# Deflection model of the machine tools.

1. INTRODUCTIONReconfigure ability of machine tools is one of the critical factors realize the responsive manufacturing systems to satisy the mass-customization production. In the machine tools designing and building exists some common steps for this process. Exist a traditional and modern ways for Machine Tool and Structure Design Process. In the following next articles it will be seen both of these tow concepts and a flow chart showing how the interaction between these steps are running till the convergence achieved to have a positive results, (Neithardt at al., 2003), (Koenigsberger et al., 1979).

In the modern machine tools structural design it can be seen some new advantages coming from the modern new tools such as Finite Element Analysis or Finite Deference Method. The most common technique is FEA "Finite Element Analysis". The cycle starts normally as in traditional way but then it goes after the machine concept for analysis for both static and dynamic with material selection to have the required material for each component. If the results is positive it can move for the detailed design then rest of the cycle as shown in figure 1. If not it should be a loop with machine main concept to have the proper results from both deflection point of and strength.

2. MACHINE TOOLS CUTTING DEFLECTIONS MODEL

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The design normally works based on a specific criteria which will be the guide if the parts then the whole machine will be ok or it will fail to do the required function. The main required function normally from all machine tools is to make cutting of different material with high accuracy. High accuracy required to have the minimum deflection of the machine tools parts including the frame. So, the criteria of failure here will be the deflection, (Benardos et al., 2006). Normally the stress should be kept under the elastic limit but in case the deflection criteria limit is respected the stress limit remain under the elastic limit and the stress concentration only should be checked to avoid the cracks under cycling loading, (Litak et al., 2007).

If the deflection is a main factor in machine tools other wise it can cause the following: Deflection can cause inaccurate parts; Deflection can cause chatter, limiting depth of cut and production rate; Chatter can cause poor surface finish; Chatter can damage tools; Axis acc/dec. can limit path accuracy and affect surface finish

The model of machine tools with work piece and the cutting tool can be simulated as shown in the fig.3. This model is used to obtain all the forces coming out from the different sources to be taken in analysis. The analysis is done by Finite Element Analysis (FEA), fig.4. The FEA technique could be explained and described in some steps as follows: Numerical method to determine structural behaviour; Solves linear equations to find response under load; Loads may be physical, acceleration, thermal; Results are deflection, stress, strain energy, modes, natural frequencies, temperatures; Results used to determine performance; Results of design analyses used to select most feasible design.

In the FEA modelling it is also required to define the contact relations between the components. In the model the stiffness volume ratio which is coming from the welding structure is higher that what is coming from casting. The FEA processing phase could be put in the following points: Stiffness calculated by solver from geometry, material, thickness; Displacement found under applied force. The static analysis (fig .5) is done for: static deflections, static stress static strain energy, natural frequencies, mode shapes modal strain energy, effect of mass.

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3. MACHINE TOOLS DYNAMICS--RESULTS

The global machine tools structure stiffness has a great effect on machine tools dynamics behaviour. The increase of the structure stiffness the ability for damping increased and this leads consequently damping convergence (Bisu, 2007) this is reflected on the tool and spindle damping convergence. Figure 6 show the relation between the stiffness increase and the frequency response. The results give also the information about the relative behaviour and absolute frequency, fig.7. To systematically generate the structure of machine tools in response to user requirements, definitions of component modules and the relations between them are required. The structure of machine tools is represented by a connectivity graph. In the connectivity graph, the nodes represent the component modules of machine tool, while the arcs mean the contact and kinematics relations between them. In this section, three modeling elements of machine tool's structure are defined: component modules, contact and kinematics relations.

This strain energy is a measure of the structure deformation obtained by applying a load. The strain energy is in a proportional relation with the stiffness. So, increasing the structure stiffness reduces the structure deflection and increasing its resistance. The total strain energy inside one assembly has a distribution and the value is different is different from one parts to another and from one subassembly to another.

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4. CONCLUSIONS

In this paper we highlighted a numerical model with an aim of determining the dynamic behaviour of the machine. At the time of modelling, we seek has to know the deflection of our spindle, or of the tool holder in the system Machine-tools/ Tool/Work piece. Evaluates machine concept in design cycle, verifies machine performance (stiffness, chatter, accuracy, reliability), reduces development resources (people, time, money), and lowers risks of non-performance. Machine doesn't chatter and doesn't break tools, machine produces quality parts, assures technology base for future developments. An experimental part will be set up permitted to validate the model and to obtain the coherence with the errors numerical which one can the given ones.

5. REFERENCES

Benardos, P. G., Mosialos, S. & Vosniakos, G. C. (2006). Prediction of workpiece elastic deflections under cutting forces in turning Robotics and Computer-Integrated Manufacturing, 22, pp 505-14.

Bisu C.F. (2007). Etudes des vibrations auto-entretenues en coupe tridimensionelle :Nouvelle modelisation appliquee eu tournage, Phd Thesis, Univ. Bordeaux 1--Univ. Politehnica Bucharest

Koenigsberger, F. & Tlusty, J. (1970). Machine Tools Structures,. Pergamon Press

Litak, G., Kasperek, R. & Zaleski, K. (2007). Effect of high-frequency excitation in regenerative turning of metals and brittle materials. Chaos Solutions and Fractals in press

Neithardt, D. & Emmrich, D. Just (2003). Structural Optimization of Machine Tools including the static and dynamic Workspace Behavior. H. Weule(1), J. Fleischer W. The 36th CIRP-International seminar on Manufacturing Systems, 03-05 June 2003, Saarbruecken, Germany

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Author: | Ispas, Constantin; Ibrahim, Ahmed; Bisu, Claudiu |
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Publication: | Annals of DAAAM & Proceedings |

Article Type: | Report |

Geographic Code: | 4EUAU |

Date: | Jan 1, 2009 |

Words: | 1075 |

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