energies Article
Energy Demand Modeling Methodology of Key State Transitions of Turning Processes Shun Jia 1, *, Qinghe Yuan 1, *, Dawei Ren 1 and Jingxiang Lv 2 1 2
*
Department of Industrial Engineering, Shandong University of Science and Technology, Qingdao 266590, China;
[email protected] Key Laboratory of Contemporary Design and Integrated Manufacturing Technology, Ministry of Education, Northwestern Polytechnical University, Xi’an 710072, China;
[email protected] Correspondence:
[email protected] (S.J.);
[email protected] (Q.Y.); Tel.: +86-532-8605-7044 (S.J.)
Academic Editor: Rick Greenough Received: 5 January 2017; Accepted: 24 March 2017; Published: 2 April 2017
Abstract: Energy demand modeling of machining processes is the foundation of energy optimization. Energy demand of machining state transition is integral to the energy requirements of the machining process. However, research focus on energy modeling of state transition is scarce. To fill this gap, an energy demand modeling methodology of key state transitions of the turning process is proposed. The establishment of an energy demand model of state transition could improve the accuracy of the energy model of the machining process, which also provides an accurate model and reliable data for energy optimization of the machining process. Finally, case studies were conducted on a CK6153i CNC lathe, the results demonstrating that predictive accuracy with the proposed method is generally above 90% for the state transition cases. Keywords: turning process; state transition; energy modeling; sustainable manufacturing
1. Introduction The report of the International Energy Agency (IEA) revealed that nearly one-third of global energy use and 40% of carbon dioxide (CO2 ) emissions are attributable to the manufacturing industry [1]. It is evident that the manufacturing industry has become one of the major sources of energy consumption and CO2 emissions, which will continue to increase by 1.9% annually if no effective action is taken [2]. Improved industrial energy efficiency is a critical cornerstone in climate change mitigation [3]. Therefore, the manufacturing industry must take responsibility and strive to adopt more energy-efficient and sustainable production techniques [4]. If energy data and information can be more effectively used and analyzed in manufacturing, it will provide considerable insights into energy-saving opportunities [5]. The machining process, as one of the major processes of manufacturing industries [6], is vital to energy saving and emission reduction. Generally, the life cycle of a product can be divided into several stages: material production; manufacture and assembly; transport; use; and end-of-life. Machine tools follow the same pattern and its Life Cycle Analysis (LCA) has shown that 95% of the environmental impact of a machine tool is associated with its use phase (assuming a 10-year lifespan). Of that use phase impact, 95% comes from energy consumption [7]. However, because the life cycle of a machine tool is usually more than 15 years, even reaching up to 20 years (with the current trends indicating that the industry will most likely want to prolong their lifecycle) [8,9], the environmental impact from the use phase of machine tools tends to be greater than 95%, even going as high to 99%. Similar results in another study [10] have shown that CO2 emissions caused by the energy consumption of a computer numerical control (CNC) machine tool (spindle power is 22 kW) over one year was equivalent to the CO2 emissions of 61 SUVs.
Energies 2017, 10, 462; doi:10.3390/en10040462
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It thus thus becomes becomes clear clear that that the the energy energy consumption consumption and and emissions emissions derived derived from from the the machining machining It process is very significant. Triggered by the necessity to improve the energy efficiency and process is very significant. Triggered to improve the energy efficiency and environmental performance performance of of the manufacturing industry, energy energy-efficiency environmental energy modeling modeling [11–16], energy-efficiency improvement [17–22] [17–22] and and carbon-emission carbon-emission reduction reduction [23,24] [23,24] of of the the manufacturing manufacturing industry industry have have improvement been studied. Experiments show that power peaks will be caused by state transitions during the been studied. Experiments show that power peaks will be caused by state transitions during the machining process process [25,26], [25,26], as as shown shown in in Figure Figure 1. 1. State State transition transition indicates indicates the the transition transition process process machining between the the two two neighboring neighboring states states during during the the machining machining process, process, such such as as spindle spindle startup, startup, rapid rapid between positioning acceleration, acceleration, coolant coolant startup, startup, tool tool change change startup, startup, etc. etc. State State transition transition generally generally relates relates to to positioning the instantaneous instantaneous startup of increase ofof torque or the of the the motor, motor,as aswell wellasasthe theinstant instantmomentum momentumthrough through increase torque moving parts, etc.,etc., which result in power increase and the phenomenon of peakofpower. or moving parts, which result in power increase andsubsequent the subsequent phenomenon peak However, intensiveintensive researchresearch about energy characteristics and models of models state transitions power. However, aboutconsumption energy consumption characteristics and of state is scarce. Toisfill this gap, an energy demand modeling method for state transition of thetransition turning process transitions scarce. To fill this gap, an energy demand modeling method for state of the is proposed in this paper. turning process is proposed in this paper.
Figure Figure 1. 1. Power Powercurve curveduring duringan an actual actual machining machining process process [25]. [25].
The peak power caused by machining state transition has been mentioned in many The peak power caused by machining state transition has been mentioned in many references [25–27]. However, the mechanism and energy demand model of the power peak has not references [25–27]. However, the mechanism and energy demand model of the power peak has not been researched in depth; the existing studies have only demonstrated the phenomenon of peak been researched in depth; the existing studies have only demonstrated the phenomenon of peak power power in the power curve. The duration of state transition is short, but the peak power caused by the in the power curve. The duration of state transition is short, but the peak power caused by the state state transition is high [27,28], making the energy demand of the state transitions significant. transition is high [27,28], making the energy demand of the state transitions significant. Moreover, state Moreover, state transitions occur frequently during the machining processes. The energy demand of transitions occur frequently during the machining processes. The energy demand of state transition state transition was not considered in reference [29]; therefore, the predicted energy is 9.3% less than was not considered in reference [29]; therefore, the predicted energy is 9.3% less than the measured the measured energy in the machining case. It can be observed that the energy demand of state energy in the machining case. It can be observed that the energy demand of state transition is a vital transition is a vital part of the energy demand of the entire machining process. part of the energy demand of the entire machining process. Although the power peak of the spindle startup was measured in the literature [30], its energy Although the power peak of the spindle startup was measured in the literature [30], its energy demand was not. The spindle and feed axis acceleration power models were studied based on the demand was not. The spindle and feed axis acceleration power models were studied based on the torque and angular velocity [31]; however, the friction torque and the torque for overcoming the torque and angular velocity [31]; however, the friction torque and the torque for overcoming the spindle rotational inertia involved in the models are very difficult to obtain, making the established spindle rotational inertia involved in the models are very difficult to obtain, making the established models difficult to apply in real machining cases. Shi et al. measured the energy consumption of models difficult to apply in real machining cases.and Shiobtained et al. measured the energy of spindle from stopping state to different speeds the spindle startupconsumption energy model spindle from stopping state to different speeds and obtained the spindle startup energy model through through quadratic function fitting [32]; the established model can be used to calculate the spindle quadratic function fitting [32]; the model can be usedthe to calculate the spindle startup startup energy from stopping toestablished the specified speed. When initial spindle speed is notenergy zero from stoppingfrom to the specified speed. thethe initial spindle speed notbezero (accelerating from low (accelerating low speed to highWhen speed), above model will is not applicable. Moreover, as speed to speed), supply the above model not be applicable. Moreover,inasour shown in the work energy supply shown inhigh the energy model of will the spindle startup established previous [33], the model can of the spindle startup in our previous [33],system the model can spindle only calculate the model only calculate theestablished energy consumption of thework spindle during speedup. energy consumption the spindle systemprocess, during spindle However, during the spindle However, during theof spindle speedup standbyspeedup. operation, X,Y,Z-axis feeding, chip speedup process, standby operation, X,Y,Z-axis feeding, chip conveying, cutting flood spraying and conveying, cutting flood spraying and other motions can also be executed. The actual energy demand of the spindle speedup is the sum of the energy demand of all the listed motions. Whether those motions are executed or not during spindle speed-up is dependent on the operating status of
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other can also be executed. The actual energy demand of the spindle speedup is the sum Energiesmotions 2017, 10, 462 3 ofof 19 the energy demand of all the listed motions. Whether those motions are executed or not during spindle the machine tool. The status of ofa the machine strongly dynamic; when speed-up is dependent on operation the operating status machinetool tool.isThe operation status ofonly a machine determining thedynamic; operating status of adetermining machine tool the spindle cantool weduring accurately tool is strongly only when theduring operating status ofspeedup a machine the calculatespeedup the totalcan energy demand of the spindle speedup process. spindle we accurately calculate the total energy demand of the spindle speedup process. In summary, summary, although although the the durations durations of of machining machining state state transitions transitions are are short, short, the the power power peak peak In caused by by the the state state transition transition is is high high and and its its energy energy demand demand cannot cannot be be ignored. ignored. Most Most of of the the caused abovementioned references have shown the peak power phenomenon to be caused by the state abovementioned references have shown the peak power phenomenon to be caused by the state transition, but energy demand of state transition is lacking. To fill transition, but the thequantitative quantitativeanalysis analysisofofthe the energy demand of state transition is lacking. Tothis fill gap,gap, an energy demand modeling methodology of key state transition of of thethe turning processes is this an energy demand modeling methodology of key state transition turning processes proposed in this paper, which can further be applied to the evaluation and optimization of energy is proposed in this paper, which can further be applied to the evaluation and optimization of energy demand of of the the machining machining process process and and provide providetheoretical theoreticalsupport supportfor forlow-carbon low-carbonmanufacturing. manufacturing. demand 2. 2. State Transition Transition Classification ClassificationBased Basedon onEnergy EnergyDemand Demand The The framework framework of the proposed proposed methodology is shown in Figure 2. Firstly, the Pareto Pareto chart chart of of energy energy demands demands of of state state transitions transitions for for the the turning turning process process is is developed. developed. Then, Then, key key state state transitions transitions and transitions are are classified according to the to established Pareto chart. Forchart. the identified and non-key non-keystate state transitions classified according the established Pareto For the key state transitions (supposing F, D, B areF,determined as the keyas state energy demand identified key state transitions (supposing D, B are determined the transitions), key state transitions), energy characteristics are researched and the energy demand formodel each type of key state demand characteristics are researched and the energymodel demand for each type oftransition key state is established. Finally, theFinally, experimental studies andstudies case studies will studies be conducted validate the transition is established. the experimental and case will betoconducted to validate the proposed energy demand model the key state transition of the turning process. The proposed energy demand model of the key stateoftransition of the turning process. The state transition state transition classification and the of the key state transitions firstdemand step for classification and the identification of identification the key state transitions are the first step are for the energy energy demand of state transitions, which is discussed modeling of statemodeling transitions, which is discussed in this section. in this section. Pareto chart Key state transitions
100%
Non-key state transitions
…… E State transitions of turning process
F
B
D
H
S
50%
0%
Key state transitions
Energy modeling
F
Energy demand modeling of F
B
Energy demand modeling of B
D
Energy demand modeling of D
Model validation
Figure 2. Framework of the proposed methodology. Figure 2. Framework of the proposed methodology.
The common state transition is summarized as follows: machine tool (off→on), machine tool The transition is summarized as follows: machine tool(on→off), (off→on), machine tool (on→off),common lighting state (off→on), lighting (on→off), cooling (off→on), cooling chip conveying (on → off), lighting (off → on), lighting (on → off), cooling (off → on), cooling (on → off), chip conveying (off→on), chip conveying (on→off), spindle rotation (Ls→Hs), spindle rotation (Hs→Ls), (off →on), chip conveying (on→off), spindle rotation →Hs), spindle rotation →Ls), positioning positioning (Ls→Hs), positioning (Hs→Ls), tool (Ls changing (off→on), tool (Hs changing (on→off), (Ls → Hs), positioning (Hs → Ls), tool changing (off → on), tool changing (on → off), material cutting material cutting (off→on), material cutting (on→off). More specifically, (off→on) indicates the state (off → on), material cutting (on → off). More specifically, (off → on) indicates the state transitions from transitions from “off” mode to “on” mode; (on→off) indicates the state transitions from “on” mode “off” mode to “on” mode;(Ls→Hs) (on→off)means indicates state transitions from “on” modemode to “off” mode. to “off” mode. Similarly, the the state transitions from “Low speed” to “High Similarly, (Ls→ Hs) means the the state transitions from “Low speed” mode speed” mode; (Hs→Ls) means state transitions from “High speed” modetoto“High “Low speed” speed” mode; mode. (Hs → Ls) means the state transitions from “High speed” mode to “Low speed” mode. Energy demand Energy demand of each state transition is analyzed by means of experiment and the key state of each state transition is analyzed by means of experiment and the key state transitions are identified transitions are identified according to the Pareto principle. Taking CK6153i CNC lathe as an according to the Pareto principle. Taking CNC as an example, demand of example, the energy demand of each stateCK6153i transition can lathe be obtained by usingthe the energy power and energy each state transition can be obtained by using the power and energy acquisition experimental device acquisition experimental device built by our research group [12]. The experimental device is built by ourofresearch group [12]. The three experimental is two composed of three current sensors, composed three current sensors, voltage device sensors, NI-9215 data acquisition cardsthree and voltage sensors, two NI-9215 data acquisition cards and one compact DAQ crate, etc. The experimental one compact DAQ crate, etc. The experimental device is connected to the main power box of the CK6153i CNC lathe. Moreover, the power and energy information is measured and stored in the Server SQL database for offline analysis. For more information about the experimental device, you can refer to Figure 10 in Section 4. The energy demands of chip conveying (off→on) and lighting
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device is connected to the main power box of the CK6153i CNC lathe. Moreover, the power and energy information is measured and stored in the Server SQL database for offline analysis. For more Energies 2017, 10, 462 4 of 19 information about the experimental device, you can refer to Figure 10 in Section 4. The energy demands of chip conveying (off→on) and lighting (off→ on)machine are the estimated values because the machine (off→on) are the estimated values because the tool mentioned above does not havetool an mentioned above does not have an automatic chip conveying device and the lighting device cannot automatic chip conveying device and the lighting device cannot be controlled separately. be In controlledbecause separately. addition, because the state transitionconveying/tool lighting/cooling/chip conveying/tool addition, the In state transition lighting/cooling/chip changing/machine tools changing/machine tools (on→closing off) onlyofinvolve instant closing of motor or lighting device, the low, energy (on→off) only involve instant motor or lighting device, the energy demand is very at demand is very low, at a value of around 5 J. The Pareto chart is obtained according to the energy a value of around 5 J. The Pareto chart is obtained according to the energy demand value of each demand value of each state transition gained byasactual measurement, state transition gained by actual measurement, shown in Figure 3. as shown in Figure 3. 3000
100%
2,795.0 90.8%
2500
93.2%
98.1% 99.3% 99.4% 99.5% 99.6% 99.7% 99.8% 99.9% 100.0% 95.2% 97.0%
86.1%
80%
80.8%
Energydemand demand (J) (J) Energy
90%
70%
2000
60% 1500
50%
54.6% 1,340.7
40% 1000
500
0
30% 20% 272.7
241.3
121.3
101.4
93.0
60.0
60.0
10% 5.0
5.0
5.0
5.0
5.0
5.0
5.0
0%
Figure 3. Pareto chart during an actual turning process. Figure 3. Pareto chart during an actual turning process.
According to the above Pareto chart and in accordance with the 80/20 rule, the top 20% of state According to the above Pareto chart in accordance the 80/20 the top 20% of transitions (top four transitions) ranked by and energy demands arewith determined as rule, key state transitions. state machine transitions four transitions) ranked by energy demands are determined as key The tool(top (off→on) includes three manually operated sub-movements: starting thestate air transitions. The machine tool (off → on) includes three manually operated sub-movements: starting switch, starting the numerical control (NC) control panel, and releasing the emergency stop button. the air switch, starting control (NC) control panel, releasing the caused emergency stop The energy demand ofthe thenumerical machine tool (off→on) is the sum ofand energy demand by these button. The energy demand of the machine tool (off→ on) is the however, sum of energy demand caused by these three sub-movements. Because they are manually operated, the duration of the machine three sub-movements. Because they are manually operated, however, the duration of the machine tool (off→on) depends on the operators. Accurate energy demand (off→on) is difficult to be obtain tool (off →on) depends operators. Accurate energy demand (off→on) is difficult to (Ls→Hs), be obtain and therefore does not on fallthe within the scope of this manuscript. Hence, spindle rotation and therefore does notcooling fall within the scope of this manuscript. Hence, spindle rotation (Ls positioning (Ls→Hs), (off→on) and tool changing (off→on) are finally determined to → beHs), the positioning (Ls → Hs), cooling (off → on) and tool changing (off → on) are finally determined to be the key state transitions (Category I), whereas other state transitions are non-key (Category II). It can be key state transitions (Category I), whereas other state transitions are non-key (Category II). It can be seen from the Pareto chart that the energy demand of key state transitions accounts for over 80% of seentotal fromenergy the Pareto chartofthat thetransitions, energy demand of key state further transitions accounts for over 80% of the the demand state thus warranting study. total energy demand of state transitions, thus warranting further study. 3. Methodology 3. Methodology 3.1. Energy Demand Model of Spindle Rotation (Ls→Hs) 3.1. Energy Demand Model of Spindle Rotation (Ls→Hs) Spindle rotation (Ls→Hs) is the transfer process of the spindle accelerating from low speed Spindle rotation (Ls→Hs) is the transfer process of the spindle accelerating from low speed (minimum is 0 r/min) to high speed under the conditions of non-cutting loading. Figure 4 shows the (minimum is 0 r/min) to high speed under the conditions of non-cutting loading. Figure 4 shows the power curves of spindle rotation (Ls→Hs) (initial speed n1 = 0 r/min, the target speed n2 = 750 r/min) power curves of spindle rotation (Ls→Hs) (initial speed n1 = 0 r/min, the target speed n2 = 750 r/min) of CK6153i CNC lathes. Energy demand of state transition spindle rotation (Ls→Hs) includes not of CK6153i CNC lathes. Energy demand of state transition spindle rotation (Ls→Hs) includes not only energy demand of the spindle system itself, but also energy demand of supporting therbligs only energy demand of the spindle system itself, but also energy demand of supporting therbligs (standby operating, lighting, etc.) during this state transition. Energy demand of spindle rotation (Ls→Hs) consists of three parts: (1) Energy demand of spindle system from spindle rotation start to peak power (ESR1); (2) Energy demand of spindle system from peak power to stable power (ESR2); (3) Energy demand of supporting therbligs during spindle rotation (Ls→Hs) (ESR3). Thus, the energy demand of state transition of spindle rotation (Ls→Hs) is written as:
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(standby operating, lighting, etc.) during this state transition. Energy demand of spindle rotation (Ls→Hs) consists of three parts: (1) Energy demand of spindle system from spindle rotation start to peak2017, power (ESR1 ); (2) Energy demand of spindle system from peak power to stable power (ESR2 Energies 10, 462 5 ); of 19 (3) Energy demand of supporting therbligs during spindle rotation (Ls→Hs) (ESR3 ). Thus, the energy Energies 2017, 10, 462 5 of 19 demand of state transition of spindle rotation (Ls→Hs) is written as:
ESRA ESR1 ESR2 ESR3
(1)
ESRA = E SR1 +EESRSR2 + E3SR3 Erotation(Ls→Hs), SRA ESR1 2 ESR where ESRA is energy demand of spindle J.
(1) (1)
where where E ESRA energydemand demandofofspindle spindlerotation(Ls→Hs), rotation(Ls→Hs),J.J. SRAisisenergy
Figure 4. Power curve of spindle rotation (Ls→Hs). Figure 4. Power curve of spindle rotation (Ls→Hs). Figure 4. Power curve of spindle rotation (Ls→Hs).
The fromspindle spindlerotation rotationstart start peak power (E) SR1 Theenergy energydemand demandof of the the spindle spindle system system from to to peak power (ESR1 is ) is The energy demand of the spindle system from spindle rotation start to peak power (E ) SR1 is calculated as:as: calculated calculated as:
Z tttSR1 SR1 SR 1
PPSR1SR1 ESR ESR1 SR= 1dtdtdt 11 00 PSR
(2) (2)(2)
0
P1SR where is thepower powerof ofthe spindle system system from spindle rotation start W; W; ttSR1 is1 is where the power of the spindle spindle system toto peak power, is PSRP where is the fromspindle spindlerotation rotationstart start peak power, SR1 1 is SR1 tSR duration from spindlerotation rotationstart start to to peak peak power, power, duration from spindle rotation start to s.s. duration from spindle power,s. The power of the spindle system during the acceleration process isis further expressed as The powerofofthe thespindle spindlesystem system during during the further expressed as [33]: [33]: The power the acceleration accelerationprocess processis further expressed as [33]: PSRP1SR P PnSR) + nTs ω Tss =s PSR P nn11 30 t t T+sTTs n1nπn 3030 /30 t+t αt SR n + 30αt/π PSR1 P = ( n T P 30 1 SR1 SR s s SR 1 s 1
(3) (3)(3)
The theoreticalderivation derivation process of of P Hence, thethe developed equation 1 is shown PSR The theoretical shownin inFigure Figure5. Hence, developed equation The theoretical derivationprocess process of P in Figure 5.5.Hence, the developed equation SR1 is shown SR1
model has a certain degree of versatility.
model has a certaindegree degreeofofversatility. versatility. model has a certain n =n1 +n
n = 60 t 2 PSR1 =PSR n1 + 60 t 2 Ts 2 n1 60 + t n = 60 t 2 PSR1 =PSR n1 + 60 t 2 Ts 2 n1 60 + t PSR1 PSR n Tss =PSR n1 +n Ts s0 + t PSR1 PSR n Tss =PSR n1 +n Ts s0 + t PSR1 =PSR n1 + 30 t Ts n1 30 + t s0 = 2 n1 60 s =s0 + t PSR1 =PSR n1 + 30 t Ts n1 30 + t = 2 n 60 s =s0 + t s0 1 s n1 s s 0 n1 Ts s0 n n Ts Figure 5. Theoretical derivation process of PSR1 .
n =n1 +n
Figure 5. Theoretical derivation process of P . Figure 5. Theoretical derivation process of P SR.1 SR1
The developed model contains some machine tool design and electrical control-related parameters (equivalent acceleration spindle tool Ts , etc.). However, the machine manual The developed model containstorque some ofmachine design and electrical control-related usually provides machine configuration-, maintenance-related information; parameters (equivalent acceleration torque ofoperationspindle Tand However, the machine manual s , etc.). descriptions of design and electrical control-related parameters are very limited (for information; technical usually provides machine configuration-, operationand maintenance-related protection reasons). coefficients of the developed model is difficult to be descriptions of designConsequently, and electricalsome control-related parameters are very limited (for technical obtained without experiments, which hinder the application of the model. To make the model easier protection reasons). Consequently, some coefficients of the developed model is difficult to be to use, the coefficients of the model (equivalent acceleration torque of spindle- T , angular obtained without experiments, which hinder the application of the model. To make thes model easier
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The developed model contains some machine tool design and electrical control-related parameters (equivalent acceleration torque of spindle Ts , etc.). However, the machine manual usually provides machine configuration-, operation- and maintenance-related information; descriptions of design and electrical control-related parameters are very limited (for technical protection reasons). Consequently, some coefficients of the developed model is difficult to be obtained without experiments, which hinder the application of the model. To make the model easier to use, the coefficients of the model (equivalent acceleration torque of spindle-Ts , angular acceleration of spindle-α, etc.) can be obtained based on the experimental studies. More specifically, each obtained coefficient value was the average value of multiple measurements. Once the coefficients of the energy model of state transitions for one machine tool are obtained, these models can be used for a long period of time. When it comes to another machine tool (of the same type of), the formula form of the energy model of state transitions can be adopted, though the coefficient values need to be updated with several simple experimental measurements. The duration from spindle rotation start to peak power tSR1 is calculated as: tSR1 =
2π (n2 − n1 ) 60α
(4)
where n1 is initial spindle speed, r/min; n2 is target spindle speed, r/min; α is angular acceleration of spindle, rad/s2 . The energy demand of spindle system ESR2 from peak power to stable power is written as ESR2 =
PSRmax + PSR (n2 ) tSR2 2
(5)
where PSRmax is power peak of spindle speedup, W; PSR is the spindle power, W; n2 is target spindle speed, r/min; tSR2 is the duration from peak power to stable power, s. tSR2 can be obtained based on experimental measurement combined with statistical analysis. The power peak of spindle speedup (PSRmax ) is spindle accelerating power at the moment (tSR1 ). According to Equation (3), the peak power of spindle speedup is expressed as: PSRmax = PSR1 (tSR1 ) = PSR n1 + 30αtSR1 /π + Ts πn1 /30 + αtSR1
(6)
The energy demand of supporting therbligs during spindle rotation (Ls→Hs) is relevant to the type and quantity of supporting therblig during state transition and the status of supporting therblig is judged by the state vector in forward-operating state [34]. The value 1 in state vector is reflected as the supporting therblig. The energy demand of supporting therbligs during spindle rotation (Ls→Hs) (ESR3 ) is calculated as: ESR3 = *
Z t SR3 * 0
*
OP · OS dt
(7)
*
where OP is the power vector of forward-operating state; OS is the state vector of forward-operating state; tSR3 is the duration of spindle rotation (Ls→Hs), s. The detail explanations of Equation (7) are shown in Figure 6. s1 ∼ s11 are the logical representations for these eleven types of therbligs, which are represented by 0–1 variables. More specifically, when the supporting therblig is executed, then s = 1 can be obtained; otherwise, s = 0 is obtained. For instance, supposing only the therblig-standby operating and therblig-lighting are executed, then s1 = s2 = 1 can be obtained, and s3 ∼ s11 are all *
*
set to be 0. As a result, the power of supporting therbligs can be expressed as: OP · OS = PSO · 1 + PL · 1 + PCFS · 0 + . . . + PMC · 0 = PSO + PL . The power model and calculation approach have been researched in our previous work [34].
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The energy demand of supporting therbligs during the state transition process (ESR3 ) is further calculated as: Z h i ESR3 =
tSR3
0
PSO · s1 + PL · s2 + PCFS · s3 + . . . + PMC · s11 dt
(8)
The duration of spindle rotation (Ls→Hs) tSR3 is calculated as: tSR3 = tSR1 + tSR2
(9)
where tSR1 is duration from spindle rotation start to peak power, s; tSR2 is duration from peak power to stable power, s. Substituting Energies 2017, 10, 462 the Formulas (2)–(8) into Equation (1) to get the energy demand of spindle rotation 7 of 19 (Ls→Hs): t SR1
Rt PSRn1n1+30αt/π 30t +TT n1 130 )dt dt ESRAE=SRA0SR10 PSR /30 +t αt (πn s s
PSRn n+1 n1 30 n2 ntSR2 t 0.5 30tSR/π TTs πn + tαt 1 + SR1 PSR + 0.5 PSR 30αt /30 + P s 2 1 1 SR1 SR1 SR SR2 i R tSR3tSRh3 PSO· ss11+ P+ Ps11 dt P + 0 0 P SO PLL ·ss22 +PCFS PCFS s·3s 3 + . . .C C · s11 dt
(10) (10)
Therblig Therblig name Therblig symbol Power vector State vector
C
OP PSO , PL , PCFS , PCC , PSR , PXF , PYF , PZF , PTS , PTC , PMC
OS s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 T
OP OS [ PSO , PL , PCFS , PCC , PSR , PXF , PYF , PZF , PTS , PTC , PMC ] [ s1 , s2 , s3 , s4 , s5 , s6 , s7 , s8 , s9 , s10 , s11 ]T PSO s1 +PL s2 +PCFS s3 +PCC s4 +PSR s5 +PXF s6 +PYF s7 +PZF s8 +PTS s9 +PTC s10 +PMC s11 Note: PSO , PL , PCFS , PCC , PSR , PXF , PYF , PZF , PTS , PTC , PMC represent the power of therblig-standby operating /-lighting/-cutting flood spraying/-chip conveying/-spindle rotating/-X-axis feeding/-Y-axis feeding/ -Z-axis feeding/-tool selecting/-tool changing/-material cutting, respectively;
s1 ~ s11 are the logical representations for eleven types of therbligs, which are represented by 0-1 variables
Figure 6. Detail explanations of Equation (7). Figure 6. Detail explanations of Equation (7).
3.2. Energy Demand Model of Positioning (Ls→Hs) 3.2. Energy Demand Model of Positioning (Ls→Hs) Positioning isthe thetransfer transfer process of feeding system low feeding speed Positioning(Ls→Hs) (Ls→Hs) is process of feeding system from low from feeding speed (minimum (minimum is 0 r/min) to the maximum feeding speed. For a given feeding system, the maximum is 0 r/min) to the maximum feeding speed. For a given feeding system, the maximum feed speed feed of each axis is Taking definite. Takinglathe CK6153i as anthe example, the maximum speed of speed each axis is definite. CK6153i as anlathe example, maximum feed speed feed of X-axis is of X-axis is 6 m/min and maximum feed speed of Z-axis is 10 m/min [35]. Figure 7 shows the power 6 m/min and maximum feed speed of Z-axis is 10 m/min [35]. Figure 7 shows the power curve of curve of positioning Z-axis positioning of CNClathe CK6153i lathe speed vf0 = 0 mm/min, Z-axis (Ls→Hs)(Ls→Hs) of CNC CK6153i (initial feed(initial speed vfeed f0 = 0 mm/min, maximum maximum feed rate v f1 = 10,000 mm/min). Similar to the state transition spindle rotation feed rate vf1 = 10,000 mm/min). Similar to the state transition spindle rotation (Ls →Hs),(Ls→Hs), energy energy demand of positioning (Ls→Hs) includes not only energy demand of the feeding system itself, but also energy demand of supporting therbligs (standby operating, lighting, etc.) during this state transition. Hence, the energy demand of positioning (Ls→Hs) consists of two parts: (1) Energy demand of feeding system during positioning (Ls→Hs) (EF1); (2) Energy demand of supporting therblig during positioning (Ls→Hs) (EF2). Thus, energy demand of positioning (Ls→Hs) is
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demand of positioning (Ls→Hs) includes not only energy demand of the feeding system itself, but also energy demand of supporting therbligs (standby operating, lighting, etc.) during this state transition. Hence, the energy demand of positioning (Ls→Hs) consists of two parts: (1) Energy demand of feeding system during positioning (Ls→Hs) (EF1 ); (2) Energy demand of supporting therblig during positioning (Ls→Hs) (EF2 ). Thus, energy demand of positioning (Ls→Hs) is calculated as: EFA = EF1 + EF2 where the FA is10, EnergiesE2017, 462energy demand of positioning (Ls→Hs), J.
(11) 8 of 19
Figure 7. Power curve of positioning (Ls→Hs). Figure 7. Power curve of positioning (Ls→Hs).
Generally, the rapid positioning accelerations of each axis of a CNC machine is very large, some Generally, the1 rapid of positioning each axis of (Ls→Hs) a CNC machine veryalthough large, some being more than g [36].positioning Therefore, accelerations the duration of is very is short, it being more than 1 g [36]. Therefore, the duration of positioning (Ls → Hs) is very short, can cause large power peaks (corresponding to the maximum feed speed). For each feed axis,although there is ita can cause large power peaks to the maximum For each axis, critical feeding distance Lf0. (corresponding When the feeding distance is Lf feed < Lf0speed). , the feeding axisfeed begins there is a critical feeding distance L . When the feeding distance is L < L , the feeding axis begins f0 f power f0 deceleration before reaching the maximum feeding speed. Because the peak does not reach deceleration before reaching the maximum feeding speed. Because the power peak does not reach the the maximum value, the duration of positioning (Ls→Hs) is very short, subsequently leading to the maximum value, the duration of positioning (Ls→Hs) is very subsequently the low low energy demand in this condition. Therefore, when theshort, feeding distance isleading Lf < Lf0to , energy energy demand in this condition. Therefore, when the feeding distance is L < L , energy demand f0f0, the feed axis canof demand of positioning (Ls→Hs) is negligible. When the feeding distance is fLf ≥ L positioning (Lsthe →Hs) is negligible. thecorresponding feeding distance is Lf ≥ Lf0 , thea feed axis canpower accelerate accelerate to maximum speedWhen and the power reaches maximum peak.to the maximum and thefocuses corresponding powerdemand reaches aofmaximum power peak. when Therefore, this Therefore, thisspeed subsection on the energy positioning (Ls→Hs) feeding subsection focuses on the energy demand of positioning (Ls → Hs) when feeding distance is L ≥ L f f0 . distance is Lf ≥ Lf0. The can be beexpressed expressedas as[33]: [33]: Thecritical critical feeding feeding distance distance LLf0 f0 can 2 22 vvrmax vv2rmax rmax L L f 0f 0= + rmax 7200a f 7200 df f 7200a 7200d
(12) (12)
wherevvrmax where maximum feeding feedingspeed speedof offeed feedtable, table,mm/min; mm/min;a fa f isisacceleration accelerationininfeed feedtable, table, rmax is the maximum 2 2 mm/s d f isisdeceleration vrmaxcan can obtained from machine manual a faf deceleration of of feed feed table, table, mm/s mm/s2 .vrmax bebe obtained from thethe machine manual mm/s2;; d f . design information. and d f can be calculated according to the machine d f energy and The can be calculated to the machine design information. demand ofaccording feeding system during positioning (Ls→Hs) EF1 is calculated as: The energy demand of feeding system during Z t F positioning (Ls→Hs) EF1 is calculated as: EF1 = t PF1 (t) dt E F 1 0 PF 1 (t ) dt F
0
(13) (13)
where (Ls→Hs). F1 ((tt)) is wherePP ispower powerfunction function of of feeding feeding system system during during positioning positioning (Ls→Hs). F1 For a given feeding system, the maximum feeding speed vrmax and feeding acceleration a f of For a given feeding system, the maximum feeding speed vrmax and feeding acceleration a f of positioning (Ls→Hs) is definite, and the initial feed rate of positioning (Ls→Hs) is 0 mm/min. Hence, positioning (Ls→Hs) is definite, and the initial feed rate of positioning (Ls→Hs) is 0 mm/min. for each feed axis, when the feeding distance is Lf ≥ Lf0 , the energy demand of feeding system Hence, EF1 and for each feed axis, when the feeding distance is Lf ≥ Lf0, the energy demand of feeding system EF1 and transfer time tF of positioning (Ls→Hs) are definite values, which can be obtained by experimental measurements combined with statistical analysis. The supporting therbligs during positioning (Ls→Hs) need to be judged by the state vector in the forward-operating state [34]. The value 1 in the state vector is reflected as the supporting therblig.
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transfer time tF of positioning (Ls→Hs) are definite values, which can be obtained by experimental measurements combined with statistical analysis. The supporting therbligs during positioning (Ls→Hs) need to be judged by the state vector in the forward-operating state [34]. The value 1 in the state vector is reflected as the supporting therblig. The energy demand of the supporting therblig (EF2 ) during positioning (Ls→Hs) is calculated as: EF2 =
Z tF h 0
i PSO · s1 + PL · s2 + PCFS · s3 + . . . + PC · s11 dt
(14)
where t F is the duration of positioning (Ls→Hs), s. The energy demand of positioning (Ls→Hs) is obtained by substituting the Formula (13) and (14) Energies 2017, 10, 462 9 of 19 into Formula (11) The energy demand of positioning Z tF Z t F h(Ls→Hs) is obtained by substituting the Formulai (13) and (14) into Formula EFA (11) = PF1 (t) dt + PSO · s1 + PL · s2 + PCFS · s3 + . . . + PC · s11 dt (15) 0
tF
0
PF 1 (t ) dt
tF
PSO s1 PL s2 PCFS s3 PC s11 dt 0 3.3. Energy Demand Model of Cooling (off→0on) E FA
(15)
Cooling (off→on) means the transfer process of the cooling device from “off” state to “power 3.3. Energy Demand Model of Cooling (off→on) on” state. The energy demand of this state transition includes not only energy demand of the cooling Cooling (off→on) means the transfer process of the cooling device from “off” state to “power on” device itself, but also energy demand of supporting therbligs (standby operating, lighting, etc.) during state. The energy demand of this state transition includes not only energy demand of the cooling the state transition. Figure 8 shows a power curve of the cooling (off→on) process for the CK6153i device itself, but also energy demand of supporting therbligs (standby operating, lighting, etc.) CNCduring lathe. the Energy demand of cooling (off→on) includes two parts: (1) Energy demand of cooling state transition. Figure 8 shows a power curve of the cooling (off→on) process for the device during cooling →on) (ECF1 );of (2) Energy demand of supporting therblig CK6153i CNC lathe.(off Energy demand cooling (off→on) includes two parts: (1) Energy during demandcooling of (off→cooling on) (ECF2 ). Therefore, the energy demand →on) of can be calculated as: during device during cooling (off→on) (ECF1);of(2)cooling Energy(off demand supporting therblig cooling (off→on) (ECF2). Therefore, the energy demand of cooling (off→on) can be calculated as:
ECFA = ECF1 + ECF2 ECFA ECF1 ECF 2
(16)
(16)
where ECFAEis the energy demand of cooling (off→on), J. where CFA is the energy demand of cooling (off→on), J.
Figure 8. Power curve of cooling (off→on).
Figure 8. Power curve of cooling (off→on).
For a given CNC machine tool, energy demand of the cooling system (ECF1) and transfer time of
For given (off→on) CNC machine demand of the cooling system (ECF1 transfer time the a cooling processtool, (tCF)energy are stable values, which can be obtained by) and experimental measurement combined with statistical analysis. of the cooling (off→on) process (tCF ) are stable values, which can be obtained by experimental The supporting during cooling (off→on) need to be judged by the state vector in the measurement combinedtherbligs with statistical analysis. forward-operating state. The value 1 in the state vector reflected as the supporting The in The supporting therbligs during cooling (off →on)is need to be judged by thetherblig. state vector energy demand of supporting therbligs during cooling (off→on) (ECF2) is calculated as: the forward-operating state. The value 1 in the state vector is reflected as the supporting therblig. t The energy demand of supporting ECF 2 therbligs PL s2 cooling PCFS s3 (off → PCon) s11 (E PSO s1 during dtCF2 ) is calculated as:(17)
0
CF
Z h CF where t F is the duration of tcooling (off→on) process, s.
ECF2 =
i PSO · s1 + PL · s2 + PCFS · s3 + . . . + PC · s11 dt
The energy demand of 0cooling (off→on) can be obtained by substituting the Formula (17) into (16). ECFA ECF 1
tCF
0
PSO s1 PL s2 PCFS s3 PC s11 dt
(18)
3.4. Energy Demand Model of Tool Changing (off→on) Tool changing (off→on) is the transfer process of a tool device changing from “off” state to
(17)
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where t F is the duration of cooling (off→on) process, s. The energy demand of cooling (off→on) can be obtained by substituting the Formula (17) into (16). ECFA = ECF1 +
Z t h CF 0
i PSO · s1 + PL · s2 + PCFS · s3 + . . . + PC · s11 dt
(18)
3.4. Energy Demand Model of Tool Changing (off→on) Tool changing (off→on) is the transfer process of a tool device changing from “off” state to “steady power” state. Figure 9 shows an actual power curve of tool changing (off→on) of CK6153i CNC lathe. Energies 2017, 10, 462several power peaks occur in the power curve. The reason is that the tool changing 10 of 19 It can be seen that (off→on) process includes several sub-actions, such as tool changing motor rotating startup, turret startup, turret rotation and motor braking. In this paper, the energy demand of tool changing rotation and motor braking. In this paper, the energy demand of tool changing (off→on) is viewed as (off→on) is viewed as the sum of energy demand of power peak caused by the sub-actions. the sum of energy demand of power peak caused by the sub-actions. Therefore, the energy demand of Therefore, the energy demand of tool changing (off→on) can be calculated as: tool changing (off→on) can be calculated as: Kp
∆p E ETCA K TCpk
ETCA =
k 1 ETC∆pk ∑
(19) (19)
k =1
where ETCA is energy demand of tool changing (off→on), J; ETCpk is energy demand of power peak where ETCA is energy demand of tool changing (off→on), J; ETC∆pk is energy demand of power peak caused by sub-action k when the rotating position number of the turret is p , J; K p is the number caused by sub-action k when the rotating position number of the turret is ∆p, J; K∆p is the number p; E can be obtained power peakswhen whenthe therotating rotatingposition position number number of the of of power peaks the turret turret isis ∆p; ETC can be obtainedbyby TC∆pk pk experimental measurement experimental measurementcombined combinedwith withthe thestatistical statistical analysis analysis method. method.
Figure 9. Power curve of tool changing (off→on). Figure 9. Power curve of tool changing (off→on).
Generally, the rotation method of turret of CNC lathe is the unidirectional tool changing order. Generally, the rotation method of CNC the unidirectional tool changing order. p lathe Hence, the rotating position numberofofturret the turret can beiscalculated as: Hence, the rotating position number of the turret ∆p can be calculated as: , T pt T pi T pt T pi ( p (20) Tpt − Tpt T pi , Tptpt ≥T T pi pi T p pi ∆p = (20) Tp − Tpt − Tpi , Tpt < Tpi where T pi is the initial position of the turret; Tpt is the target position of the turret; Tp is the total where the initial position of the turret; Tpt is the target position of the turret; Tp is the total posts postsTpi of is the turret. of the turret. 4. Case Study 4. Case Study 4.1. Description of State Transition Cases 4.1. Description of State Transition Cases Case studies of spindle rotation (Ls→Hs), positioning (Ls→Hs), cooling (off→on) and tool Case studies of spindle rotation (Ls→Hs), positioning (Ls→Hs), cooling (off→on) and tool changing (off→on) were carried out to show the feasibility of the proposed method. The state changing (off→on) were carried out to show the feasibility of the proposed method. The state transition transition cases were performed on a CK6153i CNC lathe, with a spindle speed range of 30~2000 r/min, and rapid-positioning speeds of X, Z-axes at 6000, 10,000 mm/min, respectively. In order to compare the forecast energy demand of state transition with the actual energy consumption value, an energy acquisition system was set up by our research group [12]. As shown in Figure 10, the current sensor and voltage sensor are connected with the CNC machine tool to obtain the current and voltage signal and collect the real-time data through two NI-9215 data acquisition cards. The power and
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cases were performed on a CK6153i CNC lathe, with a spindle speed range of 30~2000 r/min, and rapid-positioning speeds of X, Z-axes at 6000, 10,000 mm/min, respectively. In order to compare the forecast energy demand of state transition with the actual energy consumption value, an energy acquisition system was set up by our research group [12]. As shown in Figure 10, the current sensor and voltage sensor are connected with the CNC machine tool to obtain the current and voltage signal and collect the real-time data through two NI-9215 data acquisition cards. The power and energy information of the CNC machine tool are obtained by using LabVIEW software before being stored in the Server SQL database. The sampling interval of the energy acquisition system was set to 0.111s.of 19 Energies 2017, 10, 462 Energies 2017, 10, 462
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Figure Figure10. 10.Experimental Experimentalsetup setupof of energy energy acquisition acquisition system. system. Figure 10. Experimental setup of energy acquisition system.
Based six state state transitions transitions were were Basedon onthe themodeling modelingmethod methodproposed proposed in in Section Section 3, 3, case case studies studies of of six Based on the modeling method proposed in Section 3, case studies of six state transitions were carried out on the CK61563i CNC lathe. The determining process of experimental cases is shown in carried out on the CK61563i CNC lathe. The determining process of experimental cases is shown in carried out on the CK61563i CNC lathe. The determining process of experimental cases is shown in Figure 11. The principle is that the cases should cover all types of key state transitions. For the state Figure 11. The principle is that the cases should cover all types transitions. For the state Figure 11. The principle is that the cases should cover all types of key state transitions. For the state transition spindle speed speed isis transitionspindle spindlerotation rotation(Ls→Hs), (Ls→Hs), two two conditions conditions should should be be considered: initial spindle transition spindle rotation (Ls→ two considered: initial spindle speed is zero speed isisHs), not Therefore, spindle rotation (Ls→Hs)-[0→750 r/min] and zeroand andinitial initialspindle spindle speed notzero. zero.conditions Therefore,should spindlebe (Ls→Hs)-[0→750 r/min] and zero and initial spindle speed is not zero. Therefore, spindle rotation (Ls → Hs)-[0 → 750 r/min] and (Ls→Hs)-[500→1000 (Ls→Hs), due due to to the the (Ls→Hs)-[500→1000r/min] r/min]were wereselected selected for for the the state state transition transition positioning (Ls→Hs), (Ls → Hs)-[500 → 1000 r/min] were selected the state transition positioning (Ls→ Hs), direction). due to the fact that only feeding directions can applied for CNC (X-axis and Z-axis direction). fact that onlytwo two feeding directions canbe befor applied for the the CNC lathe Z-axis fact thatpositioning-Z-axis-[0→10,000 only two feeding directions can be applied forpositioning-X-axis the CNC lathe (X-axis and Z-axis direction). Hence, mm/min] and mm/min] were Hence, positioning-Z-axis-[0→10,000 mm/min] and positioning-X-axis [0→6000 mm/min] were Hence, positioning-Z-axis-[0 → 10,000 mm/min] and positioning-X-axis [0 → 6000 mm/min] were selected condition should should selectedasasexperimental experimentalcases. cases.For Forthe thestate state transition transition cooling cooling (off→on), only one condition selected as experimental cases. For the state transition cooling (off → on), only one condition should be considered:cooling coolingdevice device isis transiting transiting from from “off” “off” state state to “on” state (cooling bebeconsidered: (cooling (off→on) (off→on) was was considered: cooling device is transiting from “off” state to the “on” state (cooling (off→from on) was selected).For For thestate state transition toolchanging changing (off→on), the cutting one position selected). the transition tool (off→on), cutting tool changes from one selected). position For the state transition tool changing (off → on), the cutting tool changes from one position of the turret the turret turret toto another. another. The The most most commonly commonly used used changing changing was selected: tool ofof the tool changing changing to(off→on)-[T another. The most used changing was selected: tool changing (off→on)-[Tpi = 1, Tpt = 2]. 1,TTptpt=commonly =2]. 2]. (off→on)-[T pi pi= =1,
Figure 11. Determining process of experimental cases. Figure Figure 11. Determining Determining process process of experimental cases.
The above-mentioned six cases cover all the four type of key state transitions, and the main The above-mentioned six cases cover all the four type of key state transitions, and the main parameters of the above cases are shown in Table 1. parameters of the above cases are shown in Table 1.
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Table 1. Main parameters of state transition cases. State Transition Energies 2017, 10, 462
Initial Parameter
Main Parameters Target Parameter
Supporting Therbligs12 of 19
Spindle rotation (Ls→Hs) n2 = 750 r/min standby operating/lighting n1 = 0 r/min 0→750 r/min The above-mentioned Spindle rotation (Ls→Hs) six cases cover all the four type of key state transitions, and the main n2 = 1000 r/min standby operating/lighting n1 = 500 r/min 500→1000 r/min cases are shown in Table 1. parameters of the above Positioning (Ls→Hs) vrmin = 0 mm/min vrmax = 10,000 mm/min standby operating/lighting Z-axis Table 1. Main parameters of state transition cases. Positioning (Ls→Hs) vrmax = 6000 mm/min standby operating/lighting vrmin = 0 mm/min Main Parameters X-axis State Transition Cooling (off→on) OffParameter state On state standby operating/lighting Initial Target Parameter Supporting Therbligs Tool changing (off→on) T pi = 1 T pt = 2 standby operating/lighting Spindle rotation (Ls→Hs) 0→750 r/min
n1 = 0 r/min
n2 = 750 r/min
standby operating/lighting
Takingrotation spindle (Ls→Hs)-[500→1000 r/min] as an example, coefficients TS and α of the Spindle (Lsrotation →Hs) n1 = 500 r/min n2 = 1000 r/min standby operating/lighting 500→1000 r/min AH transmission chain can be obtained according to spindle startup experiment (TS = 28.42 N·m, 2)→ (Ls Hs) Z-axis vrmin = values 0 mm/min vrmax = 10,000 operating/lighting α = Positioning 39.78 rad/s [33]. The coefficient are substituted intomm/min (3) and (4)standby to obtain the expressions Positioning →Hs) X-axis = 0 mm/min v = 6000 mm/min standby operating/lighting rmax of the spindle(Ls speedup power vPrmin and the duration from spindle rotation start to peak power tSR1 SR1 Cooling (off→CK61563i on) Off state for the researched CNC lathe. Tool changing (off→on)
Tpi = 1
On state
standby operating/lighting
Tpt = 2
standby operating/lighting
PSR1 PSR n1 380t 2.98n1 1130.7t 0 t tSR1
(21)
Taking spindle rotation (Ls→Hs)-[500→1000 r/min] as an example, coefficients TS and α of the tSRaccording n2 n1 startup experiment (TS = 28.42 N(22) 1 0.002632 AH transmission chain can be obtained to spindle ·m, 2 α = 39.78 rad/s ) [33]. The coefficient values are substituted into (3) and (4) to obtain the expressions The duration from peak power to stable power t SR 2 is related to the target spindle speed n2 . of the spindle speedup power PSR1 and the duration from spindle rotation start to peak power tSR1 for t Based on the measured at different target spindle speeds n2 (see Table 2), linear regression SR 2 lathe. the researched CK61563i CNC between t SR 2 and n2 is conducted (as shown in Figure 12) to establish the duration model from PSR1 = PSR (n1 +(23)). 380t) + 2.98n1 + 1130.7t(0 < t ≤ tSR1 ) (21) peak power to stable power (Equation tSR1 = 0.002632 −) n 1) Table 2. Duration from peak power to stable power(n(t2SR2 under different target spindle speeds.
(22)
The duration from peak power to stable power tSR2 is related Target Spindle Speed n2 (r/min) tSR2 to (s) the target spindle speed n2 . Based on the measured tSR2 at different target spindle speeds n2 (see Table 2), linear regression 250 0.09 between tSR2 and n2 is conducted (as shown in Figure 12) to establish the duration model from peak 500 0.12 power to stable power (Equation (23)). 750 0.14 1000 0.16 ) 2 tSR2 = 0.037 + 1.471 × 10−4 n2 (R = 0.9479 (23) 1250 0.20 1500 which indicates that 0.26 The correlation coefficient is R2 = 0.9479, the established model can well 1750 0.32 describe tSR2 under different target spindle speeds.
Figure 12. Linear fitting between tSR2 and n2. Figure 12. Linear fitting between tSR2 and n2 .
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Table 2. Duration from peak power to stable power (tSR2 ) under different target spindle speeds. Target Spindle Speed n2 (r/min)
tSR2 (s)
250 0.09 13 of 19 500 0.12 750 0.14 1000 0.16 t SR 2 0.0371250 1.471 10 4 n2 (R 2 =0.9479) (23) 0.20 1500 0.26 The correlation coefficient is R2 = 0.9479, 1750 which indicates that 0.32the established model can well
Energies 2017, 10, 462
describe t SR 2 under different target spindle speeds.
Taking spindle rotation (Ls→Hs) as an example, the known information is the initial speed Taking spindle rotation (Ls→Hs) as an example, the known information is the initial speed
n1 0 r/min and target speed n2 750 r/min. Based on the proposed method in Section 3.1, the n1 = 0 r/min and target speed n2 = 750 r/min. Based on the proposed method in Section 3.1, the
ESRA calculated, as as shown shown in in energy spindle rotation rotation (Ls (Ls→Hs)-[0→750 r/min] ((E SRA )) can energy demand demand of of spindle →Hs)-[0→750 r/min] can be be calculated, Figure of intermediate intermediate variables variables are are Figure 13. 13. The The input input data, data, reference equations and calculation results of clearly clearly shown shown in in this figure.
n1 0 r / min
n2 750 r / min
n1 0 r / min n2 750 r / min
tSR1 0.002632 n2 n1
n1 0 r / min
PSR1 PSR n1 380t 2.98n1 1130.7t
PSR1 PSR 380t 1130.7t
n1 0 r / min n2 750 r / min
PSR1 PSR 380t 1130.7t
PSR1 =1.09 380t +41.12
PSR 1.09n 41.12
tSR1 1.97 s
tSR1 1.97 s
+1130.7t
PSR1 1.09 380t 41.12 1130.7t ESR1
t SR1
0
PSR1 dt
ESR1 3078.8 J
n2 750 r / min
tSR 2 0.037 1.471 104 n2
tSR 2 0.15 s
n2 750 r / min
PSR (n2 ) 1.09n2 41.12
PSR 750 858.6 W
tSR1 1.97 s n1 0 r / min n2 750 r / min tSR 2 0.15 s tSR1 1.97 s
tSR 2 0.15 s
PSRmax PSR1 tSR1 PSR1 PSR n1 380t 2.98n1 1130.7t
ESR 2 =
PSRmax +PSR n2 2
t SR 2
tSR 3 tSR1 tSR 2
s1 1
PSO 312.1 W PL 20 W
s2 1
ESR 3
ESR1 3078.8 J ESR 2 295.7 J ESR 3 704.1 J
PSRmax =3084.6 W
PSR 1.09n 41.12
tSR 3
0
PSO s1 PL s2 dt
ESRA ESR1 ESR 2 ESR 3
PSR 750 858.6 W
PSRmax 3084.6 W
ESR 2 295.7 J
tSR 3 2.12s ESR 3 704.1 J ESRA 4078.6 J
Figure 13. Calculation process of energy demand of spindle rotation (Ls→Hs)-[0→750 r/min]. Figure 13. Calculation process of energy demand of spindle rotation (Ls→Hs)-[0→750 r/min].
Similarly, energy demands of the other five state transitions can also be computed according to the established models in Section 3. The obtained energy demands of state transitions-spindle rotation (Ls→Hs)-[0→750 r/min], state transitions-spindle rotation (Ls→Hs)-[500→1000 r/min], positioning (Ls→Hs)-[Z-axis], positioning (Ls→Hs)-[X-axis], cooling (off→on) and tool changing (off→on) are 4078.6 J, 5056.8 J, 277.5 J, 117.2 J, 241.3 J and 116.8 J, respectively.
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Similarly, energy demands of the other five state transitions can also be computed according to the established models in Section 3. The obtained energy demands of state transitions-spindle rotation (Ls→Hs)-[0→750 r/min], state transitions-spindle rotation (Ls→Hs)-[500→1000 r/min], positioning (Ls→Hs)-[Z-axis], positioning (Ls→Hs)-[X-axis], cooling (off→on) and tool changing (off→on) are 4078.6 J, 5056.8 J, 277.5 J, 117.2 J, 241.3 J and 116.8 J, respectively. Energies 2017, 10, 462 14 of 19 4.2. Discussion 4.2. Discussion By using the energy acquisition system shown in Figure 10, the actual energy consumptions of By using the energy acquisition system shown in Figure 10, the actual energy consumptions of these demand values values of of these these six six state state thesesix sixstate statetransitions transitionswere weremeasured. measured. The The predicted predicted energy energy demand transitions are compared to the measured energy values, as shown in Figure 14. It can be seen that transitions are compared to the measured energy values, as shown in Figure 14. It can be seen that most predictive accuracies of the state transition cases are above 90%, which shows that the proposed most predictive accuracies of the state transition cases are above 90%, which shows that the energy demand models of key state of transitions well describe thedescribe energy consumption behaviors of proposed energy demand models key statecan transitions can well the energy consumption the state transitions of turning processes. behaviors of the state transitions of turning processes. 109.2 116.8
Tool changing(off→on)
261.6 241.3
Cooling(off→on)
Measured value
Predicted value
127.8 117.2
Positioning(Ls→Hs)
283.8 277.5
Positioning(Ls→Hs)
5231.7 5056.8
Spindle rotating(Ls→Hs)
4709.2
Spindle rotating(Ls→Hs)
4078.6
0
1000
2000
3000
4000
5000
Figure14. 14.Predicted Predictedenergy energyvalues values vs. vs. measured measured values values of of state Figure state transitions. transitions.
For the state transition spindle rotation (Ls→Hs), sometimes average machining power of state For thewas stateused transition spindle →Hs), sometimes machining power of transition to calculate therotation energy (Ls consumption during average state transition. Compared tostate the transition was used to calculate the energy consumption during state transition. Compared to the model model without considering the energy demand of state transitions, the accuracy can be improved to without considering the energy demand of state transitions, the accuracy can be improved to a certain a certain extent via applying the average machining power of state transitions. However, the extent via applying the average power of stateas transitions. However,model. the accuracy of the accuracy of the average powermachining model is not optimistic this is a simplistic The energy average power model is not optimistic as this is a simplistic model. The energy demand models proposed demand models proposed in this paper can further improve the energy predictive accuracy of the instate this paper can further improve the energy predictive accuracy of the state transitions compared spindle with the transitions compared with the average power model. Taking the state transition average power model. Taking the state transition spindle rotation (Ls → Hs)-[0 → 750 r/min] of CK6153i rotation (Ls→Hs)-[0→750 r/min] of CK6153i as an example, the energy demand of spindle as(Ls→Hs)-[0→750 an example, the energy of obtained spindle (Ls →Hs)-[0 750proposed r/min] has been in obtained basedby onthe the r/min] demand has been based on → the model this paper proposed model in this paper by the aforementioned calculating processes: E = 4078.6 J ( briefly SRA aforementioned calculating processes: ESRA 4078.6 J ( briefly shown in Figure 15). Moreover, if the shown in Figure Moreover, average power model is used predict energy consumption, average power 15). model is used iftothe predict energy consumption, thetocalculating process and resultthe is calculating process and result is also shown in Figure 15. It can be seen that the energy demand of also shown in Figure 15. It can be seen that the energy demand of the state transition spindle rotation the state transition spindle rotation (Ls → Hs)-[0 → 750 r/min] calculated by using the average power (Ls→Hs)-[0→750 r/min] calculated by using the average power model is ESRA 2524.3 J. Similarly, model is ESRA = 2524.3 J. Similarly, predicted energy values with the average power model and this predicted energy values with the average power model and this paper’s model can be calculated paper’s model can be calculated from the state transition spindle rotation (Ls→Hs)-[500→1000 r/min]. from the state transition spindle rotation (Ls→Hs)-[500→1000 r/min]. The comparison of the The comparison of the predicted energy values with these two models for the state transition spindle predicted energy values with these two models for the state transition spindle rotation (Ls→Hs) is rotation →Hs) 16. is shown in Figure 16. shown (Ls in Figure
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n2 750 r / min n2 750 r / min
n1 0 r / min n1 0 r / min
n2 750 r / min n2 750 r / min
ESR1 3078.8 J ESR1 3078.8 J
PSR 1.09n 41.12 PSR 1.09n 41.12
PSR 1.09 750 41.12 858.6 W PSR 1.09 750 41.12 858.6 W PSO 312.1 W PL 20 W PSO 312.1 W PL 20 W
ESR 2 295.7 J ESR 2 295.7 J
Pavg PSR PSO PL 1190.7 W Pavg PSR PSO PL 1190.7 W t SR 2 0.15 s tSR1 1.97 s t SR 2 0.15 s tSR1 1.97 s
ESR 3 704.1 J ESR 3 704.1 J
tavg tSR1 tSR 2 2.12 s tavg tSR1 tSR 2 2.12 s
ESRA Pavg tavg 2524.3 J ESRA Pavg tavg 2524.3 J
ESRA ESR1 ESR 2 ESR 3 4078.6 J ESRA ESR1 ESR 2 ESR 3 4078.6 J
Figure 15. Energy demand calculated with the model proposed in this paper and the average Figure 15. Energy demand demand calculated calculated with with the the model model proposed proposed in in this this paper paper and and the the average Figure 15. Energy average power model. power model. power model. 6000 6000 4000 4000 2000 2000 0 0
4078.6 4078.6
4709.2 4709.2
4000 4000
2524.3 2524.3
预测值(平均功率) 预测值(平均功率)
6000 6000
2000 2000 预测值(所提方法) 预测值(所提方法)
测量值 测量值
0 0
5056.8 5056.8
5231.7 5231.7
预测值(所提方法) 预测值(所提方法)
测量值 测量值
2194.8 2194.8
预测值(平均功率) 预测值(平均功率)
Figure 16. Comparison of predicted values and measured values for (a) spindle rotation Figure 16. Comparison of predicted values and for rotation Figure 16. Comparison values(Ls→Hs)-[500→1000 and measured measured values values for (a) (a) spindle spindle rotation (Ls→Hs)-[0→750 r/min] andof(b)predicted spindle rotation r/min]. (Ls→Hs)-[0→750 r/min] and (b) spindle rotation (Ls→Hs)-[500→1000 r/min]. (Ls→Hs)-[0→750 r/min] and (b) spindle rotation (Ls→Hs)-[500→1000 r/min].
It can be seen from Figure 16a that the predicted energy value with the average power model It can be seen from Figure 16a that the predicted energy value with the average power model for the state rotation (Ls→Hs)-[0→750 is 2524.3 J (the actual It can be transition seen from spindle Figure 16a that the predicted energyr/min] value with the average power measured model for for the state transition spindle rotation (Ls→Hs)-[0→750 r/min] is 2524.3 J (the actual measured energy value is 4709.2 J); the predictive accuracy is thus only 53.60% when using the average energy power the state transition spindle rotation (Ls→Hs)-[0→750 r/min] is 2524.3 J (the actual measured energy value is 4709.2 J); the predictive accuracy is thus only 53.60% when using the average power model. to the accuracy state transition spindle rotation r/min], the value is When 4709.2 it J); comes the predictive is thus only 53.60% when(Ls→Hs)-[500→1000 using the average power model. model. When it comes to the state transition spindle rotation (Ls→Hs)-[500→1000 r/min], the predictive accuracy is also not satisfactory (41.95%). The reason is that the power during state When it comes to the state transition spindle rotation (Ls→Hs)-[500→1000 r/min], the predictive predictive accuracy is also not satisfactory (41.95%). The reason is that the power during state transition treated a single value in theThe average power model and theduring dynamic power change accuracy isis also notas satisfactory (41.95%). reason is that the power state transition is transition is treated as a single value in the average power model and the dynamic power change and power were notin considered. Indeed, average is far less thanchange the peak power of treated as apeak single value the average powerthe model andpower the dynamic power and power and power peak were not considered. Indeed, the average power is far less than the peak power of the state transition, particularly in the transition spindle rotation theofproposed peak were not considered. Indeed, thestate average power is far less than(Ls→Hs). the peak With power the state the state transition, particularly in the state transition spindle rotation (Ls→Hs). With the proposed method this paper, the state predicted energy value for (Ls the→state transition spindlemethod rotation transition,inparticularly in the transition spindle rotation Hs). With the proposed in method in this paper, the predicted energy value for the state transition spindle rotation (Ls→Hs)-[0→750 r/min] is 4078.6 J. Hence, the predictive accuracy is 88.61%, improving the this paper, the predicted energy value for the state transition spindle rotation (Ls→Hs)-[0→750 r/min] (Ls→Hs)-[0→750 r/min] is 4078.6 J. Hence, the predictive accuracy is 88.61%, improving the accuracy 33.01%the compared with the average powerimproving model. A similar result isbyalso obtained in the is 4078.6 by J. Hence, predictive accuracy is 88.61%, the accuracy 33.01% compared accuracy by 33.01% compared with the average power model. A similar result is also obtained in the case state transition spindle (Ls→Hs)-[500→1000 The predictive is with of thethe average power model. A rotation similar result is also obtainedr/min]. in the case of the stateaccuracy transition case of the state transition spindle rotation (Ls→Hs)-[500→1000 r/min]. The predictive accuracy is raised from 41.95% to 96.66%, i.e., 54.71% improvement is achieved. The results show that the spindle rotation (Ls→Hs)-[500→1000 r/min]. The predictive accuracy is raised from 41.95% to 96.66%, raised from 41.95% to 96.66%, i.e., 54.71% improvement is achieved. The results show that the energy demand model proposed in thisThe paper can further improve the energy-predictive accuracy of i.e., 54.71% improvement is achieved. results show that the energy demand model proposed in energy demand model proposed in this paper can further improve the energy-predictive accuracy of the transitions compared the average power model. of the state transitions compared with thisstate paper can further improvewith the energy-predictive accuracy the state transitions compared with the average power model. the average power model. 5. Conclusions 5. Conclusions State transitions occur frequently during the turning process, and energy demand of the State transitions occur frequently during the turning process, and energy demand of the machining state transition is an important part of that entire process. The establishment of energy machining state transition is an important part of that entire process. The establishment of energy demand models of the key state transitions could significantly improve the accuracy of a turning demand models of the key state transitions could significantly improve the accuracy of a turning
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5. Conclusions State transitions occur frequently during the turning process, and energy demand of the machining state transition is an important part of that entire process. The establishment of energy demand models of the key state transitions could significantly improve the accuracy of a turning process energy model. The state transitions are classified according to energy characteristics, and the key state transitions for turning processes are identified. Then, the energy demand model of four types of key state transitions are respectively researched and established. Finally, experimental studies and case studies are performed on a CK6153i CNC lathe, the results showing that predictive accuracy with the proposed method is generally above 90% for the state transition cases. In particular, the predictive accuracy can be improved by 33.01% and 54.71% for the two state transition cases (spindle rotations (Ls→Hs)-[0→750 r/min] and (Ls→Hs)-[500→1000 r/min]) compared with the average power model. The proposed method in this paper can provide more accurate energy models and reliable data of state transitions for energy optimization of turning processes. Although this study presents energy demand modeling of key state transitions of the turning process, the dynamic distribution of key state transitions and total energy demand of state transitions throughout the machining process have not yet been investigated. Further research will be carried out to analyze key state transition distribution during the machining process and propose an energy demand modeling method of state transitions for all stages of the machining process. Acknowledgments: The authors sincerely thank editors and anonymous reviewers for their helpful suggestions on the quality improvement of our paper. This research is supported by the Shandong Provincial Natural Science Foundation, China (No. ZR2016GQ11), Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (No. 2015RCJJ049). Author Contributions: Qinghe Yuan and Dawei Ren proposed the paper structure, Shun Jia and Jingxiang Lv designed and performed the experiments. Shun Jia conceived the paper, analyzed the data and wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature af ap df ECFA ECF1 ECF2 EFA EF1 EF2 ESRA ESR1 ESR2 ESR3 ETCA ETC∆pk IEA K∆p Lf Lf0 LCA n n1 n2
acceleration in feed table (mm/s2 ) depth of cut (mm) deceleration of feed table (mm/s2 ) energy demand of cooling (off→on) (J) energy demand of cooling device during cooling (off→on) (J) energy demand of supporting therblig during(off→on) (J) energy demand of positioning (Ls→Hs) (J) energy demand of feeding system during positioning (Ls→Hs) (J) energy demand of supporting therblig during positioning (Ls→Hs) (J) energy demand of spindle rotation (Ls→Hs) (J) energy demand of spindle system from spindle rotation start to peak power (J) energy demand of spindle system from peak power to stable power (J) energy demand of supporting therbligs during spindle rotation (Ls→Hs) (J) energy demand of tool changing (off→on) (J) energy demand of power peak caused by sub-action k when the rotating position number of the turret is ∆p(J) International Energy Agency number of power peak when the rotating position number of the turret is ∆p feeding distance (mm) critical feeding distance (mm) Life Cycle Analysis spindle speed (r/min) initial spindle speed (r/min) target spindle speed (r/min)
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*
OP
power vector of forward-operating state
OS PCC PCFS PF1 (t) PL PMC PSO PSR PSR1 PSRmax PTC PTS PXF PYF PZF si tCF tF tSR1 tSR2 tSR3 Tp Tpi Tpt Ts vf0 vf1 vrmax α ωs ∆p
state vector of forward-operating state
*
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power of therblig-chip conveying (W) power of therblig-cutting flood spraying (W) power function of feeding system during positioning (Ls→Hs) power of therblig- lighting (W) power of therblig- material cutting (W) power of therblig-standby operating (W) spindle power (W) power of spindle system from spindle rotation start to peak power (W) power peak of spindle speedup (W) power of therblig-tool changing (W) power of therblig-tool selecting (W) power of therblig-X-axis feeding (W) power of therblig-Y-axis feeding (W) power of therblig-Z-axis feeding (W) logical representations for ith type of therbligs transfer time of cooling (off→on) process (s) transfer time of positioning (Ls→Hs) (s) duration from spindle rotation start to peak power (s) duration from peak power to stable power (s) duration of spindle rotation (Ls→Hs) (s) total posts of the turret initial position of the turret target position of the turret equivalent acceleration torque of spindle (N·m) initial feed speed (mm/min) maximum feed rate (mm/min) maximum feeding speed of feed table (mm/min) angular acceleration of spindle (rad/s2 ) angular velocity of spindle rotation (rad/s) rotating position number of the turret
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