Energy Consumption Model for Drilling Processes Based on Cutting Force

applied sciences

Article Energy Consumption Model for Drilling Processes Based on Cutting Force

Qi Wang, Dinghua Zhang, Bing Chen * , Ying Zhang and Baohai Wu

The Key Laboratory of High Performance Manufacturing for Aero Engine (Northwestern Polytechnical University), Ministry of Industry and Information Technology, Xi’an, Shaanxi 710072, China; [email protected] (Q.W.); [email protected] (D.Z.); [email protected] (Y.Z.); [email protected] (B.W.) * Correspondence: [email protected]

Received: 17 October 2019; Accepted: 7 November 2019; Published: 10 November 2019

Abstract: Accurate energy consumption modelling is critical for the improvement of energy efficiency in machining. Existing energy models of machining processes mainly focus on turning or milling, and there are few energy models for drilling. However, since drilling is often applied to roughing and semi-finishing, and the cutting parameters are large, the energy consumption is huge, and it is urgent to study the consumption of energy during the drilling process. In this paper, an energy consumption model for drilling processes was proposed. Idle power, cutting power, and auxiliary power were included in the proposed energy consumption model, using the cutting force to obtain the cutting power during drilling. Further, the relationship between cutting power and auxiliary power was analyzed. Cutting experiments were then carried out which confirmed the correctness of the proposed model. In addition, compared with several existing energy consumption models, the proposed model had better accuracy and applicability. It is expected that the proposed energy consumption model will have applications for the minimization of energy consumption and improvement of energy efficiency but not limited to only drilling energy consumption prediction.

Keywords: drilling; cutting power; energy consumption modelling; energy saving

1. Introduction In recent years, with the intense discussion of a low-carbon economy [1] and carbon trading [2], energy issues have once again caused widespread concern [3]. As energy prices continue to rise, the manufacturing industry, which is the largest energy consumer industry, is paying more and more attention to energy consumption in the manufacturing process, and reducing energy consumption has become a goal pursued by the manufacturing industry. In particular, drilling is widely used in the aerospace manufacturing process [4]. Studies have shown that, during the manufacture of a medium-sized aircraft, more than 6500 holes need to be machined, most of which are drilled [5]. At the same time, drilling is the main processing technology for the roughing and semi-finishing of holes; however, the processing efficiency is relatively low which leads to huge levels of energy consumption during processing [6]. Therefore, finding a solution to the problem of reducing energy consumption and increasing energy utilization during drilling processes is worth studying. To obtain a high utilization of energy in manufacturing processes, the first step is to understand and characterize how energy is consumed in manufacturing [7]. Recently, a number of energy consumption models have been proposed, particularly for machining. These existing models can be broadly classified into two categories: material removal rate (MRR)-based and detailed parameter (DPT)-based models [8]. The MRR-based models predict total energy consumption based on the assumption that the total energy assumption and MRR are linearly related. Gutowski et al. [9] pioneered the idea that machining

Appl. Sci. 2019, 9, 4801; doi:10.3390/app9224801 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 4801 2 of 14 energy consumption is related to the MRR. Kara and Li [10] proposed a specific energy consumption model, which proved to be of high accuracy for both lathes and milling machines. Li et al. [11] improved the MMR-based energy consumption model by considering the effects of no-load conditions and spindle speed on energy consumption. Costa et al. [12] studied how to obtain the minimum roughness and maximum material removal rate. Zhong et al. [13] proposed a decision rule for minimum energy consumption during turning based on the material removal rate. Differently from MRR-based models, DPT-based models calculate the total energy consumption by using different parameters which are obtained based on different theories. Many studies have pointed out that the cutting parameters are the major factors affecting energy consumption. Guo et al. [14] proposed an approach which combines energy consumption with surface roughness and applied it to finish turning; Xu et al. [15] proposed a tool path planning algorithm for five-axis milling with the goal of minimizing energy consumption. However, the accuracy of their model was found to be less than satisfactory in some cases. Some energy models are based on cutting forces including the work of Draganescu et al. [16] and Rodrigues and Coelho [17] who noted that the transformation of the cutting force caused by the tool edge geometry directly affects specific energy consumption (SEC). Research by Li and Kara [18] suggests that energy consumption models based solely on cutting forces only reflect the minimal energy consumption and not the maximum energy demand. To further improve the above energy models, Liu et al. [19] proposed a method based on the cutting force to establish an energy consumption model for the milling. Shi et al. [20] improved the energy consumption model of Liu [19] by introducing no-load power to establish a milling energy consumption model and a milling energy consumption model considering tool wear [21]. As already alluded to, although many of these existing energy models are comprehensive and detailed, most of the above energy models, whether MRR- or DPT-based, are built for turning or milling. There are very few studies on energy consumption for drilling. However, drilling is widely used in aerospace manufacturing processes [22]. Whether these existing models can accurately describe the energy consumption of the drilling process is yet to be verified. Besides, as the name suggests, in an MRR-based model, the only considered variable is MRR. However, the same MRR can be combined from many different processing parameters; cutting experiments have shown that energy consumption is not always the same at the same MRR, as many other affecting factors need to be considered. In addition, DPT-based models, such as Liu et al. [19], only consider the relationship between cutting power and total power; the coefficients in their model are purely obtained by mathematical regression thus lacking a clear theoretical basis. In this paper, an energy consumption model for drilling processes was proposed. Idle power, cutting power, and auxiliary power were included in the proposed energy consumption model. The performance of the machine determines the idle power which can be calculated from the spindle speed. The cutting power was calculated from the cutting forces on the cutting edge. The auxiliary power was calculated from the cutting power by establishing its relationship to the cutting power. The model was validated in experiments and achieved high prediction accuracy.

2. Energy Consumption in Drilling Processes

2.1. Energy Composition in a Drilling Process A complete machining process generally consists of three operational states: the start-up state, the idle state, and the machining state. Figure1 shows a general power consumption proﬁle for a drilling process; it is composed of three drilling operations with constant drilling parameters. Appl. Sci. 2019, 9, 4801 3 of 14 Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 14

Figure 1. The power proﬁle in a drilling process. Figure 1. The power profile in a drilling process. A machine tool generally comprises the drive tables, the motors for the spindle and tables, the A machine tool generally comprises the drive tables, the motors for the spindle and tables, the mechanical transmissions, and other mechanical components. Although, during machining, the energy mechanical transmissions, and other mechanical components. Although, during machining, the consumption of each component is complex, the total energy consumption of the machine tool can energy consumption of each component is complex, the total energy consumption of the machine be roughly divided into the idle power (Pidle), the cutting power (Pcutting), and the auxiliary power tool can be roughly divided into the idle power (Pidle), the cutting power (Pcutting), and the auxiliary (Pauxiliary), which can be expressed as: power (Pauxiliary), which can be expressed as:

P𝑃total == P𝑃idle++𝑃Pcutting++𝑃Pauxiliary (1)(1)

2.2. The Idle Power 2.2. The Idle Power According to Li et al. [11] and Ma et al. [23], the idle power is deﬁned as energy consumption that According to Li et al. [11] and Ma et al. [23], the idle power is defined as energy consumption only includes the rotation of the spindle, so the idle power (Pidle) can be expressed as: that only includes the rotation of the spindle, so the idle power (Pidle) can be expressed as:

Pidle = g(n) (2) 𝑃 = 𝑔(𝑛) (2) wherewheren 𝑛is is the the spindle spindle speed. speed.

2.3.2.3. TheThe CuttingCutting PowerPower InIn this this paper, paper, cutting cutting force force was was adopted adopted to calculate to calculate cutting cutting power power as shown as shown in Figure in2 Figure. The cutting 2. The forcescutting in forces drilling in candrilling be modelled can be modelled as [24,25 ]:as [24,25]: d𝐹 (𝑧) = 𝐾 d𝐴 +𝐾 ∆𝑏 (3a) dFt(z) = KtcdA + Kte∆b (3a)

d𝐹(𝑧) = 𝐾d𝐴 +𝐾∆𝑏 (3b) dF f (z) = K f cdA + K f e∆b (3b) d𝐹(𝑧) = 𝐾d𝐴 +𝐾∆𝑏 (3c) dFr(z) = KrcdA + Kre∆b (3c) 2 where 𝐾, 𝐾, and 𝐾 (N/mm ) and 𝐾, 𝐾, and 𝐾 (N/mm) are the specific cutting and edge 2 whereforce coefficients;Ktc, K f c, and d𝐴 K(mmrc (N2)/ mmis an )area and ofK tea ,chipK f e, differential and Kre (N /lipmm) removed, are the and specific it can cutting be calculated and edge by force coefficients; dA (mm2) is an area of a chip differential lip removed, and it can be calculated by d𝐴(𝑧) = ∆𝑏∙ℎ; ℎ (mm) is the chip thickness, and it can be calculated by ℎ= 𝑠𝑖𝑛𝜅; ∆𝑏 is the chip c dA(z) = ∆b h; h (mm) is the chip thickness, and it can be calculated by h = 2 sinκt; ∆b is the chip width, and it· can be calculated by ∆𝑏 = dz ; 𝜅 is the taper angle; and z (mm) is the axial position. width, and it can be calculated by ∆b = ;κ is the taper angle; and z (mm) is the axial position. cosκt t The components of the elemental cutting force components (d𝐹, d𝐹, d𝐹) can be calculated in The components of the elemental cutting force components (dFt, dF f , dFr) can be calculated in thethex ,𝑥y, ,𝑦z, directions𝑧 directions (see (see Figure Figure2): 2): ( ) d𝐹 𝑧  𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝛾 𝑠𝑖𝑛𝑖  d𝐹 dFx(z) cosθ sinγ sini dFt d𝐹(𝑧) = 𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝛾 ∙𝑐𝑜𝑠𝜅d 𝑠𝑖𝑛𝑖 ∙ 𝑠𝑖𝑛𝛾 ∙𝑐𝑜𝑠𝜅  d𝐹 (4)    − −    dFy(z)  =  sinθ cosγ cosκt sini sinγ cosκt  dF  (4) d𝐹(𝑧)   0𝑐𝑜𝑠𝛾 ∙𝑠𝑖𝑛𝜅d 𝑐𝑜𝑠𝑖 ∙ 𝑐𝑜𝑠𝜅 +𝑠𝑖𝑛𝑖∙𝑠𝑖𝑛𝛾d ∙𝑠𝑖𝑛𝜅 f d𝐹    − − · · ·   dFz(z) 0 cosγd sinκt cosi cosκt + sini sinγd sinκt dFr where 𝜃 is the angle between the cutting· velocity and· the x-axis;· 𝛾 ·is the angle among the two velocity components (a component perpendicular to the cutting edge and a component of the cutting speed in the y-axis); 𝑖 is the angle between the cutting velocity and normal to the cutting edge. Appl. Sci. 2019, 9, 4801 4 of 14

where θ is the angle between the cutting velocity and the x-axis; γd is the angle among the two velocity components (a component perpendicular to the cutting edge and a component of the cutting speed in the y-axis); i is the angle between the cutting velocity and normal to the cutting edge. Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 14

FigureFigure 2. 2. MechanicsMechanics model model of of a a twist twist drill. drill.

EnergyEnergy consumption consumption during during the the drilling drilling process process is ca isused caused by bythe therelative relative motion motion of the of tool the and tool workpieceand workpiece material. material. Rotary Rotary drive drive and andfeed feed drive drive are arethe the main main modes modes of of this this relative relative movement. movement. ModellingModelling two two different diﬀerent modes modes of of motion motion can can be be us useded to to calculate calculate the the cutting cutting energy energy consumption consumption of of thethe drill drill during during machining. machining.

InIn the the rotary rotary motion, motion, since since d𝐹dFf andand d𝐹dFr are perpendicular to to the the cutting cutting speed, speed, they they do do not not contributecontribute to thethe generationgeneration ofof rotational rotational motion motion power, power, and and the the diff differentialerential powers powers consumed consumed at each at eachtiny finitetiny finite element element cutting cutting edge edge in tangential, in tangential feed,, feed, and radialand radial directions directions can be can established be established as: as: d𝑃 = d𝐹 ∙𝑉(𝑧) (5a) dP, = dFt V(z) (5a) rotation,t · d𝑃, = 0 (5b) dProtation, f = 0 (5b) d𝑃, = 0 (5c) dProtation,r = 0 (5c) where 𝑉(𝑧) (m/s) is the cutting speed. whereTherefore,V(z) (m/ s)due is theto the cutting rotational speed. motion, the total power consumed in the tiny finite element cuttingTherefore, edge can duebe expressed to the rotational as: motion, the total power consumed in the tiny finite element cutting edge can be expressed as: d𝑃 = d𝐹 ∙𝑉(𝑧) (6) dP = dFt V(z) (6) rotation · In the feed motion, d𝐹 is perpendicular to the feed direction, which has no effect on feed power, In the feed motion, dFt is perpendicular to the feed direction, which has no effect on feed power, andand the the differential differential powers are:

d𝑃dP,f eed,t = 00 (7a) (7a)

d𝑃d,P == d𝐹d F∙𝑐𝑜𝑠𝛾cosγ ∙𝑠𝑖𝑛𝜅sinκt ∙f /𝑓/6000060000 (7b) (7b) f eed, f f · d· · d𝑃,dP = d𝐹=(d 𝑐𝑜𝑠𝑖Fr( cosi cos ∙ 𝑐𝑜𝑠𝜅κ+𝑠𝑖𝑛𝑖∙𝑠𝑖𝑛𝛾t + sini sinγ sin∙𝑠𝑖𝑛𝜅κt))f ∙/ 60000𝑓/60000 (7c) (7c) f eed,r · · d· · wherewhere ff (mm/min)(mm/min) is is the the feed feed rate. rate. TheThe total total power power in in the the tiny tiny finite ﬁnite element element cutti cuttingng edge edge caused caused by by the the feed feed motion motion can can be be expressedexpressed as: as:

d𝑃 = d𝐹 ∙𝑐𝑜𝑠𝛾n ∙𝑠𝑖𝑛𝜅 +d𝐹(𝑐𝑜𝑠𝑖 ∙ 𝑐𝑜𝑠𝜅 +𝑠𝑖𝑛𝑖∙𝑠𝑖𝑛𝛾 ∙𝑠𝑖𝑛𝜅o ) ∙ 𝑓/60000 (8) dP = dF cosγ sinκt + dFr(cosi cosκt + sini sinγ sinκt) f /60000 (8) f eed f · d· · · d· · Substituting Equation (4) into Equation (8), Equation (8) can be expressed as:

d𝑃 = d𝐹(𝑧) ∙ 𝑓/60000 (9) Finally, the instantaneous cutting power consumption can be calculated by: Appl. Sci. 2019, 9, 4801 5 of 14

Substituting Equation (4) into Equation (8), Equation (8) can be expressed as:

dP = dFz(z) f /60000 (9) f eed · Finally, the instantaneous cutting power consumption can be calculated by: R R P = P +P = dP + dP cutting f eed rotation R f eed R rotation (10) = f /60000 dFz(z) + V(z) dFt(z) · · 2.4. The Auxiliary Power The auxiliary power is attributed to the cutting load. Hu et al. [26,27] proposed that auxiliary power is a linear or quadratic function of the cutting power as follows.

Pauxiliary = C0Pcutting (11a)

2 Pauxiliary = C0Pcutting + C1Pcutting (11b) where C0 and C1 are coefficients that can be obtained from the physical cutting experiment. The coefficient of Equation (11a) is easier to obtain, but Equation (11b) is more accurate. Therefore, the load loss coefficient is determined using Equations (11a) or (11b) based on other parameters (such as machine performance, machining process, etc.).

2.5. The Power Consumption Model In the stable drilling state, the total power consumption of the machine tool can be expressed as: Ptotal = Pidle + Pcutting + Pauxiliary = Pidle + Pcutting + f Pcutting (12)

For Equation (12), it is generally agreed that Pidle only depends on the speciﬁc machine tool and Pcutting depends on the workpiece material and processing parameters such as cutting speed, feed rate, and coolant conditions. Moreover, Ptotal, Pidle, and Pcutting can all be accurately measured, respectively, by means of an electrical power logger and cutting force sensors and the calculation function (f (Pcutting)) of Pauxiliary can be obtained experimentally. In the next two sections, we report a physical cutting experiment that demonstrates how to establish the function f (Pcutting).

3. Energy Consumption Model Calibration Experiments In the following experiments, two sets of drilling operations were carried out. One set of experiments was used to calibrate the coeﬃcients in the model, and another set of experiments was used to validate the proposed model.

3.1. Experiment Details The experiments were carried out on a 3 axis machining center (YH850Z). The workpiece material was GH4169. The tool was a twist drill, the diameter was 10 mm, and the helix angle was 30◦, wet cutting. Table1 provides the cutting parameters used in Experiment-I. A total of 16 combinations were selected. In Experiment-II, some diﬀerent cutting parameters from Experiment-I were chosen to verify the accuracy of the model. As a result, four sets of processing parameters were selected for experimental veriﬁcation. Appl. Sci. 2019, 9, 4801 6 of 14

Table 1. Cutting parameters for Experiment I.

n (rpm) c (mm/r) 400 0.08 0.11 0.14 0.17 550 0.08 0.11 0.14 0.17 700 0.08 0.11 0.14 0.17 850 0.08 0.11 0.14 0.17

The setup of the experiments is shown in Figure3. All data on forces were collected using a Kistler-9123C rotary dynamometer, and all power data were collected using the PW3360 power logger duringAppl. Sci. the 2019 experiments., 9, x FOR PEER REVIEW 6 of 14 Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 14

(a)( a) (b)( b) Figure 3. The experimental setup: (a) force and (b) power signal processing and collection. FigureFigure 3. 3. TheThe experimental experimental setup: setup: (a ()a )force force and and (b (b) )power power signal signal processing processing and and collection. collection.

3.2.3.2.3.2. Energy Energy Energy Consumption Consumption Consumption Model Model Model Calibration Calibration Calibration

TheTheP Ptotalwas was equal equal to toP Pidlewhen whenthe the machine machine was was in in the the non-cutting non-cutting state. state. In In the the non-cutting non-cutting The Ptotaltotal was equal to Pidleidle when the machine was in the non-cutting state. In the non-cutting state,state, the the PW3360 PW3360 was was used used to to collect collect the the total total power power ((PPtotal) at different different spindle speeds, and and the the PPidle at state, the PW3360 was used to collect the total power (Ptotaltotal) at different spindle speeds, and the Pidle atidle atdifferent different spindle spindle speeds speeds was obtained. Then, thethe relationshiprelationship betweenbetweenP Pidle andand thethe spindle spindle speed speed different spindle speeds was obtained. Then, the relationship between Pidleidle and the spindle speed couldcouldcould be be be established. established. established. Figure Figure Figure 44 showsshows4 shows the the the experimental experimental experimental data data data and and and the the the numerically numerically fitted fitted fitted curve curve which which clearlyclearlyclearly resembles resembles resembles a a quadratica quadratic quadratic relationship. relationship. relationship.

1600 1600 2 Pidle = 0.0003n2 + 0.0524n + 1221 Pidle = 0.0003n + 0.0524n + 1221 1500 R² = 0.9956 1500 R² = 0.9956

1400 1400

1300 1300 Idle power (W) power Idle Idle power (W) power Idle 1200 1200

1100 1100 0 200 400 600 800 1000 0 200Spindle 400 rotation 600 speed (rpm) 800 1000 Spindle rotation speed (rpm) FigureFigure 4. 4. The idle power at different spindle speed. Figure 4. TheThe idle idle power power at at different diﬀerent spindle spindle speed. speed.

Explicitly,Explicitly, the the experimental experimental data data in Figurein Figure4 shows 4 shows that that the idlethe poweridle power ( Pidle ()P canidle) can be expressed be expressed as: Explicitly, the experimental data in Figure 4 shows that the idle power (Pidle) can be expressed as: as: 2 Pidle = 0.0003n + 0.0524n + 1221 (13) 𝑃 = 0.0003𝑛 + 0.0524𝑛 + 1221 (13) 𝑃 = 0.0003𝑛 + 0.0524𝑛 + 1221 (13) Reliable cutting force coefficients must be obtained before Pcutting is calculated according to Reliable cutting force coefficients must be obtained before Pcutting is calculated according to Equation (3a–c) which can be calculated using the proposed force experiments [28]. According to Equation (3a–c) which can be calculated using the proposed force experiments [28]. According to EquationEquation (10), (10), it isit onlyis only necessary necessary to tocalibrate calibrate the the cutting cutting force force coefficients coefficients in inthe the tangential tangential and and the the z z directions.directions. According According to tothe the experimental experimental data, data, th eth cuttinge cutting force force coefficient coefficient can can be be obtained obtained as: as:

K = [Ktc Kte Kzc Kze]T = [4196.8 202.6 5395.7 339.2]T K = [Ktc Kte Kzc Kze]T = [4196.8 202.6 5395.7 339.2]T FigureFigure 5 shows5 shows the the comparison comparison of ofthe the predicted predicted cutting cutting force force and and experimental experimental cutting cutting force, force, whichwhich were were calculated calculated using using the the obtained obtained cutting cutting fo rceforce coefficient coefficient under under several several different different processing processing parameters.parameters. The The results results show show that that the the error error betw betweeneen the the predicted predicted cutting cutting force force and and experimental experimental cuttingcutting force force was was acceptable, acceptable, and and that that the the obtain obtaineded cutting cutting force force coeffi coefficientscients were were reliable. reliable. Appl. Sci. 2019, 9, 4801 7 of 14

Reliable cutting force coefficients must be obtained before Pcutting is calculated according to Equation (3a–c) which can be calculated using the proposed force experiments [28]. According to Equation (10), it is only necessary to calibrate the cutting force coefficients in the tangential and the z directions. According to the experimental data, the cutting force coefficient can be obtained as:

T T K = [Ktc Kte Kzc Kze] = [4196.8 202.6 5395.7 339.2]

Figure5 shows the comparison of the predicted cutting force and experimental cutting force, which were calculated using the obtained cutting force coefficient under several different processing parameters.Appl. Sci. 2019, 9 The, x FOR results PEER showREVIEW that the error between the predicted cutting force and experimental7 of 14 cutting force was acceptable, and that the obtained cutting force coefficients were reliable.

3500 3500 Fz Ft Fz Ft Fz predict Ft predict Fz predict Ft predict

2500 2500

(N) 1500

(N) 1500 F F

500 500

-500 -500 0 5 10 15 20 25 30 35 40 0 2.5 5 7.5 10 12.5 15 17.5 20 Time (s) Time (s) (a) (b) 3500 3500 Fz Ft Fz Ft Fz predict Ft predict Fz predict Ft predict

2500 2500 (N) 1500 (N) 1500 F F

500 500

-500 -500 01234567891011 012345678910 Time (s) Time (s) (c) (d)

FigureFigure 5.5. ComparisonComparison ofof predictedpredicted andand experimentalexperimental valuesvalues ofof cuttingcutting forceforce underunder didifferentﬀerent cuttingcutting conditions:conditions: (a) n = 400400 rpm, rpm, ff == 3232 mm/min; mm/min; (b (b) )n n= =550550 rpm, rpm, f =f =6060 mm/min; mm/min; (c) (cn) =n 700= 700 rpm, rpm, f = f98mm/min;= 98mm/min; (d) ( dn) =n 850= 850 rpm, rpm, f = f144= 144 mm/min. mm/min.

TableTable2 2lists lists the the data data from from Experiment-I. Experiment-I. The TheP Ptotatotall isis thethe measuredmeasured datadata obtainedobtained byby thethe powerpower recorder.recorder. TheTheP Pidleidle waswas calculatedcalculated byby EquationEquation (13).(13). TheTheP Pcuttingcutting was calculated by the EquationEquation (10).(10). Based on these results, the auxiliary power, Pauxiliary, can then be calculated from Equation (11a) as shown in Figure 6.

Table 2. The measured total power (Ptotal) and the calculated cutting power (Pcutting) in Experiment-I.

Based on these results, the auxiliary power, Pauxiliary, can then be calculated from Equation (11a) as shown in Figure6.

Table 2. The measured total power (Ptotal) and the calculated cutting power (Pcutting) in Experiment-I.

No. n (rpm) f (mm/min) Ptotal (W) Pidle (W) Pcutting (W) 1 400 32 1625.0 1290.0 262.4 2 400 44 1679.0 1290.0 313.4 3 400 56 1744.6 1290.0 364.4 4 400 68 1781.4 1290.0 415.6 5 550 44 1750.0 1340.6 360.9 6 550 60.5 1837.4 1340.6 430.9 Appl. Sci. 2019, 9, x FOR7 PEER550 REVIEW 77 1937.0 1340.6 501.1 8 of 14 8 550 93.5 2001.8 1340.6 571.5 10 9 700700 56 77 1906.1 1988.8 1404.7 1404.7 459.3 548.4 11 10 700700 77 98 1988.8 2117.4 1404.7 1404.7 548.4 637.8 12 11 700700 98 119 2117.4 2217.9 1404.7 1404.7 637.8 727.4 12 700 119 2217.9 1404.7 727.4 13 850 68 2067.9 1482.3 557.7 13 850 68 2067.9 1482.3 557.7 14 850 93.5 2217.5 1482.3 665.9 14 850 93.5 2217.5 1482.3 665.9 15 15 850850 119 119 2354.8 2354.8 1482.3 1482.3 774.4 774.4 16 16 850850 144.5 144.5 2474.4 2474.4 1482.3 1482.3 883.2 883.2

120 Pauxiliary = 0.1336Pcutting R² = 0.9749 100

80 [W]

60 auxiliary P 40

0 0 200 400 600 800 1000 Pcutting [W] FigureFigure 6.6. TheThe auxiliaryauxiliary powerpower atat didifferentﬀerent cuttingcutting powers.powers.

ItIt cancan be be seen seen from from the the experimental experimental data data that th underat under the currentthe current processing processing parameters, parameters, the linear the relationshiplinear relationship used to used describe to describe the relationship the relationship between P betweenauxiliary and PauxiliaryPcutting andhad Pcutting reached had highreached accuracy, high soaccuracy, that in order so that to simplifyin order theto simplify calculation the process,calculation the equationprocess, the for calculatingequation forPauxiliary calculatingcan be P obtainedauxiliary can bybe Equationobtained (11a):by Equation (11a): Pauxiliary = 0.1336Pcutting (14) 𝑃 = 0.1336𝑃 (14) Finally, the Ptotal was expressed as the equation for Pidle and Pcutting, where both Pidle and Pcutting Finally, the Ptotal was expressed as the equation for Pidle and Pcutting, where both Pidle and Pcutting can can be calculated by Equations (13) and (10), the Ptotal can be expressed as: be calculated by Equations (13) and (10), the Ptotal can be expressed as:

P𝑃total == P𝑃idle++1.1336 1.1336𝑃Pcutting (15)(15)

InIn summary,summary, inin orderorder toto more more clearly clearly show show thethe calculation calculation processprocess ofof thethe energyenergy consumptionconsumption model,model, thethe energyenergy consumptionconsumption calculationcalculation processprocess ofof thethe drillingdrilling processprocess cancan bebe describeddescribed byby thethe followingfollowing ﬂowchartflowchart (Figure(Figure7 ):7): Appl. Sci. 2019, 9, 4801 9 of 14 Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 14

Workpiece material Tool parameters

Measured cutting fitting Cutting force force profiles coefficient K

calculate Cutting parameters Ft , Fz

Pidle Pcutting

Machine Tool

Pauxiliary

Ptotal

Figure 7. Flowchart of the drilling process energy consumption calculation.

In the next section,section, the experimental data underunder didifferentﬀerent processing parameters are compared and analyzed between the proposed modelmodel andand thethe existingexisting model.model.

4. Results and Discussions In this section, with the data from Experiment-II,Experiment-II, the proposed power power model model was was first ﬁrst verified. veriﬁed. Subsequently, the results from Experiment-I and II were used to compare the proposed model with some existing models.

4.1. Model Validation The setup of Experiment-II was used to verify thethe proposedproposed model.model. The four sets of processing parameters, which were different diﬀerent from Experiment-I,Experiment-I, are shown in Table3 ,3, togethertogether withwith thethe corresponding measured actual power P, and the Pidle, Pcutting, predicting power (P **), and accuracy corresponding measured actual power P, and the Pidle, Pcutting, predicting power (P ), and accuracy were calculatedcalculated underunder eacheach setting.setting.

Table 3. Cutting conditions and power dada in Experiment-II. Table 3. Cutting conditions and power dada in Experiment-II. 3 No. n (rpm) f (mm/min) MRR (mm /3s) P (W) Pidle (W) Pcutting (W) P* *(W) Accuracy No. n (rpm) f (mm/min) MRR (mm /s) P (W) Pidle (W) Pcutting (W) P (W) Accuracy 1 1400 400 76.4 76.4 100 100 1851.0 1851.0 1290.01290.0 472.1 472.1 1826.11826.1 98.66%98.66% 2 2550 550 76.4 76.4 100 100 1925.7 1925.7 1340.61340.6 507.9 507.9 1917.31917.3 99.57%99.57% 3 700 76.4 100 2010.6 1404.7 543.9 2022.4 99.41% 3 4700 850 76.4 76.4 100 100 2105.2 2010.6 1482.31404.7 580.2 543.9 2141.12022.4 98.30%99.41% 4 850 76.4 100 2105.2 1482.3 580.2 2141.1 98.30%

Among allall thethe settings,settings, the the MRR MRR was was kept kept unchanged unchanged while while the the spindle spindle speed speed was was varied varied in four in levels.four levels. It can It becan seen be seen from from the the experimental experimental data data (Table (Table3) that, 3) that, when when the the MRR MRR was was constant, constant, the theP P varied with the different processing parameters. Therefore, the simple model for predicting power with the material removal rate was not accurate enough. On the other hand, under the same feed Appl. Sci. 2019, 9, 4801 10 of 14 varied with the diﬀerent processing parameters. Therefore, the simple model for predicting power with the material removal rate was not accurate enough. On the other hand, under the same feed rate, the Pidle changed with the spindle speed, so it was also not accurate enough to use Pcutting to predict the power. It can be seen that the predicting power (P *) calculated by the prediction model was nearly 99% accurate compared with the four sets of experimental data, and it is proved that the model is reliable for predicting the energy consumption of drilling.

4.2. Model Comparison In order to prove the validity and accuracy of the new model, a comparative study was used to compare it with the three existing models (the form of each model is listed in Table4): Model-1 [ 10], Model-2 [11], and Model-3 [19]—all of which were established based on the same machine tool, and with the same data from our experiments. First of all, the coeﬃcients of the three models were calculated by the data from Experiment-I which are shown in Table4:

Table 4. Three comparison models.

Power Form Power Expression 1 Model-1 P = C0MRR + C1 P = 5.749MRR + 1393.6 2 Model-2 P = k0MRR + k1n + k2 P = 5.801MRR + 0.334n + 1170.5 3 Model-3 P = C0Pcutting + C1 P = 1.404Pcutting + 1237.9

Then, the data collected from Experiment I and Experiment II were used to compare the proposed power model, P *, with the three types of models. Table5 shows the comparison results based on the data of Experiment-I, where P(W) is the measured total power. As can be seen in Table5, on average, the proposed model prediction error was 1.13% which is the smallest error in the comparison experiments. Model 1 and Model 2 (based on the MRR) had prediction errors of 3.09% and 2.39%, respectively, and their prediction errors were greater than the 2.09% of Model 3 (based on cutting force). This indicates that the MRR was not suﬃcient to fully characterize the total energy consumption compared to the cutting force. Although Model 3 also gave acceptable predictions, the accuracy was not as good as the proposed model which may be due to the large inﬂuence of idle power on total power, while Model 3 ignores this.

Table 5. Comparing diﬀerent power models with the data from Experiment-I.

No. P (W) P * (W) P1 (W) P2 (W) P3 (W) 1 1625.0 1587.5 1635.6 1547.0 1606.7 2 1679.0 1645.2 1726.3 1638.0 1687.3 3 1744.6 1703.1 1817.1 1729.1 1750.6 4 1781.4 1761.1 1907.8 1820.2 1860.1 5 1750.0 1749.6 1726.3 1688.1 1745.9 6 1837.4 1829.0 1851.1 1813.4 1843.4 7 1937.0 1908.6 1975.9 1938.6 1964.7 8 2001.8 1988.4 2100.7 2063.8 2096.2 9 1906.1 1925.3 1817.1 1829.3 1830.4 10 1988.8 2026.4 1975.9 1988.7 1985.6 11 2117.4 2127.7 2134.7 2148.1 2205.7 12 2217.9 2229.2 2293.5 2307.4 2265.8 13 2067.9 2114.5 1907.8 1970.5 2000.3 14 2217.5 2237.2 2100.7 2164.0 2146.6 15 2354.8 2360.2 2293.5 2357.5 2301.7 16 2474.4 2483.5 2486.4 2551.1 2445.4 Average prediction error - 1.13% 3.09% 2.39% 2.09% Appl. Sci. 2019, 9, 4801 11 of 14

In addition, Figure8 shows the specific prediction error of each model under 16 sets of experimental parameters. The maximum values of the fluctuation range of Models 1, 2, and 3 were approximately 8%,Appl. 5%,Sci. 2019 and, 9 5%,, x FOR respectively. PEER REVIEW The maximum value of the proposed model fluctuation range11 wasof 14 about 2%. It can be seen that the fluctuation of the prediction error of the other three models was models was significantly higher than that of the proposed model which clearly shows the stability of significantly higher than that of the proposed model which clearly shows the stability of the proposed the proposed model prediction. model prediction.

10.0% 10.0% P* P1 8.0% 8.0%

6.0% 6.0% Error Error 4.0% 4.0%

2.0% 2.0%

0.0% 0.0% 0 4 8 12 16 0 4 8 12 16 Parameter setting Parameter setting (a) (b) 10.0% 10.0% P2 P3 8.0% 8.0%

6.0% 6.0% Error Error 4.0% 4.0%

2.0% 2.0%

0.0% 0.0% 0 4 8 12 16 0 4 8 12 16 Parameter setting Parameter setting (c) (d)

FigureFigure 8.8. TheThe predictionprediction errorserrors of of the the four four models models (Experiment-I): (Experiment-I): (a )(a proposed) proposed model; model; (b) ( modelb) model 1; ( c1;) model(c) model 2; ( d2;) model(d) model 3. 3.

1 2 Similarly,Similarly, TableTable6 6lists lists the the predicted predicted powers powers of of our our model modelP P** andand thethe threethree benchmarksbenchmarks PP1,, PP2, 3 andand PP3 against the actual power consumption P. FromFrom thethe table,table, itit cancan bebe foundfound thatthat thethe proposedproposed modelmodel hadhad thethe smallestsmallest predictionprediction errorerror (1.02%),(1.02%), andand thethe fluctuationfluctuation ofof errorerror waswas smallersmaller asas wellwell (see(see FigureFigure9 9).). ForFor Model-1,Model-1, thethe errorserrors of of the the No. No. 11 andand 44 experiments experiments werewere relatively relatively large large as as compared compared withwith thatthat ofof thethe No.No. 22 andand 3.3. ForFor thethe secondsecond benchmark,benchmark, sincesince Model-2Model-2 consideredconsidered thethe influenceinfluence ofof spindlespindle speedspeed onon energyenergy consumptionconsumption onon thethe basisbasis ofof Model-1,Model-1, thethe predictionprediction errorerror (1.73%)(1.73%) waswas muchmuch smallersmaller thanthan thatthat ofof Model-1,Model-1, butbut thethe errorerror waswas alsoalso largerlarger thanthan ours.ours. ForFor Model-3,Model-3, thethe predictionprediction accuracyaccuracy waswas equivalentequivalent toto thatthat ofof Model-2.Model-2. Model-3Model-3 usedused thetheP Pcuttingcutting toto predict predict energy consumption, butbut sincesince thethe PPidleidle at different different spindle speeds was not considered, there was stillstill nono higherhigher predictionprediction accuracyaccuracy (1.77%)(1.77%) thanthan ours.ours.

Table 6. Comparing the different models with the data from Experiment-II.

No. P (W) P* (W) P1 (W) P2 (W) P3 (W) Error* Error 1 Error 2 Error 3 1 1851.0 1826.1 1971.6 1884.2 2.16% 1.34% 6.52% 1.80% 2.72% 2 1925.7 1917.3 1971.6 1934.3 1.31% 0.43% 2.39% 0.45% 1.31% 3 2010.6 2022.4 1971.6 1984.4 0.47% 0.59% 1.94% 1.30% 0.47% 4 2105.2 2141.1 1971.6 2034.5 2.93% 1.70% 6.35% 3.36% 2.56% Average prediction error 1.02% 4.30% 1.73% 1.77% Appl. Sci. 2019, 9, 4801 12 of 14

Table 6. Comparing the diﬀerent models with the data from Experiment-II.

No. P (W) P * (W) P1 (W) P2 (W) P3 (W) Error * Error 1 Error 2 Error 3 1 1851.0 1826.1 1971.6 1884.2 2.16% 1.34% 6.52% 1.80% 2.72% 2 1925.7 1917.3 1971.6 1934.3 1.31% 0.43% 2.39% 0.45% 1.31% 3 2010.6 2022.4 1971.6 1984.4 0.47% 0.59% 1.94% 1.30% 0.47% 4 2105.2 2141.1 1971.6 2034.5 2.93% 1.70% 6.35% 3.36% 2.56% Average prediction error 1.02% 4.30% 1.73% 1.77% Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 14

7.00% P* 6.00% P1 P2 5.00% P3 4.00%

3.00%

Prediction errorPrediction 2.00%

1.00%

0.00% 1234 Parameter setting Figure 9. The prediction errors of the four models (Experiment-II).

5. Conclusions In this paper, anan energyenergy consumptionconsumption modelmodel forfor drillingdrilling processesprocesses waswas proposed.proposed. It is based on an equation consisting of the idle power, calculatedcalculated based on the spindle speed, the cutting power, power, calculated from the cutting force, and the auxiliar auxiliaryy power, power, calculated based based on on the the cutting cutting power. power. This proposedproposed model model was was implemented implemented and and verified verified during during the drilling the drilling process process on a three-axis on a three-axis vertical machiningvertical machining center. Comparativecenter. Comparative experiments experiment showeds thatshowed the proposedthat the proposed model had model higher had accuracy higher thanaccuracy the existingthan the MRR-based existing MRR-based model, the model, model the based model on thebased MRR on and the spindleMRR and speed, spindle and speed, the model and basedthe model only based on cutting only force.on cutting force. Although the new power model from this work is only specificspecific to thethe particularparticular machine tool and the specificspecific workpiece material on which the experimentsexperiments were carried out, we believe they are applicable to the majority of machine tools and workpiece materials, albeit with different different coefficients coefficients in the model. On the potential future study of the subject, the eeffectffect of tooltool wearwear onon energyenergy consumptionconsumption should bebe considered, considered, especially especially in thein drillingthe drilling of diffi ofcult-to-machine difficult-to-machine materials materials wherein thewherein roughing the stageroughing often stage has radicaloften has cutting radical parameters. cutting parameters. This calls This for the calls consideration for the consideration of the impact of the of impact tool wear of ontool energy wear consumption.on energy consumption. Secondly, the Secondly, proposed the model proposed only considers model only the energy considers consumption the energy of simpleconsumption holes, of which simple may holes, not bewhich applicable may not for be deep applicable hole drilling, for deep and hole further drilling, research and further on the research energy consumptionon the energy ofconsumption deep hole drilling of deep should hole drilling be carried should out. be carried out. Author Contributions: Conceptualization, Q.W., D.Z. and B.C.; Methodology, Q.W., Y.Z. and B.W.; Statistical analysis,Author Contributions: Q.W. and Y.Z.;Formal Conceptualization, analysis and investigation, Qi Wang, Dinghua Q.W. and Zh B.C.;ang Writing—originaland Bing Chen; Methodology, draft preparation, Qi Wang, Q.W.; Writing—reviewYing Zhang and Baohai and editing, Wu; Statistica B.C. andl Y.Z.;analysis, Supervision, Qi Wang B.W.; and Ying Project Zhang; administration Formal analysis and funding and investigation, acquisition, B.C.,Qi Wang Y.Z. and and Bing B.W. Chen; Writing—original draft preparation, Qi Wang; Writing—review and editing, Bing Chen Funding:and Ying Zhang;This research Supervision, was funded Baohai by Wu; [the Project Major admi Nationalnistration Science and and funding Technology acquisition, Projects] Bing grant Chen, number Ying [No.2017ZX04011011]Zhang and Baohai Wu. and [the China Scholarship Council] grant number [No. 201706295033] and [the Shaanxi Key Research and Development Program in Industrial Domain] grant number [No.2018ZDXM-GY-063] and [the FundamentalFunding: This Research research Funds was funded for the Centralby [the Universities]Major Nation grantal Science number and [No.31020190505003]. Technology Projects] grant number Conflicts[No.2017ZX04011011] of Interest: The and authors [the China declare Scholarship no conflict Counc of interest.il] grant number [No. 201706295033] and [the Shaanxi Key Research and Development Program in Industrial Domain] grant number [No.2018ZDXM-GY-063] and [the Fundamental Research Funds for the Central Universities] grant number [No.31020190505003].

Conflicts of Interest: The authors declare no conflict of interest.

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