A Comprehensive Micro-milling Force Model for A Low-stiffness Machining System

Abstract Micro-milling is widely used in various crucial fields with the ability of machining micro- and meso-scaled functional structures on various materials efficiently. However, the micro-milling force model is not comprehensively developed yet when tool feature sizes continually decrease to under two hundred microns in a low-stiffness system. This paper proposes an analytical force model considering the influence of tool radius, size effect, tool runout, tool deflection, and the actual trochoidal trajectories and the interaction of historical tool teeth trajectories (IHTTT). Different micro-milling status are recognized by analyzing the cutting process of different tool teeth. Conditions of single-tooth cutting status are determined by a proposed numerical algorithm, and entry angle and exit angle are analyzed under various cutting conditions for the low-stiffness system. Three micro-milling status, including single-tooth cutting status, are distinguished based on the instantaneous undeformed chip thickness resulting in three types of material removal mechanisms in predicting micro-milling force components. Discontinuous change rates of undeformed chip thickness are found in the low-stiffness micro-milling system. The proposed micro-milling force model is then verified through experiments of micro slot milling Elgiloy alloy with a 150-µm-diametrical two-teeth micro-end-mill. The experimental results show a Root-Mean-Square Error (RSME) of 0.092 N in the predicted resultant force, accounting for approximately 5.12% of the measured force, by which the proposed theoretical model is verified to be of good prediction accuracy.

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Prediction of Nonlinear Micro-Milling Force with a Novel Minimum Uncut Chip Thickness Model

Micromachines ◽

10.3390/mi12121495 ◽

2021 ◽

Vol 12 (12) ◽

pp. 1495

Author(s):

Tongshun Liu ◽

Kedong Zhang ◽

Gang Wang ◽

Chengdong Wang

Keyword(s):

Cutting Force ◽

Chip Thickness ◽

Micro Milling ◽

Force Model ◽

Force Coefficient ◽

Uncut Chip Thickness ◽

Milling Force ◽

Minimum Uncut Chip Thickness ◽

Cutting Force Coefficient ◽

Milling Force Model

The minimum uncut chip thickness (MUCT), dividing the cutting zone into the shear region and the ploughing region, has a strong nonlinear effect on the cutting force of micro-milling. Determining the MUCT value is fundamental in order to predict the micro-milling force. In this study, based on the assumption that the normal shear force and the normal ploughing force are equivalent at the MUCT point, a novel analytical MUCT model considering the comprehensive effect of shear stress, friction angle, ploughing coefficient and cutting-edge radius is constructed to determine the MUCT. Nonlinear piecewise cutting force coefficient functions with the novel MUCT as the break point are constructed to represent the distribution of the shear/ploughing force under the effect of the minimum uncut chip thickness. By integrating the cutting force coefficient function, the nonlinear micro-milling force is predicted. Theoretical analysis shows that the nonlinear cutting force coefficient function embedded with the novel MUCT is absolutely integrable, making the micro-milling force model more stable and accurate than the conventional models. Moreover, by considering different factors in the MUCT model, the proposed micro-milling force model is more flexible than the traditional models. Micro-milling experiments under different cutting conditions have verified the efficiency and improvement of the proposed micro-milling force model.

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Model of the instantaneous undeformed chip thickness in micro-milling based on tooth trajectory

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405416639890 ◽

2016 ◽

Vol 232 (2) ◽

pp. 226-239 ◽

Cited By ~ 10

Author(s):

Xiaohong Lu ◽

Zhenyuan Jia ◽

Furui Wang ◽

Guangjun Li ◽

Likun Si ◽

...

Keyword(s):

Cutting Forces ◽

Chip Thickness ◽

Milling Process ◽

Cutting Edge ◽

Micro Milling ◽

Undeformed Chip Thickness ◽

Single Tooth ◽

Extended Length ◽

Manufacturing Errors ◽

Tooth Cutting

Instantaneous undeformed chip thickness is one of the key parameters in modeling of micro-milling process. Most of the existing instantaneous undeformed chip thickness models in meso-scale cutting process are based on the trochoidal trajectory of the cutting edge, which neglect the influences of cutter installation errors, cutter-holder manufacturing errors, radial runout of the spindle and so forth on the instantaneous undeformed chip thickness. This article investigates the tooth trajectory in micro-milling process. A prediction model of radial runout of cutting edge is built, with consideration of the effects of the extended length of micro-milling cutter and the spindle speed. Considering the effects of cutting-edge trochoidal trajectory, radial runout of cutting edge and the minimum cutting thickness, a novel instantaneous undeformed chip thickness model is proposed, and the phenomenon of single-tooth cutting in micro-milling process is analyzed. Comparisons of cutting forces under different chip thickness models and experimental data indicate that this new model can be used to predict cutting forces.

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Research on Error Compensation of Corner Milling Process Based on Milling Force Prediction

Materials Science Forum ◽

10.4028/www.scientific.net/msf.800-801.761 ◽

2014 ◽

Vol 800-801 ◽

pp. 761-765

Author(s):

Hui Nan Shi ◽

Fu Gang Yan ◽

Yun Peng Ding ◽

Xian Li Liu ◽

Rui Zhang

Keyword(s):

Error Compensation ◽

Chip Thickness ◽

Milling Process ◽

Force Model ◽

Deformation Model ◽

Milling Force ◽

Element Analysis ◽

The Finite Element Analysis ◽

Flexible Deformation ◽

Milling Force Model

In cavity die corner-machining, tool flexible deformation caused by the milling force resulting in the surface error, a method of off-line error compensation is put forward. Instantaneous chip thickness model and the corner milling force model is established based on differential and the characteristics of the corner. Combining the theory of cantilever beam and the finite element analysis, cutting tool elastic deformation model is established.

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Coupled thermal and mechanical analyses of micro-milling Inconel 718

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405418774586 ◽

2018 ◽

Vol 233 (4) ◽

pp. 1112-1126 ◽

Cited By ~ 10

Author(s):

Xiaohong Lu ◽

Hua Wang ◽

Zhenyuan Jia ◽

Yixuan Feng ◽

Steven Y Liang

Keyword(s):

Inconel 718 ◽

Cutting Temperature ◽

Milling Process ◽

Micro Milling ◽

Force Model ◽

Temperature Model ◽

Milling Force ◽

Mechanical Coupling ◽

Milling Forces ◽

Milling Force Model

Micro-milling forces, cutting temperature, and thermal–mechanical coupling are the key research topics about the mechanism of micro-milling nickel-based superalloy Inconel 718. Most current analyses of thermal–mechanical coupling in micro-milling are based on finite element or experimental methods. The simulation is not conducive to revealing the micro-milling mechanism, while the results of experiments are only valid for certain machine tool and workpiece material. Few analytical coupling models of cutting force and cutting temperature during micro-milling process have been proposed. Therefore, the authors studied coupled thermal–mechanical analyses of micro-milling Inconel 718 and presented a revised three-dimensional analytical model of micro-milling forces, which considers the effects of the cutting temperature and the ploughing force caused by the arc of cutting edge during shear-dominant cutting process. Then, an analytical cutting temperature model based on Fourier’s law is presented by regarding the contact area as a moving finite-length heat source. Coupling calculation between micro-milling force model and temperature model through an iterative process is conducted. The novelty is including cutting temperature into micro-milling force model, which simulates the interaction between cutting force and cutting temperature during micro-milling process. The established model predicts both micro-milling force and temperature. Finally, experiments are conducted to verify the accuracy of the proposed analytical method. Based on the coupled thermal–mechanical analyses and experimental results, the authors reveal the effects of cutting parameters on micro-milling forces and temperature.

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Development of micro milling force model and cutting parameter optimization

Transactions of Nonferrous Metals Society of China ◽

10.1016/s1003-6326(12)61815-9 ◽

2012 ◽

Vol 22 ◽

pp. s851-s858 ◽

Cited By ~ 7

Author(s):

Shih-ming WANG ◽

Da-fun CHEN ◽

Min-chang JANG ◽

Shambaljamts TSOOJ

Keyword(s):

Parameter Optimization ◽

Micro Milling ◽

Force Model ◽

Milling Force ◽

Cutting Parameter ◽

Cutting Parameter Optimization ◽

Milling Force Model

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Modeling and Simulation of Milling Forces for Ball-End Cutter with Considering Comprehensive Factors

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.121-126.2098 ◽

2011 ◽

Vol 121-126 ◽

pp. 2098-2104

Author(s):

Xiu Lin Sui ◽

Ping Zhang

Keyword(s):

Chip Thickness ◽

Milling Process ◽

Differential Method ◽

Physical Factors ◽

Force Model ◽

Milling Force ◽

Cutter Deflection ◽

Set Up ◽

Milling Forces ◽

Milling Force Model

In this paper, influence mechanism of variously physical factors for milling force in any feed direction is studied during the milling process. Firstly, the effects of spindle eccentricity, cutter deflection and cutter vibration for the instantaneously undeformed cutting thickness are analyzed, and the mathematical expressions of chip thickness is set up. Then,on this basis of cutting force and chip load, the milling force model of ball-end mill with considering integrated physical factors is established though the differential method, and a simulation system for prediction of milling forces during the milling process is developed. This milling force model is verified through simulation and analysis of milling forces.

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Instantaneous Uncut Chip Thickness Model in End Milling Based on an Improved Method

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.764.399 ◽

2018 ◽

Vol 764 ◽

pp. 399-407

Author(s):

Yue Zhang ◽

Zhi Qiang Yu ◽

Tai Yong Wang

Keyword(s):

End Milling ◽

Chip Thickness ◽

Transcendental Equation ◽

Milling Process ◽

Force Model ◽

Uncut Chip Thickness ◽

Milling Force ◽

Milling Force Model ◽

Instantaneous Uncut Chip Thickness ◽

Taylor’S Series

The instantaneous uncut chip thickness is an important parameter in the study of milling force model. By analyzing the real tooth trajectory in milling process, accurate instantaneous uncut chip thickness can be obtained to solve the complex transcendental equation. Traditional chip thickness models always simplify the tooth trajectory to get approximate solution. A new instantaneous uncut chip thickness model is proposed in this paper. Based on real tooth trajectory of general end milling cutter, a Taylor's series is used to approximate the involved infinitesimal variable in the transcendental equation, which results in an explicit expression for practical application of the uncut chip thickness with higher accuracy compared to the traditional model.

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Modeling and Simulation of Milling Force in Virtual Numerical Control Milling Process

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.392-394.697 ◽

2008 ◽

Vol 392-394 ◽

pp. 697-702

Author(s):

Xiu Lin Sui ◽

Jia Tai Zhang ◽

Jiang Hua Ge ◽

Ya Ping Wang ◽

H. Yuan

Keyword(s):

Modeling And Simulation ◽

Chip Thickness ◽

Milling Process ◽

Cutting Edge ◽

Numerical Control ◽

Force Model ◽

End Mill ◽

Ball End Mill ◽

Milling Force ◽

Milling Force Model

A parameter equation based on cutting edge of ball-end mill is set up by analyzing the parameters of ball-end mill influence the milling force in virtual NC milling process. The relationship among elemental cutting force, instantaneous radial chip thickness and cutting edge length is analyzed, and the dynamic milling force of ball-end mill at arbitrary feed direction is established. The milling force parameter model by quadratic regression equation in different cutting conditions is built. Through experiments in NC machining center and using orthogonal combination and principal components analysis, the regression coefficients are calculated. The correctness of milling force model is testified by experiments. All these can provide theoretical basis for physics modeling and simulation of virtual numerical control milling.

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