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.

Cutting Force Model for Contour Surface Machining of Gear Indexing Cam with Flat End Milling

2004 ◽  
Vol 471-472 ◽  
pp. 122-126 ◽  
Author(s):  
P.Q. Guo ◽  
Chuan Zhen Huang ◽  
Ping Zhao
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Chip Thickness ◽  
Depth Of Cut ◽  
Force Model ◽  
Uncut Chip Thickness ◽  
Thickness Change ◽  
Flat End Milling ◽  
Axial Depth

This paper presents a model to predict the cutting forces for flat end milling as machining gear indexing cam. Rotation feeding makes axial depth of cut and uncut chip thickness change during cutting process. The development of the model is based on the analysis of cutting edge expression. According to the existing the relationship of the local cutting force and chip load and assuming the cutter to be divided into a number of differential elements in the axial direction of the cutter, the model is derived by summarising the cutting forces produced by each differential cutter disc engaged in the cut. The equation for calculating uncut chip thickness of differential disc is educed. In order to avoid the complex computing for axial depth of cut of the entire edge, a unit square window function and its criterion are introduced to estimate whether a segment of edge is in engaging range.

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.

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.

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.

Identification of Cutter Axis Tilt in End Milling

1997 ◽  
Vol 119 (2) ◽  
pp. 178-185 ◽  
Author(s):  
Li Zheng ◽  
S. Y. Liang
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Chip Thickness ◽  
Cutting Parameters ◽  
Milling Process ◽  
Mathematical Representation ◽  
Thickness Variation ◽  
Dynamic Force ◽  
Force Components

The scope of the paper is to discuss the identification of cutter axis tilt in end milling process via cutting force analysis. Cutter axis tilt redistributes the chip load among flutes thereby generating minor frequency components of cutting forces. These minor components can be utilized to infer the tilt geometry during the cutting action. This study involved the mathematical representation of chip thickness variation due to tilt, the modeling of local forces in relation to instantaneous chip thickness, the formulation of total cutting forces through convolution integration in the angle domain, the derivation of dynamic force components in the frequency domain, and the solution for tilt geometry from the dynamic cutting forces. Results show that the tilt magnitude and orientation can be estimated given the dynamic cutting force components along with the tool/work geometry, cutting parameters, and machining configuration. Numerical simulation results confirmed the validity of the angle domain convolution approach, and the end milling experimental data agreed with the analytical model.

Analytical Convolution Model of Cutting Forces in 3-D Ball End Milling

2001 ◽  
Author(s):  
Richard Y. Chiou ◽  
Bing Zhao
Keyword(s):  
Cutting Force ◽  
Frequency Domain ◽  
Cutting Forces ◽  
End Milling ◽  
Force Model ◽  
Three Dimensional Model ◽  
Calculation Algorithm ◽  
Ball End Milling ◽  
Convolution Model ◽  
Force Calculation

Abstract This paper presents an analytical convolution model of dynamic cutting forces in ball end milling of 3-D plane surfaces. The model takes into account the instantaneous slope on a sculptured surface to establish the chip geometry in cutting force calculation algorithm. A three-dimensional model of cutting forces in ball end milling is presented in terms of material properties, cutting parameters, machining configuration, and tool/work geometry. Based on the relationship of the local cutting force, chip load and engaged boundary, the total cutting force model is established via the angle domain convolution integration of the local forces in the feed, cross feed, axial direction, and inclination angle. The convolution integral leads to a periodic function of cutting forces in the angle domain and an explicit expression of the dynamic cutting force components in the frequency domain. Following the theoretical analysis, experimental study is discussed to illustrate the implementation procedure for force identification, and frequency domain data are presented to verify the analytical results.

Analysis of Cutting Force in Elastomer End-Milling

2017 ◽  
Vol 11 (6) ◽  
pp. 958-963
Author(s):  
Koji Teramoto ◽  
◽  
Takahiro Kunishima ◽  
Hiroki Matsumoto
Keyword(s):  
Parameter Identification ◽  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Process Models ◽  
Force Model ◽  
Cutting Force Model ◽  
Cutting Force Prediction ◽  
Force Prediction ◽  
The Stability

Elastomer end-milling is attracting attention for its role in the small-lot production of elastomeric parts. In order to apply end-milling to the production of elastomeric parts, it is important that the workpiece be held stably to avoid deformation. To evaluate the stability of workholding, it is necessary to predict cutting forces in elastomer end-milling. Cutting force prediction for metal workpiece end-milling has been investigated for many years, and many process models for end-milling have been proposed. However, the applicability of these models to elastomer end-milling has not been discussed. In this paper, the characteristics of the cutting force in elastomer end-milling are evaluated experimentally. A standard cutting force model and its parameter identification method are introduced. By using this cutting force model, measured cutting forces are compared against the calculated results. The comparison makes it clear that the standard cutting force model for metal end-milling can be applied to down milling for a rough evaluation.

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.

A Mechanistic Model of Cutting Forces in Micro-End-Milling With Cutting-Condition-Independent Cutting Force Coefficients

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Han Ul Lee ◽  
Dong-Woo Cho ◽  
Kornel F. Ehmann
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Cutting Conditions ◽  
Thickness Effect ◽  
Force Model ◽  
Cutting Force Coefficients ◽  
Force Coefficients ◽  
Micro End Milling ◽  
Cutting Mechanisms

Complex three-dimensional miniature components are needed in a wide range of industrial applications from aerospace to biomedicine. Such products can be effectively produced by micro-end-milling processes that are capable of accurately producing high aspect ratio features and parts. This paper presents a mechanistic cutting force model for the precise prediction of the cutting forces in micro-end-milling under various cutting conditions. In order to account for the actual physical phenomena at the edge of the tool, the components of the cutting force vector are determined based on the newly introduced concept of the partial effective rake angle. The proposed model also uses instantaneous cutting force coefficients that are independent of the end-milling cutting conditions. These cutting force coefficients, determined from measured cutting forces, reflect the influence of the majority of cutting mechanisms involved in micro-end-milling including the minimum chip-thickness effect. The comparison of the predicted and measured cutting forces has shown that the proposed method provides very accurate results.

An AI-Based Model for Predicting Instananeous Cutting Force in End Milling

Manufacturing ◽  
2002 ◽  
Author(s):  
Hazim El-Mounayri ◽  
Vipul Tandon
Keyword(s):  
Cutting Force ◽  
Frequency Domain ◽  
Cutting Forces ◽  
End Milling ◽  
Depth Of Cut ◽  
Feed Speed ◽  
Ann Model ◽  
Force Signal ◽  
Input Variables ◽  
Artificial Neural Network Ann

An Artificial Neural Network (ANN) model is developed to accurately predict the instantaneous cutting forces in flat end milling. A unique frequency domain approach is presented and is seen to simulate instantaneous cutting forces reasonably well. A set of eight input variables is chosen to represent the machining conditions and frequency domain parameters of the cutting force signal are generated. Three input parameters are varied, namely Feed, Speed and Depth of Cut. Four output parameters are suggested as a sufficient set to adequately reproduce the instantaneous cutting forces. Exhaustive experimentation is conducted to collect data (consisting of Fx, Fy, and Fz) to train and validate the model.

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