End Milling Force Model Calibration Using Measured Force Profiles

2012 ◽  
Author(s):  
Yong Zhao ◽  
Robert B. Jerard ◽  
Barry K. Fussell
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Chip Thickness ◽  
Force Sensor ◽  
Force Model ◽  
Experimental Conditions ◽  
Cutting Coefficients ◽  
Force Profile ◽  
Milling Force Model ◽  
Force Profiles

This paper introduces a method to use the cutting force profile, measured from a Kistler dynamometer, to calibrate a mechanistic based force model containing four cutting coefficients. The undesirable effects of tool vibration and force sensor dynamics are minimized by carefully choosing experimental conditions. Cutting force profiles provide an array of force versus chip thickness based values that can be used in a regression fit to find the model coefficients. Results show that different ranges of chip thickness used in the calibration process result in slightly different cutting coefficients, which implies chip thickness has an effect on cutting coefficients. The force profile based cutting coefficients are then used in the cutting force model to estimate the peak resultant cutting force. Comparison of model estimates and measured values show less than 10% error.

Identification of Polynomial Cutting Coefficients for a Dual-Mechanism Ball-end Milling Force Model

2019 ◽  
Vol 13 (3) ◽  
pp. 232-240
Author(s):  
Zhixin Feng ◽  
Meng Liu ◽  
Guohe Li
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Least Square ◽  
Force Model ◽  
Cutting Force Coefficients ◽  
Milling Force ◽  
Ball End Milling ◽  
Force Coefficients ◽  
Cutting Coefficients ◽  
Milling Force Model

Background: Calibration of cutting coefficients is the key content in modeling a mechanistic cutting force model. Generally, in modeling cutting force for ball end milling, the tangent, radial and binormal cutting force coefficients are each considered as a polynomial, respectively. This fact is due to the dependency between the cutting force coefficients and the cutting edge inclination angle which is variable in ball-end mills. Objective: This paper presents an approach to determine the polynomial cutting force coefficients. Methods: In this approach, the cutting force coefficients are expressed as explicit linear equations about the average slotting forces. After analysis of the least square regression method which is utilized in the cutting coefficients evaluation, the principle of cutting parameters choice in calibration experiment and the relationship between the order of polynomial and the number of experiments are presented. Besides, a lot of patents on identification of polynomial cutting coefficients for milling force model were studied. Results: Finally, a series of semi-slotting verification cutting tests were arranged, the measured force agrees well with the predicted force, which demonstrates the effectiveness of this approach. Conclusion: Based on the calibration method proposed in this paper, the cutting coefficients can be determined through (m+2) slotting experiments for m-degree shearing coefficients polynomial theoretically.

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.

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.

Force Modeling of Five-Axis Microball-End Milling

2015 ◽  
Vol 3 (3) ◽  
Author(s):  
Chi Xu ◽  
James Zhu ◽  
Shiv G. Kapoor
Keyword(s):  
End Milling ◽  
Elastic Recovery ◽  
Chip Thickness ◽  
Force Model ◽  
End Mill ◽  
Data Simulation ◽  
Force Modeling ◽  
Static Indentation ◽  
Five Axis ◽  
Milling Force Model

This paper presents a five-axis ball-end milling force model that is specifically tailored to microscale machining. A composite cutting force is generated by combining two force contributions from a shearing/ploughing slip-line (SL) field model and a quasi-static indentation (ID) model. To fully capture the features of microscale five-axis machining, a unique chip thickness algorithm based on the velocity kinematics of a ball-end mill is proposed. This formulation captures intricate tool trajectories as well as readily allows the integration of runout and elastic recovery effects. A workpiece updating algorithm has also been developed to identify tool–workpiece engagement. As a dual purpose, historical elastic recovery is stored locally on the meshed workpiece surface in vector form so that the directionality of elastic recovery is preserved for future time increments. The model has been validated through a comparison with five-axis end mill force data. Simulation results show reasonably accurate replication of end milling cutting forces with minimal experimental data fitting.

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.

Convolution Analysis of Milling Force Pulsation

1994 ◽  
Vol 116 (1) ◽  
pp. 17-25 ◽  
Author(s):  
J.-J. Junz Wang ◽  
S. Y. Liang ◽  
W. J. Book
Keyword(s):  
Cutting Force ◽  
Density Function ◽  
Cutting Forces ◽  
End Milling ◽  
Chip Thickness ◽  
Closed Form Expression ◽  
Thickness Variation ◽  
Depth Of Cut ◽  
Force Model ◽  
Frequency Multiplication

This paper presents the establishment of a closed form expression for the dynamic forces as explicit functions of cutting parameters and tool/workpiece geometry in milling processes. Based on the existing local cutting force model, the generation of total cutting forces is formulated as the angular domain convolution of three cutting process component functions, namely the elementary cutting function, the chip width density function, and the tooth sequence function. The elemental cutting force function is related to the chip formation process in an elemental cutting area and it is characterized by the chip thickness variation, and radial cutting configuration. The chip width density function defines the chip width per unit cutter rotation along a cutter flute within the range of axial depth of cut. The tooth sequence function represents the spacing between flutes as well as their cutting sequence as the cutter rotates. The analysis of cutting forces is extended into the Fourier domain by taking the frequency multiplication of the transforms of the three component functions. Fourier series coefficients of the cutting forces are shown to be explicit algebraic functions of various tool parameters and cutting conditions. Numerical simulation results are presented in the frequency domain to illustrate the effects of various process parameters. A series of end milling experiments are performed and their results discussed to validate the analytical model.

Calibration of a Milling Force Model Using Feed and Spindle Power Sensors

2008 ◽  
Author(s):  
Bryan Javorek ◽  
Barry K. Fussell ◽  
Robert B. Jerard
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Machining Process ◽  
Force Model ◽  
Cutting Force Model ◽  
Drive Power ◽  
Average Force ◽  
Force Monitoring ◽  
Milling Force Model

Changes in cutting forces during a milling operation can be associated with tool wear and breakage. Accurate monitoring of these cutting forces is an important step towards the automation of the machining process. However, direct force sensors, such as dynamometers, are not practical for industry application due to high costs, unwanted compliance, and workspace limitations. This paper describes a method in which power sensors on the feed and spindle motors are used to generate coefficients for a cutting force model. The resulting model accurately predicts the X and Y cutting forces observed in several simple end-milling tests, and should be capable of estimating both the peak and average force for a given cut geometry. In this work, a dynamometer is used to calibrate the feed drive power sensor and to measure experimental cutting forces for verification of the cutting force model. Measurement of the average x-axis cutting forces is currently presented as an off-line procedure performed on a sacrificial block of material. The potential development of a continuous, real-time force monitoring system is discussed.

The prediction of cutting force in end milling titanium alloy (Ti6Al4V) with polycrystalline diamond tools

2016 ◽  
Vol 231 (1) ◽  
pp. 3-14 ◽  
Author(s):  
Wencheng Pan ◽  
Songlin Ding ◽  
John Mo
Keyword(s):  
Titanium Alloy ◽  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Polycrystalline Diamond ◽  
Force Model ◽  
Machining Parameters ◽  
Diamond Tools ◽  
Cutting Coefficients ◽  
Titanium Alloy Ti6al4v

Cutting force coefficients were conventionally described as the power function of instantaneous uncut chip thickness. However, it was found that the changes in the three controllable machining parameters (cutting speed, feed and axial cutting depth) could significantly affect the values of cutting coefficients. An improved cutting force model was developed in this article based on the experimental investigation of end milling titanium alloy (Ti6Al4V) with polycrystalline diamond tools. The relationships between machining parameters and cutting force are established based on the introduction of the new cutting coefficients. By integrating the effects of varying cutting parameters in the prediction model, cutting forces and the fluctuation of cutting force in each milling cycle were calculated. Validation experiments show that the predicted peak values of cutting forces highly match the experimental results; the accuracy of the model is up to 90% in predicting instantaneous cutting forces.

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