scholarly journals A Mathematical Modeling to Predict the Cutting Forces in Microdrilling

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Haoqiang Zhang ◽  
Xibin Wang ◽  
Siqin Pang
Keyword(s):  
Mathematical Modeling ◽  
Cutting Forces ◽  
Chip Thickness ◽  
Cutting Edge ◽  
Force Model ◽  
Cutting Mechanism ◽  
Line Field ◽  
Slip Line Field ◽  
Cutting Model ◽  
Secondary Cutting

In microdrilling, because of lower feed, the microdrill cutting edge radius is comparable to the chip thickness. The cutting edges therefore should be regarded as rounded edges, which results in a more complex cutting mechanism. Because of this, the macrodrilling thrust modeling is not suitable for microdrilling. In this paper, a mathematical modeling to predict microdrilling thrust is developed, and the geometric characteristics of microdrill were considered in force models. The thrust is modeled in three parts: major cutting edges, secondary cutting edge, and indentation zone. Based on slip-line field theory, the major cutting edges and secondary cutting edge are divided into elements, and the elemental forces are determined by an oblique cutting model and an orthogonal model, respectively. The thrust modeling of the major cutting edges and second cutting edge includes two different kinds of processes: shearing and ploughing. The indentation zone is modeled as a rigid wedge. The force model is verified by comparing the predicted forces and the measured cutting forces.

Mathematical Modeling of Cutting Forces in Microdrilling

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
Kumar Sambhav ◽  
Puneet Tandon ◽  
Shiv G. Kapoor ◽  
Sanjay G. Dhande
Keyword(s):  
Mathematical Modeling ◽  
Slip Line ◽  
Cutting Forces ◽  
Chip Thickness ◽  
Rake Angle ◽  
Cutting Mechanism ◽  
Line Field ◽  
Slip Line Field ◽  
Effective Rake Angle ◽  
Secondary Cutting

In drilling, the primary and secondary cutting lips of the drill shear the material while the central portion of the chisel edge indents the workpiece, making the cutting process complex to understand. As we go for microdrilling, it exhibits an added complexity to the cutting mechanism as the edge radius gets comparable to chip thickness at low feeds. The presented work models the forces by the primary cutting lip of a microdrill analytically using slip-line field that includes the changes in the effective rake angle and dead metal cap during cutting for cases of shearing as well as ploughing. To study the variation of forces experimentally, the primary cutting lip and chisel edge forces are separated out by drilling through pilot holes of diameter slightly above the drill-web thickness. Finally, the analytical and experimental results are compared and the model is calibrated.

Mathematical Modeling of Cutting Forces in Micro-Drilling

2012 ◽  
Author(s):  
Kumar Sambhav ◽  
Puneet Tandon ◽  
Shiv G. Kapoor ◽  
Sanjay G. Dhande
Keyword(s):  
Mathematical Modeling ◽  
Chip Thickness ◽  
Rake Angle ◽  
Cutting Mechanism ◽  
Line Field ◽  
Slip Line Field ◽  
Effective Rake Angle ◽  
Micro Drilling ◽  
Micro Drill ◽  
Secondary Cutting

In drilling, the primary cutting lips and the secondary cutting lips of the drill shear the material while the central portion of the chisel edge indents the workpiece, making the cutting process complex to understand. As we go for micro-drilling, it exhibits an added complexity to the cutting mechanism when the edge radius gets comparable to chip thickness at low feeds. The presented work models the forces by the primary cutting lip of a micro-drill analytically using slip-line field that includes the changes in the effective rake angle and dead metal cap during cutting for cases of shearing as well as ploughing. To study the variation of forces experimentally, the primary cutting lip and chisel edge forces are separated out by drilling through pilot holes of diameter slightly above the drill-web thickness. Finally, the analytical and experimental results have been compared and the model has been calibrated.

scholarly journals A Slip-Line Field for Ploughing During Orthogonal Cutting

1998 ◽  
Vol 120 (4) ◽  
pp. 693-699 ◽  
Author(s):  
D. J. Waldorf ◽  
R. E. DeVor ◽  
S. G. Kapoor
Keyword(s):  
Slip Line ◽  
Cutting Forces ◽  
Orthogonal Cutting ◽  
Chip Thickness ◽  
Great Promise ◽  
Uncut Chip Thickness ◽  
Workpiece Material ◽  
Line Field ◽  
Slip Line Field ◽  
Edge Radius

Under normal machining conditions, the cutting forces are primarily due to the bulk shearing of the workpiece material in a narrow zone called the shear zone. However, under finishing conditions, when the uncut chip thickness is of the order of the cutting edge radius, a ploughing component of the forces becomes significant as compared to the shear forces. Predicting forces under these conditions requires an estimate of ploughing. A slip-line field is developed to model the ploughing components of the cutting force. The field is based on other slip-line fields developed for a rigid wedge sliding on a half-space and for negative rake angle orthogonal cutting. It incorporates the observed phenomena of a small stable build-up of material adhered to the edge and a raised prow of material formed ahead of the edge. The model shows how ploughing forces are related to cutter edge radius—a larger edge causing larger ploughing forces. A series of experiments were run on 6061-T6 aluminum using tools with different edge radii—including some exaggerated in size—and different levels of uncut chip thickness. Resulting force measurements match well to predictions using the proposed slip-line field. The results show great promise for understanding and quantifying the effects of edge radius and worn tool on cutting forces.

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.

Investigation of the Dynamics of Microend Milling—Part I: Model Development

2006 ◽  
Vol 128 (4) ◽  
pp. 893-900 ◽  
Author(s):  
Martin B. G. Jun ◽  
Xinyu Liu ◽  
Richard E. DeVor ◽  
Shiv G. Kapoor
Keyword(s):  
Cutting Force ◽  
Chip Formation ◽  
Model Development ◽  
Chip Thickness ◽  
Fault System ◽  
Formation Mechanisms ◽  
Force Model ◽  
Line Field ◽  
Fault Parameters ◽  
Microend Milling

In microend milling, due to the comparable size of the edge radius to chip thickness, chip formation mechanisms are different. Also, the design of microend mills with features of a large shank, taper, and reduced diameter at the cutting edges introduces additional dynamics and faults or errors at the cutting edges. A dynamic microend milling cutting force and vibration model has been developed to investigate the microend milling dynamics caused by the unique mechanisms of chip formation as well as the unique microend mill design and its associated fault system. The chip thickness model has been developed considering the elastic-plastic nature in the ploughing process. A slip-line field modeling approach is taken for a cutting force model development that accounts for variations in the effective rake angle and dead metal cap. The process fault parameters associated with microend mills have been defined and their effects on chip load have been derived. Finally, a dynamic model has been developed considering the effects of both the unique microend mill design and fault system and factors that become significant at high spindle speeds including rotary inertia and gyroscopic moments.

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.

Problem Solving Techniques Taught Through Validation of an Instantaneous Rigid Force Model

2014 ◽  
Author(s):  
Richard B. Mindek ◽  
Joseph M. Guerrera
Keyword(s):  
Problem Solving ◽  
Undergraduate Students ◽  
Cutting Forces ◽  
Engineering Students ◽  
Force Model ◽  
Limited Time ◽  
Undergraduate Engineering ◽  
Laboratory Courses ◽  
Milling Operations ◽  
Cutting Model

Educating engineering students in the appropriate methods for analyzing and problem solving fundamental manufacturing processes is a challenge in undergraduate engineering education, given the increasingly limited room in the curriculum as well as the limited time and resources. Although junior and senior level laboratory courses have traditionally been used as a pedagogical platform for conveying this type of knowledge to undergraduate students, the broad range of manufacturing topics that can be covered along with the limited time within a laboratory course structure has sometimes limited the effectiveness of this approach. At the same time, some undergraduate students require a much deeper knowledge of certain manufacturing topics, practices or research techniques, especially those who may already be working in a manufacturing environment as part of a summer internship or part-time employment. The current work shows how modeling, actual machining tests and problem solving techniques were recently used to analyze a manufacturing process within a senior design project course. Specifically, an Instantaneous Rigid Force Model, originally put forward by Tlusty (1,2) was validated and used to assess cutting forces and the ability to detect tool defects during milling operations. Results from the tests showed that the model accurately predicts cutting forces during milling, but have some variation due to cutter vibration and deflection, which were not considered in the model. It was also confirmed that a defect as small as 0.050 inches by 0.025 inches was consistently detectable at multiple test conditions for a 0.5-inch diameter, 4-flute helical end mill. Based on the results, it is suggested that a force cutting model that includes the effect of cutter vibration be used in future work. The results presented demonstrate a level of knowledge in milling operations analysis beyond what can typically be taught in most undergraduate engineering laboratory courses.

scholarly journals Mechanics and Dynamics of Serrated End Mills

Manufacturing ◽  
2002 ◽  
Author(s):  
S. Doruk Merdol ◽  
Yusuf Altintas
Keyword(s):  
Time Domain ◽  
Cutting Forces ◽  
Chip Thickness ◽  
Cutting Edge ◽  
Chatter Stability ◽  
Edge Point ◽  
Oblique Cutting ◽  
Edge Geometry ◽  
End Mills ◽  
Chatter Stability Lobes

Mechanics and dynamics of serrated milling cutters are presented in the article. The serrated flute design knots are fitted to a cubic spline, which is then projected on helical flutes. Cutting edge geometry at any point along the serrated flute is represented by its immersion angle and tangent vectors in radial, tangential and helix directions. The chip thickness removed by each cutting edge point is determined by using previously proposed exact kinematics of dynamic milling. The cutting forces are evaluated by orthogonal to oblique cutting mechanics transformation. The experimentally proven model is able to predict the cutting forces and chatter stability lobes in time domain.

Identification of the Cutting Forces Coefficients via Milling Process Simulation

2011 ◽  
Author(s):  
Sergey A. Voronov ◽  
Igor A. Kiselev ◽  
Maxim G. Yakovlev
Keyword(s):  
Cutting Forces ◽  
Chip Thickness ◽  
Element Model ◽  
Optimization Method ◽  
Milling Process ◽  
Force Model ◽  
Processed Material ◽  
A New Technique ◽  
The Mathematical Model ◽  
The Given

The paper is devoted to the description of a new technique (numerical and experimental) identification of the dependences between cutting forces and instantaneous chip thickness. It is required to measure only the cutting forces versus cutting conditions. Experimentally, for the given pair the processed material – the tool, coefficients of the cutting forces model are calculated by means of the optimization method (Nelder-Mead algorithm). The mathematical model of the milling process developed by authors on each step of the Nelder-Mead method is used for the process numerical simulation under given coefficients of the cutting force model. The elaborated numerical modeling algorithm allows investigating the dynamics and the kinematics of the milling process. The dynamic model of the tool, the algorithm of geometrical modeling of the instantaneous chip thickness, the finite element model of the detail are embedded into the whole model of the milling process.

Influence of Reground Tool Sharpness on Micro-Cutting Process

2010 ◽  
Vol 37-38 ◽  
pp. 550-553
Author(s):  
Xin Li Tian ◽  
Zhao Li ◽  
Xiu Jian Tang ◽  
Fang Guo ◽  
Ai Bing Yu
Keyword(s):  
Cutting Forces ◽  
Orthogonal Cutting ◽  
Cutting Tools ◽  
Chip Thickness ◽  
Cutting Edge ◽  
Cutting Process ◽  
Micro Cutting ◽  
Temperature Distributions ◽  
Edge Radius ◽  
1045 Steel

Tool edge radius has obvious influences on micro-cutting process. It considers the ratio of the cutting edge radius and the uncut chip thickness as the relative tool sharpness (RST). FEM simulations of orthogonal cutting processes were studied with dynamics explicit ALE method. AISI 1045 steel was chosen for workpiece, and cemented carbide was chosen for cutting tool. Sixteen cutting edges with different RTS values were chosen for analysis. Cutting forces and temperature distributions were calculated for carbide cutting tools with these RTS values. Cutting edge with a small RTS obtains large cutting forces. Ploughing force tend to sharply increase when the RTS of the cutting edge is small. Cutting edge with a reasonable RTS reduces the heat generation and presents reasonable temperature distributions, which is beneficial to cutting life. The force and temperature distributions demonstrate that there is a reasonable RTS range for the cutting edge.

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