The Ultra-light Cellular Structure for The High-end Numerical Control Machine Tool Optimal Design Applications C.Y.Ni 25.Jan.2008 Supervised by Prof. T.J Lu Advised by Prof. C.Q.Chen

Background High-end numerical control machine tool (accuracy,acceleration ) On of the 16 grave special projects for the state medium- term and long-term develop plan Trend of development  High speed  High degress of accracy  Multiplicity  Intelligence  Flexibility and integration  lightweight  stiffness  damp  elimination of heat Challenges

Background Proper distribution of the rib reinforcement can increase the stiffness and natural frequency of the beam (from C.L.Luo et al.) Box structures are well applied in new style machine tool As the structure requirement, the beam must be hollowness Ultra-light cellular 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 Here we just consider the 2D honeycomb structure as the rib reinforcement Background Take the beam for example to try to do some optimal design for the structure 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

Analysis example Background

Static stiffness analysis Simplified model  To the Load Tool box hanging on the beam  To the Boundary condition The beam is located on the guide rail,considering the static stiffness  To the Structure According to mechanical acknowledge Simple support Combination effect of the moment of flexion and torque a sandwich bar whose outer layer is a closed-cell thin wall bar and the inner layer is a core bar

Static stiffness analysis Simple mechanical mode 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

Relative density is the cellular structure density is the material density For honeycomb cell wall with a thickness to length ratio of Its relative density can be expressed as It has grave effect on the dynamical character for the cellular structure (from Lorna J.Gibson Michael F.Ashby) Static stiffness analysis Definition:

is the weight and is the density of the material 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 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 Solving the geometric parameter: We conclude that : Torsional stiffness Solving the geometric parameter We conclude that: Closed-cell thin bar torsional stiffness formula: Beam bending formula: Static stiffness analysis

For the inner layer equivalent continuous bar Using the same method to conclude that: Bending stiffness Using the principle of superposition to produce the static stiffness of the beam Square cross-section bar torsional formula: Static stiffness analysis Torsional stiffness

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.

For the beam we choose several usual rib reinforcement structures to carry on the analysis The analysis of the natural frequency and modal is a basic and important content in dynamical analysis of the structure FEA of the natural frequency and modal

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

Concluding the first 10 grades natural frequency as follow: FEA of the natural frequency and modal

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 FEA of the natural frequency and modal

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