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.

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.

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.

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.

Mechanistic Cutting Force Prediction Model for Plunge Milling Considering Cutter Runout

2017 ◽  
Author(s):  
Kejia Zhuang ◽  
Xiaohu Xu ◽  
Ruiqi Xiao ◽  
Dahu Zhu ◽  
Shunsheng Guo ◽  
...  
Keyword(s):  
Cutting Force ◽  
Metal Cutting ◽  
End Milling ◽  
Chip Thickness ◽  
Force Model ◽  
Cutter Runout ◽  
Rough Machining ◽  
Plunge Milling ◽  
Side Milling ◽  
Cutting Mechanisms

As a kind of promising process for mass material removal in rough and semi-rough machining of hard-to-machine materials, plunge milling receives wide concerns and is often considered as one of the most effective methods in metal cutting operation, especially in aircraft industry. The cutting force in plunge milling operation differs from that in side milling or end milling for the complex geometries. To clarify the force based cutting mechanisms, a systematic study on cutting force modeling is conducted in this paper based on the precise cutting geometry which considers both the real-time uncut chip thickness calculation and cutter runout. The deduced cutting force model can be used for different cutting conditions in plunge milling process. Then, series of plunge milling operations with various cutting steps are implemented to verify the proposed force model. The results indicate that the predicted values show quite good agreement with the measured cutting forces.

A Mechanistic Cutting Force Model for 3D Ball-end Milling

2000 ◽  
Vol 123 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Hsi-Yung Feng ◽  
Ning Su
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Chip Thickness ◽  
Milling Process ◽  
Force Model ◽  
Cutting Force Model ◽  
Ball End Milling ◽  
End Milling Process ◽  
Force Relationship

This paper presents an improved mechanistic cutting force model for the ball-end milling process. The objective is to accurately model the cutting forces for nonhorizontal and cross-feed cutter movements in 3D finishing ball-end milling. Main features of the model include: (1) a robust cut geometry identification method to establish the complicated engaged area on the cutter; (2) a generalized algorithm to determine the undeformed chip thickness for each engaged cutting edge element; and (3) a comprehensive empirical chip-force relationship to characterize nonhorizontal cutting mechanics. Experimental results have shown that the present model gives excellent predictions of cutting forces in 3D ball-end milling.

Model of End Milling Force Based on Undeformed Chip Surface with NURBS in Peripheral Milling

2010 ◽  
Vol 33 ◽  
pp. 356-362 ◽  
Author(s):  
Xionig Ying Pu ◽  
Wei Jun Liu ◽  
Ji Bin Zhao
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Chip Thickness ◽  
Contact Length ◽  
Force Model ◽  
Cutting Force Model ◽  
Peripheral Milling ◽  
Chip Surface ◽  
Chip Area ◽  
Differential Element

A new cutting force model for peripheral milling is presented based-on a developed algorithm for instantaneous undeformed chip surface with NURBS. To decrease the number of the differential element, the contact cutting edges of end-milling cutter with the part and the chip thickness curve are represented by NURBS helix, and the instantaneous undeformed chip is constructed as a ruled surface with the two curves. The cutting force generated by the edge contact length and the uncut chip area. Using the cutting coefficients from Budak[1] , the cutting-force model verified by simulation. The simulation results indicate that new cutting-force model predict the cutting forces in peripheral milling accurately.

On the segmentation-driven vibration in milling titanium alloy

2016 ◽  
Vol 232 (9) ◽  
pp. 1508-1522 ◽  
Author(s):  
Jiahao Shi ◽  
Qinghua Song ◽  
Zhanqiang Liu ◽  
Yi Wan
Keyword(s):  
Titanium Alloy ◽  
Cutting Force ◽  
Natural Frequency ◽  
End Milling ◽  
Chip Morphology ◽  
Milling Process ◽  
Force Model ◽  
Tool Vibration ◽  
Segmented Chip ◽  
Cutting System

Numerous hard, brittle metals have been shown to form segmented chips during machining operations, which has been shown to be linked to high vibration levels in turning and milling processes. This article concerns quantitative comprehension of segmentation-driven vibration in end-milling process. First, dynamic model of milling process with impact of segmented chip is presented, and a periodic cutting force model related with segmented chip is proposed. Second, for experimental observation, a series of tests are carried out concerning modal test of cutting system; chip morphology, tool vibration during cutting, surface location error, and high-frequency sampling measurements of cutting force signal are realized. The method used for calculating the frequency of segmentation chip by oblique cutting is deduced. It is found that at low feed rate, the periodic cutting force is affected by the natural frequency of cutting system, segmentation chip, and tool vibration. Finally, amplitude–frequency response for quasi-single degree of freedom is employed to elaborate the relationship between segmentation frequency and natural modes of system. The results show that when the ratio (frequency of segmented chip to natural frequency of system) is a noninteger value or above 3, no significant vibrations of cutting system are observed in milling titanium alloy Ti6Al4V.

An Improved Cutting Force Model Considering the Size Effect in End Milling

2000 ◽  
Author(s):  
Won-Soo Yun ◽  
Dong-Woo Cho
Keyword(s):  
Size Effect ◽  
Cutting Force ◽  
Cutting Forces ◽  
Measurement Problem ◽  
End Milling ◽  
Mechanistic Model ◽  
Chip Thickness ◽  
Force Model ◽  
Cutting Force Model ◽  
Approximate Methods

Abstract In this paper, a mechanistic model is first constructed to predict three-dimensional cutting forces, and the uncut chip thickness is calculated by following the movements of the position of the center of a cutter, which varies with the nominal feed, cutter deflection and runout. For general implementation to a real machining, this paper presents the method that determines constant cutting force coefficients, irrespective of the cutting conditions or cutter rotation angles. In addition, this study presents the approach which estimates runout-related parameters, the runout offset and its location angle, using only one measurement of cutting forces. For more accurate cutting force predictions, the size effect has to be considered in the cutting force model. In this paper, two approximate methods are suggested since the strict approach is practically impossible due to a measurement problem. The size effect is individually considered for narrow and wide cuts.

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