Identifying the lead angle limit to achieve required surface roughness in ball-end milling

doi:10.21203/rs.3.rs-1454249/v1

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Research Article

Identifying the lead angle limit to achieve required surface roughness in ball-end milling

https://doi.org/10.21203/rs.3.rs-1454249/v1

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When milling generally-shaped surfaces with a ball-end milling tool, machined surface roughness and accuracy as well as machining productivity are often monitored. Improving one of these parameters often causes a decrease in the other monitored parameters. Therefore, knowing possible ways of influencing these parameters is important for achieving the optimum result, if possible, in all requirements. A deep understanding of how some technological parameters influence finished surface roughness is still lacking, as well as detailed knowledge of the relationships among some roughness parameters. In response, an experiment entailing machining of planar samples at different orientation angles was carried out to identify the influence of the studied parameters on the transverse roughness of the final surface. A finding was made, that the resulting surface roughness is dependent on the cutting edge geometry of the particular ball-end milling tools used and the achieving of the required surface roughness can be guaranteed by setting the specific lead angles. Furthermore, it was verified that a minimum lead angle limit can be found based on the geometric properties of the specific milling tool, and the relationship between the evaluated roughness parameters Ra and Rz was found as well.

milling

surface roughness

ball-end-milling tool

scallop

real cutting diameter

lead angle

When milling generally-shaped surfaces, the machined surface quality, shape and dimensional accuracy of the final surface and machining productivity are very important aspects of finishing machining. Roughness, which plays the largest role in evaluation of machined surface quality, is a directly measured parameter that must be achieved when machining a part. Tools with a circular cutting edge, known as ball-end mills, are used to finish shaped surfaces. When a surface is point milled using this type of tool, the main geometric parameters that determine the resulting surface roughness are the tool diameter and the spacing between the single passes of the toolpath (step-over). These parameters determine the height of the remaining material on the machined surface, known as the scallop [1]. The structure of the final surface is also influenced by factors such as the choice of cutting speed and feed rate. The surface roughness can be evaluated in the direction of tool movement (along the tool path – longitudinal roughness) or perpendicular to the direction of tool movement (across the toolpath – transverse roughness). Based on the nature of the shape of the remaining material, the scallop parameter can be compared to the resulting roughness Rz (roughness depth parameter, defined by ISO 4287), evaluated perpendicular to the direction of tool movement. The surface roughness in the direction of tool movement is mainly determined by the tool rotation and feed per tooth. If the cutting conditions are set optimally, the roughness perpendicular to the direction of tool movement has a predominant influence on the resulting surface. Thus, the scallop is a parameter that can be selected during machining operation set-up in the CAM system and used to determine the expected machined surface roughness. However, there is no direct information about the relationship between the scallop parameter and the resulting Ra value (the average arithmetic roughness according to ISO 4287), which is often the only defined parameter to be achieved after surface machining. The relationship between the parameters Rz and Ra is addressed in DIN 4763, which provides only a relatively wide range of values (not very detailed) and several papers can be found describing experiments with data measurements monitoring a narrow range of conditions [2–5]. Other parameters that are not included in the scallop calculation also need to be taken into account and examined through experiments. The experiments mentioned below demonstrate that changing some technological parameters results in a different surface quality (parameter Ra) for the same scallop value. These parameters include, for example, cutting speed, tool orientation angle, tool diameter, the choice of material to be machined and the relationship to tool wear.

Other parameters that are used when setting the toolpath for machining shaped surfaces are the lead angle or the tilt angle of the tool axis. The lead and tilt angles directly affect the cutting speed achieved with a specific spindle speed at the point of contact with the material. The smaller the tool lead angle, the less material is machined at the effective tool diameter and therefore the lower the cutting speed. If machining is carried out with a zero tool axis orientation angle, the material is removed by the tool area close to the tool centre where the effective diameter is very small and therefore the cutting speed decreases rapidly. A low cutting speed and low effective diameter have a negative impact on the resulting transverse roughness [6] [7]. This is one of the reasons why a lead angle or tool tilting is used in milling. However, some specific machining cases do not allow for significant lead and tilting angles and only angles in the order of units of degrees are possible (e.g. milling of narrow inter-blade spaces, etc.). In three-axis milling of a shaped area, where the tool orientation is constant (perpendicular to the plane of the machine tool table), the angle of orientation of the tool from the workpiece surface is determined by the particular shape of the workpiece (its curvature and orientation at a given point). Thus, at certain toolpath points, the near centre of the tool is used during machining. Batista et al. [6] experimentally verified the surface finish when machining WNr 1.2367/X38CrMoV5-3 steel with a zero-tilt angle cutter. Cycloid-shaped traces are visible on the workpiece surface which correspond to the ploughing of the material. These cycloids have a constant pitch, which is determined by the feed rate. A similar finding was made by Mali [8], who investigated the effect of changing the direction of the point milling toolpath and cutting conditions during three-axis milling of a shaped workpiece of Duralloy EN AW 7075.

De Souza [9] investigated force loads when machining an AISI P20 steel shaped workpiece using a ball-end mill. The experiment showed that the highest force load occurs in the tool centre where the material is formed rather than machined. By increasing the cutting speed, the area of this significant increase in cutting forces near the tool centre can be narrowed and the force load at all locations of the shaped workpiece can also be reduced. The effective milling diameters are also monitored as a function of the machining direction at a particular location. A similar experiment was also carried out by Scandiffio [10] when milling AISI D6 tool steel. He discussed the relationship of the effective cutting diameter to different milling directions, force loads and the resulting surface roughness. For three tilting angles, pulling the tool resulted in lower roughness and lower cutting forces than when it was pushed. Beno obtained similar findings when machining a generally-shaped surface [11], observing the resultant quality when the rows were machined in different directions with respect to the workpiece shape. Aspinwall et al. [12] demonstrated the effect of cutter orientation on the machinability of Inconel 718 through experiments. The orientation of the tool axis relative to the machined surface was defined by a fixed angle of 45°. The effect of different surface rows (pulling, pushing) was investigated and for comparison the surface was machined at a 0° tool orientation (three-axis milling). The experiment showed that the toolpath direction and tool axis orientationhave a clear effect on tool life, cutting forces and the resulting surface roughness. Wojciechowski drew similar conclusions [13] [14]. Vavruska [15] proposed an algorithm for calculating the cutting speed and feedrate depending on the current effective diameter at a specific location on the workpiece, which leads to achievement of selected cutting conditions. Käsemodel [16] subsequently carried out a machining experiment using a new computational algorithm based on previous findings. Erdim [17] optimized the feed on the shape path by calculating the material removal at a specific location according to the contact point in order to increase productivity (reduction of machining time). Rybicki [18] adopted a similar approach but also varied spindle speed in addition to feed rate, and achieved a lower tool load and constant roughness of the machined surface alongside a reduction of machining time.

Matras [19] addressed machining of hardened steel with a CBN ball mill. He proposed a cutting force prediction algorithm that takes into account the tool contact point at a specific location of the shaped workpiece during three-axis milling. He optimized cutting conditions, supported by an experiment verifying cutting condition settings (especially feed rate) and the effect of this change on cutting force magnitude. Lazoglu [20] optimized the machining path to achieve the lowest possible force load. The proposed force optimization is more suitable for semi-finishing operations since toolpath modification affects the resulting surface texture. Costes [21] predicted surface roughness based on changes in the position on the shaping toolpath. Author predicted tool vibration locations and experimentally verified the calculations using laser sensors. The roughness measurements correspond to the calculations. No et al. [22] focused on a reverse engineering simulation of cutting forces and tool orientation for selected cutting conditions. Data from a 3D scan of the tool (cylindrical cutter) were used for the prediction, for which the scanned points around the cutting edge are essential.

There are also various analytical (mathematical prediction) studies that aim to predict the resulting surface roughness. Mikó et al. [23] defined the mathematical relationships for predicting scallop height depending on input parameters such as toolpath density or lead angle. It is a prediction-model of the scallop that emerges during changes to the toolpath spacing (also called step-over). Chen et al. [1] modelled the longitudinal and transversal surface roughness with respect to changes of the feed per tooth. While the cutter diameter changed, the step-over was kept constant and the feed per tooth was increased. Thus, there is a decrease in Rz in the transverse direction (scallop parameter in the design) but an increase in longitudinal roughness (an effect of increasing the feed rate). In his study, Shchurov [24] alluded to the problem of projecting the toolpath onto a curved surface (specifically a spherical canopy). He proposed a mathematical model that ensures uniform distribution of the toolpath passes on the workpiece shape in order to achieve constant spacing and therefore constant roughness over the entire curved surface. In summary, he concluded that given the vastness of the problem, the development of a mathematical algorithm capturing all cases of curvature change (convex-concave transitions, etc.) requires further work. Similarly, [25] Liu improved his previous mathematical algorithm [26] which aims to adjust the CL data to obtain the best possible scalloped shape surface in terms of the scallop parameter. Yang [27] used the NURBS method to simulate the residual surface after sphere milling. He observed the effect of the machined surface curvature on the resulting roughness and discussed the relationship between tool compliancy and tool vibration at larger tilt angles.

Changing the tool orientation angle as well as the milling direction plays an important role when machining difficult-to-cut materials. Matras [28] investigated the dependence of the resulting surface roughness on the selected angle of pulling/pushing when machining 16MnCr5 steel. The angle is varied in 10° increments from − 90° to 90° (0°- machining through the centre of the tool). The results showed that the worst roughness occurred near 0°. However, the step of changing the tool tilt angle is quite coarse for a detailed analysis of the behaviour of the resulting surface roughness. Stejskal et al. [29] conducted an experiment machining Duralloy EN AW 7075 and duplex steel DIN 1.4462 and focused on the relationship between the contact point parameter of the ball-end mill and the actual cutting speed. From the surface roughness measurements of the planar specimens, they found an approximate limiting lead angle value from which the resulting surface finish remains unchanged as the lead angle increases. Here, the lead angle was varied near the tool centre in small increments (1°) but the quality was assessed from a visual perspective rather than by comparison with the theoretical scallop value from the CAM system. The findings led to the development of an optimization algorithm that adjusts the tool orientation vector on the machining toolpath of the general shape surface.

Based on the findings from many of these references, it is evident that a detailed understanding of the effects of parameter settings on the nature of surface roughness is very important for optimal setting of machining operations. If the point milling operation settings using the ball-end mill are unsuitable, then either the required surface roughness for the production of the part will not be achieved in many sections on the machined surface or, on the contrary, the resulting quality is too high in relation to the setting requirements. This can result in the production of a scrap part or, on the other hand, part production is too costly due to the increased production time and machine and tool costs. This wastes machining time, degrades the part material and wears out the tool. The area that has been least investigated to date is the setting of a suitable tool lead angle, which, if increased, would no longer cause such a pronounced influence on the required machined surface roughness perpendicular to the direction of the cutter movement which arises from the geometric indeterminacy of the engagement conditions near the tool centre. Different results can also be expected when usingvarious types and diameters of the ball-end milling tools. Therefore, this paper aims to increase knowledge of the effects on the achieved surface roughness at a certain tool axis orientation angle and to deepen knowledge of the dependence of the achieved machined surface roughness on the input data that can be influenced when setting the toolpath, which in turn increases the reliability of achieving the required roughness in the transverse direction to the tool movement (i.e. transverse roughness).

The analysis of the current state of the art shows that one of the main parameters directly influencing the machined surface’s final transverse roughness is the actual effective tool cutting diameter at the contact point between the tool and the workpiece. The actual effective tool cutting diameter in turn directly affects the actual cutting speed at the contact point. Specifically, with a ball-end mill, it is the section of the cutting edge defined by the original surface of the workpiece and the bottom of the toolpath, newly created during the point milling operation. However, the effect of the tool cutting edge geometry itself has not yet been analysed experimentally. It is therefore necessary to design a suitable experimental setup to analyse the transverse roughness achieved on the machined surface according to the actual tool lead angle relative to the machined surface, as well as the influence of the nominal diameter of the ball-end of the milling tool and of the cutting edge geometry itself.

A suitable experimental setup is shape machining where the tool contact point is variable depending on the workpiece shape. For simplicity, the machined specimens are considered as planar and the tool always has a fixed lead angle during milling, thus inducing specific contact point conditions as would occur at specific sections during machining of the shaped surface. The spindle speed is set so that the cutting speed on the tool diameter at the top of the machined groove is constant (Fig. 1), diameter at section "3"). For the case at hand, the effective diameter D_ef at a certain point of the cutting edge can be calculated according to Eq. (1) when D is the nominal tool diameter [mm], α is the tool lead angle [°] and Sc is the selected scallop value [mm]:

$${D}_{ef}=D*\text{sin} \left[\alpha +arc\text{cos}\left(\frac{D-2* Sc}{D}\right)\right] \left(1\right)$$

The corresponding cutting speed v_c [m/min] at a given location is then calculated from Eq. (2), where S is the spindle speed [1/min]:

$${v}_{c}=\frac{\pi *{D}_{ef}*S}{1000} \left(2\right)$$

For the smallest lead angle (or for zero), the value of the effective diameter reaches a minimum, and therefore the cutting speed reaches a maximum. Here the cutting speed is set to respect the spindle speed limit of the machine tool. Logically, a higher cutting speed can be set for higher tool diameters due to machining at higher effective diameters. Given the observation of the roughness parameter in a direction perpendicular to the tool movement (when the roughness in the groove is not observed), a constant feed per tooth is selected for machining. The four most common nominal diameters of the ball-end of the milling tool are chosen (see Table 1) and their effects on the achieved transverse roughness are analysed. The depth of cut corresponds to the material removal during finishing and is set to one fixed value for all measurements. All of the cutting parameters are summarised in Table 1.

Table 1

Cutting parameters for each tool
Parameter /Factor
Tool diameter	D	mm	4	6	8	12
Cutting speed	v_c	m/min	40	55	70	90
Feed per tooth	f_t	mm	0.08
Axial depth of cut	a_p	mm	0.1

A description of the contact points between the tool and the workpiece is presented as part of a more detailed analysis of the assumptions (Fig. 1). The tool tip is represented by point 0 and the points on the left and right side of the tool when moving through the groove are defined by points 2 and 2̍. The main points of observation in this experiment are marked 1 and 3. These are the points that include the minimum (point 1) and maximum (point 3) of the effective cutting diameter D_ef. The observed effective tool cutting diameter at these points is denoted as D_ef1 and D_ef3 and the corresponding cutting speeds v_c1 and v_c3. In

Figure 2, a linear increase in the effective cutting diameter at both monitored points can be observed as a function of the lead angle for the selected nominal tool diameter D6. The linearly increasing trend in cutting speed v_c1 must be reflected while v_c3 is constant (greater than the lead angle of 0°). The dependence of the cutting speeds on the lead angle at the two points for tool D6 can be seen in Fig. 3. These characteristics are related to the spherical shape of the ball-end mill envelope. The lead angles are set so that attention is paid to the section where other experiments have shown that there are significant changes in the resulting roughness. Lead angles greater than 4° are represented only by two additional values, as no significant difference in the resulting surface roughness is expected here.

The experiment design minimises the number of variable parameters that are not the main subject of investigation. The intention is to obtain results that can conclusively explain the influence of the monitored parameters on the resulting surface quality.

3.1 Workpiece material, tools and machine tool used

The chosen workpiece material is aluminium alloy with the designation EN-AW7075 - T651. This alloy is often used in aerospace manufacturing and its advantages include high tensile strength, good machinability and low weight. It is assumed that for this material, the effect of cutting conditions on the intensity of cutting edge wear will be negligible, thus excluding the effect of wear in the experiment measurements. The material does not tend to adhere to the cutting edge, which could potentially affect the machined surface. The blank is a drawn flat bar pre-machined to 190 x 110 x 25 mm. The test blank is provided with a pair of through holes for M8 countersunk head screws. These screws are used to clamp the blank to the machine table via the stones in its T-slots. Emulsion liquid (Blasocut Combi) at a concentration of 5% is used for cooling during machining and the supply to the cut is provided by two external nozzles. For the experiment, double-bladed uncoated cylindrical shank ball-end milling tools from Iscar with a grade of IC08, nominal diameters of 4, 6, 8 and 12 mm and overall lengths of 50, 51, 63 and 71 mm were chosen. The specific manufacturer code designations are EB-A2 04-06C06E50, EB-A2 06-07C06E51, EB-A2 08-09C08E63 and EB-A2 12-14C12E71. Thermal clamps were selected for tool clamping. The experiment was carried out on a five-axis MCVL1000 milling centre (manufactured by Kovosvit MAS Machine Tools) equipped with a Nikken tilt-turn table. The working range of the machine tool is: X = 1016 mm; Y = 610 mm; Z = 660 mm. The range of working feeds of all machine axes is identical: (2 to 12000) mm/min. The electric spindle of the machine with the HSK E40 clamping interface has a maximum speed of 42000 1/min.

3.2 Toolpaths and chosen strategy

One square sample is machined for each tool and lead angle combination. The set of samples is evenly distributed on the face of the blank. The dimension of one machined sample is 7 x 7 mm, with the exact scallop value based on Eq. (3), where Rsm (spacing of the grooves according to ISO 4287) is rounded down to make the sample width an integral multiple thereof. The tool movement (Fig. 4) is based on a zig strategy with a left-to-right rowing direction to ensure climb cut (down-milling). The desired workpiece tilt orientation is set by indexing the table by tilting it in the B axis. The toolpath for milling samples is implemented through interpolation of the X and Z axes and the step-over direction takes place in the Y axis.

$$Sc=\frac{D}{2}-\frac{\sqrt{{D}^{2}-{Rsm}^{2}}}{2} \left(3\right)$$

3.3 Selection of the lead angle

The logic used to set the lead angle change was that the discrepancy between the desired and actual measured surface roughness would be highest for small angles, therefore the lead angle change is set with a small spacing for small angles. For larger lead angles, the assumption is that the surface roughness results would be relatively constant. Thus, there is no bigger setting step change in this range of angles. To ensure constant cutting edge engagement conditions, one tool orientation variation was chosen, namely pull milling.

3.4 Implementation of the experiment

Before machining, the cutting edge envelopes of the ball-end milling tools were measured. They deviated from the ideal nominal ball by -0.006 to + 0.006 mm with respect to the nominal diameter. The radial runout of the tools clamped in the chuck and into the machine spindle was also measured to eliminate the effect of runout on the measurements. The tool radial runout during all tests ranged from 0.005 to 0.008 mm. The machine tool setup during sample milling with the D12 ball-end mill is shown in Fig. 5.

3.5 Tool analysis

The actual tool cutting edge geometry was determined with an Alicona InfiniteFocus G5 scanning digital microscope. The cutting edges of each milling tool were analysed by converting the STL file into CAD software. Differences in the geometry of the cutting edges, which were sharpened on the individual tools, may affect the differing texture of the resulting machined surface of the samples.

The surface roughness of the samples was measured using a Mahr LD130 roughness instrument with an LP C 25-15-2_90 measuring transducer. The characteristics were evaluated according to ISO 4287, using a Gaussian filter ISO 16610-21 with a cutoff wavelength LC of 0.8 mm. Roughness measurements were performed perpendicular to the direction of tool movement in the trace (as shown on Fig. 6). The texture of the machined surface on the samples was also optically observed on a Keyence VHX-7000 microscope (Fig. 7) with a VH-ZST Dual Objective Zoom Lens.

The following tables show the measurements of the roughness parameters Rz (Table 2) and Ra (Table 3) for the tool lead angles that had been set. These are the averages of five repeated measurements on each sample. In Table 2, the scallop values Sc are also indicated.

Table 2

Rz parameter measurements
Lead angle α [°]	0	1.5	2	2.5	3	3.5	4	7	10	30
Tool diameter	Rz [µm]										Sc [µm]
D4	5.28 ± 0.05	6.03 ± 0.05	5.91 ± 0.08	5.92 ± 0.13	5.76 ± 0.1	5.47 ± 0.08	4.93 ± 0.05	4.19 ± 0.06	4.18 ± 0.07	4.53 ± 0.03	4.2
D6	5.22 ± 0.17	5.09 ± 0.2	4.94 ± 0.24	4.66 ± 0.24	4.92 ± 0.23	5.02 ± 0.2	5.1 ± 0.25	4.51 ± 0.1	4.53 ± 0.17	4.48 ± 0.12	4.1
D8	7.95 ± 0.28	7.65 ± 0.09	7.69 ± 0.3	7.20 ± 0.31	6.46 ± 0.33	5.38 ± 0.25	4.74 ± 0.3	4.47 ± 0.25	4.48 ± 0.12	4.42 ± 0.1	4.4
D12	10.86 ± 0.5	11.63 ± 0.41	10.99 ± 0.48	11.09 ± 0.35	10.22 ± 0.31	9.00 ± 0.32	6.89 ± 0.42	4.40 ± 0.35	4.57 ± 0.4	4.68 ± 0.43	4.5

Table 3

Ra parameter measurements
Lead angle α [°]	0	1.5	2	2.5	3	3.5	4	7	10	30
Tool diameter	Ra [µm]
D4	1.29 ± 0.02	1.30 ± 0.07	1.31 ± 0.1	1.34 ± 0.15	1.34 ± 0.08	1.26 ± 0.07	1.12 ± 0.07	1.01 ± 0.03	1.01 ± 0.02	1.08 ± 0.01
D6	1.39 ± 0.07	1.26 ± 0.05	1.16 ± 0.04	1.10 ± 0.08	1.07 ± 0.04	1.14 ± 0.05	1.11 ± 0.09	1.03 ± 0.03	1.07 ± 0.07	1.04 ± 0.02
D8	2.05 ± 0.17	1.93 ± 0.05	2.02 ± 0.15	1.97 ± 0.13	1.59 ± 0.14	1.21 ± 0.1	1.09 ± 0.1	1.03 ± 0.15	1.05 ± 0.07	1.05 ± 0.05
D12	2.87 ± 0.2	3.09 ± 0.21	2.75 ± 0.12	2.70 ± 0.07	2.45 ± 0.13	2.14 ± 0.15	1.59 ± 0.17	0.95 ± 0.08	1.04 ± 0.1	1.07 ± 0.09

Figure 8 shows the dependence of parameter Ɛ_sc on lead angle change. Ɛ_sc is the ratio of the Rz measurements to the set Sc. This figure shows the lead angle range up to 8°; for larger lead angles, the constant value of (epsilon) was achieved. The larger the tool diameter, the larger the difference between the measured Rz and scallop for a given lead angle. However, this type of dependence was not found for the D6 tool, which exhibits a relatively consistent Ɛ_sc ratio over the entire range of selected lead angles. It is also evident that for the diameters of tools D8 and D12, the measured Rz corresponds to the theoretical Sc value only with larger lead angles than for tools D4 and D6. For all tools, it was true that from a certain threshold lead angle, the Ɛ_sc ratio was close to the desired value of 1 for all higher values. To determine the nature of this phenomenon, the geometry of the spherical part of the tools of all diameters is analysed in the next step.

The tool cutting edge geometry was evaluated in the tool tip area corresponding to the lead angle where the change in the achieved transverse roughness had been found. Figure 9 highlights the two main tool surface areas: rake face (2) and primary relief (3). A detailed analysis of the cutting edge geometry of the tools of all diameters showed design differences in the transitional part of the blade (the outline of the blade around the tool axis). This detail can be described by the circle (1), hereinafter referred to as the circular transition boundary.

Figure 10 highlights the material removal zone for tool lead D6 at an angle of 3°. The area boundary diameters are D_ef1 (inner) and D_ef3 (outer), as shown in Fig. 1. In this case, the circle C1 (1) created by tool sharpening does not interfere with the contact area (2).

Figure 11 shows a comparison of the effective cutting diameters D_ef1 for lead angles ranging from 0° to 8°. The measured significant diameters of the grinded geometry transition C1 for each tool are indicated (horizontal dashed line). The D6 tool has a circle intersection with the engagement zone close to the 1.5° lead angle. The other tools have a circle intersection with the engagement zone at a greater lead angle values (between 3° and 4.5°).

Table 4 summarises the measured diameters C1 for each tool diameter and the exact values of limit lead angles obtained by comparing the C1 values and the dependence of diameter D_ef1 on the lead angle.

Table 4

Measured diameters C1 and the limit lead angles for each tool diameter
Tool diameter	C1 [mm]	Limit lead angle [°]
D4	0.24	3.3
D6	0.14	1.3
D8	0.52	3.7
D12	0.87	4.1

Figure 12 shows the contact zone for a lead angle of 3° and the circle C1, corresponding to the circular transition boundary. For tools D4, D8 and D12, the contact zone and circle C1 intersect and for tool D6, this circle does not interfere with the contact zone. As shown in Fig. 13, this is the cause of the poor surface roughness and the significant increase in Ɛ_sc above 1, as shown in the graph in Fig. 8. The interference of the cutting edge section with the circular transition boundary causes irregular tool marks on the machined surface (for all tools except D6 in this case) and this leads to an increase in Rz compared to the predicted Sc value. The larger the area of this part of the tool cutting edge that performs chip removal, the higher the resulting Ɛ_sc value; see Fig. 8.

Figure 14 shows the contact zone for a lead angle of 4° and the circle C1, corresponding to the circular transition boundary. In the case of tool D12, the contact zone and circle C1 intersect; for tools D4, D6 and D8, this circle does not interfere with the contact zone. Figure 15 shows that for the surfaces finished with tools D4, D6 and D8, the tool trace has a regular form, while the undesired tool impression is still present in the tool D12 sample. This corresponds to the Ɛ_sc value, which is still quite high for tool D12 (over 1.5). On the other hand, for the other tool samples, the Ɛ_sc value achieves a constant level even for larger lead angles, i.e. close to the desired value of 1, as shown in the graph in Fig. 8.

The observed relationship between the shape and regularity of the marks left by the ball-end mill during leading on the machined surface and the contact point between the tool and the workpiece is consistent with the observed dependencies of the surface roughness measurements and Ɛ_sc ratio for a particular lead angle setting. The results point to the conclusion that for a given tool geometry, the diameter C1 may be determined by analysing the tool cutting edge shape. Using this diameter, it is possible to derive the minimum tool lead angle from which the transverse roughness of the machined surface will correspond to the value which is a theoretical assumption based on the tool path setting. In contrast, it is evident that this value is independent of the nominal tool diameter.

The results of the surface roughness measurements also indicate the possibility of determining the ratio of two surface roughness parameters - Rz and Ra. This ratio (Fig. 16) is constant even for small lead angles, although here the dependence is not completely linear (the X-axis is truncated, while the other measured values are constant). Thus, Ra can be derived from this ratio for the given conditions if we know Rz or scallop (parameter Sc). The relationship between Rz and Ra is tentatively defined by the standard [DIN 4768]. The results thus signify a significant refinement of parameter dependence. The larger Rz is, the larger Ra is (valid for all cutter diameters). As the lead angle increases above the point where the Ɛ_sc ratio stabilises close to 1, the Rz/Ra ratio varies between 4.1 and 4.6. When the lead angle is below this limit, the Rz/Ra ratio range increases to between 3.7 and 4.6. In general then, if Rz is known, Ra for the least favourable case can be determined for a given setup by the formula Ra = Rz/3.8.

The parameter Ra is the average arithmetic roughness value. It can be obtained as the arithmetic mean of all parts of the roughness profile values according to Eq. (4). When comparing the Ra parameter for different roughness profiles, the amplitude of the profile and the nature of the profile in the regions between the amplitudes are important, as seen in Fig. 17.

$${R}_{a}=\frac{1}{l}{\int }_{0}^{L}\left|Z\left(x\right)\right|dx \left(4\right)$$

The parameter Rz represents the depth of roughness, namely the arithmetic mean of the different depths of roughness Rzi occurring in the measured section of the profile ln, which can be calculated according to Eq. (5). The parameter Rz, unlike Ra, only considers the values of the profile amplitudes in the given profile sections, not the nature of the profile between amplitudes, as seen in Fig. 18.

$${R}_{z}=\frac{1}{n}({R}_{z1}+{R}_{z2}+...+{R}_{zn}) \left(5\right)$$

Figure 19 illustrates why the Rz/Ra ratio is constant even when the measured Rz differs significantly from the theoretical scallop value. The two profiles of the measured roughness for lead angles of 1.5° and 4.5° show that although the peak amplitudes are different, their frequencies (parameter Rsm) and especially the waveforms are identical. Under these assumptions, it follows that whatever the amplitude of the peaks, the average Ra value will always be the same multiple of the value of that amplitude (hence Rz).

The machined surface roughness on the shaped part perpendicular to the tool movement can be influenced by various parameters. In this experiment, attention was paid to lead angle variation for four selected ball-end mill diameters. The other machining parameters were held constant to eliminate other effects on machined surface roughness.

1. The result shows a discrepancy between the theoretical scallop roughness value and the actual measured parameter Rz (Ɛ_sc ratio), where for small lead angles the measured Rz value is higher than the theoretical value resulting from the setting of the machining strategy and the applied conditions.

2. The result further leads to the finding that the specific tool geometry influences the possibility of achieving the required surface roughness, rather than a low cutting speed on a small effective diameter (the actual diameter of the tool-workpiece contact). It is not the nominal diameter that plays a role, but the particular cutting edge geometry on the affected effective diameters.

3. If the resulting chip is also generated by the curling part below the circular transition boundary, the surface has an irregular character. As a consequence, the real surface roughness Rz does not correspond to the theoretical (expected) value. An important and new finding is therefore that for a given tool, it is possible to find, from a simple macroscopic analysis of its geometry, an effective diameter which determines the limiting minimum tool lead angle from which the transverse roughness of the machined surface will correspond to the value which is theoretically required during pre-production setting of toolpath and cutting conditions. This can significantly help technologists efficiently set milling operations and avoid repeated re-setting for better machining results.

4. Another advantage is that the results also allow a general and relatively accurate determination of the Rz-Ra ratio when milling EN AW 7075 material with a ball-end milling tool. The obtained ratio applies to all of the tools used.

Author contribution Not applicable.

Funding The authors acknowledge support from the EU Operational Programme Research, Development and Education, and from the Centre of Advanced Aerospace Technology (CZ.02.1.01/0.0/0.0/16_019/0000826), Faculty of Mechanical Engineering, Czech Technical University in Prague.

Data availability Not applicable.

Code availability Not applicable.

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Reviewers invited by journal
21 Mar, 2022
Editor assigned by journal
18 Mar, 2022
First submitted to journal
15 Mar, 2022

You are reading this latest preprint version

Identifying the lead angle limit to achieve required surface roughness in ball-end milling

Status:

Version 1

Abstract

Figures

1 Introduction

2 Parameters And Assumptions Affecting Transverse Surface Roughness

3 Experiment Execution

3.1 Workpiece material, tools and machine tool used

3.2 Toolpaths and chosen strategy

3.3 Selection of the lead angle

3.4 Implementation of the experiment

3.5 Tool analysis

4 Results And Discussion

5 Conclusion

Declarations

References

Status:

Version 1