Advancement in machining technology of curved surfaces for various engineering applications is increasing. Various methodologies and computer tools have been developed by the manufacturers to improve efficiency of freeform surface machining. Selection of the right sets of cutter path strategies and appropriate cutting conditions is extremely important in ensuring high productivity rate, meeting the better quality level, and lower cutting forces. In this paper, cutting force as a new decision criterion for the best selection of tool paths on convex surfaces is presented. Therefore, this work aims at studying and analyzing different finishing strategies to assess their influence on surface texture, cutting forces, and machining time. Design and analysis of experiments are performed by means of Taguchi technique and analysis of variance. In addition, the significant parameters affecting the cutting force in each strategy are introduced. Machining strategies employed include raster, 3D-offset, radial, and spiral. The cutting parameters were feed rate, cutting speed, and step over. The experiments were carried out on low curvature convex surfaces of stainless steel 1.4903. The conclusion is that radial strategy provokes the best surface texture and the lowest cutting forces and spiral strategy signifies the worst surface texture and the highest cutting forces.
CNC milling is today the most effective, productive, and flexible manufacturing method for machining of curved surfaces. Ball end tools are used for machining of 2.5D and 3D surfaces for dies, molds, and various parts, such as aerospace components, due to the fact that the cutter readily adapts well to machining of these parts [1, 2].
The machining of curved surfaces is generally performed in accordance with a given machining strategy. However, as competition grows among manufacturing companies, greater emphasis has been placed on product quality and process efficiency, and this is subsequently promoting and standardizing widespread use of predetermined machining strategy within product design. That is to say, industries require high efficiency machining strategies for curved surface machining, before any machining process to be done, due to the increasing demand for higher accuracy, higher surface integrity, lower machining time, and lower cutting forces. All of these terms resulted from employing an appropriate cutter path strategy.
Different possible strategies in finish milling can be used. The finish milling operations employed in this study were spiral, radial, 3D-offset, and raster tool paths. Spiral machining creates a spiral tool path from a given focal point while keeping a constant contact between the cutter and workpiece. Radial machining converges tool paths to a central point with the ability to stop short of the center of the radial passes where they become very dense. In raster machining, the passes are parallel in the -plane and follow the surface in -direction, in this strategy, in order to reduce machining time, the machining direction offered to be chosen along the long side of the workpiece. In 3D-offset milling, the cutter starts at the periphery to the inner of the surface to be machined or the cutter may start at the center of the workpiece and then proceeds outwards. The cutter recurs to the starting point in each cycle and then cuts outwards to the next outer cycle [3, 4]. It should be noted that in all strategies mentioned above, up and down milling are performed. Figure 1 illustrates schematically the 3D-tool paths of the strategies tested.
Figure 1: Various 3D-tool path strategies.
Precision parts with curved surfaces are required in many manufacturing industries. Due to the inherently low stiffness of end mills during manufacturing processes of such parts, cutting forces can cause tool deflections and these deflections have a significant effect on the geometric and dimensional errors in the machined part . Hence, choosing the cutter path strategy in which the lower cutting forces could be resulted might be one method to prevent any catastrophic tool breakage and unfavorable machined surface quality. Ng et al.  showed that specific force values when machining with vertical downward strategy are higher than the vertical upward. This explains the extremely short tool life experienced when using this operating mode. Kim et al.  conducted simulation and experiments of cutting forces on inclined surfaces and showed that cutting forces were in general lower in horizontal cutter path orientations as compared to milling in vertical cutter path orientations. Chu et al.  revealed that although vertical upward orientation at low inclination angles reached at better stability than vertical downward orientation, faster cutting speeds with the former resulted in lower cutting forces. Several researches have also addressed the influence of cutter path on surface roughness, although few studies focus on the impact of tool path strategies on surface texture [9, 10].
Most of the previous researches focused on comparing cutting forces with respect to cutter path orientations, but none of them investigate cutting forces regarding cutter path strategies specially when machining low curvature curved surfaces.
Thus, appraisal of cutter path strategies regarding cutting force, surface texture, and relevant workpiece machining characteristics, when milling of convex surfaces, deserves more merit. Firstly, the objective of this study is to analyze different machining strategies including raster, 3D-offset, spiral, and radial tool paths in 3-axis milling of a low curvature convex geometry. Secondly, the influence of machining parameters on cutting forces based on the tool path strategy employed is investigated and the most significant parameter affecting cutting force in each milling strategy is identified by using analysis of variance (ANOVA). Taguchi design method is also used for the design of experiments. The machining parameters used in this study are cutting speed, feed rate, and step over. Cutting forces and machining time are measured and surface texture is analyzed.
2. Experimental Works
The aim of experimental work is to investigate the effect of cutter path strategies and cutting parameters on operating performance when ball nose end milling of a typical low curvature convex surface.
2.1. Workpiece Material and Cutting Tool
The workpiece material was X10CrMoVNb9-1DIN stainless steel 1.4903, which is used in turbine and boiler construction, turbine blades, chemical industry, and reactor engineering. Its nominal composition is of 8.26% Cr, 0.91% Mo, 0.37% Mn, 0.29% Si, 0.19 V, 0.15% Cu, 0.13 Ni, 0.11% C, 0.06% Nb, 0.02% W, 0.015% P, and Fe balance (all weights percent). Table 1 shows the mechanical properties of this material. The workpieces are machined into curved blocks with dimensions of 82 mm × 60 mm × 16 mm (see Figure 2).
Table 1: Mechanical properties of stainless steel 1.4903.
Figure 2: Workpiece specimen’s geometry and dimensions.
In order to avoid the transient state, the comparison between the strategies took place within a restrictive domain of surface curvature angle (0–32 degrees with respect to -axis). Otherwise, the result of performance characteristics will be changed when using different domains of workpiece surface curvature. The CAD model of the part and the surface curvature angle of parts are illustrated in Figure 3.
Figure 3: Geometry part used to analyze the milling strategies.
The cutting tool selected is two flutes inserted coated carbide ball nose end mill by TiN with 12 mm in diameter made by Walter Company. Table 2 shows the geometrical properties of the cutting tool. The milling tools are changed after three operations in order to assure that tool wear does not affect the result.
Table 2: Geometrical properties of cutting tool.
2.2. Experimental Equipment and Procedure
All machining trials are carried out on a vertical 3-axis CNC machining center HARTFORD with FANUC-OM controller (Figure 4). This has a maximum spindle speed 8000 rpm, maximum power 11 KW, and feed rates up to 10 m/min. A continuous mineral oil based emulsion coolant is employed during machining. Oil is mixed with water to form an emulsion. Emulsion coolant or water soluble coolant is used to reduce friction between the contact metal parts. In addition, whenever removing chips from the workpiece surface was required, air pressure was delivered through a nozzle and directed at the cutting zone.
Figure 4: Milling machine.
2.2.1. Cutting Forces and Surface Texture Measurements
Cutting force measurements (, , and ) are made using a Kistler 3-component piezoelectric type 9255B platform dynamometer. This has a resonant frequency of 30 KHz in the - and -axes and 30 KHz in the -axis. The dynamometer is connected to a series of charge amplifiers, which in turn are connected to a four-channel oscilloscope with a maximum sampling rate of 3000 M samples/s. The whole system was checked and calibrated prior to use. The cutting force data is downloaded from oscilloscope and information on cutting force signatures is stored onto a PC and after processing of the cutting force data analysis is performed using software.
Surface textures are obtained using an optical microscope Olympus (1000X). The surface roughness is measured by Mahr Roughness Tester at different places in each strategy.
2.3. Experimental Design Based on Taguchi Method
The Taguchi method is an experimental design technique, which is useful in decreasing the number of experiments considerably by using orthogonal arrays and also tries to minimize effects of the factors out of control. The basic philosophy of the Taguchi method is to ensure quality in the design phase . The greatest advantages of Taguchi method are to reduce the experimental time, to decline the cost, and to find out significant factors in a shorter period of time. Moreover, Taguchi method employs a special design of orthogonal array to investigate the effects of the entire machining parameters through small number of experiments. Recently, the Taguchi method is widely employed in several industrial fields and research works .
Taguchi uses the signal-to-noise () ratio as the quality characteristic of choice. Here the term “signal” represents the desirable value (mean) and the “noise” represents the undesirable value (standard deviation). So the ratio determines the amount of variation that exists in the quality characteristic . There are three types of ratios according to the objective of quality characteristic (performance characteristic). They include the lower-the-better, the higher-the-better, and the nominal-the better, which are displayed in the following equations.
Smaller the better characteristics:Larger the better characteristics:Nominal the better characteristics:where denotes the ratio calculated from the observed values (unit: dB), represents the experimentally observed value of the th experiment, is the repeated number of each experiment, and is the average of observed data and is the variance of . Regardless of the performance characteristic, the larger ratio corresponds to the better performance characteristic. Therefore, the optimal level of the process parameters is the level with the highest ratio .
The analysis of variance (ANOVA) is used to indicate statistically significant machining parameters and the percent contribution of these parameters on the performance characteristics (output parameters). In fact, ANOVA is a computational technique to estimate quantitatively the relative contribution which each controlled parameter makes on the overall measured response and is expressed as a percentage. Thus information about how significant the effect of each controlled parameter is on the experimental results can be obtained. The total variation in response is the variation due to various controlled factors and due to the error involved in the experimentation. The ANOVA can be done with the raw data or with the data. Based on the raw data, it signifies the factors which affect the average response rather than reducing the variation. But based on the data, both of these aspects are taken into account . Therefore, it is used in this research.
2.4. Experimental Conditions
The experimental design for each strategy is set according to an L9 orthogonal array based on Taguchi method. The orthogonal array is the L9 (33) that has 9 rows corresponding to the number of experiments (three factors with three levels each). Three factors are determined as controllable cutting parameters including cutting velocity (), feed rate (), and step over (), as shown in Table 3. The levels of each machining condition are determined by taking the cutter and workpiece materials into consideration. The amount of axial depth of cut is set 0.5 mm based on a typical finishing operation and it is fixed throughout all tests. All 9 tests are performed for each strategy and the effect of employing different cutter path strategies when finish milling of stainless steel 1.4903 is investigated.
Table 3: Machining parameters and their levels.
It is also should be noted that in the field of freeform surface machining, CAM software allows management of various modes of tool path leaning on the geometry of the surface to be machined. Various machining strategies can be used for the same shape. Nevertheless, the choice of a machining strategy remains an expert field . Thus, the cutter path strategies used in this study are simulated on CAM software before machining process.
3. Results and Discussion
The machining time is measured for each strategy in all experiments (Table 4). Also, the cutting length is attained from CAM software simulation. Figure 5 provides an exemplary graphical overview of machining time and length cut taking experiments 1 to 3 for each strategy. It can be seen that by increasing feed rate and step over, machining time decreases with length cut regardless of cutter path strategies applied. On the other hand, radial strategy shows higher machining time and length cut in comparison to the other strategies. Furthermore, compared to radial strategy, machining time could be reduced by employing spiral and raster strategies at about 67% and by using 3D-offset strategy at nearly 63%. It should be noted that the machining time difference between 3D-offset, spiral, and raster strategies is partial, which is mainly due to the small dimensions of parts geometry.
Table 4: Standard orthogonal array with experiment measurements for machining time.
Figure 5: Machining time and length cut versus experiment numbers for different cutter path strategies.
In fact, total machining time consists of cutting time and rapid traversal time as illustrated in Figure 6 for different strategies taking the test 1 to 3, for instance. Obviously, rapid traversal time in each strategy includes small portion of total machining time, because cutter path alternations at opposite directions (up and down) result in continuous cutting. Therefore, the machining time difference between different cutter path strategies is not caused by the rapid traversal time variations.
Figure 6: Machining time includes rapid and cutting time separately versus experiment numbers for different tool paths.
As said elsewhere, the other parameters used in this research to compare the relative advantages of the strategies are the surface texture and the cutting forces.
3.1. Cutting Forces
Cutting forces are the main factors governing machining accuracy, surface quality, machine tool vibration, power requirements, and tool life . Proper selection of the cutter path strategy is crucial in achieving desired machined surfaces. Without considering the impact of appropriate cutter path selection regarding cutting forces, the result can lead to catastrophic cutter failure and therefore lead to unnecessary waste of time, cost, and poor surface quality . In other words, employing cutter path strategies with minimum cutting forces in milling of ruled surfaces can lead to achieve high accuracy and productivity. Therefore, cutting force measurements are carried out to determine the effects of using different tool path strategies in milling of convex surfaces. Figure 7 depicts the cutting force components, the feed force, pick feed force, and axial force. Three components of cutting force in each strategy fluctuate and consist of many periods. Each period in every strategy determines one track of tool path. Firstly, the maximum absolute value of the cutting force waves in one cutting period is measured. Then, the average values of amongst all cutting periods in one milling experiment are taken as the three force components , , and .