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 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.

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.

Experimental investigation of a slip-line field model for a worn cutting tool

2013 ◽  
Vol 228 (8) ◽  
pp. 1398-1404 ◽  
Author(s):  
Alper Uysal ◽  
Erhan Altan
Keyword(s):  
Wear Rate ◽  
Slip Line ◽  
Field Model ◽  
Cutting Tool ◽  
Flank Wear ◽  
Cutting Speed ◽  
Chip Thickness ◽  
Rake Angle ◽  
Uncut Chip Thickness ◽  
Line Field

In this study, the slip-line field model developed for orthogonal machining with a worn cutting tool was experimentally investigated. Minimum and maximum values of five slip-line angles ( θ1, θ2, δ2, η and ψ) were calculated. The friction forces that were caused by flank wear land, chip up-curl radii and chip thicknesses were calculated by solving the model. It was specified that the friction force increased with increase in flank wear rate and uncut chip thickness and it decreased a little with increase in cutting speed and rake angle. The chip up-curl radius increased with increase in flank wear rate and it decreased with increase in uncut chip thickness. The chip thickness increased with increase in flank wear rate and uncut chip thickness. Besides, the chip thickness increased with increase in rake angle and it decreased with increase in cutting speed.

Impact of Spindle Speed on Micro-Milling Stability

2012 ◽  
Author(s):  
Eric B. Halfmann ◽  
C. Steve Suh
Keyword(s):  
Slip Line ◽  
Chip Thickness ◽  
Rake Angle ◽  
Micro Milling ◽  
Work Piece ◽  
Formation Mechanisms ◽  
Lumped Mass ◽  
Effective Rake Angle ◽  
Helical Angle ◽  
Force Mechanism

Milling efficiency is hampered by excessive tool vibrations that negatively impact the work-piece quality. This is more of a concern in micro-milling where sudden tool breakage occurs before the operator can adjust cutting parameters. Due to different chip formation mechanisms in micro-milling, an increased tool-radius to feed-rate ratio, and higher spindle speeds, micro-milling is a highly non-linear process which can produce multiple and broadband frequencies which increase the probability of tool failure. Micro-milling is studied through the development and analysis of a 3-D nonlinear micro-milling dynamic model. A lumped mass, spring, damper system is assumed for modeling the dynamic properties of the tool. The force mechanism utilized is a slip-line field model that provides the advantages of being highly dynamic by accounting for the constantly changing effective rake angle and slip-line variables. Accurate prediction of the chip thickness is important in correctly predicting the dynamics of the system since the force mechanism and its variables are a function of the chip thickness. A novel approach for calculating the instantaneous chip thickness which accounts for the tool jumping out of the cut and elastic recovery of the work-piece is presented. The effective rake angle and helical angle is accounted for resulting in a 3-D micro-milling model. The model is shown to resolve the high frequency force components that are seen in experimental data available in literature. Also, exciting the system at various spindle speeds results in dynamic states of motion that negatively impact the process through increased vibration amplitude and a broad frequency bandwidth.

On the non-uniqueness of the machining process

1978 ◽  
Vol 360 (1703) ◽  
pp. 587-610 ◽  
Keyword(s):  
Shear Stress ◽  
Slip Line ◽  
Interfacial Shear Stress ◽  
Rake Angle ◽  
Interfacial Shear ◽  
The Other ◽  
Machining Process ◽  
Line Field ◽  
Slip Line Field ◽  
Orthogonal Machining

The elimination of a class of possible slip-line field solutions for orthogonal machining indicates that the process is not uniquely defined. The range of possible solutions for any value of tool rake angle and interfacial shear stress is shown to be associated with large variations in the curvature of the machined chip. Machining conditions are split into two types, for one of which the machined chip will always curl, while the other has the Lee & Shaffer slip-line field as a lower limit of the solution range. The extent of the solution range for any value of friction is found to decrease with increasing rake angle. The analysis is shown to be consistent with certain experimental work available.

High Speed Non-Linear Micro-Milling Dynamics

2012 ◽  
Author(s):  
Eric B. Halfmann ◽  
C. Steve Suh
Keyword(s):  
Slip Line ◽  
Chip Thickness ◽  
Rake Angle ◽  
Micro Milling ◽  
Work Piece ◽  
Formation Mechanisms ◽  
Effective Rake Angle ◽  
Non Linear ◽  
Force Mechanism ◽  
Milling Dynamics

The efficiency of the milling process is limited due to excessive vibrations that negatively impact the tool and work-piece quality. This becomes even more of a concern in micro-milling where sudden tool breakage occurs before the operator can adjust cutting parameters. Due to different chip formation mechanisms in micro-milling, an increased tool-radius to feed-rate ratio, and higher spindle speeds, micro-milling is a highly non-linear process which can produce multiple and broadband frequencies which increase the probability of tool failure. This paper investigates micro-milling through the development and analysis of a 3-D nonlinear micro-milling dynamic model. A lumped mass, spring, damper system is assumed for modeling the dynamic properties of the tool. The force mechanism utilized is a slip-line field model that provides the advantages of being highly dynamic by accounting for the constantly changing effective rake angle and slip-line variables. Accurate prediction of the chip thickness is important in correctly predicting the dynamics of the system since the force mechanism and its variables are a function of the chip thickness. A novel approach for calculating the instantaneous chip thickness which accounts for the tool jumping out of the cut and elastic recovery of the work-piece is presented. The derivation for the effective rake angle is given and the helical angle is accounted for resulting in a 3-D micro-milling model. The results of simulating the model demonstrate its capability of producing the high frequency force components that are seen in experimental data available in literature. The advantages of using this approach over the constant empirical force coefficient approach when studying micro-milling dynamics is discussed and the instability of the system is investigated utilizing instantaneous frequency.

Numerical Research on the Changing of the Slip-Line Field in Hard Turning of Case Hardened Steels

2014 ◽  
Vol 474 ◽  
pp. 399-404
Author(s):  
Gergely Szabó ◽  
János Kundrák
Keyword(s):  
Numerical Simulation ◽  
Slip Line ◽  
Hard Turning ◽  
Rake Angle ◽  
Stagnation Zone ◽  
Line Field ◽  
Slip Line Field ◽  
Hardened Steels ◽  
Numerical Research ◽  
Chip Removal

The article examines the change of the slip-line fields structure with the help of numerical simulation (FEM) in the case of hard turning by gradually decreasing the tool rake angle. During the examination the influencing effect of the stagnation zone on the chip removal was taken into consideration. The stagnation zone is typical of the cutting done by a negative rake angle and it is generally present in front of the tool tip.

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