Transcript Document

The Ultra-light Cellular Structure for The
High-end Numerical Control Machine
Tool Optimal Design Applications
C.Y.Ni
Supervised by Prof. T.J Lu
Advised by Prof. C.Q.Chen
25.Jan.2008
Background
On of the 16 grave special projects for the state mediumterm and long-term develop plan
High-end numerical control machine tool
(accuracy  1 m ,acceleration  5g )
Trend of development
High speed
High degress of accracy
Multiplicity
Intelligence
Flexibility and integration
Challenges
lightweight
stiffness
damp
elimination of heat
Background
Box structures are well applied in new style machine tool
Proper distribution of the rib
reinforcement can increase the
stiffness and natural frequency of
the beam
(from C.L.Luo et al.)
As the structure requirement ,
the beam must be hollowness
Ultra-light cellular structure
Background
Take the beam for example to try to do some optimal design for the structure
The beam is the master part of a machine tool ,the rationality of its structural
design can influence the stiffness and the precision of the machine tool directly
Objective
Build simplified theoretical model for the beam
Analyze the static stiffness of the beam with different
cellular structure to find the optimal design in theory
FEA of the natural frequency and modal for the beam
with different cellular structure to find the optimal design
Here we just consider the 2D honeycomb structure as the rib reinforcement
Background
Analysis example
Static stiffness analysis
Simplified model
To the Load
Combination effect of
the moment of flexion
and torque
Tool box hanging on the beam
To the Boundary condition
The beam is located on the guide rail ,considering the static
stiffness
Simple support
To the Structure
According to mechanical acknowledge
a sandwich bar whose outer layer is
a closed-cell thin wall bar and the
inner layer is a core bar
Static stiffness analysis
The honeycomb structure can be transferred to the continuous
homogeneous structure using equivalent method in order to
solve discrete structure by the theory of continuous medium
(from Lorna J.Gibson Michael F.Ashby)
Here we just consider four kinds
of classic honeycomb structures
equivalent structure
Simple mechanical mode
H  550mm, h  209mm, L  286mm, l  215mm, t0  30mm, X  2320mm
Static stiffness analysis
Relative density
Definition:

s

r
s
is the cellular structure density
is the material density
It has grave effect on the dynamical character for the cellular structure
For honeycomb cell wall with a thickness to length ratio of
Its relative density can be expressed as
t
l

t
 C1
s
l
(from Lorna J.Gibson Michael F.Ashby)
Static stiffness analysis
Considering a core structure composed of one row honeycomb cell
the relative density can be expressed by the macroscopic parameters
of the core structure
For the given core
structure we can
determine the relative
density directly
W is the weight and 
is the density of the material
Static stiffness analysis
In-plane equivalent stiffness of the honeycomb structure
(from A.-J.Wang and D.L.McDowell)
Static stiffness analysis
The simplified model reveals that the static stiffness of the beam contain
the torsional stiffness and the bending stiffness
For outer layer closed-cell thin wall bar
Bending stiffness
Beam bending formula:
1


M
K1
Solving the geometric parameter:
We conclude that:
K1  EI
I z  2.01e9
K1  2.01e9 Es
Torsional stiffness
Closed-cell thin bar torsional stiffness formula:
Solving the geometric parameter
We conclude that:
4A2G
GJ 
S
D1  8.87e8Gs
Static stiffness analysis
For the inner layer equivalent continuous bar
Using the same method to conclude that:
K2  1.81e9 E
Bending stiffness
Torsional stiffness
Square cross-section bar torsional formula:
D2  ab G
3
D2  4.92e8G
Using the principle of superposition to produce the static
stiffness of the beam
P  K1  K2  D1  D2
Static stiffness analysis
Basing on the conclusion above, we can determine the stiffness
using the macroscopic parameters of the beam
For the beam whose inner layer with different core shape we get
the conclusion as follow:
Static stiffness analysis
Conclusion
Analyze the static stiffness of the beam with the
theoretical simplified model
Find the hexagon honeycomb core structure is the
optimal structure in this four structures.
FEA of the natural frequency and modal
The analysis of the natural frequency and modal is a basic and
important content in dynamical analysis of the structure
For the beam we choose several usual rib reinforcement
structures to carry on the analysis
Strucure 1 Square honeycomb-like core (original beam structure)
Structure 2 Fold-like core
Structure 3 Dummy plate core
Structure 4 Fold-like structure
Structure 5 Hexagon-like core
FEA of the natural frequency and modal
Concluding the first 10 grades natural frequency as follow:
FEA of the natural frequency and modal
频率（HZ）
440
247
246
245
244
243
242
241
240
239
238
237
410
380
350
320
290
260
230
200
结构一
结构二
结构三
结构四
频率（HZ）
二阶固频
三阶固频
一阶固频
结构五
各结构前三阶固频比较图
Conclusion
Hexagon-like structure is the best among these five structures
by analyzing the natural frequency and modal of the structures
This conclusion also certificates the rationality of the theory
simplification above in certain extent
Conclusions
Find that the relative density of the cellular structure is not only
relative to the microscopic parameters but also can be determined
by the macroscopic parameters
A simplified model has been suggested to analyze the
mechanical performance for the beam of the machine tool
The simplified model is applied to analyze the static stiffness of
the beam structure and we find that hexagon honeycomb
structure is the optimal design of the four structures
FEA of the natural frequency and modal for the beam structure
also finds that hexagon honeycomb structure is the best one of
the five structures
The conclusion of the modal analysis certificates the rationality
of the simplified model in certain extent
Future work
For the static and dynamical performance, we can do the optimal
design from theory model building ,computer simulation and experiment
research three aspects to expect concluding the general analysis
model
The optimal approach should contain topological optimization and
general optimization
For the machining accuracy, we may progress the global error
analysis ,and reduce the global error by controlling the local accuracy.
Considering the optimal design for the structure undergoing extreme
loads
At the same time, we also should make full use of the multifunctional
character of the ultra light cellular structure
Thanks