Natural frequencies and modal shapes of machine tools have position-dependent characteristics owing to their dynamic behaviors changing with the positions of moving parts. It is time-consuming and difficult to evaluate the dynamic behaviors of machine tools and their machining accuracy at different positions. In this paper, a Kriging approximation model coupled with finite element method is proposed to substitute the dynamic equations for obtaining the position-dependent natural frequencies of a machine tool, as well as relative positions between the tool and the workpiece during the machining process. Based on the proposed method, dynamic performance optimization design of the machine tool is conducted under the condition of minimum relative positions. Three case studies are illustrated to demonstrate the implementation of the proposed method.
HongJTalbotDKahramanA. Load distribution analysis of clearance-fit spline joints using finite elements. Mech Mach Theory2014; 74: 42–57.
3.
HuoDChengKWardleF. A holistic integrated dynamic design and modelling approach applied to the development of ultraprecision micro-milling machines. Int J Mach Tool Manuf2010; 50: 335–343.
4.
HuPTangK. Improving the dynamics of five-axis machining through optimization of workpiece setup and tool orientations. Comput-Aided Des2011; 43: 1693–1706.
5.
DuncanGSTummondMFSchmitzTL. An investigation of the dynamic absorber effect in high-speed machining. Int J Mach Tool Manuf2005; 45: 497–507.
6.
ZaehMSiedlD. A new method for simulation of machining performance by integrating finite element and multi-body simulation for machine tools. CIRP Ann-Manuf Technol2007; 56: 383–386.
7.
Zatarain M. Modular synthesis of machine tools. Ann CIRP 1998; 47.
8.
SilvaMMBrülsOSweversJet al.Computer-aided integrated design for machines with varying dynamics. Mech Mach Theory2009; 44: 1733–1745.
9.
SeguraMMCeligJT. A new dynamic reanalysis technique based on modal synthesis. Comput Struct1995; 56: 523–527.
10.
LawMAltintasYSrikanthaPA. Rapid evaluation and optimization of machine tools with position-dependent stability. Int J Mach Tool Manuf2013; 68: 81–90.
11.
LawMIhlenfeldtSWabnerMet al.Position-dependent dynamics and stability of serial-parallel kinematic machines. CIRP Ann-Manuf Technol2013; 62: 375–378.
12.
YadavVSinghAKDixitUS. An approximate method for computing the temperature distributions in roll and strip during rolling process. Proc IMechE, Part B: J Engineering Manufacture2014; 228: 1118–1130.
13.
LeeJSongCY. Estimation of submerged-arc welding design parameters using Taguchi method and fuzzy logic. Proc IMechE, Part B: J Engineering Manufacture2013; 227: 532–542.
14.
YildizYSundaramMMRajurkarKP. Statistical analysis and optimization study on the machinability of beryllium-copper alloy in electro discharge machining. Proc IMechE, Part B: J Engineering Manufacture2012; 226: 1847–1861.
15.
LeePHChungHLeeSW. Optimization of micro-grinding process with compressed air using response surface methodology. Proc IMechE, Part B: J Engineering Manufacture2011; 225: 2040–2050.
16.
Timothy S. Comparison of response surface and kriging models for multidisciplinary design optimization. In: 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, St Louis, MO, USA, 2–4 September 1998.
17.
Papalambros PY and Wilde DJ. Principles of optimal design: Modeling and computation. 2nd ed. Cambridge: The Edinburgh Building, 2000.
SimpsonTWPoplinskiJDKochPNet al.Metamodels for computer-based engineering design: survey and recommendations. Eng Comput-Germany2001; 17: 129–150.
20.
BuiTQNgocNMZhangC. A moving Kriging interpolation-based element-free Galerkin method for structural dynamic analysis. Comput Methods Appl Mech Eng2011; 200: 1354–1366.
21.
LamXBKimYSHoangADet al.Coupled aerostructural design optimization using the Kriging model and integrated multiobjective optimization algorithm. J Optimiz Theory Appl2009; 142: 533–556.
22.
MayerRMirYAVafaeesefatAet al.Touch probe radius compensation for coordinate measurement using Kriging interpolation. Proc IMechE, Part B: J Engineering Manufacture1997; 211: 11–18.
23.
QinWJHeJQ. Optimum design of local cam profile of a valve train. Proc IMechE, Part C: J Mechanical Engineering Science2010; 224: 2487–2492.
24.
LeeKH. A robust structural design method using the Kriging model to define the probability of design success. Proc IMechE, Part C: J Mechanical Engineering Science2010; 224: 379–388.
25.
HuYLiB. Robust design and analysis of 4PUS-1RPU parallel mechanism for a five-degree-of-freedom hybrid kinematic machine. Proc IMechE, Part B: J Engineering Manufacture2011; 225: 685–698.
26.
JangHLChoHChoiKKet al.Reliability-based design optimization of fluid-solid interaction problems. Proc IMechE, Part C: J Mechanical Engineering Science2014; 228: 1724–1742.
27.
DingRXGuoCZhuZCet al.Piezoelectric-based non-destructive monitoring of contact pressures in fine-blanking process. Proc IMechE, Part B: J Engineering Manufacture2014; 228: 927–936.
28.
LaiXZhangYWangC. A new robust design method for path-generating linkages with multi-stochastic noises. Proc IMechE, Part B: J Engineering Manufacture2015; 229: 860–869.
29.
TlustyJZatonWIsmailF. Stability lobes in milling. Annals of the CIRP1983; 32: 309–313.
