Use of a virtual milling system to generate power-aware tool paths for 2.5-dimensional pocket machining

Abstract

Traditional (direction-parallel and contour-parallel) and non-traditional (trochoidal) tool paths are generated by specialized geometric algorithms based on the pocket shape and various parameters. However, the tool paths generated with those methods do not usually consider the required machining power. In this work, a method for generating power-aware tool paths is presented, which uses the power consumption estimation for the calculation of the tool path. A virtual milling system was developed to integrate with the tool path generation algorithm in order to obtain tool paths with precise power requirement control. The virtual milling system and the tests used to calibrate it are described within this article, as well as the proposed tool path generation algorithm. Results from machining a test pocket are presented, including the real and the estimated power requirements. Those results were compared with a contour-parallel tool path strategy, which has a shorter machining time but has higher in-process power consumption.

Keywords

Cutting process modelling and planning computer-aided manufacturing tool path generation power consumption

Introduction

For several years, there has been a significant increase in the consumption of electric energy in several sectors in the world.¹ The industry sector is responsible for the consumption of 42% of electricity¹ and for 21% of greenhouse gas (GHG) emissions.² This effect is a result of the energy demand from the processes carried out in the manufacture of products in several sectors.

In the manufacturing perspective, machining processes are widely used for making products and, therefore, it is very important to develop researches that seek to reduce the consumption of electrical energy in machining processes.^3–7

The energy consumption of machining processes has been the focus of many studies as a consequence of the interest in reducing the ecological footprint of manufacturing systems.^8–11 The high electrical power demand of machining equipment has been recognized as an important component of this footprint.^12,13 In this context, Balogun and Mativenga¹⁴ presented a comparison of some recent publications where different models and methods are used to study the electrical power demand of machining processes.

Aramcharoen and Mativenga¹⁵ proposed to identify and characterize power consumption, associating it with different machine components and auxiliary equipment. As machining centres are complex machines having multiple components, this task is usually not trivial.^16–18 One of the difficulties is that components such as fans and lubrication pumps have a power requirement that changes over time.¹⁹ However, those studies should help machine designers and builders to make more efficient systems.⁸

Although the machining tool path strategy is known to influence power consumption,^8,15,20,21 a large amount of research works that propose tool path generation methods normally focus on the relationship between material removal rate (MRR) and the processing time.^22,23 Also, they do not consider proposing the generation of tool paths that take into account power consumption.

In this context, this article describes a system that generates power-aware tool paths, that is, tool paths that depend on the machining power requirement. The generated power-aware tool paths are compared with the traditional contour-parallel (CP) tool path strategy, and an analysis of the results is carried out.

Literature review

A significant amount of researchers have published methods to model and minimize power consumption. For instance, Lv et al.,¹⁷ Yoon et al.,²⁴ Yan and Li²⁵ and Mori et al.²⁶ proposed methods to optimize the machine power consumption by studying the relationship between the operating parameters and the power requirement. They repeated a relatively simple cut varying the cutting parameters. For every cut, the power requirement is measured and the output is analysed using a statistical method in order to identify an optimal combination of parameters.

He et al.²⁷ proposed a method to estimate energy consumption of machining, based on the correlation of numerical control (NC) codes and energy-consuming components of machine tools. The test performed in the C45 steel prismatic part corresponded to a linear slotting (full immersion milling) tool path.

Liu et al.²⁸ presented a model to predict energy consumption in machining. Their energy consumption model is hybrid, that is, cutting power is obtained analytically through calculation of cutting forces, and experimental data from slot milling were used to obtain empirically the relationship between total power and cutting power. They compared their model with other models under different cutting conditions, and very good results were obtained considering either MRR only or both MRR and spindle speed.

Sealy et al.²⁹ studied the characteristics of energy consumption in hard milling, including process parameters and tool wear. AISI H13 tool steel (50 HRC) was machined, and they inferred that tool wear has the greatest influence on net cutting specific energy compared with feed rate and cutting speed. Also, energy efficiency increased with MRR. However, a simple one-way linear tool path was used in the experiments.

Deng et al.³⁰ proposed a method to optimize the machining parameters in order to reduce the specific energy consumption and the processing time. Real constraint conditions were considered, and the model was solved using a genetic algorithm. However, the influence of different tool paths on power consumption was not considered.

Peng and Xu⁹ developed an energy analysis system that uses a hybrid energy consumption modelling, which includes the STEP-NC standard.³¹ Tests were performed in three and five-axis machines, leading to a significant reduction in energy consumption and machining time. However, the performed operations corresponded to slot milling.

Diaz et al.³² proposed setting a lower limit to the MRR value (75 mm³/s in their machine-material setup), establishing that machining cuts with MRR values lower than that should be avoided, since such values would lead to a high specific energy.

The studies cited heretofore in this section consider the machining tool path an important factor, but they do not assess how different tool paths affect the electric energy consumption, beyond the relationship between MRR and the processing time.

Avram and Xirouchakis³³ proposed a method to evaluate and reduce energy consumption considering some 2.5-dimensional (2.5D) machining strategies and machine components interactions. The employed strategies were as follows: (a) zigzag face milling, (b) contour milling a shoulder and (c) contour milling a pocket. Dry, minimum quantity lubrication and wet lubrication were tested in the machining of aluminium Al-7022 parts, and a high value of spindle speed (19,500 r/min) was used in some tests. They concluded that their method can be used to calculate the total energy required by a machine tool system for milling a 2.5D part. In order to reduce energy consumption in machining, they suggested a significant reduction of the non-cutting activities (e.g. amount of tool changes and the tool change time). They did not perform the generation of a power-aware tool path.

Kong et al.²¹ developed a method to estimate the energy consumption and GHG emissions of a computer numerical control (CNC) machine. They considered acceleration and deceleration of machine tool axes in the operations, as well as the direction of axes movement. The tool path strategies that were considered include zigzag, spiral linear, spiral circular and trochoidal. They concluded that the moving direction of the tool path influences the energy demand, and that the geographic location of the machine results in different amounts and characteristics of GHG emissions. No power-aware tool path was considered in their analysis.

Aramcharoen and Mativenga¹⁵ presented a methodology to predict energy demand for milling operations comparing different tool paths for pocket milling: zag, zigzag, contour and spiral. Up and down-milling were considered, as well as machining in different machine axes. Surface roughness, tool wear and machining time were also taken into account. They inferred the following: (a) their model can be used to estimate energy requirement with high accuracy when compared to online monitoring, (b) contour and spiral milling enables reducing energy demand by more than five times compared to zigzag milling and (c) tool path strategies can lead to significant energy savings in machining and recommend that more studies should be carried out on tool paths.

Shin et al.³⁴ presented a component-based energy-modelling methodology to implement online optimization. Component models were proposed, which sought to predict energy at the tool path-level in different machining configurations. STEP-NC³¹ and MTConnect Institute³⁵ standard interfaces were used to enable data and model exchange. The methodology was applied to a 2.5D part with features such as profile, slot, pocket and hole, and the following tool paths were considered: contouring, slotting and zigzag. No new tool paths were proposed.

Edem et al.⁸ investigated the influence of tool path strategies and machine tool axis configurations on the electrical energy consumption in pocket milling. Zag, zigzag, rectangular contour and spiral were the tool path strategies considered, which were tested in two three-axis CNC machines. Milling was performed at constant MRR. They inferred that the electrical energy efficiency of tool paths varies from one machine to another depending on their structural configurations. They studied traditional tool path strategies and did not attempt to generate and investigate a new type of tool path.

An approach that can be applied in order to relate the tool path to power consumption is the investigation of how the tool path influences the specific cutting force k_c. Although k_c is usually related to process stability and tool life, it can also be used to calculate an estimated value of cutting power, by multiplying it by the MRR value. However, the value of k_c is not constant and depends on many factors, including the undeformed chip geometry.

In this context, in order to investigate the variations of the cutting force, Hinduja et al.³⁶ analysed an offset tool path and concluded that slotting occurred 40% of the distance travelled. On the other hand, when the radial depth of cut was less than half the tool diameter, the time was more than 30% in that specific tool path. This variation of radial depth produces an uneven cutting force,^37,38 leading to irregular values of cutting power.

Some researchers proposed to modify the tool path in order to control the cutting force.^39,40 Such modifications include the following approaches: (a) adjust the feed rate in order to compensate the radial depth variations,⁴¹ (b) use trochoidal tool path strategy^42–45 and (c) use spiral tool path strategy.⁴⁶

In order to have a precise estimation of the power requirement of the process, Borgia et al.⁴⁷ used a computer simulation of the tool–material interaction. Using computational solid geometry libraries, they calculated the instantaneous MRR along the tool path.

In this work, a further step was taken: a computer simulation referred to as virtual milling system (VMS) was integrated with the tool path generation process, enabling the estimation of the power consumption along every tool path segment, leading to the generation of a power-aware tool path. A detailed description of the proposed power-aware tool path generation system is given in the next section.

Proposed method for power-aware tool path generation

Components of the power required for machining

The power required by a machining process can be divided into four portions: P_idle is the power consumed by all machine devices and accessories (e.g. computers, communication devices, small motors, lamps and other accessories) while the machine is turned on; P_spindle is the power required to rotate the spindle without performing any cut; P_feed is the power for feeding (positioning) the tool; and P_cut is the power necessary to perform the cut.

In practice, each of those power elements represents a demand that occurs in a certain time span during the process. For example, the CNC control is constantly demanding power from the machine start-up to its shutdown, while lubrication pumps and cooling vents are activated only when needed. On the other hand, the spindle is activated only during limited time spans starting seconds before the cutting process and stopping some seconds after completing the operation.

The total power requirement is given by equation (1). It is clear that a decrease in any of the individual power elements will reduce the total power required for the process

P_{total} = P_{idle} + P_{spindle} + P_{feed} + P_{cut}

(1)

The method proposed in this article attempts to manage the value of P_cut. This power can be approached by using the specific cutting force (equivalent to the specific energy consumption), which is the power required to machine a unitary cube (usually 1 mm³) and adjust the value by using one or more correction factors to reflect the actual conditions of the cut. A commonly used formula corresponds to equation (2)^48,49

k_{c} = k_{c 1} \times h_{m}^{- m_{c}} \times (1 - \frac{γ_{o}}{100})

(2)

where k_c is the specific cutting force (N/mm²), k_c1 is the specific cutting force per 1 mm² (N/mm²), h_m is the mean chip thickness (mm), m_c is a constant based on the part material and γ_o is the rake angle of the tool on the orthogonal plane.

Specific cutting force tests

Initially, in order to provide a good estimation of the milling power requirement, a series of milling tests with different cutting parameters were performed, all of them without the use of cutting fluid. Initially, some values of cutting speed V_c and feed per tooth f_z were used in order to verify the stability of the process, and the selected values for further tests were V_c = 180 m/min, and f_z = 0.15 mm/tooth, since higher values resulted in the occurrence of chatter.^37,50

The machine used in this research was a 7.5-kW Charles MVC-955 machining centre, with a Siemens Sinumerik CNC 840Di. It was equipped with the power measurement device Kron Mult-K120⁵¹ (Figure 1), which was connected to a computer using a Modbus interface in order to generate a power consumption graph. The machined material was a P20 tool steel with 31 HRC hardness. A 20-mm indexable end mill was used for machining, having three BDMT 11T308ER-JT carbide inserts with PR-1225 PVD coating, and Kyocera MEC 20-S20-11T tool holder.

Figure 1.

Power measurement device Kron Mult-K120.⁵¹

The tests consisted of removing through down-milling a volume with cross section a_e (radial depth of cut), a_p (axial depth of cut) along a straight line with length L (Figure 2) and recording the power consumption (in Watt) by the cut. A graph was created for every test (Figure 3), and mean power was calculated for idle and cutting conditions (dwell time was added before the cut). The difference between those means was recorded as cutting power for that specific parameter combination.

Figure 2.

Variables considered in the milling tests.

Figure 3.

Graph obtained from a cutting test.

A total amount of 60 combinations were used to measure the power requirement in each cut by varying the values of radial and axial depths of cut. Table 1 presents the parameters used in the tests.

Table 1.

Values of the cutting parameters used in the machining tests.

Parameter	Values
a_e (mm)	2, 4, 6, 8, 10, 12, 14, 16, 18, 20^a
a_p (mm)	0.5, 1.0, 1.5, 1.75, 2.0, 2.25
f_z (mm/tooth)	0.15
V_c (m/min)	180

Corresponding to a slotting operation (D_tool = 20 mm).

Every test combination was used four times, and resulting averaged cutting power requirement for each (a_e, a_p) combination is presented in Figure 4.

Figure 4.

Measured average P_cut from experimental tests.

MRR is given by equation (3),⁵² and it was calculated for each (a_e, a_p) combination

MRR = a_{e} \times a_{p} \times v_{f}

(3)

where MRR is the material removal rate, a_e is the radial depth of cut, a_p is the axial depth of cut and v_f is the feed speed.

Then, the specific cutting force k_c for each (a_e, a_p) combination was determined using equation (4),⁵³ and the obtained points are shown in Figure 5. The estimated error was calculated based on the standard deviation and the number of tests, and it was included in Figure 5

k_{c} = \frac{P_{cut}}{MRR}

(4)

Figure 5.

Obtained specific cutting force k_c values with the estimated error.

Figure 6 shows the mean values of the curves in Figure 4 plotted as a surface, with the two depths (a_p and a_e) in different axes. It can be inferred from the results shown in Figure 6 that there is a region in which the specific cutting force is minimum and almost constant. This occurs for a_e values between 8 and 18 mm, and when a_p is larger than 2.0 mm. On the other hand, the worst values of k_c are those for a_e values lower than 4 mm, and k_c values increase significantly in a slotting operation (a_e = D_tool). A possible cause for this behaviour is the relationship between the undeformed chip thickness and the value of k_c. As it was shown by Balogun et al.,⁵⁴ three different mechanisms (rubbing, ploughing and shearing) can occur. When the undeformed chip thickness is small, rubbing and ploughing are the dominant mechanisms, causing an increase in the specific cutting energy. This condition occurs at the starting point of the cut for up milling, and at the end for down-milling. In slotting operations, this mechanism takes place both at the start and end points of the cut. As the graphs represent the mean k_c for the whole cut, the k_c value in slotting operations is not as high as the k_c value for small a_e values (a_e < 8 mm).

Figure 6.

Average specific cutting force for different values of axial and radial depths of cut.

Thus, for a_p values greater than 1.5 mm, in order to keep k_c values low, tool path segments that result in a_e values outside the 8- to 18-mm range should be avoided. Also, the tool path should keep a_e values as close as possible to 18 mm, since this value results in a higher MRR.

Mean chip thickness

In milling, since the geometry of the chip changes continuously along every cut, chip thickness changes continuously. The instantaneous chip thickness value depends on the feed per tooth f_z and the relative position of the part from the tool direction of feed. In this work, the mean chip thickness h_m is used so as to take in account this variation.

The variation of the mean chip thickness for a radial depth of cut a_e can be obtained by dividing the cutting area by the cutting length (ϕ_s). As the feed is constant, the cutting area is obtained by multiplying f_z by a_e, while the cutting length is obtained by multiplying the cutter swept angle by the tool radius (equation (5))

h_{m} = \frac{A_{c}}{l_{c}} = \frac{f_{z} \cdot a_{e}}{ϕ_{s} (\frac{D}{2})}

(5)

The cutter sweep angle (ϕ_s) can be obtained with equation (6)

ϕ s = \arccos (1 - \frac{2 \cdot a_{e}}{D})

(6)

The graphs of the cutter swept angle, the mean chip thickness and the cutting area as a function of the radial depth of cut are shown in Figure 7.

Figure 7.

Graphs showing the (a) cutter swept angle, (b) mean chip thickness and (c) radial depth of cut.

Similarly, the mean chip thickness for an axial depth of cut a_p is obtained by dividing the lateral cutting area by the cutting edge length. The area is obtained by multiplying f_z and a_p, whereas the cutting edge length (for a toroidal cutter) is obtained by multiplying the cutter swept angle by the tool radius. The resulting h_m graph is shown in Figure 8.

Figure 8.

Graphs showing the (a) cutter line length, (b) mean chip thickness and (c) axial depth of cut.

Some conclusions can be drawn from those two graphs. First, regarding a_e (Figure 7), if up or down-milling is used, a higher value of h_m/f_z is obtained using an a_e/D = 0.845 (which corresponds to an a_e = 16.9 mm with the used tool). On the other hand, Figure 8 shows that increasing a_p leads to a higher value of h_m/f_z, tending to 1.

By combining the results shown in Figures 7 and 8, the mean chip thickness resulting from this combination is shown in Figure 9. This graph shows that an increase in a_p/RE (axial depth of cut divided by the tool nose radius) results in a more efficient cut (due to the direct relationship between k_c and h_m in Kienzle’s equation), whereas for a_e/D (radial depth of cut divided by the tool diameter), there is an optimal zone where there is some cutting efficiency for both very low values and for high values.

Figure 9.

Dimensionless mean chip thickness (h_m/f_z).

Modified mean chip thickness

The experimental values of the specific cutting force k_c and the dimensionless mean chip thickness (shown in Figure 9) were used to obtain constants k_c1 and m_c of equation (2). The fitted curve, corresponding to the dashed line in Figure 10, gives an approximate value of k_c. Nevertheless, when comparing this fitted curve with the points generated for each a_p (as shown in Figure 11), it is evident that every graph has the same characteristic shape: a minimum value of k_c is reached when a_e increases, and then, after achieving the maximum value of mean chip thickness, k_c increases again, but this time up to a value above the fitted curve.

Figure 10.

Fitted curve for k_c for different values of h_m and a_p.

Figure 11.

Fitted curve for k_c, and the k_c points for different values of h_m, a_e and a_p.

While the reason for this behaviour is not obvious, it may be a consequence of the difference from the nominal value with the real chip thickness, whose values may differ due to the occurrence of unbalanced forces and vibration.

Thus, in order to have more precise values for k_c used in the VMS, the mean chip thickness value for every (a_p, a_e) combination was modified from the one shown in Figure 9 to the values shown in Figure 12. These values were calculated using equation (2) to obtain the h_m value from the experimental k_c, and the fitted k_c1 and m_c values. Figure 12 shows that the values of h_m remain almost constant in the area above the 0.52 curve (combinations with a_p/RE = 2.25 and 0.4 < a_e/D < 0.8).

Figure 12.

Modified dimensionless mean chip thickness h_m.

VMS

Given the initial workpiece, the tool geometry and the tool path, the developed VMS calculates the interaction between the tool and the workpiece. The system was implemented in a tree-like structure where the part is composed of cubes, which are referred to as voxels (‘volume elements’).^55,56 When the tool gets in contact with a voxel (which corresponds to an intersection), the voxel is automatically divided into sub-voxels recursively until a certain subdivision limit is reached. This limit is a configuration parameter of the system, and it was set to three, that is, each voxel can be subdivided up to three times, corresponding to 3 × 3 × 3 sub-voxels for each initial voxel. This recursive process is shown in Figure 13.

Figure 13.

Virtual milling system and the subdivision of voxels resulting from the relative position between the tool and the workpiece.

When the tool gets in contact with a leaf voxel (which is the minimum sub-voxel), it is set as being removed, and the time step in which the material was removed is also assigned to the voxel. Moreover, the voxel’s geometric location relative to the tool and the tool path is recorded for further analysis (Figure 14).

Figure 14.

Data collected from voxels removed by the tool.

Given that voxels are aligned, the tool (e.g. a flat end milling tool moving along the z direction) initially does not intersect any voxel, but then it intersects simultaneously a large number of voxels in a small pass, and all these voxels will be removed at the same time (Figure 15(a)). In order to avoid this effect, the interaction between the tool and the leaf voxel is calculated using a point within the voxel, which is generated randomly and is located anywhere within the voxel (Figure 15(b)). This process generates some noise in the system output, but it does not interfere with the proposed tool path generation algorithm.

Figure 15.

Interaction between the tool and the part: (a) voxels with their geometric centres and (b) voxels with randomized points representing their centres.

In order to have an estimated value of the power required in each feed movement, the following values are calculated: (a) the volume of material removed, determined by counting the number of voxels removed multiplied by the voxel volume and (b) the a_e value, which is the difference between the relative linear position of the rightmost removed voxel and the position of the leftmost removed voxel. This process is shown in Figure 16.

Figure 16.

Calculation of the a_e value, which uses the positions of the rightmost and leftmost removed voxels.

The proposed architecture allows the system to undo one or more steps related to the movement of the tool, restoring a previous state. This ability is essential for the tool path generation algorithm proposed in this article. The number of steps that can be undone is limited by the system memory and, in order to limit the memory usage, a garbage collector module was implemented to free memory when certain parts of the path are not modified.

Localized Voronoi mountain gradient mesh

The proposed algorithm requires the generation of the Voronoi mountain of the pocket geometry^57–59 (Figure 17).

Figure 17.

An L-shaped pocket and its Voronoi mountain.

The used algorithm was described in Ochoa González and Ferreira,⁶⁰ where a grid is formed by some rectangular cells stored in a structure in which every cell has one or more related boundary lines (or ‘sites’), including all the sites that are nearest every point in the cell.

This grid is obtained through the following procedure: (a) the endpoints of every pocket boundary are used to subdivide the cells, forcing all end points to coincide with cell corners; (b) the distance from every cell to the pocket boundary lines (or sites) is determined, keeping all those who apply as the nearest site to some of the points in that cell; (c) if there are two or more related sites, the cell is subdivided and the process is repeated with the obtained cells, else the cell is not altered.

The output of this process is a selectively refined mesh containing the following information for each cell: the minimal distance to a boundary element, an approximate Voronoi mountain gradient and a list of the nearest sites, enabling a fast point-to-boundary distance calculation.

Power-aware tool path generation algorithm

The direction-parallel and CP tool path strategies^61,62 do not usually keep the a_e value constant (or even constrain a_e to a specific range), especially for complex pockets. Thus, in order to provide some control of the a_e value, the following algorithm is proposed:

The a_p value and the number of passes are selected, based on the depth of the pocket and the characteristics of the tool. In the test setup, the value used for a_p corresponded to the largest a_p that divided the total pocket depth in equal cuts. Thus, for a pocket depth of 8 mm, a_p = 2 mm (four equal cuts).

Using this a_p value and either the power requirement graph P_cut (for a tool path limited by the power requirement, Figure 4) or the specific cutting force (for an energy-efficient tool path, Figure 5), the value of a_e that will result in the desired power/energy, called a_etarget, is calculated.

The a_etarget value is used as an upper limit, and a lower limit value is established (a_emin). For the example tool paths presented in this article, a value of a_emin = (a_etarget − 2 mm) was used.

The tool uses a helical path to start the cut. This helix is centred in some of the highest points of the Voronoi mountain.

After the tool enters the workpiece, the tool path is built by adding path segments, evaluating the a_e value and modifying the segments if necessary. Initially, starting from the tool entry point, the tool path is pointed towards a direction descending from the Voronoi mountain. The tool feed direction is measured always relative to the Voronoi mountain height map, with three possible directions: (a) neutral (perpendicular to the gradient), (b) ascending (positive to the gradient), and (c) descending (contrary to the gradient) (Figure 18).

The tool advances in the direction given in the last step.

If this movement takes the tool out the pocket, a step is undone, and the direction is made neutral. The algorithm jumps to step 6. In order to evaluate the tool-boundary interaction, the minimum distance between the centre of the tool and the pocket boundary is compared with the tool radius. This process is accomplished using the previously obtained Voronoi mountain.

The removed material and the a_e value are calculated, and these values are used to determine (a) the required cutting power P_cut (with the Kienzle equation –equation (2)) and (b) the modified mean chip thickness h_m.

If the a_e value is larger than a_etarget, a number of steps (n_jumpback) are undone, and the direction is made positive. On the other hand, if the a_e value is lower than a_emin and the tool is not in contact with the pocket boundary, a number of steps (n_jumpback) are undone, and the direction is made negative. Those steps backwards allow a tool path with limited curvature, by changing the direction before the limits are attained, as shown in Figure 19.

If the a_e value is in the High Critical Range, the direction is modified to a positive value, but no steps are undone (Figure 19(b)).

If the a_e value is in the Low Critical Range, the direction is modified to a negative value, but no steps are undone (Figure 19(d)). This rule has an exception: if the tool is in contact with the pocket boundary but the material not yet removed is on the other side of the tool, the direction is modified to a more positive value as shown by the black arrow in Figure 20. Again, in order to evaluate tool–boundary interaction, the minimum distance between the tool centre and the pocket boundary is compared with the tool radius.

If a complete loop in contact with the boundary of the pocket is detected, end the tool path generation, else go to step 6.

Figure 18.

Directions of the Voronoi mountain: (a) neutral, (b) ascending and (c) descending.

Figure 19.

Steps 9, 10 and 11 of the power-aware tool path generation algorithm.

Figure 20.

Step 11 exception: moving the tool away from a machined wall.

Generated tool paths for the example pocket

The proposed algorithm was implemented in the Python⁶³ language, and an important library that was used in the development of the system was NumPy.⁶⁴ The algorithm was used to generate power-aware tool paths to mill the flat bottom pocket with two islands shown in Figure 21.

Figure 21.

Machined test pocket.

The following upper limits of a_e were used to generate the tool paths: 14.0, 16.0, 18.0 and 19.6 mm (these test points are shown in Figures 4 and 5). A constant axial depth of cut a_p = 2.0 mm was used in the tests. By examining the graph in Figure 4, the maximum power requirement should be 1460, 1690, 1930 and 2212 W, respectively.

The resulting power-aware tool paths are shown in Figure 22, while Figure 23(a) and (b) shows two CP tool paths (a_e equal to 18.0 and 14.0 mm, respectively), both generated using Siemens NX 7.5 software. Finally, Figure 24 shows a trochoidal tool path generated using the algorithm proposed in Ferreira and Ochoa González.⁵⁹ It should be pointed out that, in all the tool paths generated, the tool enters the workpiece in a helical path. In this way, after the tool enters the pocket, the material that has not yet been removed is the same in all tool path strategies. The place of entry usually corresponds to one of the highest points of the Voronoi mountain. In every case, the CPU time to generate the tool paths was about 200 s in an i5 processor computer.

Figure 22.

Generated power-aware tool paths for different a_e values: (a) 14 mm, (b) 16 mm, (c) 18 mm and (d) 19.6 mm.

Figure 23.

Generated contour-parallel tool paths using Siemens NX 7.5 software: (a) a_e = 18 mm and (b) a_e = 14 mm

Figure 24.

Generated trochoidal tool path using the algorithm proposed by Ferreira and Ochoa⁵⁹ (a_e = 18 mm)

The generated tool paths were analysed using the VMS. Histogram plots of a_e for the tool paths in Figures 22 –24 are presented in Figure 25. It can be noticed in the graphs of Figure 25 that the proposed algorithm generates tool paths in which the largest amount of cutting segments have an a_e value below the desired target, while the traditional CP tool paths have most of its a_e values exceeding the target a_e value. On the other hand, the trochoidal tool path is capable to meet the target a_e value, but it produces more cuts with small a_e values, which, as shown in Figure 6, will result in higher values of specific cutting force.

Figure 25.

VSM generated histograms of a_e counts for each tool path shown in: (a) 14.0 mm, (b) 16.0 mm, (c) 18.0 mm, (d) 19.6 mm, (e) contour-parallel (a_e = 18.0 mm), (f) contour-parallel (a_e = 14.0 mm) and (g) trochoidal (a_e = 18.0 mm).

Experimental results

The parts were machined using all the obtained tool paths, and during the process, the NC program (G-code) line number, tool position and power consumption were recorded. The tests were carried out in 300 × 200 × 50 mm³ P20 tool steel parts (same material used in the previous tests), and cutting was carried out in dry condition.

For each tool path used to mill the pocket, one replicate experiment was conducted, and the resulting P_cut + P_feed values were averaged. The obtained data were analysed in order to identify the higher power peak. By numerically integrating the area below the P_cut curve, the total cutting energy E_cut was calculated. Finally, the specific cutting force was obtained by dividing the E_cut value by the total removed material volume. Also, the specific cutting force (corresponding to P_feed and P_cut) was obtained by numerically integrating the area under the power graph and dividing the result by the total removed material volume. The results are presented in Table 2 and Figure 26.

Table 2.

Pocket milling tool path results.

Programmed a_e (mm)	Maximum P_cut (W)	Total E_cut (kJ)	Specific cutting force k_c (N/mm¹)
14.0	1340	104.0	2601
16.0	1498	104.4	2609
18.0	1731	104.8	2620
19.6	1991	107.8	2693
18.0 (CP)^a	2154	108.0	2699

Contour-parallel (CP) path generated using a CAM software, used for comparison.

Figure 26.

Pocket milling tool path results: (a) average P_cut and (b) average E_cut and calculated k_c.

It can be noticed that the tool paths generated by the proposed algorithm achieve lower values of maximum P_cut compared with the CP tool path with a_e = 18 mm. However, it is important to emphasize that these values correspond only to the cutting energy. Considering the P_idle value and the fact that the CP tool path processing time is shorter than the machining time of the proposed method, the CP tool path leads to a lower value of the total energy consumed.

In Figure 27, three process power consumption graphs are presented for the tool path shown in Figure 22(c). Figure 27(a) shows the power consumption measured directly at the machine, while Figure 27(b) illustrates the power requirement graph resulting from the VMS. Figure 27(c) depicts the power consumption by the machine operating without machining the part (it includes motor usage).

Figure 27.

Power consumption graphs: (a) actual milling, (b) simulated by VMS and (c) no machining (measured).

Conclusion

In this work, a system for generating power-aware tool paths was proposed, which is based on the power consumption estimation along every tool path segment. Since CAM software usually does not generate tool paths that take power consumption into account, it is important to carry out researches that seek to generate such tool paths due to the need to reduce energy consumption in manufacturing systems.

Based on the results obtained, the proposed method generates tools paths that have a lower in-process power consumption compared with the CP tool path strategy, but a longer machining time. Better energy efficiency can be obtained by selecting an adequate value of a_e and its management along the tool path. However, as the gain is relatively small, the global efficiency could be worsened because the processing times are usually longer.

The proposed VMS system and its calibration by using the data from experimental tests can be used to have an estimation of the needed process power.

It is suggested as a future work the assessment of other tool path generation algorithms that use the proposed VMS. It is also suggested extending VMS to evaluate the power requirement in four and five-axis milling tool paths. As it is possible that the consideration of a_e and a_p will not be sufficient to characterize properly the cutting geometry, some other parameters could be included. Also, it is suggested the machining of harder materials (e.g. hardness of about 55 HRC), which are also commonly used in dies and moulds, since the cutting power will be higher than the one obtained for the less hard material (31 HRC) machined in this work, and compare the total energy consumption with traditional tool path strategies such as CP. Finally, it is suggested to investigate the use of mechanistic modelling of cutting forces^65,66 for the generation of power-aware tool paths.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Council for Scientific and Technological Development (CNPq) of Brazil.

ORCID iDs

David Manuel Ochoa González

Joao Carlos Espindola Ferreira

References

International Energy Agency (IEA). Key world energy statistics. Paris: IEA, 2017.

United States Environmental Protection Agency. Global greenhouse gas emissions data, https://www3.epa.gov/climatechange/ghgemissions/global.html (2018, accessed June 2018).

Dahmus

Gutowski

TG.

An environmental analysis of machining. In: Proceedings of the ASME international mechanical engineering congress and RD&D exposition, Anaheim, CA, 13–19 November 2004. New York: ASME.

Fysikopoulos

Pastras

Alexopoulos

, et al. On a generalized approach to manufacturing energy efficiency. Int J Adv Manuf Tech 2014; 73(9–12): 1437–1452.

Zhang

Review of recent advances on energy efficiency of machine tools for sustainability. Proc IMechE, Part B: J Engineering Manufacture 2015; 229(12): 2095–2108.

Shokrani

Dhokia

Newman

ST.

Energy conscious cryogenic machining of Ti-6Al-4V titanium alloy. Proc IMechE, Part B: J Engineering Manufacture 2018; 232(10): 1690–1706.

Peng

Tang

Energy modeling and a method for reducing energy loss due to cutting load during machining operations. Proc IMechE, Part B: J Engineering Manufacture 2019; 233: 699–710.

Edem

Balogun

Mativenga

PT.

An investigation on the impact of toolpath strategies and machine tool axes configurations on electrical energy demand in mechanical machining. Int J Adv Manuf Tech 2017; 92(5–8): 2503–2509.

Peng

An interoperable energy consumption analysis system for CNC machining. J Clean Prod 2017; 140: 1828–1841.

10.

Liu

Guo

Sealy

, et al. Energy consumption and process sustainability of hard milling with tool wear progression. J Mater Process Tech 2016; 229: 305–312.

11.

Campatelli

Lorenzini

Scippa

Optimization of process parameters using a Response Surface Method for minimizing power consumption in the milling of carbon steel. J Clean Prod 2014; 66: 309–316.

12.

Zhang

Deng

, et al. A process parameters optimization method of multi-pass dry milling for high efficiency, low energy and low carbon emissions. J Clean Prod 2017; 148: 174–184.

13.

Balogun

Edem

Mativenga

PT.

E-smart toolpath machining strategy for process planning. Int J Adv Manuf Tech 2016; 86(5–8): 1499–1508.

14.

Balogun

Mativenga

PT.

Modelling of direct energy requirements in mechanical machining processes. J Clean Prod 2013; 41: 179–186.

15.

Aramcharoen

Mativenga

PT.

Critical factors in energy demand modelling for CNC milling and impact of toolpath strategy. J Clean Prod 2014; 78: 63–74.

16.

Zhou

, et al. Energy consumption model and energy efficiency of machine tools: a comprehensive literature review. J Clean Prod 2016; 112: 3721–3734.

17.

Tang

Jia

, et al. Experimental study on energy consumption of computer numerical control machine tools. J Clean Prod 2016; 112: 3864–3874.

18.

Yingjie

Energy efficiency techniques in machining process: a review. Int J Adv Manuf Tech 2014; 71: 1123–1132.

19.

Zein

Kara

, et al. An investigation into fixed energy consumption of machine tools. In: Hesselbach

Herrmann

(eds) Glocalized solutions for sustainability in manufacturing. Berlin; Heidelberg: Springer, 2011, pp.268–273.

20.

Newman

Nassehi

Imani-Asrai

, et al. Energy efficient process planning for CNC machining. CIRP J Manuf Sci Tech 2012; 5(2): 127–136.

21.

Kong

Choi

Yasui

, et al. Software-based tool path evaluation for environmental sustainability. J Manuf Syst 2011; 30: 241–247.

22.

Rauch

Hascoet

JY.

Selecting a milling strategy with regard to the machine tool capabilities: application to plunge milling. Int J Adv Manuf Tech 2012; 59(1–4): 47–54.

23.

Kara

Unit process energy consumption models for material removal processes. CIRP Ann: Manuf Techn 2011; 60(1): 37–40.

24.

Yoon

Lee

Kim

, et al. Empirical power-consumption model for material removal in three-axis milling. J Clean Prod 2014; 78: 54–62.

25.

Yan

Multi-objective optimization of milling parameters – the trade-offs between energy, production rate and cutting quality. J Clean Prod 2013; 52: 462–471.

26.

Mori

Fujishima

Inamasu

, et al. A study on energy efficiency improvement for machine tools. CIRP Ann: Manuf Techn 2011; 60(1): 145–148.

27.

Liu

, et al. Analysis and estimation of energy consumption for numerical control machining. Proc IMechE, Part B: J Engineering Manufacture 2012; 226(2): 255–266.

28.

Liu

Zhang

WF.

A hybrid approach to energy consumption modelling based on cutting power: a milling case. J Clean Prod 2015; 104: 264–272.

29.

Sealy

Liu

Zhang

, et al. Energy consumption and modeling in precision hard milling. J Clean Prod 2016; 135: 1591–1601.

30.

Deng

Zhang

, et al. Optimization of process parameters for minimum energy consumption based on cutting specific energy consumption. J Clean Prod 2017; 166: 1407–1414.

31.

International Organization for Standardization (ISO) 14649-1:2003. Industrial automation systems and integration – physical device control – data model for computerized numerical controllers: part 1 – overview and fundamental principles (Geneva: ISO, 2003).

32.

Diaz

Redelsheimer

Dornfeld

Energy consumption characterization and reduction strategies for milling machine tool use. In: Hesselbach

Herrmann

(eds) Glocalized solutions for sustainability in manufacturing. Berlin; Heidelberg: Springer, 2011, pp.263–267.

33.

Avram

Xirouchakis

Evaluating the use phase energy requirements of a machine tool system. J Clean Prod 2011; 19(6–7): 699–711.

34.

Shin

Woo

Rachuri

Energy efficiency of milling machining: component modeling and online optimization of cutting parameters. J Clean Prod 2017; 161: 12–29.

35.

MTConnect Institute. MTConnect standard part 1 – overview and protocol. McLean, VA: The Association for Manufacturing Technology, 2014.

36.

Hinduja

Barrow

Determination of the radial width of cut and cutting modes in milling. Int J Mach Tool Manu 1995; 35(5): 689–699.

37.

Altintaş

Budak

Analytical prediction of stability lobes in milling. CIRP Ann: Manuf Techn 1995; 44(1): 357–362.

38.

Insperger

Stépán

Updated semi-discretization method for periodic delay-differential equations with discrete delay. Int J Numer Meth Eng 2004; 61(1): 117–141.

39.

Bouard

Pateloup

Armand

Pocketing toolpath computation using an optimization method. Comput Aided Design 2011; 43(9): 1099–1109.

40.

Kim

HC.

Tool path generation and modification for constant cutting forces in direction parallel milling. Int J Adv Manuf Tech 2011; 52(9–12): 937–947.

41.

Bae

Kim

, et al. Automatic feedrate adjustment for pocket machining. Comput Aided Design 2003; 35(5): 495–500.

42.

Ibaraki

Yamaji

Kakino

, et al. Tool path planning using trochoid cycles for hardened steel in die and mold manufacturing (1st report). In: Proceedings of the 2003 international conference on agile manufacturing, Beijing, China, 4–6 December 2003, pp.435–442. Beijing, China: China Machine Press.

43.

Elber

Cohen

Drake

MATHSM: medial axis transform toward high speed machining of pockets. Comput Aided Design 2005; 37(2): 241–250.

44.

Otkur

Lazoglu

Trochoidal milling. Int J Mach Tool Manu 2007; 47(9): 1324–1332.

45.

Ibaraki

Yamaji

Matsubara

On the removal of critical cutting regions by trochoidal grooving. Precis Eng 2010; 34(3): 467–473.

46.

Held

Spielberger

A smooth spiral tool path for high speed machining of 2D pockets. Comput Aided Design 2009; 41(7): 539–550.

47.

Borgia

Albertelli

Bianchi

A simulation approach for predicting energy use during general milling operations. Int J Adv Manuf Tech 2017; 90(9–12): 3187–3201.

48.

Kienzle

Einfluss der Wärmebehandlung von Stählen auf die Hauptschnittkraft beim Drehen. Stahl Eisen 1954; 74(9): 530–551.

49.

Tönshoff

Denkena

Basics of cutting and abrasive processes. Berlin: Springer, 2013.

50.

Dong

Zhang

Deng

The reconstruction of a semi-discretization method for milling stability prediction based on Shannon standard orthogonal basis. Int J Adv Manuf Tech 2016; 85(5–8): 1501–1511.

51.

Kron. Kron Mult-K 120, http://www.kronweb.com.br/br/produto-13-mult-k-120-multimedidor-energia-agua-gas (2018, accessed May 2018).

52.

Rai

Brand

Slama

, et al. Optimal selection of cutting parameters in multi-tool milling operations using a genetic algorithm. Int J Prod Res 2011; 49(10): 3045–3068.

53.

Guo

Loenders

Duflou

, et al. Optimization of energy consumption and surface quality in finish turning. Proc CIRP 2012; 1: 512–517.

54.

Balogun

Edem

Adekunle

, et al. Specific energy based evaluation of machining efficiency. J Clean Prod 2016; 116: 187–197.

55.

Kaufman

Cohen

Yagel

Volume graphics. Computer 1993; 26(7): 51–64.

56.

Requicha

Rossignac

JR.

Solid modeling and beyond. IEEE Comput Graph 1992; 12(5): 31–44.

57.

Held

VRONI: an engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments. Comput Geom 2001; 18(2): 95–123.

58.

Seth

Stori

JA.

Optimal tool selection for 2.5D milling, part 1: a solid-modeling approach for construction of the Voronoi mountain. Int J Comp Integ M 2005; 18(4): 294–307.

59.

Ferreira

JCE

Ochoa González

. A method for generating trochoidal tool paths for 2½D pocket milling process planning with multiple tools. Proc IMechE, Part B: J Engineering Manufacture 2013; 227(9): 1287–1298.

60.

Ochoa González

Ferreira

JCE.

Self-refining mesh algorithm to determine the Voronoi diagram. In: Proceedings of the 36th ABCM Ibero-Latin American congress on computational methods in engineering (CILAMCE), Rio de Janeiro, Brazil, 2015, https://doi.org/10.20906/CPS/CILAMCE2015-0204

61.

Kim

Choi

BK.

Machining efficiency comparison direction-parallel tool path with contour-parallel tool path. Comput Aided Design 2002; 34(2): 89–95.

62.

Hansen

Arbab

An algorithm for generating NC tool paths for arbitrarily shaped pockets with islands. ACM T Graphic 1992; 11(2): 152–182.

63.

Python Software Foundation. Python, http://www.python.org/ (2018, accessed February 2018).

64.

NumPy, http://www.numpy.org/ (2018, accessed April 2018).

65.

Lee

Altintaş

Prediction of ball-end milling forces from orthogonal cutting data. Int J Mach Tool Manu 1996; 36(9): 1059–1072.

66.

Wang

Guan

, et al. Comparison of different polynomial functions for predicting cutting coefficients in the milling process. Int J Adv Manuf Tech 2018; 94(5–8): 2961–2972.