Recently, manufacturing industry is rapidly developing towards the 4th industrial revolution.
Accordingly, global demand for an intelligent manufacturing that can be applied to the decision-making process is emerging. In this chapter, digital twin is implemented for the virtual machining. Then, collected data from digital twin is utilized to predict and analyze the energy consumption, which is considered as key machining performance indicator. Firstly, framework of digital twin is described.
Then, cutting power model in drilling process is presented based on material removal rate. The model established above is combined with digital twin to predict the cutting power in real-time. Lastly, specific cutting energy is obtained from empirical results.
4.1 Framework of digital twin 4.1.1 Configuration of digital twin
In digital twin, virtual model is synchronized with the physical machine. To achieve the accurate mapping from the physical space to the virtual space, data acquisition system with communication should be constructed [36-39]. As shown in Fig. 4-1, integrated framework is established beforehand to manage the large quantity of the data. The framework of digital twin consists of three parts:
communication platform, data acquisition and data analysis [40].
Fig.4-1. Schematic diagram of the digital twin
22 Data acquisition
The data acquisition system is constructed to synchronize the physical robot arm and the virtual robot arm in real-time. The tool-path is generated and imported to the physical robot in advance. Based on the real-time motion data such as position and velocity of the robot, mapping between physical and virtual space can be achieved. Then, virtual machine performs machining simulation, computation of material removal rate, prediction of energy consumption and calibration for drilling perpendicularity.
Communication platform
In communication platform, data is transmitted, integrated, and stored through industrial networks.
Since data is distributed across several data sources, transmitted data needs to be integrated in unified system for monitoring and analyzing [41, 42]. Overall network system includes several protocols such as Ethernet and OPC UA. In case of OPC UA, it standardizes data from different devices. Therefore, interoperability of data can be ensured. In addition, wireless transmission is established via WIFI.
Communication platform consists of two parts: data server and client. Robot controller and sensors act as a data server transmitting raw data to the client. Graphic-based client integrates and analyze data to monitor, control and make a diagnosis of the machine status in real-time.
Data analysis
The data analysis system mainly consists of visualization of virtual space and decision-making parts.
Various data sources include robot controller, sensors such as dynamometer and laser sensor. The raw data from different sources is integrated and visualized in graphic user interface (GUI) created based on Unity game engine. The GUI provides both 2D and 3D forms of display to the end-users. During the machining simulation, status of the robot can be monitored and predicted in real-time. Based on the simulation, virtual machining supports decision-making. In this study, material removal rate computed via virtual machining is used as a parameter for the predictive model of cutting power. The results of current predicted energy consumption are utilized to optimize machining parameters to meet the required conditions. In addition, tool-path can be adjusted in real-time. The feedback system suggested in chapter 3 ensures precision drilling.
4.1.2 Tool-workpiece engagement regions
Cutting power predictive model based on material removal rate (MRR) is combined with ModuleWorks software. The ModuleWorks software computes removed volume of the virtual workpiece based on the tool-workpiece engagement regions. Each time the tool moves along the tool path and interferes with the workpiece, it removes the engaged volume of the virtual workpiece [43-
23
45]. As shown in Fig. 4-2, virtual model and simulation is set based on the geometric modeling of the tool-workpiece engagement regions. Among various geometric modeling techniques, tri-dexel model is adopted in ModuleWorks software [46]. Tri-dexel model is used to update the in-process geometry of the virtual workpiece. The basic concept of tri-dexel model is discretizing an object using parallel grid segments. Then, it updates geometry by length-based calculation [43, 47-52]. The mesh engaged is computed and performs the cutting operation.
Fig. 4-2. Illustration of tool-workpiece engagement.
4.2 Cutting power model based on material removal rate 4.2.1 digital twin-based cutting power estimation
To predict the cutting power for arbitrary tool-workpiece engagement regions during drilling process, cutting power model based on material removal rate is established. Basically, power consumption in drilling process consists of three components: the idle power ๐๐๐๐๐, the cutting power ๐๐๐ข๐ก๐ก๐๐๐ and the additional power loss ๐๐๐๐ ๐ .
total idle cutting loss
P =P +P +P (4-1)
According to [53], the idle power ๐๐๐๐๐ is the energy consumption generated purely by the rotation of the spindle. Therefore, it is expressed only by the spindle speed. The cutting power ๐๐๐ข๐ก๐ก๐๐๐ is the energy consumed only for the material removal. ๐๐๐ข๐ก๐ก๐๐๐ is divided again into two parts: the feed power generated by the feed motion, ๐๐๐๐๐ and the rotational power generated by the rotational motion, ๐๐๐๐ก๐๐ก๐๐๐. The additional power loss ๐๐๐๐ ๐ is the power consumption caused by the cutting loss on the system. In this paper, cutting power, generated purely by material removal, is considered and modelled.
24
The cutting power during drilling process is expressed as a function of the material removal rate:
cutting c
P =K MRR๏ (4-2)
where ๐พ๐ is specific cutting energy, which is empirical constant. Specific cutting energy is defined as energy required to remove a unit volume of material. MRR is virtually computed in real-time based on digital twin system.
4.2.2 Experimental cutting power
For the verification of power estimated by the digital twin, the data of experimentally measured cutting power should be collected. Experimental cutting power can be obtained in two ways. Firstly, it can be measured directly through the power-energy collecting devices such as power meter. Second method measures cutting power indirectly by using the existing cutting power model which has drilling force and machining parameters as variables. The first method has a limitation that it requires additional power measurement devices. Therefore, second method was adopted to obtain the experimental cutting power. The cutting power, one of the parameters of cutting power model, is obtained through the dynamometer which can measure the cutting power in x, y and z directions.
Fig. 4-3. Elemental cutting section in drilling.
As mentioned above, drilling forces are key parameters of cutting power model as shown in Fig. 4- 3. The elemental drilling forces dFt,dFf,dFr can be converted to the drilling forces in x, y and z directions [54].
( ) cos sin sin
( ) sin cos cos sin sin cos
( ) 0 cos sin cos cos sin sin sin
x d t
y d t d t t
z d t t d t t
dF z i dF
dF z i dF
dF z i i dF
๏ฑ ๏ง
๏ฑ ๏ง ๏ซ ๏ง ๏ซ
๏ง ๏ซ ๏ซ ๏ง ๏ซ
โ โ
๏ฉ ๏น ๏ฉ ๏น ๏ฉ ๏น
๏ช ๏บ ๏ช= โ โ ๏ ๏ ๏ ๏บ ๏ช ๏บ
๏ช ๏บ ๏ช ๏บ ๏ช ๏บ
๏ช ๏บ ๏ช ๏ ๏ + ๏ ๏ ๏บ ๏ช ๏บ
๏ซ ๏ป ๏ซ ๏ป ๏ซ ๏ป
(4-3)
25
where is the angle between cutting velocity and the x-axis. is the angle between the cutting speed perpendicular to the cutting edge and the that of y-axis. is the angle between normal of cutti
d
i
๏ฑ ๏ง
These are geometric parameters of the tool.
ng adge and the cutting velocity.
Rotational power is also referred as material drilling power, since it is the power required for the actual removal of material [55]. The power consumption with respect to the rotational motion is expressed as:
( ) ( )
rotation t
dP =V z dF z๏ (4-4)
where V(z) is the cutting speed in m/s. Only tangential cutting force contributes to the rotational motion.
In feed motion, only axial force in feed direction affects the feed power. Therefore, the feed power can be expressed as:
6000 ( )
feed z
dP = f ๏dF z (4-5)
where f is feed rate in mm/min.
The total cutting power is the sum of feed power and rotation power.
( ) ( ) ( )
6000
6000
cutting feed rotation
z z
z t
P P P
f dF z V z dF z
f F V F
= +
= + ๏
= + ๏
๏ฒ ๏ฒ ๏ฒ
(4-6)Since machining parameters and tool geometry are known values, total cutting power can be obtained by measuring the cutting forces experimentally.
4.3 Experimental observation of specific cutting energy
Specific cutting energy should be obtained before calculating ๐๐๐ข๐ก๐ก๐๐๐ based on Eq. 4-2. Specific cutting energy is taken as an empirical function of feed and the tool diameter. The specific cutting energy increases with a decrease in the product of ๐ ยท ๐, which corresponds to uncut chip area. According to the power law relationship, specific cutting energy can be expressed as [56]:
( )n
Kc=A f d๏ (4-7)
Where A and n is parameters that need to be determined by the regression. These empirical constants are obtained by the experiment under the cutting conditions given in Table 4-1.
26 Material Tool diameter
(mm)
Spindle speed
(rpm) Feed (mm/rev) A n
Unidirectional
CFRP plate 1 6000 0.03 /0.04 /0.05
0.06 /0.07 /0.08 0.09
9.994 -0.822 Table 4-1. Cutting conditions and result of empirical coefficient.
Fig. 4-4 shows the empirical results of specific cutting energy obtained by the regression parameters A and n. The specific cutting energy is adopted as empirical constant to estimate the cutting power based on digital twin model suggested in Eq.
Fig. 4-4. Experimental results of specific cutting energy
4.4 Summary
In chapter 4, digital twin-based energy consumption was estimated. During virtual drilling process, tool-workpiece engagement area based on mesh model automatically calculated material removal rate.
Considering material removal rate and specific cutting energy, which is empirical constant together, cutting power was calculated in real-time. To evaluate the twin model, experimental cutting power model was suggested as a comparison. Verification of digital twin-based power prediction is presented in chapter 5.
0.03 0.04 0.05 0.06 0.07 80
100 120 140 160 180 200
Experimental Kc Data fiftted
Kc (N/mm2)
f.d (mm2/rev)
27