別紙41 (課程博士(英文))Date ofsubmission (m01〕th day, year):0708,2021

Departmenlof
Studen11D Nunlber

D165111

Mechanical Engineering
Pplica11t's n田11eSupervlsors

Uchiyama Naoki
Sato Kaiji

Enock圦liⅡiamNshama

Abstract 田od0釣Title oflhesis

Multi、objective optimization Approach to Energy'savin牙 Motion Ti'ajectory
Gena'ation with H地h'speed and High・Accuracy for lndustrial Feed Drive
Systems

Approx.800 ＼Nolds

Ihe ever・gro、入ling breakt1Ⅱ'oughs in science and techl〕010gy perpetua11y pressurize theInanufacturing industry to increase accuracy and production rates il〕 processes. such increases
Come at a price, the price ofan enlarging carbon footprint with lilnited reliable ena'gy sources.
Colnputa' nun〕erical contr01(CNC) machine tools are typica11y used in the industry due to theiraccuracy and repetitive task execution speed. Due to the afore・n〕entioned production and energy
Pressures, d〕e objectives ofin)proving accuracy, cycle time, and energy consumption are majorreseω'ch drivers. since these objectives are contradictory, pareto optilnization methods arenecesS砥、y to obtain optimal operatlng conditionsIhere are typica11y t11ree possible actions for achieving the aforenamed objectives: h砥'dW砥'e
UP即'ades, internals0丘Ware n〕odifications, and trajectory optilnizations. H砥'd工入7m'e uPσrades are
UsuaⅡy avoided since tl〕ey are relatively expensive. Most con〕1nercial cNc lnachine tools'inten〕al soft、入lare is inaccessible; hence trajectory optimization presents a feasible and cost・
effective action.工入7ith this rationale, trajectory optimization is the study field explored in thisthesisIhis tl〕esis discusses sevel'al propositions for trajectoly optilnization in industrial feed drive
Systenls: pareto optimization of ena'gy and tolerance in motion trajectory gena'ation (chapter3), a u'ade・off between energy saving and cycle time reduction by pareto‑optimal corner
Smoothing (chapter 4), and pareto optimization ofcycle time and n〕otion accuracy (chapter 5).
Feed drive dynamics, energy modeling, trajectory profiHng, a n〕ulti・objective optimlzation
Problem formulation, and a paret0 丘onti肌' generation algorithm 雛'e described in thePreliminaries chapter (chapter 2). The thesis is completed with a conclusion and future 圦70rks
Chapta'(chapter 6)
A method of generating piecewise linear trajectories with smoothed con)ers optimizing twoObjectives: energy consun)ption and cornering tolerance for feed drive systelns is proposed i11
Chapta' 3. An ena'gy model ofan industrial biaxial feed drive system is used to forn〕ulate a bi・
Objective optimization problem. The linear and slnooth corner segments are respectively
described using jerk・1imited acceleration profiles (JLAPS) and kinematic c01'ner smoothing
technique with interrupted acceleration (KCSIA).1he optimization problem is formulated with
the norn〕alized normal constraints method, where sequential quadratic programming is used toSolve it. A divide and conquer algorithm is utilized to generate pareto optimal solutions
recursively.1he best trade・off solution is obtained as the one that lninimizes botl〕 objectives
Optimization results for an industrial biaxial machine are iⅡUstrated, wh飢'e the best trade‑off
Solution acl〕ieves 64% ofthe energy・saving potential with a moderate cornering t01飢'ance of30μm

Chapter 4 Proposes a method of gena'aung pareto optimal con)er slnootl〕ing trajectories that
U'ade・off the contradicting objectives of minimizing cycle tin〕e and energy consumptlon
Sevelalstudies have proposed corner slnoothing lned〕odsthatimplove cycle time for piecewise
Iine釘' paths by exploiting axial Hmits to achieve time・optilnaltr勾ectories. Energy‑savlng ls not
Considered an objective in these 111ethods. The trajectories along Hneω' paths and smoothedCorna's are respectively described using JLAps and kinematic corner smootl〕ing n〕ethods (i.e.,
1くCSIA and kinelnauc corner smoothing with uninterrupted acce1仇'ation (KCSUA)). An ena'gy
Consumption model of an il〕dustrialtlNO・axis feed drive systeln is identified by least sqU砥'esestin〕ation and used in solving the bi・objective optimization probleln (BOOP). A contrast andCon)P砥'ison ω・e lnade between KCSIA,1くCSUA, and point・to・point (PIP) n〕̲otion protiles. TheOptilnization results show that the KCSIA pareto frontier is closest to the utopia polnt, where itis experilnenta11y vil〕dicated that the besttrade・offtrajectory ad〕ieves 66% and 60% ofthetin)e and energy・savil〕g potentials, respectively.1n tenns of contouring performance of best
trade・off trajectories, INhile KCSUA reduces the average error by 7少、0, KCSIA decreases themaxilnum error by

19% relative to plp

A method ofP雛'eto optilnizing tl〕e conaicting objectives ofreducing cycle time and increasingCon〕ering accuracy for piece、刃ise linear contours is proposed in chapter 5.1t has been sholNn in
the literature tl〕飢 non・Z磁'o cornering velocities deteriorate contouring perfonnance 工入lhileteducing cycle til〕〕e. To resolve the set of conaicting objectives, the norlnalized nonnal
Constraint formulation of tl)e Boop is described with lower and upper cornering tolerances ateach con〕er described as inequality conS11'ain{S. This method's effecliveness is investigated withIinear and slnoothed con〕ersegn〕el〕1SJ'espectively, defined by JLAp and KCSIA.1he optin〕ized
KCSIA is refa1でd to as KCSIA* wh飢'e its Pω'et0 丘onti引' shows lhat tl〕e original KCSIA
Produces a don〕inated solulion. Hence,1くCSIA* soluti01〕S ω'e superlor colnpared to KCSIAExperin〕ental results furth飢' en〕phaslze tl〕1S poinl by showu〕g thalthe lくCSIA* had a lo＼NerContouring 引'ror than KCSIA, wha'e {he best lrade・off solulion reduceS 11〕e maximum andaverage contouring 田1冷rs by 29ツ0 and 12% INhile increasing cycle tln〕e by 3少'o colnpared
to KCSIA

Concluding remarks and tentative future 、入70rks ofthis thesis are Hlustrated ln chapta' 6.1heProposed lnethods can be extended to five・axis cNc machines by including to01 0rientation
tolerances at cornels.1n the case of lnachining operations, cutting forces il〕crease the an〕ount
Of energy consulnption. Hence, a cutting force model can be incorporated into the previously

Used energy consumption model.1he proposed methods can be generaHzed by considering
asymn〕etrical corner smoothing togetl)er with cotnering transitions other than line・to‑1ine ones