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Journal of Manufacturing Systems 31 (2012) 420– 428

Contents lists available at SciVerse ScienceDirect

Journal of Manufacturing Systems

journa l h o me pag e: www.elsev ier .com/ locate / jmansys

echnical Paper

ptimization of machining processes from the perspective of energyonsumption: A case study

.M. Bia, Lihui Wangb,∗

Department of Engineering, Indiana University Purdue University Fort Wayne, Fort Wayne, IN, USAVirtual Systems Research Centre, University of Skövde, Skövde, Sweden

r t i c l e i n f o

rticle history:eceived 31 May 2012eceived in revised form 3 July 2012ccepted 8 July 2012vailable online 28 July 2012

eywords:nergy modeling

a b s t r a c t

One of the primary objectives of sustainable manufacturing is to minimize energy consumption in itsmanufacturing processes. A strategy of energy saving is to adapt new materials or new processes; butits implementation requires radical changes of the manufacturing system and usually a heavy initialinvestment. The other strategy is to optimize existing manufacturing processes from the perspective ofenergy saving. However, an explicit relational model between machining parameters and energy cost isrequired; while most of the works in this field treat the manufacturing processes as black or gray boxes.In this paper, analytical energy modeling for the explicit relations of machining parameters and energy

omputer aided processing planningomputer aided manufacturingustainable manufacturing

consumption is investigated, and the modeling method is based on the kinematic and dynamic behaviorsof chosen machine tools. The developed model is applied to optimize the machine setup for energy saving.A new parallel kinematic machine Exechon is used to demonstrate the procedure of energy modeling. Thesimulation results indicate that the optimization can result in 67% energy saving for the specific drillingoperation of the given machine tool. This approach can be extended and applied to other machines to

dels

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establish their energy mo

© 2012 The Soc

. Introduction

Manufacturing is the backbone of industrialized society. In thenited States, manufacturing sector is responsible for a significant

hare of US economic production, generating $1.6 trillion in GDP in006, which was about 12.2% of the total US GDP. Besides, manu-acturing sector uses trillions of dollars’ worth of commodities andervices as inputs. Therefore, having a strong base of manufactur-ng is important as it stimulates all the other sectors of a country’sconomy [1,2]. However, manufacturing is one of major sources ofhe global warming. The survey on the electric energy consumptionas shown that up to 54% of electric energy is used in productionrocesses, which are mainly on production machines [3]. A simi-

ar situation happened to Europe. For example, the industrial sectoronsumes about 25% of the entire energy consumption in Germany;articularly for the electric energy, the industrial sector has theighest consumption of over 43% [4].

On the other hand, people are becoming more and moreonscious about the deterioration of today’s environment. Sustain-

bility of economy, society and environment has been recognizeds the priority to fundamental engineering research [5]. Increas-ngly, manufacturers are required to be more environmentally

∗ Corresponding author.E-mail address: lihui.wang@his.se (L. Wang).

278-6125/$ – see front matter © 2012 The Society of Manufacturing Engineers. Publishettp://dx.doi.org/10.1016/j.jmsy.2012.07.002

for sustainable manufacturing.f Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

responsible with respect to their products and processes. In thearea of manufacturing, new system paradigms related to sustain-ability have been proposed, e.g. sustainable manufacturing (SM),green manufacturing, and environmentally conscious manufacturing,to name a few [6].

In order to design an SM system, one of the primary tasks isto define the metrics of SM. The role of metrics in system designand optimization cannot be overstated [7]. The metrics for sus-tainable manufacturing have been extensively discussed in [8,9],where carbon footprint has been used as a measure of the impactthat manufacturing activities have on the environment. It relates tothe amount of CO2 produced in product life cycles (PLC), which iscommonly evaluated by Life-Cycle Assessment (LCA). Reich-Weiseret al. [9] proposed a methodology of LCA which including energyuse, global climate change, non-renewable resources consumption,and water consumption. However, the SM principles have beenmainly applied to product design instead of manufacturing systemdesign. The linkage between sustainability of a manufacturing sys-tem and the use of information technologies is still missing; designof a manufacturing system from the environmental perspective is,in most cases, not realized [10].

The authors of this paper are motivated by the fact that very lim-

ited works have been conducted in developing applicable energymodels of machine tools, which possess direct relations to thedesign parameters of manufacturing processes. The energy mod-els are desirable for minimizing energy cost of the manufacturing

d by Elsevier Ltd. All rights reserved.

Z.M. Bi, L. Wang / Journal of Manufactu

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Fig. 1. Classification of energy modeling.

rocesses. To this end, the paper first provides a comprehensiveiterature review on energy modeling of SM and identifies the lim-tations of existing works. The concept of energy modeling basedn kinematics and dynamics of machine is introduced. Then, a par-llel kinematic machine is used to illustrate the deriving process ofn energy model. An example is introduced to highlight the effec-iveness of the developed energy model in optimizing machineetups for drilling processes. Finally, conclusions and future workre outlined.

. Literature review

Improving energy efficiency can enhance the competitiveness of manufacturer, since the production cost is decreased and depen-ency on non-renewable energy sources may also be reduced.nergy consumption is directly related to sustainable environ-ents. Energy efficiency can be improved by process substitution,

hanging fuel structure, feedstock effect and recycling [11,12].owever, all of the aforementioned areas would cause some radicalhanges to a manufacturing system. In order to define metrics ofnergy-value of a product, one has to measure the energy consump-ion of the product during all the stages of its lifecycle includingesign, manufacturing, distribution, use, disposal and recycle [13].mong many other methods, energy modeling is a critical step to

mplement SM.

.1. Existing work on energy modeling

A sustainable manufacturing strategy requires metrics for deci-ion making at all levels of an enterprise [1]. Herrmann et al. [14]uggested using a multi-dimensional metrics (economic, environ-ental, and social) to evaluate sustainability; from the perspective

f strategies, the aspects include efficiency, consistency, and suf-ciency; in terms of system structure, the evaluations are madet network, company, factory, and process layers. A similar workas reported by Reich-Weiser et al. [9]; their proposed metrics isivided into five levels: machine tool, line, factory, supply chain, and

ife cycle.In manufacturing, the portion of energy is consumed in material

ow. As shown in Fig. 1, the material flow begins with the extrac-ion of raw materials from natural resources, manufacturing of parts,

ssembly of product, reuse/remanufacturing of parts/products, andnally ends in products disposal. At each phase, corresponding toolsextracting tools, manufacturing tools, assembly tools, remanufac-uring tools and disposal tools) are required to transform a product

ring Systems 31 (2012) 420– 428 421

from one phase to another along its lifecycle. The operations of thetools consume energy and generate wastes. Within the context,energy consumption can be modeled at different levels in differentscopes related to both the material flow and/or tool flow. Existingworks on energy modeling are thus classified into four types (seeFig. 1) and discussed as follows.

2.1.1. Life-cycle assessment approachesThe approaches under this category assess energy consump-

tion from the perspective of material flow. Energy consumed bymaterial-processing tools is treated as static. They are usuallyapplied at higher level of a system, e.g. to design new prod-ucts/processes and to optimize the supply chains of the system.

Jayal and Balaji [15] emphasized the importance of materialchoices and product features on sustainability. A choice amongalternative designs was made on the quantitative scores over thelife of the product. Pineda-Henson and Culaba [16] integrated LCAand AHP (analytic hierarchy process) for sustainable productivityperformance and measurement. Simulation is found to be an appro-priate means to estimate energy cost over the lifecycle of a product.Among many research efforts [17–21], Sekulic and Sankara [20]reported an interesting work to quantify the energy cost based onthermodynamics. Their approach might be helpful in determiningthe theoretically minimal energy that is required by manufacturingoperations as well as in modeling the energy conversion processes.Jayal and Balaji [15] commented that the scope of this exercise canbe daunting, posing unfortunate obstacles to the practical imple-mentation of sustainability initiatives. Fang et al. [22] introduceda mathematical model for the scheduling optimization with theconsideration of power consumption; the power consumptionscorresponding to a set of machining parameters were assumed.Their purpose of establishing this model and its solution was toachieve the multi-objective optimization in shortening cycle timeand reducing carbon footprint.

2.1.2. Tool-flow measurement approachesThe approaches under this category assess energy consumption

from the viewpoint of tool flow, and quantify energy consumptionbased on the measures of energy-related inputs (e.g. time, force,torque, etc.) of machine tools. A machine tool is treated as a blackor gray system, whose physical model is not necessarily knowncompletely. They were developed mainly for machine tool buildersto design/improve their machine tools without considerations ofspecific applications in manufacturing.

Energy consumption in tool flow depends on cutting methods,cutting parameters, geometries of tools, and cutting fluids [23].There has been extensive works in characterizing the impact ofspecific types and technologies of machining operations. Jeswietand Kara [24] defined a carbon emission signature for correlatingelectrical energy use to greenhouse gas emissions for some man-ufacturing processes. To optimize the material cutting, Gutowshiet al. [25] investigated the impact of cutting fluid and other con-sumable materials on energy consumption of material removal. Toincrease the efficiency of a machine, Roman and Bras [26] estab-lished the energy model for industrial cleaning processes; they didnot take into account how the machine was actually used. Rajemiet al. [27] modeled a turning process and optimized it for the min-imized energy footprint. Critical parameters in minimizing energyuse have been identified. The total energy consists of the energy for(i) machine setup, (ii) material removal operation, (iii) tool changes,and (iv) tool and tool edge preparation. It was assumed that theenergy on the production of workpiece material is independent

of the machining strategy and does not affect the optimizationof production parameters. However, the energy consumption wassimplified as the multiplication of power and the time of action.Dhanorker and Ozel [28] applied finite element modeling for end

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22 Z.M. Bi, L. Wang / Journal of Man

illing to predict forces, stresses and temperature distributions.hese quantities were used to estimate energy consumptions inanufacturing processes. Fratila [29] reported a comparative study

f machines. By selecting a pool of machines and workpieces withifferent materials, experiments were conducted to acquire dataor the evaluation of machine candidates under various machin-ng conditions. The energy consumption relates to temperature.fefferkorn et al. [30] investigated the impact of thermal assis-ance on the productivity of machining. A specific thermal energynd minimum preheating power are applied to guide the designf thermal energy delivery in thermally assisted manufacturing.ower consumption predictions can help operators to determinehe most effective cutting parameters. Quintana et al. [31] analyzedhe power consumption in high-speed ball-end milling operations,nd developed an artificial neural network to predict power con-umption during the operations. Besides, interested readers areeferred to [12,32,33] for other works on the energy consumptionf material removal.

.1.3. Tool-flow historiographical approachesThe approaches under this category assess energy consump-

ion from the same viewpoint of the previous type, but quantifynergy consumption based on measures of energy-related outputse.g. watt, temperature, heat, etc.) of machine tools. Similar to theool-flow measurement approaches, a machine tool is treated as alack box whose physical model is unknown. Energy consumed by

machine tool consists of the energy required by the tool tip foraterial removal and the energy used for auxiliary functions. Tra-

itionally, the energy required for the cutting process is estimatedased on cutting force prediction equations. However, this estima-ion is limited to the energy consumption of the tool tip [34,35].esides the energy required for removing a certain amount of mate-ial, a cautious consideration must be given to energy consumed by

machine tool and its auxiliary equipment [36].In the experiment of a type of ball-end milling machine tool,

uintana et al. [31] found that the theoretical power required toenerate the material removal rate is very low compared to theeal power consumed in the actual metal removal operation (i.e.,heoretical required power is 0.34% of actual power consumption).he power used to produce relative movement between tool andorkpiece through spindle rotation and axes movements is veryigh compared to the power needed to remove extra material inhe form of chips; conventional machines are very inefficient inontrast to micro machines. A similar conclusion was made by Liow37] that a conventional machine consumes 800 times more energyhan a micro milling facility. The bulk of the energy used by theonventional machine was for driving the spindle where most ofhe torque available was not required for the job. It is crucial toptimize the machining process to reduce the energy footprint of

machined product.One of the key components of a machine tool is spindle. A spindle

onsumes a large portion of energy in machining. Altintas and Cao38,39] presented an integrated simulation model of the spindle,ool holder, and cutting process. They used a finite element modelo predict the forces and energy flow occurred to the spindle. Theirbjective was to optimize the spindle dimensions for the maxi-um material removal rate. In designing a large milling machine,

ulaika et al. [40] investigated the feasibility of mass reduction forobile structural components to maximize material removal rate;

heir experiments showed an increase of 100% productivity, accom-lished at the same time, and with 13% of energy saving. Li andara [34] developed a simplified model to predict the total energy

onsumption of a turning machine tool; however, they requiredxperiments to measure power consumption under various cut-ing conditions. It was expected to provide a reliable predication ofnergy consumption of the given process parameters.

ring Systems 31 (2012) 420– 428

Industrial robots have been widely used in manufacturing; oneof the research topics is to improve robotic motions to achievemaximal speed, optimal path, and minimized energy costs. Someworks have been reported on using the minimized energy con-sumptions for design of robots and for the path and trajectoryplanning. For examples, Yang and Chen [41] and Bi and Zhang[42] investigated the optimal design of modular robots with theconsideration of multiple objectives including energy consump-tion. In the path planning of cooperation for multiple manipulators,Garg and Kumar [43] used the minimized torque as their designobjective; the optimization was conducted by Genetic Algorithm.UR-Rehman et al. [44] considered the path placement optimizationfor Orthoglide parallel robots; the multi-objective design crite-ria include energy consumption, shaking forces and maximumactuators torques. One consideration in the machining cell is therelative location between the workpiece and a machine tool. Lopesand Pires [45] proposed an optimization method based on thequality of workpiece and minimized energy cost. Zhang and Khosh-nevis [46] considered specifically on contour crafting processes;the tool paths of contour crafting were optimized to increase theefficiency of the construction of complicated products. Capi et al.[47] applied the minimum consumed energy as the design crite-rion for trajectory planning of a biped robot. Balasubramanian andBalch [48] investigated the trajectory planning for over-actuatedrobots for energy saving. Smetanova [49] investigated the influ-ences of movement parameters on energy consumption duringrobotic operations, where mathematical models were experimen-tally verified. Energy consumption was calculated from acquiredforces and torques during the operations. In addition, Van Duijsenand Chen [50] discussed the representations of energy in differ-ent media, e.g. electricity, solar power, wind power, hydro power,and wave power. These representations can be used to optimizethe generation, transportation, storage, as well as planning andcontrol of energy. Computer numerically controlled machining isone of the fundamental manufacturing technologies and its mainenvironmental impact is attributed to electrical energy use. Thepower requirement of an operation depends on machining param-eters, cutting tools, and materials. Anderberg et al. [51] developedan extended economic cost model for machining operations withinternal cost for energy use, which was based on the handbook for-mulae for machining cost estimations. Energy-saving activities canbe towards the machine tool to minimize idle energy consumptionand to introduce more energy efficient cooling systems.

2.1.4. Physics-based integration approachesPhysics-based integration approaches assess energy consump-

tion at both of the material- and tool-flows, and quantify the energyconsumption using physics-based models (kinematics, dynam-ics, control, etc.) of machine tools. It takes into consideration ofthe interface between material removal and machine tool. Theapproaches of this type can be applied not only to design newmachine tools but also to optimize manufacturing processes whena machine tool is given in a system.

Narita et al. [52,53] proposed new machine tools called FutureOriented Machine Tools (FOMT). To reduce energy consumption,both of machine tools and machining processes were modeledand their interactions were considered. However, such a machinetool was simplified as a servo motor, spindle motor, NC controller,and compressor. The electrical energy consumption was calculatedbased on the required torque. The energy consumption of machin-ing process was calculated from cutting force, coolant quantity andso on. Their recent efforts were extended to a virtual machining

simulator (VMSim) for flat end mill [54,55]. VMSim was proposedto replace numerous cutting tests for optimization of cutting condi-tions. A few researchers have studied the optimization of machinetools or actuators for energy saving. Santos et al. [23] reported

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Z.M. Bi, L. Wang / Journal of Man

he energy modeling work for a press-brake device. The compari-on and modeling of electricity consumption of hydraulic/electricystems were investigated. The energy consumption of differentomponents was estimated based on the measurements of the elec-rical variables such as voltage, current, power factor, frequency,nd harmonics. Anderberg et al. [51] showed that productivitynd cost efficiency can be improved alongside energy savings in

computer numerically controlled machining environment. Theelationship between machining parameters, machining costs, andnergy consumption were evaluated. Their research was based on

machining cost model and experiments where energy consump-ion was monitored together with tool wear. Draganescu et al. [56]arried out experiments for statistic modeling of machine tools.he efficiency of a machine tool and its energy consumption haseen determined as functions of different machining parameters.he models are based on the relationship between the process effi-iency and major cutting parameters. Note that models for differentperations can be varied significantly; this method cannot eas-ly be generalized for other processes and machine configurations.

oreover, supplementary aggregates of machines are disregarded,ven though they may have a major impact on the overall energyalance. Diaz et al. [57] discussed the relations of process param-ters on power consumption for end-milling operations. Energyonsumption relates to the quality of machining as well. Lee andiang [58] proposed to improve the smoothness of segmented tool-aths based on the minimized strain energy. The composite curvesmong segments can achieve the continuity of the second order oferivatives without oscillations.

.2. Summary of literature review

A brief summary below reveals our findings from the literaturen energy modeling for machine tools and machining processes.

The methodologies of energy modeling can be classified into fourtypes: life-cycle assessment approaches, tool-flow measurementapproaches, tool-flow historiographical approaches, and physics-based integrated approaches. The majority of reported works fallsinto the first three, while the last one has not attracted enoughattention due to the complexity in developing complete physics-based models for machine tools.The majority of works treaded a machine tool as a black box,and energy consumption was modeled based on experimentsand measurements. While measurement- or monitoring-basedapproaches are active, what has been missing is a practicalmethod to predict the actual energy consumption that is depen-dent on the way a machine tool works.Neither production machine builders nor their customers have aclear picture about the energy utilization of their machines andproduction lines [59]. Research efforts to explore direct relation-ships among energy consumption, design variables of machines,and operation parameters of manufacturing processes are lim-ited. Most of the existing works are confined to industrial robotsor serial machine tools; the criterion of the minimized energyconsumption was dealt with a minor objective in the multi-objective optimizations. Few works have quantified the actualenergy saving by taking into consideration of the energy require-ments in optimization.

Besides the aforementioned findings from the literature review,he reported works in this paper are also motivated by the followingspects:

Relevant researches mostly treated the minimized energy cost asa minor design criterion in the multi-objective operations. Therole of this criterion in the optimization has not been thoroughly

ring Systems 31 (2012) 420– 428 423

investigated. For example, the question of what the energy savingwill be from such a multi-optimization has not be answered.

• In contrast to the other costs occurred to a machine tool, theincrease of energy efficiency will be generated in a smaller scale.The optimization of energy saving likely results in a substantiallyhigh cost machine tool [27,51]. To reduce energy cost effectively,a desirable strategy is to improve the machining processes basedon existing machine tool.

• Energy consumption depends on machining parameters, cuttingtools, and workpiece materials. In other words, it is strongly cou-pled to the running state of machine tools. It is, therefore, anatural and promising choice to develop energy models based onkinematic and dynamic models of machine tools. Note that theimprovement was made by integrating the energy model withrobot programming; no extra investment in hardware is required.

In what follows, we will focus on the energy modeling of aparallel kinematic machine Exechon for its machining operationssuch as drilling and friction-stir welding. Those operations requirelarge machining forces. This type of energy models possessesunique opportunity for energy saving in contrast to other relevantresearches. In comparison with the energy models of industrialrobots, most of industrial robots have very limited load capacity,the required torques from actuators are small, and further reduc-tions will not cause significant energy saving. On the other hand,in comparison with the energy models for conventional machinetools, these machine tools are usually very bulky. Even thoughthe machine tools can generate large machining forces, the energyconsumption directly related to the machining processes is verysmall with respect to the energy on the movements of machines’body. The optimization of machining operations for energy savingbecomes insignificant. Parallel kinematic machines have light mov-ing mass yet are capable of generating large machining forces; theoptimization of the machining operations based on energy savingbecomes significant.

3. An Exechon machine tool

From this section onwards, a new Exechon machine [60] is usedas an example to explain the energy modeling procedures and howits energy consumption can be reduced through optimization. Asshown in Fig. 2(a) [61], the Exechon machine is a hybrid serial-parallel kinematic machine with five degrees of freedom (DOF). Itsparallel structure is of 3-DOF and is used to support a tool holder.The tool holder (to hold an end-effector) has a 2-DOF serial struc-ture. Fig. 2(b) shows the entire Exechon machine mounted on agantry, with an enlarged motion range for operations of large-sizeaircraft components.

Within the context, the optimization is for the machine setupduring drilling operations over aircraft components. Since the sizeof an aircraft component is much larger in comparison to the sizeof the Exechon machine. The gantry system must be mobile inorder to cover the entire working area. Therefore, the parametersof machine setup need to be treated as process parameters, whichcan then be optimized to reduce the energy consumption duringthe drilling operations.

As shown in Fig. 2(a), the tool-holder unit is supported by threeparallel legs. At the home position, Leg 1 and Leg 3 are symmetricalwith respect to Leg 2, and are connected to a base by a universaljoint followed by a prismatic joint. Both Leg 1 and Leg 3 have 4-DOF. Leg 2 is slightly different from Leg 1 and Leg 3 in the sense

that there are two revolute joints after the universal joint to thebase. Therefore, Leg 2 has 5-DOF. All three legs are each connectedto the tool-holder unit by a rotational joint. The prismatic joints areactuated, and the rest of the joints only have passive motions.

424 Z.M. Bi, L. Wang / Journal of Manufactu

3

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Fig. 2. An Exechon with hybrid structure [60].

.1. Kinematic modeling

A simplified structure of the Exechon machine is shown in Fig. 3or the ease of understanding. The centers of universal joints on thease are denoted as A1, A2, and A3, and the mounting locations of the

egs to the tool holder are denoted by B1, B2, and B3, respectively.

he global coordinate system is {Ob–XbYbZb}, where Ob is the cen-ral point of A1A3. Xb is a vector from A1 to A3, Yb is perpendicularo A1A3 and towards A2, and Zb is downwards to the tool holder.

local coordinate system is attached to the tool holder, given as

Fig. 3. Simplified structure of the Exechon machine.

ring Systems 31 (2012) 420– 428

{Oe–XeYeZe}, where Oe is the central point of B1B3. Xe is a vectorfrom B1 to B3, Ye is perpendicular to B1B3 and towards B2, and Ze isdownwards to the tool holder.

The pose of the tool holder is fully described by {Oe−XeYeZe} andis known by inverse kinematics. Its relations to the intermediatevariables can be defined as

[Re (xe, ye, ze) Oe (xe, ye, ze)

]=

⎡⎢⎣

ck 0 sk xe

s ̨ · sk c ̨ −s ̨ · ck ye

−c ̨ · sk s˛ c ̨ · ck ze

⎤⎥⎦(1)

where Re (xe, ye, ze) is the matrix for the orientation of the toolholder, which is the function of the position of the tool holder (xe, ye,ze) expressed in the coordinate system {Ob−XbYbZb}; s representsthe sine function and c the cosine function; k and ̨ are dependentintermediate variables described as

k = tan−1 xe − xA1

c˛(

ze − zA1

)− s˛

(ye − yA1

) ̨ = tan−1

(−ye/ze

)⎫⎬⎭ (2)

After all the intermediate variables are obtained, the location ofBi (i = 1, 2, 3) can be defined, while position Ai (i = 1, 2, 3) is fixedon the base platform. The displacement of the actuated prismaticjoints can be found easily by

qi =∣∣AiBi

∣∣ (3)

where qi (i = 1, 2, 3) is the joint position. More details about thekinematic model can be found in our earlier work [62].

3.2. Dynamic modeling

Energy consumption relates to the driving forces/torques fromactuators. Once the external load conditions are given, an inversedynamic model of a machine determines the functions of the driv-ing forces/torques with respect to time. The energy consumptionfor a task can be obtained by integrating the accumulated poweralong the trajectory of the task. Therefore, inverse dynamic mod-els are discussed here. The Newton–Euler formulation is used toobtain the internal/external forces of all components in the struc-ture. A system model is then assembled from all the equations ofthe individual components.

3.2.1. Inertia force/torque of componentsAs shown in Fig. 4, the structure of the Exechon machine is

decomposed into four components: three legs and one tool holder.In order to calculate the inertial forces/torques of the individualcomponents, local coordinate systems {Oe−XeYeZe} and {Oi−XiYiZi}are established and used as inertia coordinate systems of the toolholder and leg i, respectively. According to Newton’s law and Euler’sequation, the inertia forces/torques of the components can be cal-culated as follows.

For the tool holder,

he = meR−1e ae

ne = Ie

(R−1

e �e

)+

(R−1

e �e

)×

(Ie

(R−1

e �e

))}

(4)

For the legs,

hi = miR−1i ai

ni = Ii

(R−1

i εi

)+

(R−1

i ωi

)×

(Ii

(R−1

i ωi

))}

(i = 1, 2, 3) (5)

where he and hi are the inertial forces of the tool holder and leg i,respectively; ne and ni are the inertial torques of the tool holder andleg i, respectively; me and mi are the masses of the tool holder andleg i, respectively; Ie and Ii are the matrices of the inertia of the tool

Z.M. Bi, L. Wang / Journal of Manufacturing Systems 31 (2012) 420– 428 425

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Table 1Properties of Exechon X700 components.

Center (m) Mass (kg) Inertia

Leg 1 d1 = 0.5913 158.432

[47.11 0 −2.73

0 46.67 0−2.73 0 2.16

]

Leg 2 d2 = 0.5913 158.432

[47.11 0 −2.73

0 46.67 0−2.73 0 2.16

]

Leg 3 d3 = 0.5913 158.432

[47.11 0 −2.73

0 46.67 0−2.73 0 2.16

][

8.39 −0.01 0]

Fig. 4. Components and applied forces/torques.

older and leg i, respectively; �e, ae and �e are angular velocity,inear and angular accelerations of the tool holder; and �i, ai andi are angular velocity, linear and angular accelerations of leg i.

.2.2. Force equilibriumUnder the local coordinate system {Oe−XeYeZe}, the force and

orque balances of the tool holder can be found as

fe −3∑

i=1

R−1e ·

(RifBi

)+ meR−1

e g = he

−3∑

i=1

(R−1

e ·(

RitBi

)+ re,i ×

(R−1

e ·(

RifBi

)))+ te = ne

⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭

(6)

here fe and te are the known external working force and torquender the local coordinate system {Oe−XeYeZe}; fBi and tBi are theeaction force and torque from leg i to the tool holder in the oppositeirections of those from the tool holder to leg i; re,i is the vectorrom Oe to Bi in {Oe−XeYeZe}; and Ri and Re are the matrices ofrientations of the components, which can be calculated when theool-holder position is given.

Similarly, under local coordinate system {Oi−XiYiZi}, the forcend torque balances of leg i can be found as

fAi+ fBi

+ miR−1i g = hi

ri,Ai× fAi

+ ri,Bi× fBi

+ tAi+ tBi

= ni

}(7)

here fAi and tAi are the reaction force and torque from the base toeg i; fBi and tBi are the reaction force and torque from leg i to theool holder; and ri,Ai, ri,Bi are the vectors from Oi to Ai and from Oio Bi, respectively.

.2.3. Dynamic model and solutionCombining Eqs. (6) and (7) gives a set of 24 linear equations

ith a total of 26 unknown parameters. However, note that for Leg and Leg 3, redundant components of internal torques (tA1,z andB1,z, tA3,z and tB3,z) are involved. One can set tA1,z = tA3,z = 0 to obtainufficient number of equations for the inverse dynamic model. In

pplying this dynamic model, once the motion and force profiles ofhe tool holder are given, third-party tools can be used to solve thequations to obtain all internal forces/torques as well as the drivingorces at the joints.

Tool holder Oe 265.240 −0.01 7.40 0.100 0.10 11.43

3.3. Energy modeling

The energy consumption of a given task can be obtained byintegrating the accumulated power along the trajectory of the taskas

E =tstop∫tbegin

⎡⎣ i=nl∑

i=0

(fi(t) · vi(t)) +j=nr∑j=0

(�j(t) · ωj(t))

⎤⎦dt (8)

where E is the energy consumption along a trajectory under a givenexternal load; nl and nr are the number of actuated linear and rotaryjoints, respectively; fi (t) is the function of driving force of a linearmotor with respect to time; �j (t) is the function of driving torqueof a rotary motor with respect to time; vi (t) is the function of thelinear velocity of actuated linear motion with respect to time; andωj (t) is the function of the angular velocity of a rotary motor withrespect to time.

When the trajectory of the task is discretized into a set of key-points (k = 1, . . ., nk), the energy consumption along the trajectorycan be approximated as

E ∼=k=nk∑k=1

⎡⎣ i=nl∑

i=0

(fi,k · vi,k) +j=nr∑j=0

(�j,k · ωj,k)

⎤⎦�t (9)

where �t is the given time step between two key-points; fi,k is thedriving force of linear motor i on key-point k; �j,k is the drivingtorque of rotary motor j on key-point k; vi,k is the linear velocityof linear motor i on key-point k; and ωj,k is the angular velocity ofrotary motor j on key-point k.

4. A case study

The developed energy models are applied in a case study formachine setup optimization. The Exechon machine is used to per-form a drilling operation along Ze at a given position (xb, yb). Assumethat the orientations {Xb, Yb, Zb} and {Xe, Ye, Ze} are aligned, but therelative positions of the origins Ob and Oe can be further optimizedin terms of machine setup to reduce the energy consumption duringthe drilling operation.

Exechon X700 [60] is chosen for the case study. Under their localcoordinate systems, the properties of the tool holder and legs arecalculated and listed in Table 1.

Some typical parameters for drilling operations are chosen inthis case study as follows:

Spindle speed: n = 6000 rpm

Drilling forces: Fx = Fy = 0.0 N, Fz = 3000.0 NDrilling torques: Tx = Ty = 0.0 Nm, Tz = 1.5 NmFeed rate: v = 0.02 m/sDrilling depth: d = 0.01 m

426 Z.M. Bi, L. Wang / Journal of Manufacturing Systems 31 (2012) 420– 428

Fig. 5. Steps (key points) of the drilling operation.

r

w

FdZturdt

oyT

Fig. 7. Velocity along drilling trajectory.

Fig. 6. Displacement of Ze along drilling trajectory.

Based on these parameters, the required energy for materialemoval during drilling is calculated as

= Fz · d + Tz · 2n�

60d

v= 77.1 Nm (10)

The steps of the drilling operation along Ze are shown in Fig. 5.irstly, the drilling tool must be moved to d = 0.01 m above therilling position; secondly, the drilling tool is accelerated alonge until its tip touches the top surface of the aircraft component;hirdly, the tool begins to drill in a constant feed-rate of v = 0.02 m/sntil it drills through the workpiece; finally, the drilling tool isetreated and decelerated until it stops at the starting position. Theisplacement, velocity and, acceleration of the tool with respect toime along the drilling trajectory is shown in Figs. 6–8, respectively.

Assume that the machine setup for the drilling operation is maden the cross-section of workspace with ze = 0.8 m. The position (xe,e) is, however, to be determined based on the energy consumption.o achieve this goal, the cross-section ze = 0.8 m of the workspace is

Fig. 9. Distribution of energy c

Fig. 8. Acceleration along drilling trajectory.

divided into a 30 × 30 array. Each cell is represented by its centralposition. Using the developed energy model, the energy consump-tions during the drilling operation from each central position areevaluated and the distribution of the energy consumptions is ana-lyzed.

Fig. 9 illustrates the energy consumption of drilling operation

when the origin of the machine is set up at a point on the specifiedcross-section of workspace. The X–Y plane corresponds to the cross-section, and Z-axis represents the total energy consumption alongthe drilling path when its origin is set up. The given origin provides

onsumption of drilling.

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Z.M. Bi, L. Wang / Journal of Man

he complete information about the drilling path under the globaloordinate system. The developed energy model is applied to cal-ulate the energy cost for the machine tool to perform the drillingperation along the path.

As shown in Fig. 9, the drilling tool must be able to move alonge for 0.032 m including 0.010 m of the drilling depth; only 20.4% ofll the positions over the cross-section of the workspace satisfy thisonstraint. The minimal energy consumption for the drilling oper-tion is 594.20 Nm, which occurs at the position of (−0.0035 m,.1553 m). The average energy consumption over the cross-sectionor all valid starting positions is 1873.10 Nm, and the maximalnergy consumption is 7033.81 Nm. From this case study, it is clearhat the minimal energy consumption is 31.71% and 8.4% of theverage and maximal energy consumptions, respectively. Note thathe minimal energy consumption is still 7.7 times of the requirednergy for material removal. Taking into consideration that therere over 14,000 holes to be drilled on an aircraft wing, the opti-ization of the machine setup for the energy saving is significant.

. Conclusions

It is increasingly desired to implement green and sustainableanufacturing in order to minimize not only the economic aspects

ut also the potential environmental impact. Energy consumptions one of the most important factors that impact the environment.y establishing the energy models based on kinematics and dynam-

cs of machine tools, the considerations on both the material flownd tool flow are merged mutually. The direct relationship betweennergy consumptions and the decision variables of manufacturingrocesses is thus defined. Therefore, the manufacturing processesan be optimized for energy saving. The reported works towardshis direction are summarized as follows:

The literature survey reveals that very limited works are availableon energy modeling with the consideration of physical behav-iors of machines. Exploration of explicit relations between energyconsumption and manufacturing processes is still lacking in opti-mal machine setups.The existing works on energy modeling stop at the high-leveloptimization of manufacturing systems; and the data of energyconsumption is static and has little value on the optimization ofmanufacturing processes.Our energy models, as unique contributions, are based on kine-matic and dynamic analysis of machines. Therefore, they can be auseful add-on for optimizing manufacturing processes, especiallyfor energy saving.The results of the case study show that the developed energymodel can facilitate machine setup optimization to reduce energyconsumption to as low as 1/3 of average energy usage of an arbi-trary setup.

The methodology can be extended to other types of machineools for energy assessment. Towards this end, our future work islanned to: (1) obtain more accurate geometric and dynamic char-cteristics of machines as inputs of the energy models, (2) acquireeal data of energy consumption in real manufacturing operations,nd (3) validate and improve the energy models by experiments.

The developed model focuses on the prediction of energyonsumption in machining processes. It has been validated via sim-

lation. An experimental platform of the machine tool has to beet up to measure the energy consumption in actual drilling andompare the simulation result. The two limitations of the proposedodel are:

[

ring Systems 31 (2012) 420– 428 427

1) Only the energy consumed by the machine tool has been consid-ered. Other sub-systems such as coolant systems and fixturingsystems are left out although they also consume energy. It willbe the logical extension to integrate the reported work with theenergy models of other systems to provide much more compre-hensive information for the machining processes optimization.

2) The developed model has the simplified requirements of amachining operation including cutting force, depth, and feed-rate. There are other important considerations such as toolwears and the robustness to accommodate material defects. Thesoundness of the simplification needs to be further investigated.It is also interesting to note that energy consumption relatesclosely to the tool wear. Our future work is to explore the relationbetween energy consumption and tool wear.

Acknowledgment

The first author would like to thank the financial support fromPurdue University through 2012 Summer Faculty Grant.

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