.2012 U. Bänninger 18


Idealisation of guideways

Comparison of FEM and EMA:

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Idealisation of guideways Comparison with measurements made during the university study.

This method has also been verified for several guideways suppliers. The university study

yielded results with very good agreement between measurements and simulation. The

results above were obtained with rails and carriages of the supplier “Schneeberger”.

09.11.2012 U. Bänninger 20

Mode Measurement [Hz] Simulation [Hz ] Delta abs(Delta)

1 326 314.53 3.52% 3.52%

2 432 425.78 1.44% 1.44%

3 461 460.76 0.05% 0.05%

4 464 509.65 -9.84% 9.84%

5 566 562.79 0.57% 0.57% 6 600 610.8 -1.80% 1.80%

7 775 776.69 -0.22% 0.22%

8 803 833.74 -3.83% 3.83%

9 927 956.68 -3.20% 3.20%

Mean value -1.48% 2.72%


Bushing

A bushing has 6 degrees of freedom, 3 translations and 3 rotations, all of which can be characterized by their translational and rotational stiffness, respectively.

The 3 translational DOFs and the 3 rotations DOFs are : Ux, Uy, Uz, and φ, Θ, ψ. The forces developed in the bushing are expressed as:

{F} are the forces, {T} are the torques, and [K] is the 6x6 stiffness matrix. Off diagonal terms in the matrix are coupling terms between the DOFs.

For each DOF also damping can be defined.

09.11.2012 U. Bänninger 21

z

y

x

U

U

U

KT

F


Bushing

• Definition of a Bushing:

• Disadvantage of bushing elements: Sparse Direct Solver has to be used (Lagrange multiplier exists)

09.11.2012 U. Bänninger 22


Weight Influence on accuracy

What is the meaning of this analysis?

The machine is set up at axis position (0,0,0). Positioning accuracy is absolute here.

Let’s say, the axes are moved to position (1000,1000,1000). Due to the deformation of the machine bed due to gravity, the positioning precision will not be absolute. The part will deflect and this will normally not be compensated by the command control.

09.11.2012 U. Bänninger 23


Parametric

• Position of the axis as a parameter

• Definition of bushing element for the guideway remains consistant

• Bidirectional and associative CAD Interface needed

09.11.2012 U. Bänninger 24



Variation of the deformation in z at the contact point due to gravity

09.11.2012 U. Bänninger 25

z

~3 µm

Position error < 4 µm



• Example

09.11.2012 U. Bänninger 26


Outlook: System Simulation

From component level to system level

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Model Extraction

Physic solvers

Me

ch

an

ica

l Component level

System level

Coupled physics + Control system

Where most

ANSYS users

today are involved


System Simulation The entire system is modelled into ANSYS

09.11.2012 U. Bänninger 28

Actuator

Velocity sensor

Control

Position sensor

Maschine bed

Axis

Motor Spindle

Target position f(t)


System Simulation The harmonic response of the machine-tool will be influenced by the command control. Resonances due to the command control are visible.

09.11.2012 U. Bänninger 29

Kindly provided by Gebr. Heller Maschinenfabrik GmbH


System Simulation

Possible Scenario: response to a force or perturbation.

09.11.2012 U. Bänninger 30

Control

Maschine bed

Axis

Input curve

F

Displacement

as an output


Mechatronic system with ANSYS Simplorer Study the dynamic interaction between

09.11.2012 U. Bänninger 31

2) Machine body

1) Control unit

3) Piece to machine


Mechatronic system with ANSYS Simplorer

09.11.2012 U. Bänninger 32

PID

E-motor /

Voltage

source

Rotational velocity

domain Translational domain


Mechatronic system with ANSYS Simplorer

Results:

09.11.2012 U. Bänninger 33

The force now reaches the

requested 10N

mechanische simulation an werkzeugmaschinen · ansys conference & 30. cadfem users‘ meeting...

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