Virtual Model of Gear Shaping—Part I: Kinematics, Cutter–Workpiece Engagement, and Cutting Forces

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Andrew Katz ◽  
Kaan Erkorkmaz ◽  
Fathy Ismail
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
Spur Gear ◽  
Cutting Edge ◽  
Prediction Algorithm ◽  
Force Model ◽  
Time Step ◽  
Solid Modeler ◽  
Chip Geometry ◽  
Gear Shaping

Gear shaping is, currently, the most prominent method for machining internal gears, which are a major component in planetary gearboxes. However, there are few reported studies on the mechanics of the process. This paper presents a comprehensive model of gear shaping that includes the kinematics, cutter–workpiece engagement (CWE), and cutting forces. To predict the cutting forces, the CWE is calculated at discrete time steps using a tridexel discrete solid modeler. From the CWE in tridexel form, the two-dimensional (2D) chip geometry is reconstructed using Delaunay triangulation (DT) and alpha shape reconstruction. This in turn is used to determine the undeformed chip geometry along the cutting edge. The cutting edge is discretized into nodes with varying cutting force directions (tangential, feed, and radial), inclination angles, and rake angles. If engaged in the cut during a particular time-step, each node contributes an incremental force vector calculated with the oblique cutting force model. Using a three-axis dynamometer on a Liebherr LSE500 gear shaping machine tool, the cutting force prediction algorithm was experimentally verified on a variety of processes and gears, which included an internal spur gear, external spur gear, and external helical gear. The simulated and measured force profiles correlate closely with about 3–10% RMS error.

scholarly journals Modeling Cutting Forces for Five Axis Milling of Sculptured Surfaces

2011 ◽  
Vol 223 ◽  
pp. 701-712 ◽  
Author(s):  
Yaman Boz ◽  
Huseyin Erdim ◽  
Ismail Lazoglu
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Force Model ◽  
Ball End Milling ◽  
Validation Test ◽  
Tool Accessibility ◽  
Solid Modeler ◽  
Five Axis ◽  
Machining Productivity

5-axis ball-end milling processes are used in various industries such as aerospace, automotive, die-mold and biomedical industries. 5-axis machining provides reduced cycle times and more accurate machining via reduction in machining setups, use of shorter tools due to improved tool accessibility. However, desired machining productivity and precision can be obtained by physical modeling of machining processes via appropriate selection of process parameters. In response to this gap in the industry this paper presents a cutting force model for 5-axis ball-end milling cutting force prediction. Cutter-workpiece engagement is extracted via developed solid modeler based engagement model. Simultaneous 5-axis milling tests are conducted on Al7075 workpiece material with a carbide cutting tool. Validation of the proposed model is performed for impeller hub roughing toolpaths. Validation test proves that presented model is computationally efficient and cutting forces can be predicted reasonably well. The result of validation test and detailed comparison with the simulation are also presented in the paper.

Analytical cutting force modelling of micro-slot grinding considering tool-workpiece interactions on both primary and secondary tool surfaces

2021 ◽  
pp. 1-43
Author(s):  
Ashwani Pratap ◽  
Karali Patra
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
Orthogonal Cutting ◽  
Surface Interactions ◽  
Surface Interaction ◽  
Edge Density ◽  
Force Model ◽  
Height Distribution ◽  
Force Modeling ◽  
Tool Surface

Abstract This work presents an analytical cutting force modeling for micro-slot grinding. Contribution of the work lies in the consideration of both primary and secondary tool surface interactions with the work surface as compared to the previous works where only primary tool surface interaction was considered during cutting force modeling. Tool secondary surface interaction with workpiece is divided into two parts: cutting/ ploughing by abrasive grits present in exterior margin of the secondary tool surface and sliding/adhesion by abrasive grits in the inner margins of the secondary tool surface. Orthogonal cutting force model and indentation based fracture model is considered for cutting by both the abrasives of primary tool surface and the abrasives of exterior margin on the secondary surface. Asperity level sliding and adhesion model is adopted to solve the interaction between the workpiece and the interior margin abrasives of secondary tool surface. Experimental measurement of polycrystalline diamond tool surface topography is carried out and surface data is processed with image processing tools to determine the tool surface statistics viz., cutting edge density, grit height distribution and abrasive grit geometrical measures. Micro-slot grinding experiments are carried out on BK7 glass at varying feed rate and axial depths of cut to validate the simulated cutting forces. Simulated cutting forces considering both primary and secondary tool surface interactions are found to be much closer to the experimental cutting forces as compared to the simulated cutting forces considering only primary tool surface interaction.

ANISOTROPIC CUTTING FORCE CHARACTERISTICS IN MILLING OF MARAGING STEEL PROCESSED THROUGH SELECTIVE LASER MELTING

2021 ◽  
pp. 1-16
Author(s):  
Shoichi Tamura ◽  
Takashi Matsumura ◽  
Atsushi Ezura ◽  
Kazuo Mori
Keyword(s):  
Additive Manufacturing ◽  
Cutting Force ◽  
Maraging Steel ◽  
Selective Laser Melting ◽  
Cutting Forces ◽  
Manufacturing Process ◽  
Laser Scanning ◽  
Force Model ◽  
Laser Melting ◽  
Scanning Direction

Abstract Additive manufacturing process of maraging steel has been studied for high value parts in aerospace and automotive industries. The hybrid additive / subtractive manufacturing is effective to achieve tight tolerances and surface finishes. The additive process induces anisotropic mechanical properties of maraging steel, which depends on the laser scanning direction. Because anisotropy in the workpiece material has an influence on the cutting process, the surface finish and the dimension accuracy change according to the direction of the cutter feed with respect to the laser scanning direction. Therefore, the cutting parameters should be determined to control the cutting force considering material anisotropy. The paper discusses the cutting force in milling of maraging steel stacked with selective laser melting, as an additive manufacturing process. Anisotropic effect on the cutting forces is proved with the changing rate of the cutting force in milling of the workpieces stacked by repeating laser scanning at 0/90 degrees and 45/-45 degrees. The cutting forces, then, are analyzed in the chip flow models with piling up of orthogonal cuttings. The force model associates anisotropy with the shear stress on the shear plane. The changes in the cutting forces with the feed direction are discussed in the cutting tests and analysis.

Anisotropic Cutting Force Characteristics in Milling of Maraging Steel Processed Through Selective Laser Melting

2021 ◽  
Author(s):  
Shoichi Tamura ◽  
Takashi Matsumura ◽  
Atsushi Ezura ◽  
Kazuo Mori
Keyword(s):  
Additive Manufacturing ◽  
Cutting Force ◽  
Maraging Steel ◽  
Selective Laser Melting ◽  
Cutting Forces ◽  
Manufacturing Process ◽  
Laser Scanning ◽  
Force Model ◽  
Laser Melting ◽  
Scanning Direction

Abstract Additive manufacturing process of maraging steel has been studied for high value parts in aerospace and automotive industries. The hybrid additive / subtractive manufacturing is effective to achieve tight tolerances and surface finishes. The additive process induces anisotropic mechanical properties of maraging steel, which depends on the laser scanning direction. Because anisotropy in the workpiece material has an influence on the cutting process, the surface finish and the dimension accuracy change according to the direction of the cutter feed with respect to the laser scanning direction. Therefore, the cutting parameters should be determined to control the cutting force considering material anisotropy. The paper discusses the cutting force in milling of maraging steel stacked with selective laser melting, as an additive manufacturing process. Anisotropic effect on the cutting forces is proved with the changing rate of the cutting force in milling of the workpieces stacked by repeating laser scanning at 0/90 degrees and 45/−45 degrees. The cutting forces, then, are analyzed in the chip flow models with piling up of orthogonal cuttings. The force model associates anisotropy with the shear stress on the shear plane. The changes in the cutting forces with the feed direction are discussed in the cutting tests and analysis.

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.

Improved dynamic cutting force modelling in micro milling of metal matrix composites part II: Experimental validation and prediction

2019 ◽  
Vol 234 (8) ◽  
pp. 1500-1515
Author(s):  
Zhichao Niu ◽  
Kai Cheng
Keyword(s):  
Cutting Force ◽  
Metal Matrix Composites ◽  
Cutting Forces ◽  
Metal Matrix ◽  
Micro Milling ◽  
Force Model ◽  
Matrix Composites ◽  
Cutting Force Model ◽  
Side Milling ◽  
Dynamic Cutting Force

The effects of cutting dynamics and the particles' size and density cannot be ignored in micro milling of metal matrix composites. This article presents the improved dynamic cutting force modelling for micro milling of metal matrix composites based on the previous analytical model. This comprehensive improved cutting force model, taking the influence of the tool run-out, actual chip thickness and resultant tool tip trajectory into account, is evaluated and validated through well-designed machining trials. A series of side milling experiments using straight flutes polycrystalline diamond end mills are carried out on the metal matrix composite workpiece under various cutting conditions. Subsequently, the measured cutting forces are compensated by a Kalman filter to achieve the accurate cutting forces. These are further compared with the predicted cutting forces to validate the proposed dynamic cutting force model. The experimental results indicate that the predicted and measured cutting forces in micro milling of metal matrix composites are in good agreement.

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.

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.

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