Kinematic Model of Dynamic Drilling Process

2004 ◽  
Author(s):  
Jochem C. Roukema ◽  
Yusuf Altintas
Keyword(s):  
Mathematical Model ◽  
Rigid Body ◽  
Kinematic Model ◽  
Chip Thickness ◽  
Body Motion ◽  
Depth Of Cut ◽  
Force Model ◽  
Drilling Process ◽  
Structural Vibrations ◽  
Radial Depth

A mathematical model of the torsional-axial chatter vibrations in drilling is presented. The model considers the exact kinematics of both rigid body, and coupled torsional and axial vibrations of the drill. The drill is modeled as a pretwisted beam that exhibits axial deflections due to torque and thrust loading. A mechanistic cutting force model is used to model the cutting torque and thrust as a function of feedrate, speed, radial depth of cut, and drill geometry. The drill rotates and feeds axially into the workpiece while the structural vibrations are excited by the cutting torque and thrust force. The exact location of the drill edge is predicted using the model, and the generated surface is digitized at discrete time intervals. The distribution of chip thickness, which is affected by both rigid body motion and structural vibrations, is evaluated by subtracting the presently generated surface from the previous one. The model considers nonlinearities in cutting coefficients, tool jumping out of cut and overlapping of multiple regeneration waves. The dynamic chip thickness obtained from the true kinematics model allows simultaneous prediction of force, torque, power and dimensional form errors left on the surface. The time domain simulation model allows prediction of stability lobes. The paper provides details of the mathematical model, supported by experimental results of both stable and unstable cuts.

Micro Flat End Milling Simulation Model With Instantaneous Plowing Area Prediction

2016 ◽  
Vol 4 (2) ◽  
Author(s):  
Abdolreza Bayesteh ◽  
Junghyuk Ko ◽  
Martin Byung-Guk Jun
Keyword(s):  
Feed Rate ◽  
Tool Path ◽  
End Milling ◽  
Chip Thickness ◽  
Depth Of Cut ◽  
Uncut Chip Thickness ◽  
Chip Area ◽  
Edge Radius ◽  
Wide Range ◽  
Radial Depth

There is an increasing demand for product miniaturization and parts with features as low as few microns. Micromilling is one of the promising methods to fabricate miniature parts in a wide range of sectors including biomedical, electronic, and aerospace. Due to the large edge radius relative to uncut chip thickness, plowing is a dominant cutting mechanism in micromilling for low feed rates and has adverse effects on the surface quality, and thus, for a given tool path, it is important to be able to predict the amount of plowing. This paper presents a new method to calculate plowing volume for a given tool path in micromilling. For an incremental feed rate movement of a micro end mill along a given tool path, the uncut chip thickness at a given feed rate is determined, and based on the minimum chip thickness value compared to the uncut chip thickness, the areas of plowing and shearing are calculated. The workpiece is represented by a dual-Dexel model, and the simulation properties are initialized with real cutting parameters. During real-time simulation, the plowed volume is calculated using the algorithm developed. The simulated chip area results are qualitatively compared with measured resultant forces for verification of the model and using the model, effects of cutting conditions such as feed rate, edge radius, and radial depth of cut on the amount of shearing and plowing are investigated.

Dynamic Modeling and Response Analysis of a Planar Rigid-Body Mechanism With Clearance

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
Chen Xiulong ◽  
Jiang Shuai ◽  
Deng Yu ◽  
Wang Qing
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Contact Force ◽  
Kinematic Model ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Prototype Model ◽  
Force Model ◽  
Normal Contact

In order to understand dynamic responses of planar rigid-body mechanism with clearance, the dynamic model of the mechanism with revolute clearance is proposed and the dynamic analysis is realized. First, the kinematic model of the revolute clearance is built; the amount of penetration depth and relative velocity between the elements of the revolute clearance joint is obtained. Second, Lankarani-Nikravesh (L-N) and the novel nonlinear contact force model are both used to describe the normal contact force of the revolute clearance, and the tangential contact force of the revolute clearance is built by modified Coulomb friction model. Third, the dynamic model of a two degrees-of-freedom (2DOFs) nine bars rigid-body mechanism with a revolute clearance is built by the Lagrange equation. The fourth-order Runge–Kutta method has been utilized to solve the dynamic model. And the effects of different driving speeds of cranks, different clearance values, and different friction coefficients on dynamic response are analyzed. Finally, in order to prove the validity of numerical calculation result, the virtual prototype model of 2DOFs nine bars mechanism with clearance is modeled and its dynamic responses are analyzed by adams software. This research could supply theoretical basis for dynamic modeling, dynamic behaviors analysis, and clearance compensation control of planar rigid-body mechanism with clearance.

Dynamics and Stability of Turn-Milling Operations With Varying Time Delay in Discrete Time Domain

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Alptunc Comak ◽  
Yusuf Altintas
Keyword(s):  
Time Domain ◽  
Chip Thickness ◽  
Body Motion ◽  
Depth Of Cut ◽  
Time Varying Delay ◽  
Milling Operations ◽  
Varying Time Delay ◽  
The Stability ◽  
Five Axis ◽  
Turn Milling

Turn-milling machines are widely used in industry because of their multifunctional capabilities in producing complex parts in one setup. Both milling cutter and workpiece rotate simultaneously while the machine travels in three Cartesian directions leading to five axis kinematics with complex chip generation mechanism. This paper presents a general mathematical model to predict the chip thickness, cutting force, and chatter stability of turn milling operations. The dynamic chip thickness is modeled by considering the rigid body motion, relative vibrations between the tool and workpiece, and cutter-workpiece engagement geometry. The dynamics of the process are governed by delayed differential equations by time periodic coefficients with a time varying delay contributed by two simultaneously rotating spindles and kinematics of the machine. The stability of the system has been solved in semidiscrete time domain as a function of depth of cut, feed, tool spindle speed, and workpiece speed. The stability model has been experimentally verified in turn milling of Aluminum alloy cut with a helical cylindrical end mill.

Kinematics Analysis of the Chipping Process Using the Circular Diamond Saw Blade

1999 ◽  
Vol 121 (2) ◽  
pp. 257-264 ◽  
Author(s):  
H. D. Jerro ◽  
S. S. Pang ◽  
C. Yang ◽  
R. A. Mirshams
Keyword(s):  
Kinematic Model ◽  
Chip Thickness ◽  
Depth Of Cut ◽  
Machining Parameters ◽  
New Model ◽  
Spacing Ratio ◽  
Diamond Saw ◽  
D Values ◽  
Saw Blade ◽  
Machining Parameter

One of the primary goals in the design of a diamond blade cutting system is to reduce the cutting force. By understanding the fundamentals of the kinematics of the sawing operation, these forces can be lowered and even optimized with respect to the machining parameters. In this work the material chipping geometries have been mathematically defined and derived through kinematic analysis. These geometries are bounded by four curves and depend on the parameters: depth of cut h, blade diameter D, transverse rate of the workpiece νT, peripheral speed of the saw blade νP, and grit spacing λ. From these chipping geometries, chip area and thickness relations have been obtained. A relation for the mean chip thickness to grit spacing ratio (tc/λ) has also been obtained as a function of the nondimensional machining parameter ratios, h/D and νT/νP. The effects of these parameters on tc were also investigated. It was found that increasing ω and D, reduces the chip thickness. Contrarily, increasing νT, λ, and h, increases the magnitude of the chip thickness. A review of older chipping models was performed, comparing well with the developed model. The results show an excellent agreement between the new model and the older ones. However, at moderately small to large h/D values the new model yields a more exact result. Thus, for h/D values greater than 0.08, it is recommended that the kinematic model be used to compute tc and other pertinent sawing parameters (i.e., grit force and grinding ratio) which are a function of tc.

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.

Dimension Error in the Presence of Process and Machine Error in End Milling

2010 ◽  
Author(s):  
H. N. Chiang ◽  
J. J. Wang ◽  
F. C. Hsu ◽  
Y. J. Li
Keyword(s):  
Prediction Model ◽  
End Milling ◽  
Depth Of Cut ◽  
Force Model ◽  
Surface Error ◽  
Machine Errors ◽  
Process Error ◽  
Radial Depth ◽  
Measuring Machine ◽  
Cutting Point

The contribution of process and machine errors to the dimension error of machined part was investigated in this study. End milling was performed in two different types of machine configuration (XFYZ and XYFZ) in order to evaluate the dimension error caused by process and spatial errors of machine tools. The spatial machine errors were obtained by the sequential diagonal method with the Doppler laser displacement meter. For the process error, a simple average force model for a single cutting point and the identified structure stiffness is used to calculate the force induced surface error along the tool axis direction. Surface error due to tool runout effect is also considered as a contributing factor to the process error. Finally, the prediction model of dimension error for end milling was established by analyzing the machine positioning error and process error. The error prediction model was confirmed by different radial depth of cut and cutting fluid supply parameters. The dimension error of machined part was measured by the coordinate measuring machine. The experimental results reveal that the proposed model is useful in predicting the dimension error in an end milling process.

Cutting Force Changes during One Cut in End Milling with a Throw-Away Insert - Difference between Up-Cut and Down-Cut –

2019 ◽  
Vol 825 ◽  
pp. 123-128
Author(s):  
Kota Matsuda ◽  
Ryutaro Tanaka ◽  
Katsuhiko Sekiya ◽  
Keiji Yamada
Keyword(s):  
Cutting Force ◽  
End Milling ◽  
Tangential Force ◽  
Chip Thickness ◽  
Radial Force ◽  
Depth Of Cut ◽  
Radial Depth ◽  
Aisi 1045 ◽  
Tangential Forces ◽  
Coated Carbide

In this study, the transition of cutting force in the tangential and radial direction during one cut was investigated in milling of AISI-1045, AISI-304, and Ti-6Al-4V with a TiN coated carbide throw-away insert. In the case of 1045 and Ti-6Al-4V, there was not obvious difference in tangential forces between up-cut and down-cut. However, up-cut showed larger radial force than down-cut in any material. In down-cut, tangential force showed almost the same regardless of radial depth of cut. 304 and Ti-6Al-4V caused larger radial force with the increase of radial depth of cut at the same cut chip thickness.

scholarly journals Modeling and optimization of cutting forces and effect of turning parameters on SiCp/Al 45% vs SiCp/Al 50% metal matrix composites: a comparative study

2021 ◽  
Vol 3 (7) ◽  
Author(s):  
Rashid Ali Laghari ◽  
Jianguang Li
Keyword(s):  
Mathematical Model ◽  
Cutting Force ◽  
Feed Rate ◽  
Cutting Forces ◽  
Positive Response ◽  
Cutting Speed ◽  
Machining Process ◽  
Depth Of Cut ◽  
Force Model ◽  
Sic Particles

Abstract In this study, the proposed experimental and second-order model for the cutting forces were developed through several parameters, including cutting speed, feed rate, depth of cut, and two varying content of SiCp. Cutting force model was developed and optimized through RSM and compared for two different percentages of components SiCp/Al 45% and SiCp/Al 50%. ANOVA is used for Quantitative evaluation, the main effects plot along with the evaluation using different graphs and plots including residual analysis, contour plots, and desirability functions for cutting forces optimization. It provides the finding for choosing proper parameters for the machining process. The plots show that during increment with depth of cut in proportion with feed rate are able to cause increments in cutting forces. Higher cutting speed shows a positive response in both the weight percentage of SiCp by reducing the cutting force because of higher cutting speed increases. A very fractional increasing trend of cutting force was observed with increasing SiCp weight percentages. Both of the methods such as experiment and model-predicted results of SiCp/Al MMC materials were thoroughly evaluated for analyzing cutting forces of SiCp/Al 45%, and SiCp/Al 50%, as well as calculated the error percentages also found in an acceptable range with minimal error percentages. Article Highlights This study focuses on the effect of cutting parameters as well as different percentage of SiC particles on the cutting forces, while comparing the results of both SiC particles such as SiCp/Al 45%, and SiCp/Al 50% the result shows that there isn’t fractional amount of impact on the cutting force with nominal increasing percentages of SiC particles. Cutting speed in machining process of SiCp/Al shows positive response in reducing the cutting forces, however, increasing amount of depth of cut followed by increasing feed rate creates fluctuations in cutting force and thus increases the cutting force in the cutting process. The developed RSM mathematical model which is based on the box Behnken design show excellent competence for predicting and suggesting the machining parameters for both SiCp/Al 45%, and SiCp/Al 50% and the RSM mathematical model is feasible for optimization of the machining process with good agreement to experimental values.

scholarly journals Kinematics of Serial Manipulators

2020 ◽  
Author(s):  
Ivan Virgala ◽  
Michal Kelemen ◽  
Erik Prada
Keyword(s):  
Rigid Body ◽  
Numerical Solutions ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Body Motion ◽  
Robot Kinematics ◽  
Kinematic Modeling ◽  
Open Chain ◽  
Serial Manipulators ◽  
Serial Robot

This book chapter deals with kinematic modeling of serial robot manipulators (open-chain multibody systems) with focus on forward as well as inverse kinematic model. At first, the chapter describes basic important definitions in the area of manipulators kinematics. Subsequently, the rigid body motion is presented and basic mathematical apparatus is introduced. Based on rigid body conventions, the forward kinematic model is established including one of the most used approaches in robot kinematics, namely the Denavit-Hartenberg convention. The last section of the chapter analyzes inverse kinematic modeling including analytical, geometrical, and numerical solutions. The chapter offers several examples of serial manipulators with its mathematical solution.

Autoresonant Tuning and Control in Ultrasonic Vibration Assisted Drilling Process

2006 ◽  
Vol 505-507 ◽  
pp. 823-828 ◽  
Author(s):  
Yu Chieh Chen ◽  
Yunn Shiuan Liao ◽  
J.D. Fan
Keyword(s):  
Cutting Parameters ◽  
Milling Process ◽  
Performance Characteristics ◽  
Depth Of Cut ◽  
Drilling Process ◽  
Side Milling ◽  
Relational Analysis ◽  
Radial Depth ◽  
Grey Relational ◽  
Optimal Cutting Parameters

This paper presents an optimal cutting-parameter design of heavy cutting in side milling for SUS304 stainless steel. The orthogonal array with relational analysis is applied to optimize the side milling process with multiple performance characteristics. A grey relational grade obtained from the grey relational analysis is used as a performance index to determine the optimal cutting parameters. The selected cutting parameters are cutting speed, feed per tooth, axial depth of cut, and radial depth of cut, while the considered performance characteristics are tool life and metal removal rate. Experimental results have shown that cutting performance in the side milling process for heavy cutting can be significantly improved through this approach.

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