Design of end mill cutter with applying FEM-method

Richárd, HORVÁTH 1, Gergő,MIHÁLYI 2, Sándor, dr. SIPOS 3

1 BMF/BDGBMK/AGI, Institute Engineer


3 BMF/BDGBMK/AGI, Associate Professor


In order to fulfil the increasing requirements of the industry better, the regular application of the finite element method (FEM) seems to be unavoidable. The recognition of this fact can be noticed in case of non-series tools still less, but manufacturing companies (wishing to remain competitive in the future as well) use softwares, based on the finite element method and simulating the cutting processes, also nowadays. The aim to develop these softwares is to design and produce tools, maximal fulfilling the demands of the customers and at the same time, enabling the reduction of design and production costs of the tool manufacturers. As a result of the use of the softwares we can be able to predict the occasional tool deformations, avoiding the break of the tool, the unfavourable chip deflection, the undesirable deformations of the workpiece, etc.

1. Intentions during the construction

At indexable inserted high feed milling cutters, the main cutting edge angle of the insert, mounted on the tool, has a very important role as it affects the chip thickness significantly. In case of high feed milling cutters, the main cutting edge angle usually varies between 10-17º, it results in smaller chip thickness, as compared to the tools, having a greater main cutting edge, therefore a greater feed can be achieved.

For high feed end mill cutters the radial rake angle of 0º is typically, but in case of tools with a bigger diameter – in order to achieve better chip evacuation – the negative radial rake angles are dominant. As regards the axial rake angle, positive values are dominant in order to achieve smaller force components and better chip deflection. The radial and axial rake angles, mentioned earlier, should be determined with considering the chip-breaker geometry of insert. For example, the cutter body, as it can be seen on Figure 1/a, has a positive true axial rake, thanks to the combination of the negative rake angle of the insert seat and the extreme positive rake angle shaped insert with the chip forming top face. As regards the tooth pitch, even or intentionally uneven construction can be used in case of high feed milling cutters as well. It is recommended to design the load-bearing cross section of the high feed milling cutter maximal as this type can be characterised by greater feed force components, affecting the deformation of the insert seat unfavourbale, compared to the tools with great main cutting edge angle.

1.a Positive axial rake angle [3]

1.b The resultant of the cutting force system

Figure 1. Main construcional parameters of the working part

The shaft of the high feed milling cutters is less sensitive to deformations and vibrations as the resultant of the spatial force system works in the direction of the main spindle (Figure 1/b). It results in small degree bending and decreases the vibrations. In case of arbor mounted high feed milling cutters there are no special needs, concerning the minimal length of the tool. As regards the holding parts, in case of end mill cutters the Weldon- and straigth constructions have spread, while in case of arbor mounted HFM, construction with axial or clutch keyways is dominant. Further tool holding methods are threading connection and Coromant Capto®, both available in commercial trade as well. The disadvantage of the HFM tool family is that only minimal axial depth of cut can be applied and it can be used only to roughing operations.

2. Optimisation of the tool deformation with the help of FEM

The finite element module CATIA V5 R17, applied by us, has been originally developed not for designing cutting tools, but for analyses of statical design; however, the applied mechanical model works in the range of elastic deformation with satisfying accuracy. The main aim of this design is to achieve that the tool should suffer not more than only elastic deformation during the cutting processes. One of the disadvantages of the applied software is that it is not possible to determine the force components, developing during the cutting operations. Therefore in case of cutting tool, designed by us, we have used the values, gained during force component measurements - described in the essay [1] - as these measured results contain not only the geometrical features of the workpiece and inserts, but the dynamical characteristics of the cutting process as well. The maximal values of the force components have been considered by us as secure factors, even if they have developed not at the same time. The examinations of FEM have been limited to analysing the insert seat. We have registrated the force components, where relationship between ae and D (so called tool engagement, Ψ) occured smaller than 1 [2].

Two from spatial force components, developing during the experiment, have been registered by us, they are the normal force (Fn) and the feed force (Ff) components. The FE analysis refers to an assembling model, where the question was not the deformation of the insert, but the effect of the forces, causing the deformation of the insert seat. To the tool body a steel material type, available in the data base of CATIA, has been chosen by us, seemed to be a perfect solution to our examinations: due to its elastic (Young) modulus it can be considered to be similar to the steels, applied in the tool production.

During the examination the presence of the screw has been considered as well. We have defined the screw connection by assembling the model of the screw and the force as well, necessary to fix the screw. At assembling the model, especially on the surfaces and edges, we have selected and applied coincidence constraints. The surrounding area of the insert seat has been selected to fix the constraints, so, that we could examine the deformation of the load-bearing cross section. After that the counteracting force of the measured force values [1], acting on the main edge, has been defined by us (Figure 2/a).

The examination results show that only a minimal size deformation (1-8 µm) can be noticed. This value can be considered as insignificant, so the construction of the prototype can be evaluated as appropriate. On Figure 2/b an extremely high deformation value (0,0139 mm) can be seen. This value belongs not to the load-bearing cross-section of the tool shaft: it indicates the size of movement, resulting from the unscrewing of the insert from the insert seat.

2/a: Definition of the cutting forces [2]

2/b: The deformation of the load-bearing cross-section of the insert seat [2]

Figure 2. The FE analysis of end mill cutter

The FE analysis, mentioned earlier, has occured after an analysis chain and we have managed to reduce the value of the size deformation after continuous changes of the geometrical data. We have succeeded to reduce the deformation to an appropriate value (value of µm) with setting the appropriate radial rake angle, tilting the insert, increasing the diameter of the working part and with increasing the radius of the chip-deflection surface.

3. Planning, producing and controlling the tool prototype

Not having information about the exact insert geometry, we have created more models of the insert seat (Figure 3.) with small differences in their size, in order that the prototype end mill cutter could be mounted in the best way and could work correctly. From the insert seat models the version has been chosen by us, enabling the best location (the sample with code 2, as seen on Figure 3/b). This model has been applied by us to design the construction and the production of the steel tool. As regards the material of the final tool body, it was a C60 cold-drawn rod, in annealed condition. The output parameter was Ø50mm × 125mm (Figure 4).

The short list of operations, to produce end mill cutter:

  • cutting the rod into pieces,

  • turning, roughing and contour finishing on CNC-machine,

  • turning operations (cutting off + surfacing + formation of the edge radius + centre drilling),

  • grinding (of the holding part),

  • milling/boring operations (formation of insert seat),

  • milling (formation of the Weldon-shaft),

  • thread turning,

  • burring operation.

4. The applied design of experiments, online measured force, developed during the milling

The measurements have been carried out during dry milling process, without applying cooling-lubricating liquids, with conventional milling. In order to compare the tools, the cutting conditions have been determined by us with the help of DoE (Design of Experiments). Besides the constant cutting speed value three factors have been varied by us during the measurements. With the help of preliminary examinations the minimal, the medium and the maximal setting values have been defined by us. The cutting conditions, applied during the experiments, are as follows:

vc=120 m/min (cutting speed)

ap = 0,5 – 0,63 – 0,8mm (depth of cut)

ae = 6 – 8 – 10 mm (width of cut)

fz = 0,6 – 0,8 – 1,0 mm (feed per tooth)

Due to space limitations we cannot introduce all setting values of the experiments and all force components (feed force, normal force and axial force components), measured during the test trials.

4.1. Comparison of the cutting performance of the prototype and a tool, available in commercial trade and used for similar purposes

The force measurement has been carried out with 3 component force measuring device, type: KISTLER 5019. The eight setting trials, according to the DoE, can be seen in Table 1.

Table 1.


















































Figure 5. shows the development of the average feed force components versus the different settings.

Figure 5. Feed force components vs. different settings

As it can be seen on Figure 5., the prototype tool – with except for 1-2 settings – works with very similar force values, as compared to the rival tool; even more, in case of the 6th setting value it produces smaller force values. The development of the normal force components is shown on Figure 6, in function of different settings.

Figure 6. Average normal force components vs. different settings

As it can be seen on Figure 6., the designed and produced prototype tool (with except for the first setting) has detached the chip with smaller force, arising during the process, as compared to the rival tool. The normal force component affects the production accuracy and the surface microgeometry (especially the waviness), as it works in the direction of radial depth of cut, with other words, in the direction of the workpiece. Figure 7. shows the development of average axial force components in function of different settings.

Figure 7. Average axial force components vs. different settings

Figure 7. shows that the prototype tool has produced smaller forces in case of every setting, compared to the rival tool. The axial force component affects the production accuracy, especially in case of workpieces with thin walls. Furthermore, it has an effect on the vibration tendency of the tool as well; and, as a result of it, the surface roughness parameters and the parameters of the wawiness of the machined surface become clearly better.

4.2. Further aims and tasks

It is our further aim

  • to design a prototype tool, needing less feed force than the tools, available in commercial trade.

  • to carry out tests to examine the wear process and tool life of these tools.

  • to develop a software, optimising the load-bearing cross-section of the tool holder and the insert seat in it, based on the constants and exponents of the power function, resulting from the force measurements; provided, that the milling conditions and the acceptable values of the size deformation have to be defined by the user.

5. Summary, results

The present article has summarised the reasons, making necessary the use of the finite element method during the design of end mill cutters. It has summed up the most important requirements, to be considered during the construction and to be fulfilled by high feed milling during the machining operation. The main part of the article is to optimise the deformation of the end mill cutter, analysed with the FEM.

After summarising the circumstances of the tool production (operations, tool machines, difficulties, arising during the operations, etc.) the experiences, gained during the use of the end mill cutter, the setting values, applied at DoE and the results, measured online during the milling operation have been introduced.

Finally, the designed prototype and a tool, available in commercial trade and used for similar purposes, have been tested, compared and evaluated.


[1] Tállai P. –Mihályi G.: Új konstrukciójú marószerszámok képességvizsgálata

TDK dolgozat, BMF/BDGBMK/AGI, Budapest, 2008. pp. 35

[2] Mihályi G. - Halász G.: Marószerszám végeselem módszerrel segített tervezése

TDK dolgozat, BMF/BDGBMK/AGI, Budapest, 2009. pp. 32 + pp. 16 (Append.)