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Topology Optimization of Machine Tools to improve the

Stability in high performing Metal Cutting Processes

Gebr. HELLER Maschinenfabrik GmbHDr. Gerhard Kehl, Harald Altstädter

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Manufacturing Systems for Automotive Industry

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MCH 250 G

MCH 350 GE

MCH 250 C

MCH 250 HSM

Simulation Disciplines at Machine Tools

Static Dynamic

Thermal

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Mechanical Structures in complex Systems

Designspace

Non-Desigarea

2 Volumes

3 Couplings

17 Volumes

12 elastic Couplings

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Modeling of the mechanical Structure for Optimization

+ =

Non-Design Area Designspace Simulation Model

+ =

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Optimization Strategies

Combined Topology Optimizationstatic loads + eigenfrequencies

specific frequency constraints

f1= 60 Hz > f

1*

f2= 90 Hz > f

2*

f3= 120 Hz > f

3*

Static Topology Optimization with weighted load cases (up to now max. 44)

• moving loads (weight)

• acceleration loads (quasi-static)

• process loads

Frequenz

Am

plitu

de

Ausgangsmodell

Opt imierungsergebnis

(Nachgiebigkeitsf requenzgang)

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Initial model for head (Realistic boundary conditions)

Loadcase 1(x-direction)

Flexible beam elements for

boundary conditions

Beam elements

attached

to rigid mass

Loadcase 2 (y-direction)

Beam elements

attached

to rigid mass

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Static optimization

Minimize: Maximize of { abs(ux), abs(uy)}

Mass < Mass* = 35%

Important: the static optimization

showed that the frequency responses also

have to be considered in the optimization.

The rigid mass is no

more

attached to structure !!!!

Number Eigenfrequency

1 ~0

2 ~0

3 ~0

4 2.4

5 3.0

6 3.5

}

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0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1 3 5 7 9

11

13

15

17

19

21

23

25

27

29

31

33

35

37

39

41

Frequency optimization

Maximize the eigenfrequencies from f1 to f6

Mass < Mass* = 35%

Mass constraint is not active

Important: Model the correct physical

boundary conditions. The optimization

should include static and frequency results.

Number Eigenfrequency

1 83

2 105

3 112

Shaft hardly attached to structure.

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Combined static and frequency optimization

Purpose: To improve the static stiffness for both loadcases including constraints

on the eigenfrequencies.

Objective: Minimize: Maximize of { abs(ux), abs(uy)}

Constraints: Mass < Mass* = 35%

f1> f

1* = 60 Hz f

1> f

1* = 75 Hz

f2> f

2* = 90 Hz f

2> f

2* = 100 Hz

f3> f

3* = 120 Hz f

3> f

3* = 125 Hz

f4> f

4* = 150 Hz f

4> f

4* = 150 Hz

f5> f

5* = 180 Hz f

5> f

5* = 175 Hz

f6> f

6* = 210 Hz f

6> f

6* = 200 Hz

Example 1

Example 2

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Combined static and frequency optimization: Topology

Example 1:

Number Initial example 1

1 48 60

2 60 90

3 94 137

4 137 181

5 260 256

6 265 345

Example 2:

Number Initial example 2

1 48 75

2 60 101

3 94 145

4 137 191

5 260 268

6 265 377

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Examples for Topology optimized Machine Components

Tool Changer Arm Rod and Plain Eye hydr. Rundtisch Brake

p

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Examples for Topology optimized Machine Components

Machine Stand

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Examples for Topology optimized Machine Components

Machine Stand

Milling and Boring Carriage