Can trochoidal milling be ideal?

I. Szalóki  – S. Csuka – S. Csesznok – S. Sipos dr.

Óbuda University, Donát Bánki Faculty of Mechanical Engineering


In the manufacturing technology the milling technology, used to machine surfaces with grooves and scallops, repeating cuttings (zigzag surfaces) has been completed with a new, alternative method: it is the so-called trochoidal milling, carried out in different kinematic ways. In the present article we are going to give a summary on the milling cycles, established with geometric modelling and suggested by the modern designing systems. The force demand, the productivity indicators and the microgeometrical features of surfaces, machined with different types of milling, will be examined and compared with analysing the results of the tests, planned and carried out systematically. The values, gained by us during machining of material grades, having different conditions and compositions, will be presented; and – with listing the advantages and disadvantages of each type – the question, raised in the title, will be answered as well.


Among the machining operations, the groove or slot milling is used to form torque transmitting surfaces, first of all on axis-like components; based on the accuracy of the machining, we can distinguish operations of general accuracy and of increased accuracy. To the firstly mentioned group belong slots, being necessary to the locking plates of bearings, to the second one slots of tight tolerance (more precise than tolerance class IT9), being part of fixed and movable locking connections. In case of closed keyways, having a low depth, the exact groove width has been produced with keyway milling machine and with double-edged keyway end mills, with one-way and two-way milling technologies for a long period of time [1]. With the general dispersion of CNC controlled machines, with the development of newly constructed tools and their becoming dominant, the specialised machines and the slot milling cutters have fallen into the background. The closed keyways have been machined with drilling operation by use of milling cutters, having central cutting edges, after that they have been milled – usually in one-way technology – to the appropriate size.

In case of other group of components, made with groove milling operation, the necessary depth of groove ap can achieve or even exceed (ap>d) the dimension of the tool diameter. The grooves can be machined with roughing operation, serving as cog-wheel of wind power plant or can serve as a surface for fixing blades in case of turbine production. The general milling, carried out in one step, is absolutely not ideal as a very long edge section contacts with the workpiece, the cutting force and the temperature rise, the momentary chip thickness means an uneven load to the edges, the unfavourable chip transport may lead to the re-cutting of the chip. The cutting operation is not effective, furthermore, it is accompanied with unfavourable edge durability of the tool and with the increase of machining costs. With the even more dynamic advancement of the so-called DTM-materials (DTM=difficult-to-machine materials) (titanium alloys, for example, Ti-6Al-4V in the air craft industry, HRSA-materials, for example, GTD 241 in the production of turbine blades, the pre-tempered tool steels, for example, ToolOx 33 and 44 in the tool manufacturing) the unfavourable phenomena, mentioned earlier, are increasing even more.

We talk about trochoidal milling operation when the groove width (bw), to be machined with a tool and having a diameter „d”, has a minimum value of 1.15 x d, the radial step over is in the range of 0.02…0.25 x d [2]. The movement cycle of the trochoidal milling operation is a type of cylindrical milling where the achievable accuracy and surface microgeometry depends on the applied strategy. In case if the grooves are machined according to these principles, then the radial depth of cut (ae) is in a continuous change, while the value of the radial step over, given at the generation of the tool path, will be exceeded by the value of aemax, belonging to the greatest radial contact; moreover, its value may achieve even a multiple value in every case! Calculating the exact value of aemax is essential in order to carry out the operation safely, to its calculation the formulas, known from the cutting theory and used in case of edge milling operation, can be used well.

With the help of the trochoidal milling methods, chosen by us, almost every problem can be solved as

  • beginning from tool steels of high toughness till the hardened workpieces, the machining operation can be carried out with the help of HPC (High Productive Cutting), even in case of workpieces, having small wall thickness,

  • in case of roughing operation the axial depth of cut is relatively great (having usually a value of 10-20 mm), while in case of radial depth of cut its value is smaller as usual. The productivity can be favourably raised with increasing the cutting speed and the feed per tooth,

  • the tool life and the surface roughness can be considered as favourable,

  • the progammed milling strategies spare the machining system (machine tool, workpiece clamping and tool clamping devices) as the cutting operation goes on with smaller force effects and lower vibrations,

  • despite of these facts, the effectivity of the machines increases.

Obviously, this method requires from the machine tool an intensive acceleration and deceleration from the control, and a look-ahead function will be demanded. The rigid connection of the tool clamping system and the smallest possible overhang of the milling cutter is an important requirement, to be met.

With the elaboration of the present topic it was our aim to compare the carefully modelled trochoidal milling types, to choose those which are able to meet the criteria, mentioned earlier, in the best possible way. In order to fulfil it, the productivity, the developing force effects, the quality of the machined grooves and the development of the machined surface roughness have been analyised by us.

1. The different types of trochoidal milling operation and their modelling

To programme the tool paths, serving as the base of our examination, Microsoft Office Excel application has been used by us. The description of tool movements has been made in a parametric way, it means that in case of change, made in any of the initial data (d, bw, w etc.), the programme is able to re-calculate the points of the tool path automatically, and the NC-program, prepared in ISO programming language, will be provided in a form, being easily adjustable to the applied machine tool controller (Figure 1).

In the literatures [2-8], studied by us, the schemes of different milling types could have been found, but very little information has been given, being utilizable in the programming. In our present study we are going to introduce the most important characteristics, benefits (see above) and disadvantages of the special movement cycles, taking the space limitations into consideration. On the above figure different types of tool path are shown, having different features from the point of view of cutting operation and serving as base of the modelling [9].

The simulation of the programmed tool paths on the machine tool

Figure 1. The simulation of the programmed tool paths on the machine tool (Mazak Nexus) and on its controller (Mazatrol™)

1/a Trochoidal milling operation with catia-model (catmo)

Nowadays, the strategy of the trochoidal milling operation can be found in several modern planning systems, but in the most of cases it is simplified to a great extent. On the Figure 1/A the simulation of the tool path can be seen: it has been generated with „Prismatic Machining” modul of planning system CATIA V5R20 CAD/CAM. The movement of the tool contains only interpolation of circles and straight lines, following each other: first of all, a circle form will be made, after that the interpolation of the straight line, made along on the side surface of the groove. It results in the fact that one of the sides of the slot has better surface roughness values, while on the other side there will be „laces” as a result of the radial step over, developed from the overlapping of the arcs. The acceptable value of the „laces” depends on the accuracy of the groove, and it should be considered during the planning phase. This procedure has the advantage that it can be easily programmed and down-milling operation will be carried out by the movement cycle.

1/b Cycloid forming milling (a real trochoidal operation)

In case we talk about machining operation of grooves where the tool path can be described with open or closed contours, or with straight or discretionary contour, then usually a cycloid curve can be a solution. The cycloid forming movement can be seen on Figure 1/B. The tool will be driven on a path, having a looped cycloid form – it is very favourable from the point of view of the load, made on the tool. This method can be considered as less effective due to the length of the way, to be covered by the tool, it requires a careful and circumspect planning (generation of NC-code/point lines); furthermore, approx. 50 percent of the covered way can be considered as dead time in this case as well.

To generate a cycloid path, the most important feature is the length of the chord (t), it is called as path accuracy factor. This feature means the length of all lines, forming the generated path, and determines the accuracy, „angularity” of the path. Its optimal value is in the range of t = 0.1…0.3 mm. In case if the value is greater than 0.3 mm, then it may lead to unfavourable deterioration process of the tool – as a result of the uneven load – and the tool life may decrease. If the value is lower than 0.1 mm, then the model contains too much points and this fact can cause problems when reading and storing the data. Therefore in our test series the generation of the tool path has been made with use of value of t = 0.2 mm [3].

1/c Semi-circular milling operation

The milling of semi-circular grooves (see Figure 1/C) is a solution to minimise dead time of the CATIA-strategy, serving as base of our tests, because the milling tool works from one side of the groove till the other one, covering the shortest possible way (it means the tool changes side diagonally), in this case the idle running is approx. 40 percent.

Its benefit is that

  • it can be programmed easily,

  • it works with down-milling opeartion and „produces” good surface roughness,

  • „laces” can be observed „only” on one of the groove sides.

Its disadvantage is that after finishing the semi-circle it makes one more step, therefore it is less productive.

1/d Swinging (pendulum) milling process

Compared to the versions, introduced till now, the swinging milling process, shown on Figure 1/D, eliminates the idle running, spent without machining operation: it is made in the way that it contains one-way and reversed milling sections as well. Its application is favourable especially in cases when the aim is to increase the material removal rate (V′, cm3/min) with a given tool.

The tool path will be formed from the continuous change of interpolation, containing semi-circles and straight lines. This procedure has the obvious benefits that it can be easily programmed and has good productivity indexes. This method has the disadvantage that the tool makes a straight step over (its value is w), after finishing the semi-circle; furthermore, on both sides of the groove an increased development of laces can be observed.

With applying the swinging milling operation (it is called as pendulum milling as well) to machine grooves, it becomes possible to achieve high material removal rate even on HSC-milling machines, having lower main spindle performance and without causing an overload or damage to the machine and main spindle.

1/e Stepping-swinging milling operation (developed by us)

In order to increase the productivity further, our research team has developed a special variation of the trochoidal tool path: its base is the swinging milling operation of grooves, therefore it is called as stepping-swinging milling method (see on Figure 1/E). The most important difference is that there is no dead time as the interpolation along the straight section will be spared: the milling tool works only along arcs of circle. The tool moves not along real semi-circles, but along an arc, having a radius of R2 and depending on the step over (w) and on the groove width and diameter of the milling tool; it guarantees that the tangential contact will be kept even in case when the tool recedes from the wall of the groove (see Figure 2). This requirement is important in order to keep the width and the accuracy of the groove. Knowing this principle, the process can be easily programmed, the program has low power demand and contains one-way and reversed milling sections as well.

Principle of stepping-swinging milling type

Figure 2. Principle of stepping-swinging milling type

1/f The traditional slot milling operation

This is the most general and widespread method to productively machine short grooves with low depth. It can be very easily programmed but it can be considered as the worst solution when the task is to machine grooves, having a greater depth. Due to the increasing vibrations and in order to keep the tool edge durability, it is not allowed to apply depth of cut values as in cases A-E. In order to effectively machine grooves, having a greater depth (ap>d), it is necessary to repeat cuts, but it can be made only at the expense of the productivity.

2. The results of the cutting operation, carried out under test conditions

The tests have been carried out in the machine shop of Donát Bánki Faculty of Mechanical and Safety Engineering at Óbuda University, on the vertical machining center, type: MAZAK Nexus 410A (controller: Mazatrol™), it has been installed to carry out tool tests, the trials have been executed with application of device to blow cold, compressed air. The force examination has been made easy by the dynamometer, type: Kistler 9257, the DynoWare™ software to evaluate the results, and by the data collecting system, used by us to the tool qualification, while the stereo microscope has been used to monitor the conditions of the tool edges: it has been equipped with CCD-camera and with ImagePro software (to analyse images) as well.

To the trials workpieces with a dimension of 160×50×50 mm have been used, they have had the following properties: the grade 40CrMnMo7 (DIN standard W. Nr. 1.2391) has been pre-tempered to approx. 1000 MPa, the hardness has been checked by us ((HB285±5).

The monolith cemented carbide HPC shank milling cutter (type: R215.36-12060-AC26L, see on Figure 3) has been placed to our disposal by the representative of SANDVIK Magyarország Kft. The tools have been clamped in a cold shrink adapter, with the help of clamping system PGR „powRgrip®”, produced by EMUGE-FRANKEN. The overhang of the tool was 40 mm, the run-out of the milling cutter was 0.01 mm.

HPC shank milling tool

- fine grained cemented carbide;

- modern TiAlN coating;

- λs = 60° helix angle

Figure 3. HPC shank milling tool, produced by SANDVIK (CoroMill® Plura)

The settled data and conditions, applied during the tests, have been summarised in Table 1. The feed and axial force components have been measured with the force measuring device. The trials have been completed with the following result parameters: time and productivity analyse, accuracy examination and micro geometrical measurements.

Table 1. Test milling conditions

Constant conditions

Cutting speed,

vc, m/min

Rpm, n, min-1

fz, mm

vfm, mm/min

vf, mm/min

~ 120





Varying conditions


bw, mm

w, mm

ap, mm

aemax, mm












where: fz – is the feed per tooth; vfm – circumferential feed; vf – the central feed of the tool.

2.1. The results of the on-line measurements in case of different trochoidal milling types

The tests, carried out by us till now, have brought remarkable results as regards the average feed and axial force components, measured during different trochoidal milling methods. Depicting the force components of the different methods (Figure 4) we can get a picture about the development of the forces. Based on it, it is easy to understand the truth of the question, already mentioned in the headline of the present article whether trochoidal milling can be an ideal solution from the point of view of end mills and the machine tool.

The average values of the feed force components are surprisingly low in case of every trochoidal milling method, the tool is continuously trying to „move away” the workpiece (see the upper part of Figure 4). In case of the traditional, general milling - under test conditions – approx. 3.5- 4 times greater feed forces have developed. This phenomenon can be explained by the different number of cutting edges, engaging the workpiece. The full or general milling requires significantly more power, it results in more intensive vibrations, the usage and the input power of the machine tool is increased; in addition, the noise load has a multiple value, compared to all trochoidal milling types, based on our experiences it may approach even a level, being intolerable to the human ears.

The development of feed (red) and axial force (blue) components in case of different milling methods

Figure 4. The development of feed (red) and axial force (blue) components in case of different milling methods

It is a well-kown fact that the value of the axial force and the accuracy of the groove is influenced by the helix angle to a significant degree. The axial force values (marked with blue colour on figure) are negative as the workpiece is trying to draw out the tool from the tool clamping system, or with other words, the tool is trying to lift up the workpiece from the machine table. As regards the average values of the axial force (see the lower part of Figure 4), it can be noticed that the difference between the milling methods has decreased, but its value (60 percent) can still be considered as significant. It is worth mentioning that in case of CAtmo, cycloid and semi-circular milling operations by approx. 90 percent lower axial force can be observed, compared to the traditional slot milling. It is remarkable that in case of a significant increase of axial depth of cut and step over the average values of feed and axial forces have increased only by 100 percent in case of different trochoidal milling methods.

2.2 The productivity of the modelled milling methods

To the characterization of the productivity, the material removal rate (V′, cm³/min) has been used: it sets a definite order among different types. By this order the methods will be characterised solely from one point of view, from economical point of view, and influencing factors (thermal and mechanical impacts, vibrations, power demand etc.), having effect on the process security, edge durability of the tools, furthermore, on the development of the machining costs to a great extent, will not be considered.

Material removal rates of the modelled milling methods

Figure 5. Material removal rates

of the modelled milling methods

Based on the models and tests it has become clear that the 6 milling methods can be divided into three groups, based on the productivity (Figure 5). In the first category the following milling methods can be ranked: CAtmo, cycloid and semi-circular, with these a material removal rate of 8 – 18 cm3/min can be achieved. The next category with higher productivity is represented by the swinging and stepping-swinging types, in these cases the productivity rate has achieved a value of 25 – 35 cm3/min. The general milling operation has been proved to be the most productive as the material removal rate has reached a value of 30 – 50 cm3/min. It is important to emphasise that

  • there was a tool, having an exceptional performance: it had a really good resistance against mechanical and thermal effects, till finishing the tests almost no wear has been observed on it,

  • in case of trochoidal milling operations greater feed values can be applied, compared to the general milling, as the load of the tool is much more favourable. It means that in case of greater feed values the chip volume, detached during a time unit, can be increased to a great extent.

Our further tests should be focused on to what extent the productivity can be improved without the risk of a tool break.

2.3 The accuracy and the surface texture of the machined grooves

The accuracy examinations have been carried out with the help of a calibrated sliding caliper with a resolution of 0.01 mm, equipped with a dial gauge, the device has been produced by Mitutoyo. Based on the results (shown in Table 2), the following conclusions can be drawn:

  • applying trochoidal methods, decreasing width values have been observed in case of increasing the productivity, it means that faster machining operations have caused greater „laces”, i. e. more inaccurate grooves,

  • it is obviously that the general milling operation has produced grooves, having greater width, compared to its nominal value, it can be explained by the great radial load. Having studied the video recording, made during the operation, and the results of the force measurements it can be noticed that a normal force, having a value of ± 5000 N, has developed perpendicularly to the groove (respectively to the feed) when the tool has entered the material, and it has visibly turned off the tool from the centre. This phenomenon can be reduced with applying the so-called tool sparing path. At the end of the milled way the so-called keyhole effect can be noticed, it means a new proof to the unfavourable radial load.

Table 2. Measured results of groove width

Groove width / milling methods






General milling


w = 1.2 mm







w = 2 mm







In case of surfaces, machined with roughing operation, microgeometrical inspections are carried out rarely. We were curious about the development of the laces, waviness and the surface roughness on the surface of the groove sides in case of different methods. The registratums have been made with a resolution of (R) ±100 µm in case of the roughness profile and (P) ±200 µm in case of the whole profile, the degree of the laces, developed on the surfaces, can be seen well: it is tightly connected with the accuracy and Rz roughness parameter.

The values of the maximum height of profile

Figure 6. The values of the maximum height of profile, depicted in diagrams in case of four methods – the filtered (R) and unfiltered (P) surface profiles (ap = 16 mm)

On the upper part of Figure 6, the microgeometry of the milled surfaces is shown in case of four types of trochoidal milling operations, in the event of filtered and unfiltered profiles as well. Analysing the surface of the groove, machined with the swinging methods, it can be established that the whole profile (P) has shown a completely different picture, compared to the filtered one (its detailed inspection will be made in the frame of the TÁMOP-project). Depicting the values of the maximum height of profile Rz (see on the lower part of Figure 6) it can be noticed that the roughness has the most favourable value (<10 µm) in case of general milling, while the highest values have been registered in case of swinging methods (80-100 µm). It is important to emphasise that it would be fairly subjective to evaluate the methods solely based on these data.

3. Conclusions, further tasks

Based on the comparison of the trochoidal milling methods it has become clear that in the present stage of inspections it is not possible to give a correct answer to the question, given in the headline of the article. Based on several aspects of inspections (power demand, productivity, accuracy, surface texture, edge durability, costs) a suitability order can be made among the different methods, taking the priorities into consideration. According to our experiences, gained during the tests, the general milling operation requires significantly greater forces, the process is accompanied with increased load to the tool and machine and with greater power consumption; but applying the same feed values, it is still more productive, compared to the trochoidal methods. In case of machining grooves, having a greater depth (ap>d), additional cuts are necessary in order to achieve economical general milling, but these can be the obstacle to the economical machining. On the other hand, in case of trochoidal milling methods, applying the same cutting conditions (w, ap, bw etc. have constant values), the tool wear has decreased to a significant extent. In addition, almost the whole working part of the tool can be used (ap can achieve even a value of 2xD), and it can result in the increase of chip volume, detached with one tooth.

Our further tasks include similar tool tests, sponsored by leading tool producing companies: these trials will have the aim to analyse the tool life of different types and to determine the optimal machining values. If the trochoidal milling method is successfully combined with integrated or parametrically programmmed feed regulating system, then machining of the grooves may become even more economical. It has the condition that the tool should cover the way, spent without machining, with an increased speed value.


The project was realised through the assistance of the European Union, with the co-financing of the European Social Fund, namely: TÁMOP-4.2.1.B-11/2/KMR - 2011 - 0001: Researches on Critical Infrastructure Protection.

This article was presented at the International Manufacturing
Conference (Budapest, Hungary, 14-16 November 2012, organised by GTE,
Hungarian Scientific Society for Mechanical Engineering) and has been published in
electronic form, on CD as well.


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