Virtual High Speed Machining Tests Ramón Bueno and Iraitz Etxeberria TEKNIKER Avda. Otaola, 20 20600 Eibar - Spain E-mail: [email protected]

ABSTRACT. This work submits the results of simulated tests of high speed turning through a commercial simulation programme, applied to three types of materials: aluminium alloys (Al7075-T6), carbon steel (AISI 1045) and titanium alloys (Ti6Al4V). The concept of high speed machining applied to different materials is herein discussed. The physical parameters of the materials as well as the most important cutting conditions which have an effect on the maximum temperature reached during the cutting process are analysed. The results are represented in a condensed way through non-dimensional parameters. The obtained results are compared with different results found in the bibliography. A criticism is made over the simplifications carried out during the selection of the parameters taken into account and of their influence on the obtained results. Finally, there is a description of the advantages that these simulations provide and their future prospects on their application to high speed machining. KEY WORDS: Modelling, High speed machining, Orthogonal cutting.

0. Introduction The present work refers to some high speed machining test results simulated through a commercial programme. According to the working group on modelling of machining process operations, within the technical scientific committee of cutting (STC C) of CIRP, there can be various levels of modelling [LUT 98] [LUT 98a] according to the purpose of the model which can be the design or planning of the process, the optimisation of the process, the control of the process, the simulation of the process or the equipment design. The simulation of the machining processes is still in its first stages. Recently, the method of finite elements is being used for computer simulation, analysing the chip generation process, though it still remains a long way for the industrial use of this type of models in the day to day operations, with enough degree of precision and acceptable reliability. There are, in any case, different levels of modelling depending on their object: either attending engineering needs of different degree of detail, or the needs of scientific knowledge improvement. This work seeks to find the laws of variation of the maximum temperature of the tool in terms of cutting parameters. The determination of the temperatures during the cutting process has been profusely analysed throughout history since it is intimately bound to the analytical study of the cutting theory [SHA 84]. It is worth mentioning the works that calculate those temperatures as from the heat generation in the shearing zones and in the rake face, through simplified laws of heat transfer, calculating the heat distribution between the piece, the tool and the chips, which normally obtain the maximum temperatures in the shearing zone and in the rake face, through more or less iterative procedures. The main interest of calculating the temperature in the interface between the chips and the tool is that the wear of the tool depends, to a large extent, on this matter. Of the different types of wear produced in the tools, the most meaningful wear in high speed cutting is the thermally activated one, that is to say, a form of wear fundamentally related via physical-chemical phenomena which increase rapidly with the increase of the temperature of the tool.

1. Calculation of the maximum temperature in the cutting process Through the classical analytical theories of the cutting processes, approximations for the calculation of temperatures are accomplished determining the sources of heat, mainly in the primary shearing zone and in the secondary friction zone. Simplified

models of mono and two-dimensional heat transfer are accomplished analysing the heat transmitted by conduction in the 3 bodies, i.e.: in the piece, the tool and the heat carried away by the chips. At the same time, simplified models of heat distribution are established between the considered bodies, from common temperatures in the interfaces. These semi-analytical studies lead to quite complex formulations and to iterative calculation processes, since it is necessary to estimate temperatures, to know the thermo-mechanical properties of the materials at such temperatures and to re-calculate, through the established calculation process, new temperatures which are then compared to the previous ones. It is therefore necessary to continue the iteration up to arriving to the coincidence of temperatures in consecutive iterations.

V m/min

Energy %

Workpiece

Chip

Cutting speed ft/min Figure 1. Influence of the cutting speed in the percentage of energy carried away by the 3 bodies, according to experiments made by Shaw. Energy considerations, together with some simplifications with respect to the distribution of temperatures between the 3 bodies, which are more valid at high speeds where most part of the heat is taken away by the chips (fig. 1), lead to the following type of formulations: ∆θT ≈u

vh k ρcp

[1]

in which: ∆θT = variation of temperature in relation to the environmental temperature in the interface of the rake face, u = specific cutting force, v = cutting speed, h = undeformed chip thickness, k = conductivity of the machined material, c = specific heat of the machined material, r = density of the machined material.

It is also possible to arrive to this type of formulation through the dimensional analysis developed by Shaw in 1958. A previous dimensional study to that of Shaw’s, accomplished by Kronenberg in 1949 concluded with the following formulation:  A v 2 (ρc) 2 θT ρ c = ϕ1   u k2 

   

[2]

where A represents the not deformed section of the chips, of which the formulation of Shaw is a particular case where the ϕ1 function is the function 4 .... , to which it is also possible to arrive directly grouping the thermomechanical constants in unique form of kρc. In our "virtual tests" we are going to use a non-dimensional parameter proposal analogous to that of Kronenberg´s, using instead of A, the square of the undeformed chip thickness “h” and using the following formula: θT ρ c ρ c v h  = ϕ2   u  k 

[3]

where the non-dimensional variable ρ c v h k is the square root of that considered by Kronenberg. To arrive to these proposals a large number of simplifications have been required, not taking into account thermal parameters of the tool which have influence on its heat transmission and on the distribution of the heat, neither geometric cutting conditions, the relationship between r/h, that is to say, between the radius of the cutting edge of the tool and thickness of the chips, laws of variation with temperature and the deformation speed of the parameters of the constitutive equation

of the material, friction coefficients, etc., though they do take into account some of such variables indirectly, since the specific cutting force is such at the temperature of the test and it also contains the influence of the friction. The heat transmitted to the tool is assumed to be a negligible part of the heat transported by the chips, which is reasonable considering the high speed. By means of equation [1], it is possible to try to define high speed machining. For this purpose, we put it on this form: v =C

te

k ρ c p  ∆θT 2   h  u 

[4]

Since the aim is to obtain the optimum production, in roughing as well as in finishing, the machining conditions that lead to such optimum production depend to a large degree on the wear of the tool, which in limit conditions are fundamentally determined by the maximum admissible temperature “θ” in the chips/tool interface. Such maximum temperature depends fundamentally on the specific cutting force, on the speed, on the undeformed chip thickness and on the thermal parameters of the material of the piece. The first clear issue is that the high speed, which of course, refers to the cutting speed, depends on the value of the specific cutting force of the considered material, that is to say, to obtain a temperature of θT, the bigger is the value of u, i.e. the greater difficulty of the material to be machined, the lower will be the speed. Similarly, it will be possible to obtain speeds which do not exceed the maximum temperature more easily, with small undeformed chip thickness and with high conductivity, specific heat and density values. High speed machining is, therefore, a machining strategy which intends to obtain greater production by increasing the cutting speed and reducing the thickness of the chips. The reachable speeds are greater for materials of low specific cutting force and with high conductivity, such as aluminium alloys. The development of high speed machining has been coincident with the appearing of new tool materials capable of resisting the highest temperatures without suffering a very rapid wear. The conventional machining strategy in roughing consists on making the tool work with reduced speeds and greater undeformed chip thickness, that is to say, greater feed in the case of turning processes and greater radial depth and feed in the case of end milling processes, always with lower cutting speeds.

The high speed strategy is clearly the most adequate for finishing operations and though it can be occasionally surpassed by the conventional strategy in some roughing cases, due to power availability problems, it overall presents advantages of time reduction, production increase, possibility of machining thin work-pieces, less warming up of the piece, smaller cutting forces, roughness improvement, etc., widely known. The decrease of chip thickness has a limit related to the radius of the sharp end of the tool, which should not be reduced. On the other hand, in milling operations, the small radial immersion of the milling tool at high speeds, involves a smaller ratio between the iddle cutting times of the different tips of the tools, which facilitates a better refrigeration of these. To contrast the formulations [1], [2], [3] and [4] and to see the influence of factors not taken into account up to now, several tests with different materials and different cutting conditions have been simulated, and as a result of such simulation, values of the maximum temperature in the chips/tool interface have been obtained, as well as values of the specific cutting forces, necessary for the application of such formulations. In addition, the aim is also to obtain information on variations in the shape of the chips and to examine the different basic deformation mechanisms which could occur at high speeds, analysing whether there are any substantial changes or not, as a general rule, when using the high speed machining strategy.

2. Used simulation programme The software programme on modelling of the machining process “AdvantEdge” [ANO 99] has been used, in its version of a two-dimensional and Lagrangian package of finite elements. It is composed of coupled mechanical and thermal analyses, studying the transitory regime through a step by step procedure.

2.1. Mechanical equations The set of mechanical equations represents the dynamical forces equilibrium, taking into account the internal forces (internal stresses), the external or contour forces and the inertia forces. The equations are represented in form of a matrix:

[M ]{&x&}+ [R in ]= [R ext ] [M ] = {&x&} =

mass matrix, accelerations vector,

[5]

[R ] = [R ]= in

internal forces matrix,

ext

external forces matrix.

The Newmark procedure is used for time integration, calculating the speeds and displacements as from the accelerations determined by the equation [5]. The stability limits of the steps in the integration process are taken into account, starting from the highest value of the natural frequency corresponding to the elastic problem (since the plasticity reduces the stiffness and natural frequencies).

2.2. Thermal equations The equation of the heat transfer is solved in transitory state: &} [] c {θ + [] k {θ}= {Q}

[6]

where:

[] c = [] k = {Q}=

thermal capacity matrix, conductivity matrix, sources of heat vector, which takes into account the surface sources (in the interface with the tool) and the volumetric sources (plastic deformation work converted into heat), & {θ}y θ = vectors of temperature and of their first time derivative.

{}

For the heat distribution generated in the interfaces it is assumed the continuity of temperatures, and the distribution of the heat flow is calculated according to the quotient: Q1 Q 2 = k1 ρ1 c1

k 2 ρ2 c 2 .

The heat generated by unit of volume is proportional to the plastic deformation work and the heat generated in the interfaces is proportional to the friction force multiplied by the relative speed.

2.3. Thermo-mechanical coupling The programme adopts a procedure of different steps for the coupling of the mechanical and thermal equations. A geometrically identical mesh is used for the thermal and mechanical models. The calculation is accomplished in different steps supposing constant temperature during the mechanical step and constant heat generation during thermal step. In the first

mechanical step, the initial temperature is the environmental one and the heat generated is computed from plastic working and frictional heat generation. The aforementioned heat is transferred to the thermal mesh and the distribution of temperatures is recomputed. The resulting temperatures are transferred to the mechanical mesh and incorporated into thermal softening model. The isothermal mechanical step is accomplished again recalculating the new displacement vector, speeds and accelerations, as well as the plastic deformation and friction works, repeating the cycle once and again.

2.4. Adaptive Remeshing During the machining process of the work-piece, the material is permitted to flow about the cutting edge. In the nearby of such edge the elements become very distorted and precision is lost. The programme periodically alleviates element distortion by updating FE mesh, refining the large elements, remeshing the distorted ones and coarsening the very small elements.

3. Material model The material model is defined by their constitutive equations thereof. In the deformation that takes place during the machining process, in the primary and secondary shear strain zones the strain rate is very high, of around 10-9 s-1 whereas outside these zones the strain rate is much smaller. In the programme employed, potential laws with different values of sensitivity to the strain rate are used, depending on a threshold value of the plastic strain rate ε&p . The value of the plastic strain ε p itself is also taken into consideration in order to take into account the strain hardening through a potential law. Finally there is also a model which takes into account the softening of the material by effect of the temperature, through an exponential type law. The parameters of all these laws are customised for each specific material.

4. Virtual tests carried out Through the programme described in the previous paragraph, turning tests of three types of materials have been simulated: aluminium alloys (Al7075-T6), carbon steel (AISI 1045) and titanium alloys (Ti6Al4V).

For each one of these materials, the conditions of cutting speed v and the undeformed chip thickness h, have been those in table 1: v (m/min)

h (mm)

ρc p v h

Al 7075-T6

800 - 3500

0,05 - 0,15

9,4 - 141

0,1 - 0,3

AISI 1045 (C45)

600 - 1500

0,05 - 0,2

33,7 - 338

0,075 - 0,3

60 - 180

0,06 - 0,12

18 - 113

0,125 - 0,25

Ti6Al4V

r h

k

Table 1. Conditions of cutting speed v and the undeformed chip thickness h used in the virtual simulations of the 3 studied materials. In all cases it has been simulated an orthogonal cutting with α= 6º rake angle and γ= 8º clearance angle, 0.015 mm cutting edge radius and ceramic type tool. Even though the geometry of the tools as well as their material may not be the optimum for each of the materials and cutting conditions, the purpose is to perform some tests in the same external conditions for the three materials, trying to find general laws and properties of the machined materials relating to cutting conditions that have to do with the high speed, independently of the tools.

5. Results of the tests The following are some of the results of the tests carried out: Figure 2 presents the non-dimensional temperature θTρc/u in terms of the parameters ρvch/k and r/h, for the aluminium alloy Al7075-T6. It can be observed that the results for different values of r/h are very close together and only for the highest values of those parameters the differences are more sensitive, that is to say, when the relative size of the radius of the sharp edge of the tool is significant enough. Moreover, when that high value coincides with a low cutting speed, the temperature increases because the cutting process becomes a ploughing process with built up edge phenomena, according to the results of other investigations, such as those of Schulz [SCH 96]. Figures 3, 4 and 5 present the results of non-dimensional temperature in terms of the non-dimensional speed parameter, not taking into account the influence of r/h, since the speed parameter seems to be the most influential one.

Figure 2. Influence of the parameters ρvch/k and r/h on the maximum temperature, in the aluminium alloys Al-7075-T6. Figure 3 represents the results for the aluminium alloy, figure 4 for carbon steel C45 and figure 5 for titanium alloy Ti6Al4V. The results can be presented in the following way: m

ρ c θT ρ c v h  = C1   u  k 

[7]

being the values of C1 and m, those shown in table 2: C1

m

Al 7075-T6

0,439

0,221

AISI 1045 (C45)

0,416

0,218

Ti6Al4V

0,324

0,311

Table 2. Values of C1 and m obtained for the 3 studied materials.

Figure 3. Influence of the non-dimensional speed parameters ρvch/k on the maximum temperature, in the aluminium alloy Al-7075-T6.

Figure 4. Influence of the non-dimensional speed parameters ρvch/k on the maximum temperature, in the carbon steel AISI 1045.

Figure 5. Influence of the non-dimensional speed parameters ρvch/k on the maximum temperature, in the titanium alloy Ti6Al4V. The first commentary is that the m exponent is inferior to 0,5 therefore, Shaw’s results cannot be assimilated in principle, resulting: θT = C1 u ( vh) m ⋅(ρc) m− 1 k − m

[8]

Another commentary is that the prediction of Solomon about the reduction of the maximum temperatures at very high speeds has not been reached. Finally, figures 6 and 7 show the double logarithmic adjustment and the representation with linear scales of the set of all the performed tests, resulting the values of C1 = 0,460 and m = 0,206, continuing the same trend as the particular results of each material. In order to determine the non-dimensional number θTρc/u, that is to say, in order to calculate the temperature, it is necessary to calculate the specific cutting force obtained from the simulation. In figure 8 the registered values of the cutting forces can be seen, with large fluctuations owed to the not permanent phenomenon of chip formation.

Figure 6. Influence of the non-dimensional speed parameters ρvch/k on the maximum temperature, in the 3 materials, represented in double logarithmic scale.

Figure 7. Influence of the non-dimensional speed parameters ρvch/k on the maximum temperature, in the 3 materials, represented in linear scale.

800 700 600 500 400

FX, FY

300 200 100 0

-100 -200 -300 -400 0

0.001

0.002

TIME Figure 8. Values of cutting forces when modelling a machining operation with Ti6Al4V-T6 alloy. In the case of continuous chips the variation is lower than in the case of serrated chips. In every case it is necessary to obtain the average value of the cutting force, once stabilised, for each cutting condition set. As a general rule, according to the experimental results of other authors [SCH 89], a decrease of the specific cutting force is observed when the parameter ρcpvh/k increases, like the one seen in figure 9. The main cause in these cases is the decrease of the resistance of the material to the plastic deformation, due to the softening produced by temperature. Upon effecting different simulations with the 3 materials and with different machining conditions, changes are occasionally observed in the deformation of the chips as well as in their shape. The plastic deformation can be more or less concentrated in the primary and secondary deformation zones, depending on the strain hardening. The main shearing can bring on more or less continuous or segmented chips, with different degrees of segmentation (as it can be appreciated in the figures 10 and 11).

Figure 9. Influence of the cutting speed in the values of the cutting forces, according to experiments made by Schulz.

Figure 10. Continuous type chip obtained when modelling a machining operation with the Al7075-T6 alloy.

Figure 11. Segmented type chip obtained when modelling a machining operation with the Ti6Al4V alloy. There are no general changes of the chip forming mechanisms when machining at high speeds. What occurs is a modification of the state of the material correspondent to its constitutive equation and to the conditions given in different points of the material during the process, that give way to a deformation as a consequence of all these. That is to say, it gives way to the cutting process, which, depending on each situation, seems more or less like the extreme idealised mechanisms analysed in the simplified, analytical theories, of the process.

6. Review of the results The programme, in broad outline, shows some results that qualitatively describe what occurs in the machining process of the different studied cases. Basically, the constitutive equations of the material are the ones that define the final results, as well as the variation with temperature of the physical parameters as conductivity, specific heat and density. Also, the friction laws on the rake face and those of separation in the edge of the tool can give rise to variants. In addition to all those questions referred to the physical modelling, there are problems of geometrical modelling, and also those referred to the shape and size of the meshing, the extent of the integration steps, to be integrated in the thermal as

well as in the mechanical aspects, the proper numerical integration procedures and even to the rounding problems in the numerical calculation. The simulation results do not correspond to a steady state, there are noteworthy variations in the registered cutting forces, as it happens in reality. Since the temperatures evolve more slowly, it is necessary to use the mean values of the forces to apply the formulations that relate the temperatures to the cutting forces in the cutting phenomena. Concerning the temperatures, they sometimes present prompt high values, produced by local forms of the piece/chips mesh, which are not properly adapted to the shape of the tool and which produce local temperatures in the calculation which do not seem to correspond with reality. Those values have been eliminated from the results.

7. Conclusions 1. The simplifications used in the analytical procedures provide just approximate results of the temperature calculations. 2. High speed machining has been defined as a machining strategy, that in contrast to conventional machining, tries to find the maximum productivity increasing the cutting speed and reducing the undeformed chip thickness. 3. Using a commercial simulation system, we have tried to know what happens, especially in relation to the temperatures,. 4. The results have been grouped through non-dimensional parameters. 5. It has been observed that the results can be properly represented with laws such

(ρcv c h k )m

as cpθT u = c1

where m has a value of approximately 0,2.

6. The obtained representation is general and unique for the 3 materials considered, what allows to estimate the speed ranges in terms of the physical characteristics of the material and of the maximum temperature tolerated by the tool. 7. Other parameters, such as the ratio h/r, have lower importance in the results for values superior to certain threshold. 8. The simulation provides information on the forces and type of chips, which needs to be more contrasted with the experimental tests. 9. For the different materials, the basic laws of chip formation are the same, but applied using different parameters which explain the different results. As a

general rule, there are no changes of fundamental deformation models characteristic of high speed machining. 10. The results of the virtual tests encourage to follow this working line, which provides good scientific information of the cutting phenomenon. A working line that will have to be improved contrasting it with experimental plans, headed towards knowing better the basic parameters of the material.

8. Acknowledgements The authors wish to thank the collaboration from the people responsible for the commercial programme Third Wave AdvantEdge used on this occasion.

9. References [LUT 98] LUTTERVELT, C.A. VAN, CHILDS, T.H.C., JAWAHIR, I.S., KLOCKE, F., VENUVINOD, P.K., “Present situation and future trends in modelling of machining operations. Progress Report of the CIRP Work Group ‘Modelling of Machining Operations’”. Annals of the CIRP, p. 587-626, Vol. 47/2/1998. [LUT 98a] LUTTERVELT, C.A. VAN, “The importance of suitable models for machining operations to improve machine-tool performance”, Proceedings of the International Seminar on Improving Machine Tool Performance, San Sebastián, Spain, p. 545-555, 1998. [SHA 84] SHAW, M.C., Metal Cutting Principles, Oxford University Press, 1984. [ANO 99] Third Wave AdvantEdge, A Short Course on Modelling Metal Cutting Processes, Fraunhofer Institut Produktionstechnologie, Aachen, Germany, September 22-23, 1999. [SCH 96] SCHULZ, H., High-Speed Machining, Carl Hanser Verlag, 1996. [SCH 89] SCHULZ, H., Hochgeschwindigkeitsfräsen metallischer und nichtmetallischer Werkstoffe, Carl Hanser Verlag, 1989.