Investigation of the Dynamics of Microend Milling—Part I: Model Development

2006 ◽  
Vol 128 (4) ◽  
pp. 893-900 ◽  
Author(s):  
Martin B. G. Jun ◽  
Xinyu Liu ◽  
Richard E. DeVor ◽  
Shiv G. Kapoor
Keyword(s):  
Cutting Force ◽  
Chip Formation ◽  
Model Development ◽  
Chip Thickness ◽  
Fault System ◽  
Formation Mechanisms ◽  
Force Model ◽  
Line Field ◽  
Fault Parameters ◽  
Microend Milling

In microend milling, due to the comparable size of the edge radius to chip thickness, chip formation mechanisms are different. Also, the design of microend mills with features of a large shank, taper, and reduced diameter at the cutting edges introduces additional dynamics and faults or errors at the cutting edges. A dynamic microend milling cutting force and vibration model has been developed to investigate the microend milling dynamics caused by the unique mechanisms of chip formation as well as the unique microend mill design and its associated fault system. The chip thickness model has been developed considering the elastic-plastic nature in the ploughing process. A slip-line field modeling approach is taken for a cutting force model development that accounts for variations in the effective rake angle and dead metal cap. The process fault parameters associated with microend mills have been defined and their effects on chip load have been derived. Finally, a dynamic model has been developed considering the effects of both the unique microend mill design and fault system and factors that become significant at high spindle speeds including rotary inertia and gyroscopic moments.

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

Micromachines ◽  
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.

Voxel Based Cutting Force Simulation of Ball End Milling Considering Cutting Edge Around Center Web

2018 ◽  
Author(s):  
Isamu Nishida ◽  
Takaya Nakamura ◽  
Ryuta Sato ◽  
Keiichi Shirase
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Chip Thickness ◽  
Previous Method ◽  
Cutting Edge ◽  
Force Model ◽  
End Mill ◽  
Uncut Chip Thickness ◽  
Ball End Mill ◽  
Tool Rotation

A new method, which accurately predicts cutting force in ball end milling considering cutting edge around center web, has been proposed. The new method accurately calculates the uncut chip thickness, which is required to estimate the cutting force by the instantaneous rigid force model. In the instantaneous rigid force model, the uncut chip thickness is generally calculated on the cutting edge in each minute disk element piled up along the tool axis. However, the orientation of tool cutting edge of ball end mill is different from that of square end mill. Therefore, for the ball end mill, the uncut chip thickness cannot be calculated accurately in the minute disk element, especially around the center web. Then, this study proposes a method to calculate the uncut chip thickness along the vector connecting the center of the ball and the cutting edge. The proposed method can reduce the estimation error of the uncut chip thickness especially around the center web compared with the previous method. Our study also realizes to calculate the uncut chip thickness discretely by using voxel model and detecting the removal voxels in each minute tool rotation angle, in which the relative relationship between a cutting edge and a workpiece, which changes dynamically during tool rotation. A cutting experiment with the ball end mill was conducted in order to validate the proposed method. The results showed that the error between the measured and predicted cutting forces can be reduced by the proposed method compared with the previous method.

Off-line error compensation in corner milling process

2016 ◽  
Vol 232 (7) ◽  
pp. 1172-1181 ◽  
Author(s):  
Caixu Yue ◽  
Xianli Liu ◽  
Yunpeng Ding ◽  
Steven Y Liang
Keyword(s):  
Cutting Force ◽  
Error Compensation ◽  
Tool Path ◽  
Chip Thickness ◽  
Milling Process ◽  
Process Conditions ◽  
Force Model ◽  
Tool Deflection ◽  
Profile Error ◽  
Compensation Algorithm

Tool deflection induced by cutting force could result in dimensional inaccuracies or profile error in corner milling process. Error compensation has been proved to be an effective method to get accuracy component in milling process. This article presents a methodology to compensate profile errors by modifying tool path. The compensation effect strongly depends on accuracy of the cutting force model used. The mathematical expression of chip thickness is proposed based on the true track of cutting edge for corner milling process, which considers the effect of tool deflection. The deflection of tool is calculated by finite element method. Then, an off-line compensation algorithm for corner profile error is developed. Following the theoretical analysis, the effect of the error compensation algorithm is verified by experimental study. The outcome provides useful comprehension about selection of process conditions for corner milling process.

Dynamic cutting force prediction for micro end milling considering tool vibrations and run-out

2018 ◽  
Vol 233 (7) ◽  
pp. 2248-2261 ◽  
Author(s):  
Xuewei Zhang ◽  
Tianbiao Yu ◽  
Wanshan Wang
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Chip Thickness ◽  
Milling Process ◽  
Force Model ◽  
Dynamic Cutting Force ◽  
Micro End Milling ◽  
Tool Vibrations ◽  
End Milling Process

An accurate prediction of cutting forces in the micro end milling, which is affected by many factors, is the basis for increasing the machining productivity and selecting optimal cutting parameters. This paper develops a dynamic cutting force model in the micro end milling taking into account tool vibrations and run-out. The influence of tool run-out is integrated with the trochoidal trajectory of tooth and the size effect of cutting edge radius into the static undeformed chip thickness. Meanwhile, the real-time tool vibrations are obtained from differential motion equations with the measured modal parameters, in which the process damping effect is superposed as feedback on the undeformed chip thickness. The proposed dynamic cutting force model has been experimentally validated in the micro end milling process of the Al6061 workpiece. The tool run-out parameters and cutting forces coefficients can be identified on the basis of the measured cutting forces. Compared with the traditional model without tool vibrations and run-out, the predicted and measured cutting forces in the micro end milling process show closer agreement when considering tool vibrations and run-out.

High-Quality Machining of Edges of Thin-Walled Plates by Tilt Side Milling Based on an Analytical Force-Based Model

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Gongyu Liu ◽  
Jiaqiang Dang ◽  
Weiwei Ming ◽  
Qinglong An ◽  
Ming Chen ◽  
...  
Keyword(s):  
Cutting Force ◽  
Tilt Angle ◽  
Chip Thickness ◽  
Assessment Model ◽  
Force Model ◽  
High Quality ◽  
Machined Surface ◽  
Side Milling ◽  
Thin Walled ◽  
Milling Force Model

The milling of thin-walled workpieces is a common process in many industries. However, the machining defects are easy to occur due to the vibration and/or deformation induced by the poor stiffness of the thin structures, particularly when side milling the edges of plates. To this problem, an attempt by inclining the tool to a proper tilt angle in milling the edges of plates was proposed in this paper, in order to decrease the cutting force component along the direction of the lowest stiffness of the plates, and therefore to mitigate the machining vibration and improve the machined surface quality effectively. First, the milling force model in consideration of the undeformed chip thickness and the tool-workpiece engagement (TWE) was introduced in detail. Then, a new analytical assessment model based on the precisely established cutting force model was developed so as to obtain the optimum tool tilt angle for the minimum force-induced defects after the operation. Finally, the reliability and correctness of the theoretical force model and the proposed assessment model were validated by experiments. The methodology in this paper could provide practical guidance for achieving high-quality machined surface in the milling operation of thin-walled workpieces.

scholarly journals A Mathematical Modeling to Predict the Cutting Forces in Microdrilling

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Haoqiang Zhang ◽  
Xibin Wang ◽  
Siqin Pang
Keyword(s):  
Mathematical Modeling ◽  
Cutting Forces ◽  
Chip Thickness ◽  
Cutting Edge ◽  
Force Model ◽  
Cutting Mechanism ◽  
Line Field ◽  
Slip Line Field ◽  
Cutting Model ◽  
Secondary Cutting

In microdrilling, because of lower feed, the microdrill cutting edge radius is comparable to the chip thickness. The cutting edges therefore should be regarded as rounded edges, which results in a more complex cutting mechanism. Because of this, the macrodrilling thrust modeling is not suitable for microdrilling. In this paper, a mathematical modeling to predict microdrilling thrust is developed, and the geometric characteristics of microdrill were considered in force models. The thrust is modeled in three parts: major cutting edges, secondary cutting edge, and indentation zone. Based on slip-line field theory, the major cutting edges and secondary cutting edge are divided into elements, and the elemental forces are determined by an oblique cutting model and an orthogonal model, respectively. The thrust modeling of the major cutting edges and second cutting edge includes two different kinds of processes: shearing and ploughing. The indentation zone is modeled as a rigid wedge. The force model is verified by comparing the predicted forces and the measured cutting forces.

Dynamic Response Analysis in End Milling Using Pretwisted Beam Finite Element

1995 ◽  
Vol 117 (1) ◽  
pp. 1-10 ◽  
Author(s):  
C.-L. Liao ◽  
J.-S. Tsai
Keyword(s):  
Finite Element ◽  
Cutting Force ◽  
Present Model ◽  
End Milling ◽  
Chip Thickness ◽  
Beam Element ◽  
Force Model ◽  
Milling Cutter ◽  
Tool Deflections ◽  
Cutting System

This paper develops an analytical model to estimate the dynamic responses in end milling, i.e., dynamic milling cutter deflections and cutting forces, by using the finite element method along with an adequate end milling cutting force model. The whole cutting system includes spindle, bearings and cutter. The spindle is structurally modeled with the Timoshenko-beam element, the milling cutter with the pretwisted Timoshenko-beam element due to its special geometry, and the bearings with lumped springs and dampers. Because the damping matrix in the resulting finite element equation of motion for the whole cutting system is not of proportional damping due to the presence of bearing damping, we use state-vector approach and convolution integral to find the solution of equations of motion. To assure the accuracy of dynamic response predication, the associated cutting force model should be sufficiently precise. Since the dynamic cutting force is proportional to the chip thickness, a quite accurate algorithm for the calculation of chip thickness variation due to tool geometry, runout and spindle-tool vibration is developed. A number of dynamic cutting forces and tool deflections obtained from the present model for various cutting conditions are compared with the experimental and analytical results available in the literature, and good agreement is demonstrated for these comparisons. Therefore the present model is useful for the prediction of end milling instability. Also, the tool deflections obtained by using the pretwisted beam element are found smaller than those by straight beam elements without pretwist angle. Hence, neglecting the pretwist angle in the structural model of milling cutter may overestimate the tool deflections.

On the Modeling and Analysis of Machining Performance in Micro-Endmilling, Part II: Cutting Force Prediction

2004 ◽  
Vol 126 (4) ◽  
pp. 695-705 ◽  
Author(s):  
Michael P. Vogler ◽  
Shiv G. Kapoor ◽  
Richard E. DeVor
Keyword(s):  
Cutting Force ◽  
Ductile Iron ◽  
Chip Thickness ◽  
Thickness Effect ◽  
Force Model ◽  
Machining Performance ◽  
Cutting Force Prediction ◽  
Minimum Chip Thickness ◽  
Modeling And Analysis ◽  
Deformation Force

In Part II of this paper, a cutting force model for the micro-endmilling process is developed. This model incorporates the minimum chip thickness concept in order to predict the effects of the cutter edge radius on the cutting forces. A new chip thickness computation algorithm is developed to include the minimum chip thickness effect. A slip-line plasticity force model is used to predict the force when the chip thickness is greater than the minimum chip thickness, and an elastic deformation force model is employed when the chip thickness is less than the minimum chip thickness. Orthogonal, microstructure-level finite element simulations are used to calibrate the parameters of the force models for the primary metallurgical phases, ferrite and pearlite, of multiphase ductile iron workpieces. The model is able to predict the magnitudes of the forces for both the ferrite and pearlite workpieces as well as for the ductile iron workpieces within 20%.

Research on the Ductile Chip Formation in Grinding of Brittle Materials

2011 ◽  
Vol 487 ◽  
pp. 58-62
Author(s):  
Yun Feng Peng ◽  
Zhi Qiang Liang ◽  
Yong Bo Wu ◽  
Yin Biao Guo ◽  
T. Jiang ◽  
...  
Keyword(s):  
Shear Stress ◽  
Compressive Stress ◽  
Chip Formation ◽  
Thrust Force ◽  
Brittle Materials ◽  
Chip Thickness ◽  
Force Model ◽  
Theoretical Discussion ◽  
Undeformed Chip Thickness ◽  
Formation Zone

A theoretical discussion has been presented for the ductile chip formation in grinding of brittle materials. The single abrasive grit was dealt with a top-rounded cutter removing material of varying undeformed chip thickness. The force model in the chip formation zone was established. The stress analysis showed that larger compressive stress and shear stress can be generated in the chip formation zone, which shields the growth of pre-existing flaws in the material by suppressing the stress intensity factor. When the stress intensify factor is smaller than fracture toughness and the resolved shear stress exceeds the critical flow stress of the material, the ductile chip is formed. Experiments of monocrystal silicon grinding were conducted. The results show that the thrust force is much larger than the cutting force, which ensures the larger compressive stress in the chip formation zone and the formation of ductile chip.

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