Berechnung von Werkzeugmaschinen 3 Beispiele elements available into ANSYS Workbench ... point, a...

Berechnung von Werkzeugmaschinen

3 Beispiele

Roberto Rossetti, CADFEM (Suisse) AG

grinding machine

milling machine

grinding machine

Simulation of 3 machine tool geometries

Hypothesis :

- Electric motors and their control loop are considered as infinitely rigid (the

equivalent stiffness values of the electric motors control are not considered in this

exercise)

- Contact surfaces between bodies are perfectly bonded (the bolts are stiff

enough to hold the parts together)

- The stiffness values for bearings, guideways, harmonic drives and ball screws

given by the suppliers are correct

- The geometrically simplified details have a negligible influence on the results

- As both displacements and rotations are small, a linear FEA is adequate

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)

Grinding machine 1 - Stiffness analysis

Shaft_A_axis

Z_axis

X_axis

Fixed and mobile

ballscrew support z

DesignModeler is very practical to perform such tasks

Simplification of the geometry

2 faces2 faces

5 faces

3 faces

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).

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. These are the so called

crosstalk terms.

z

y

x

U

U

U

KT

F

BUSHING

Bushing example : bearings

000000

000000

000000

00000

00000

00000

axial

radial

radial

K

K

K

K

y

z x

y

z x

Know how

Idealisation study at the ETHZ

Was is the best way to idealise guideways with FEM?

Specific elements available into ANSYS Workbench

Very good correlation between measurement and simulation

- 7 / 38-

Stiffness analysis

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%

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.

Stiffness analysis - load case

y

xz

tool side

workpiece side

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

,

0

0

1

00

00

00

2

1

2

1

2

1

2

1

2

1

2

1

z

y

x

z

y

x

,

0

1

0

00

00

00

2

2

2

2

2

2

2

2

2

2

2

2

z

y

x

z

y

x

1

0

0

00

00

00

2

3

2

3

2

3

2

3

2

3

2

3

z

y

x

z

y

x

222 fA

2

3

2

2

2

1

2

3

2

2

2

1

2

3

2

2

2

1

2

zzz

yyy

xxx

A

y

xz

(1)

(2)

y

xz

(1) stands for workpiece

(2) stands for tool

Results – rigidity matrix, influence coefficient

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


matrig_param.txt :

\prep7

*dim, resultdisp1, array, 3, 3

*dim, resultdisp2, array, 3, 3

!read results step 1

set,1

*get,resultdisp1(1,1),node,node1,u,x

*get,resultdisp1(2,1),node,node1,u,y

*get,resultdisp1(3,1),node,node1,u,z





set,2








set,3







a=sign(1,resultdisp1(1,1))*(resultdisp1(1,1)-resultdisp2(1,1))

b=sign(1,resultdisp1(2,2))*(resultdisp1(1,2)-resultdisp2(1,2))

c=sign(1,resultdisp1(3,3))*(resultdisp1(1,3)-resultdisp2(1,3))

d=sign(1,resultdisp1(1,1))*(resultdisp1(2,1)-resultdisp2(2,1))

e=sign(1,resultdisp1(2,2))*(resultdisp1(2,2)-resultdisp2(2,2))

f=sign(1,resultdisp1(3,3))*(resultdisp1(2,3)-resultdisp2(2,3))

g=sign(1,resultdisp1(1,1))*(resultdisp1(3,1)-resultdisp2(3,1))

h=sign(1,resultdisp1(2,2))*(resultdisp1(3,2)-resultdisp2(3,2))

i=sign(1,resultdisp1(3,3))*(resultdisp1(3,3)-resultdisp2(3,3))

a1=sign(1,resultdisp1(1,1))*resultdisp1(1,1)

b1=sign(1,resultdisp1(2,2))*resultdisp1(1,2)

c1=sign(1,resultdisp1(3,3))*resultdisp1(1,3)

d1=sign(1,resultdisp1(1,1))*resultdisp1(2,1)

e1=sign(1,resultdisp1(2,2))*resultdisp1(2,2)

f1=sign(1,resultdisp1(3,3))*resultdisp1(2,3)

g1=sign(1,resultdisp1(1,1))*resultdisp1(3,1)

h1=sign(1,resultdisp1(2,2))*resultdisp1(3,2)

i1=sign(1,resultdisp1(3,3))*resultdisp1(3,3)

a2=-sign(1,resultdisp1(1,1))*resultdisp2(1,1)

b2=-sign(1,resultdisp1(2,2))*resultdisp2(1,2)

c2=-sign(1,resultdisp1(3,3))*resultdisp2(1,3)

d2=-sign(1,resultdisp1(1,1))*resultdisp2(2,1)

e2=-sign(1,resultdisp1(2,2))*resultdisp2(2,2)

f2=-sign(1,resultdisp1(3,3))*resultdisp2(2,3)

g2=-sign(1,resultdisp1(1,1))*resultdisp2(3,1)

h2=-sign(1,resultdisp1(2,2))*resultdisp2(3,2)

i2=-sign(1,resultdisp1(3,3))*resultdisp2(3,3)

my_dispA_1=a*1000

my_dispA_2=b*1000

...


- 12 / 38-

T


Concept

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.

- 13 / 38-

Modal analysis

Steps

Similar to a static analysis

Define point masses replacing non-idealised parts

The liaison to the ground is very important

23 Hz

28.4 Hz

35.3 Hz

50.7 Hz

48.1 Hz

58.1 Hz

62.3 Hz

77.8 Hz

68.5 Hz

97.6 Hz

flexible behavior

rigid behavior

Modal analysis – flexible vs. Rigid bodies

Variation of the influence coefficient matrix

The plates (1) and (2) are kept in the

model. By doing so, the top surfaces of

all feet of both plates remain in the

same plane. This will become clear

when the loads are defined.

(1)

(2)

New machine bed design

our proposal:

The existing vertical plates are aligned under the 12 feet (1), vertical metal sheets

are added (2), the geometry is partially closed (3) and the 5 feet thickness is

increased to 10 mm (4).

original design

(1) and (2)

(3)(4)

New machine bed design

Static Structural : Total deformation

Mass center displacement (µm)

Deformation Probe : -1.4 (-31%) 1.57 (-44%) -0.65 (-52%)

Deformation Probe 2 : 0.36 (-36%) 1.04 (-43 %) -0.39 (+238%)

New machine bed design - Results

Modal analysis

Original design New design

76 Hz

227 Hz

203 Hz

(+167%)

262 Hz

(+15%)

New machine bed design - Results

Concept

What is the influence of a temperature difference on the accuracy?

Let’s say the machine-tool is set up at 8am. Room temperature is 22°C

During the day, the room temperature rises to 23°C. The machine-tool will

change its size due to dilatation. What is the influence on accuracy?

- 20 / 38-

Temperature difference & Accuracy

Steps

3D parts are needed to replace bushings, for example so that the spindle

expansion can be taken into account + material data

As the temperature is uniform,

• there is no gradient

• no thermal coefficients are needed.

Definition of the temperature difference.

Important is the displacement difference between tool and workpiece

- 21 / 38-

Total deformation

x-dir. 2.1 μm

y-dir. -3.0 μm

z-dir. -0.1 μm


The effect of material differences is illustrated in the figures above. The base plate

expanses more than the x and the z plates.


3 translation

axes (x, y and

z axis)

Milling machine

Concept

The machine is excited over a frequency range by a given force (1000 N).

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.

- 24 / 38-

Harmonic analysis

Steps

Similar to a static and modal analysis

Define frequency range and sampling.

- 25 / 38-

Harmonic analysis

Important is the displacement difference between tool and workpiece

MACHINE-TOOL WORKSHOP – 3 days

Table of content

WS01 : test bed guideways idealisation

WS02 : Static Structural Analysis

WS03 : Modal Analysis

WS04 : Parametric Static Structural – Stiffness

WS05 : Parametric Static Structural - gravity load

WS06 : Modal Analysis

WS07 : Thermal Dilatation

WS08 : Design Study - machine bed

WS09 : Static Analysis Milling Machine

WS10 : Modal Analysis Milling Machine

WS11 : Harmonic Analysis Milling Machine

Thanks!

CADFEM (Suisse) AG

Avenue de Cour 74

1007 Lausanne

Tél.: 021 601 70 80

[email protected]

www.cadfem.ch

mailto:[email protected]

Berechnung von Werkzeugmaschinen 3 Beispiele elements available into ANSYS Workbench ... point, a...

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