Estimation of Cutter Deflection Based on Study of Cutting Force and Static Flexibility

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Xianyin Duan ◽  
Fangyu Peng ◽  
Rong Yan ◽  
Zerun Zhu ◽  
Kai Huang ◽  
...  
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Chip Thickness ◽  
Machining Accuracy ◽  
Tool Orientation ◽  
Surface Machining ◽  
Cutter Deflection ◽  
Geometrical Constraints ◽  
Machining System ◽  
Five Axis

In the tool orientation planning for five-axis sculptured surface machining, the geometrical constraints are usually considered. Actually, the effect of nongeometrical constraints on tool orientation planning is also important. This paper studied one nongeometrical constraint which was cutting force induced static deflection under different tool orientations, and proposed a cutter deflection model based on that. In the study of the cutting force, the undeformed chip thickness in filleted end milling was modeled by geometrical analysis and coordinate transformation of points at the cutting edge. In study of static flexibility of multi-axis machine, static flexibility of the entire machining system was taken into consideration. The multi-axis machining system was divided into the transmission axes-handle (AH) end and the cutting tool end. The equivalent shank method was developed to calculate the static flexibility of the AH end. In this method, static flexibility anisotropy of the AH end was considered, and the equivalent lengths of the AH end were obtained from calibration experiments. In cutter deflection modeling, force manipulability ellipsoid (FME) was applied to analyze the static flexibility of the AH end in arbitrary directions. Based on the synthetic static flexibility and average cutting force, cutter deflections were derived and estimated through developing program realization. The predicted results were compared with the experimental data obtained by machining 300 M steel curved surface workpiece, and a good agreement was shown, which indicated the effectiveness of the cutter deflection model. Additional experiments of machining flat workpiece were performed, and the relationship of cutter deflections and tool orientations were revealed directly. This work could be further employed to optimize tool orientations for suppressing the surface errors due to cutter deflections and achieving higher machining accuracy.

scholarly journals Cutting force prediction considering force-deflection coupling in five-axis milling with fillet-end cutter

2021 ◽  
Author(s):  
Xianyin Duan ◽  
Lantao Li ◽  
Chen Chen ◽  
Sheng Yu ◽  
Zerun Zhu ◽  
...  
Keyword(s):  
Cutting Force ◽  
Tilt Angle ◽  
Prediction Models ◽  
Machining Process ◽  
Machining Accuracy ◽  
Force Model ◽  
Cutting Force Model ◽  
Lead Angle ◽  
Cutter Deflection ◽  
Five Axis

Abstract With the increasing demand for higher quality and performance of equipment and assembly in aerospace, shipbuilding, medical and other fields, the machining accuracy of parts is facing higher requirements. It is particularly important to predict the cutting force accurately, which is the main physical quantity in the machining process and basis of process inspection and quality control. In this paper, the cutting force model in five-axis milling with fillet-end cutter is proposed, which reveals the law of force-deflection coupling. Firstly, the initial cutter deflection model induced by the ideal cutting force ignoring the effect of deflection is built based on analysis of the geometric characteristics of fillet-end cutter. Then the undeformed chip thickness model is educed considering the cutter posture and cutter deflection. Further, the iterative method is utilized to resolve the coupling relationship between cutter deflection and cutting force. Finally, the cutting force model under force-deflection coupling is established for achieving more accurate prediction. To verify the effectiveness of the proposed cutting force model, the milling experiment is carried out on a five-axis milling center. The measured cutting force values are utilized to inspect the accuracy of prediction models considering and not considering force-deflection coupling respectively. The results show that the proposed method could improve the prediction accuracy of cutting force, which show the effectiveness of taking force-deflection coupling law into consideration clearly. The influence of cutter posture on cutting force is analyzed using the proposed cutting force model. The cutting force decreases with the increasing of lead angle or tilt angle, and the influence of tilt angle is greater than that of lead angle under experimental conditions of five-axis milling using the set process parameters.

Cutting Force Simulation in Minute Time Resolution for Ball End Milling Under Various Tool Posture

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Isamu Nishida ◽  
Ryuma Okumura ◽  
Ryuta Sato ◽  
Keiichi Shirase
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Chip Thickness ◽  
Cutting Edge ◽  
New Method ◽  
Uncut Chip Thickness ◽  
Tool Posture ◽  
Voxel Model ◽  
Five Axis ◽  
Milling Forces

A new cutting force simulator has been developed to predict cutting force in ball end milling. In this simulator, uncut chip thickness is discretely calculated based on fully voxel models representing both cutting edge and instantaneous workpiece shape. In the previous simulator, a workpiece voxel model was used to calculate uncut chip thickness under a complex change of workpiece shape. Using a workpiece voxel model, uncut chip thickness is detected by extracting the voxels removed per cutting tooth for the amount of material fed into the cutting edge. However, it is difficult to define the complicated shape of cutting edge, because the shape of cutting edge must be defined by mathematical expression. It is also difficult to model the voxels removed by the cutting edge when tool posture is nonuniformly changed. Therefore, a new method to detect uncut chip thickness is proposed, one in which both cutting edge and instantaneous workpiece shape are fully represented by a voxel model. Our new method precisely detects uncut chip thickness at minute tool rotation angles, making it possible to detect the uncut chip thickness between the complex surface shape of the workpiece and the particular shape of the cutting edge. To validate the effectiveness of our new method, experimental five-axis milling tests using ball end mill were conducted. Estimated milling forces for several tool postures were found to be in good agreement with the measured milling forces. Results from the experimental five-axis milling validate the effectiveness of our new method.

Effective Determination of Feed Direction and Tool Orientation in Five-Axis Flat-End Milling

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
M. Javad Barakchi Fard ◽  
Hsi-Yung Feng
Keyword(s):  
End Milling ◽  
Strip Width ◽  
Free Form ◽  
Tool Orientation ◽  
Surface Machining ◽  
Toroidal Surface ◽  
Machining Strip Width ◽  
Feed Direction ◽  
Optimal Feed ◽  
Five Axis

This paper addresses the challenging problem of determining feed direction and tool orientation at a given cutter contact (CC) point in five-axis free-form surface machining with flat-end mills. The objective is to efficiently determine a feed direction and tool orientation that will avoid both local and global tool gouging and yield a near maximum machining strip width at the CC point. Concurrent determination of the optimal feed direction and tool orientation is a very computationally intensive task and searching for the correct solution would involve exhaustive evaluations of the machining strip width at many feed directions and tool orientations. In this paper, the optimal feed directions and analytical solutions for the optimal tool orientations in five-axis flat-end milling of spherical, cylindrical, and toroidal surfaces are identified first. A toroidal surface inscription method is devised to approximate the local surface geometry at a CC point on a free-form surface by an inscribed toroidal surface. Analytical solutions for toroidal surface machining are then employed to position the flat-end mill at the CC point with the tool feeding in the best toroidal surface inscribing direction. Case studies have demonstrated that the proposed method can efficiently determine a feed direction and tool orientation, corresponding to a near maximum machining strip width.

Modification of Tool Orientation and Position to Compensate Tool and Part Deflections in Five-Axis Ball End Milling Operations

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
M. Habibi ◽  
O. Tuysuz ◽  
Y. Altintas
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Traditional Approach ◽  
Cutting Speed ◽  
Computational Time ◽  
Blade Surface ◽  
Tool Orientation ◽  
Ball End Milling ◽  
Form Errors ◽  
Five Axis

Tool-workpiece deflection is one of the major error sources in machining thin walled structures like blades. The traditional approach in industry to eliminate this error is based on modifying tool positions after measuring the error on the machined part. This paper presents an integrated model of cutting force distribution on the tool–blade contact, automatic update of blade static stiffness matrix without resorting to time-consuming finite element solutions as the material is removed, the prediction and compensation of static deflection marks left on the blade surface. The main focus of the paper is to compensate the deflection errors by respecting the maximum form errors, collision of tool/machine/workpiece, cutting speed limit at the tool tip, and ball end—blade surface contact constraints. The compensation has been carried out by two modules. The first module adjusts the tool orientation along the path to reduce the error by constructing an optimization problem. This module is computationally inexpensive and results in about 70% error reduction based on the conducted experiments. The modified tool path resulted from the first module is fed to the second module for further reduction of the form errors if needed at the violated cutter locations; hence it takes less computational time than the stand alone approach proposed in the literature. The proposed algorithms have been experimentally validated on five-axis finish ball end milling of blades with about 80% reduction in cutting force induced form errors.

Dynamics and Stability Prediction of Five-Axis Flat-End Milling

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
YaoAn Lu ◽  
Ye Ding ◽  
LiMin Zhu
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Stability Prediction ◽  
Tool Orientation ◽  
Cutting Force Prediction ◽  
Vector Method ◽  
Force Prediction ◽  
Flat End Milling ◽  
The Stability ◽  
Five Axis

The tool orientation of a flat-end cutter, determined by the lead and tilt angles of the cutter, can be optimized to increase the machining strip width. However, few studies focus on the effects of tool orientation on the five-axis milling process stability with flat-end cutters. Stability prediction starts with cutting force prediction, and the cutting force prediction is affected by the cutter-workpiece engagement (CWE). The engagement geometries occur between the flat-end cutter and the in-process workpiece (IPW) are complicated in five-axis milling, making the stability analysis for five-axis flat-end milling difficult. The robust discrete vector method (DVM) is adopted to identify the CWE for flat-end millings, and it can be extended to apply to general cutter millings. The milling system is then modeled as a two-degrees-of-freedom spring-mass-damper system with the predicted cutting forces. Thereafter, a general formulation for the dynamic milling system is developed considering the regenerative effect and the mode coupling effect simultaneously. Finally, an enhanced numerical integration method (NIM) is developed to predict the stability limits in flat-end milling with different tool orientations. Effectiveness of the strategy is validated by conducting experiments on five-axis flat-end milling.

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.

Analytical Prediction of Stability Lobes in Ball End Milling

1999 ◽  
Vol 121 (4) ◽  
pp. 586-592 ◽  
Author(s):  
Y. Altıntas¸ ◽  
E. Shamoto ◽  
P. Lee ◽  
E. Budak
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Orthogonal Cutting ◽  
Chip Thickness ◽  
Transformation Method ◽  
Quadratic Equation ◽  
Analytical Prediction ◽  
Force Coefficient ◽  
Ball End Milling ◽  
Stability Lobes

The paper presents an analytical method to predict stability lobes in ball end milling. Analytical expressions are based on the dynamics of ball end milling with regeneration in the uncut chip thickness, time varying directional factors and the interaction with the machine tool structure. The cutting force coefficients are derived from orthogonal cutting data base using oblique transformation method. The influence of cutting coefficients on the stability is investigated. A computationally efficient, an equivalent average cutting force coefficient method is developed for ball end milling. The prediction of stability lobes for ball end milling is reduced to the solution of a simple quadratic equation. The analytical results agree well with the experiments and the computationally expensive and complex numerical time domain simulations.

Virtual Five-Axis Flank Milling of Jet Engine Impellers: Part 1 — Mechanics of Five-Axis Flank Milling

2007 ◽  
Author(s):  
W. Ferry ◽  
Y. Altintas
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
Orthogonal Cutting ◽  
Chip Thickness ◽  
Friction Angle ◽  
Flank Milling ◽  
Cutting Force Prediction ◽  
Jet Engine ◽  
End Mills ◽  
Five Axis

Jet engine impeller blades are flank-milled with tapered, helical, ball-end mills on five-axis machining centers. The impellers are made from difficult-to-cut titanium or nickel alloys, and the blades must be machined within tight tolerances. As a consequence, deflections of the tool and flexible workpiece can jeopardize the precision of the impellers during milling. This work is the first of a two part paper on cutting force prediction and feed optimization for the five-axis flank milling of an impeller. In Part I, a mathematical model for predicting cutting forces is presented for five-axis machining with tapered, helical, ball-end mills with variable pitch and serrated flutes. The cutter is divided axially into a number of differential elements, each with its own feed coordinate system due to five-axis motion. At each element, the total velocity due to translation and rotation is split into horizontal and vertical feed components, which are used to calculate total chip thickness along the cutting edge. The cutting forces for each element are calculated by transforming friction angle, shear stress and shear angle from an orthogonal cutting database to the oblique cutting plane. The distributed cutting load is digitally summed to obtain the total forces acting on the cutter and blade. The model can be used for general five-axis flank milling processes, and supports a variety of cutting tools. Predicted cutting force measurements are shown to be in reasonable agreement with those collected during a roughing operation on a prototype integrally bladed rotor (IBR).

Tool Orientation Planning in Milling With Process Dynamic Constraints: A Minimax Optimization Approach

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Tao Huang ◽  
Xiao-Ming Zhang ◽  
Jürgen Leopold ◽  
Han Ding
Keyword(s):  
Tool Path ◽  
End Milling ◽  
Tool Path Generation ◽  
Optimization Approach ◽  
Path Generation ◽  
Tool Orientation ◽  
Minimax Optimization ◽  
Ball End Milling ◽  
Dynamic Constraints ◽  
Five Axis

In five-axis milling process, the tool path generated by a commercial software seldom takes the dynamics of the machining process into account. The neglect of process dynamics may lead to milling chatter, which causes overcut, quick tool wear, etc., and thus damages workpiece surface and shortens tool life. This motivates us to consider dynamic constraints in the tool path generation. Tool orientation variations in five-axis ball-end milling influence chatter stability and surface location error (SLE) due to the varying tool-workpiece immersion area and cutting force, which inversely provides us a feasible and flexible way to suppress chatter and SLE. However, tool orientations adjustment for suppression of chatter and SLE may cause drastic changes of the tool orientations and affects surface quality. The challenge is to strike a balance between the smooth tool orientations and suppression of chatter and SLE. To overcome the challenge, this paper presents a minimax optimization approach for planning tool orientations. The optimization objective is to obtain smooth tool orientations, by minimizing the maximum variation of the rotational angles between adjacent cutter locations, with constraints of chatter-free and SLE threshold. A dedicated designed ball-end milling experiment is conducted to validate the proposed approach. The work provides new insight into the tool path generation for ball-end milling of sculpture surface; also it would be helpful to decision-making for process parameters optimization in practical complex parts milling operations at shop floor.

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