Model-Based Analysis of the Surface Generation in Microendmilling—Part I: Model Development

2006 ◽  
Vol 129 (3) ◽  
pp. 453-460 ◽  
Author(s):  
Xinyu Liu ◽  
Richard E. DeVor ◽  
Shiv G. Kapoor
Keyword(s):  
Stochastic Model ◽  
Surface Topography ◽  
Deterministic Model ◽  
Elastic Recovery ◽  
Chip Thickness ◽  
Surface Generation ◽  
Generation Model ◽  
Generation Process ◽  
Floor Surface ◽  
Tool Edge

This paper presents the development of models that describe the surface-generation process for microendmilling. The surface-generation models for the sidewall and floor surfaces consist of deterministic and stochastic models. In the sidewall surface-generation model, the deterministic model characterizes the surface topography generated from the relative motion between the major cutting edge and the workpiece material. The model includes the effects of the process kinematics, dynamics, tool edge serration, and process faults (e.g., tool tip runout). The stochastic model predicts the increased surface roughness generated from ploughing due to the significant tool edge radius effect. In the floor surface-generation model, the deterministic model characterizes the three-dimensional surface topography over the entire floor surface and considers the effects of the minimum chip thickness, the elastic recovery, and the transverse vibration. The variation of the ploughing amount across the swept arc of the cutter due to the varying chip load conditions is considered in the stochastic model.

On the Modeling and Analysis of Machining Performance in Micro-Endmilling, Part I: Surface Generation

2004 ◽  
Vol 126 (4) ◽  
pp. 685-694 ◽  
Author(s):  
Michael P. Vogler ◽  
Richard E. DeVor ◽  
Shiv G. Kapoor
Keyword(s):  
Surface Roughness ◽  
Ductile Iron ◽  
Single Phase ◽  
Chip Thickness ◽  
Thickness Effect ◽  
Surface Generation ◽  
Generation Model ◽  
Generation Process ◽  
Machining Performance ◽  
Minimum Chip Thickness

This paper examines the surface generation process in the micro-endmilling of both single-phase and multiphase workpiece materials. We used 508 μm dia endmills with edge radii of 2 and 5 μm to machine slots in ferrite, pearlite, and two ductile iron materials at feed rates ranging from 0.25 to 3.0 μm/flute. A surface generation model to predict the surface roughness for the slot floor centerline is then developed based on the minimum chip thickness concept. The minimum chip thickness values were found through finite element simulations for the ferrite and pearlite materials. The model is shown to accurately predict the surface roughness for single-phase materials, viz., ferrite and pearlite. Two phenomena were found to combine to generate an optimal feed rate for the surface generation of single-phase materials: (i) the geometric effect of the tool and process geometry and (ii) the minimum chip thickness effect. The surface roughness measurements for the ductile iron workpieces indicate that the micromilling surface generation process for multiphase workpiece materials is also affected by the interrupted chip-formation process as the cutting edge moves between phases resulting in burrs at the phase boundaries and the associated increases in surface roughness.

Modeling the Material Microstructure Effects on the Surface Generation Process in Microendmilling of Dual-Phase Materials

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
A. M. Abdelrahman Elkaseer ◽  
S. S. Dimov ◽  
K. B. Popov ◽  
M. Negm ◽  
R. Minev
Keyword(s):  
Chip Thickness ◽  
Machining Process ◽  
Surface Generation ◽  
Dual Phase ◽  
Generation Process ◽  
Phase Boundaries ◽  
Material Microstructure ◽  
Workpiece Material ◽  
Multiphase Materials ◽  
Proposed Model

The anisotropic behavior of the material microstructure when processing multiphase materials at microscale becomes an important factor that has to be considered throughout the machining process. This is especially the case when chip-loads and machined features are comparable in size to the cutting edge radius of the tool, and also similar in scale to the grain sizes of the phases present within the material microstructure. Therefore, there is a real need for reliable models, which can be used to simulate the surface generation process during microendmilling of multiphase materials.This paper presents a model to simulate the surface generation process during microendmilling of multiphase materials. The proposed model considers the effects of the following factors: the geometry of the cutting tool, the feed rate, and the workpiece material microstructure. Especially, variations of the minimum chip thickness at phase boundaries are considered by feeding maps of the material microstructure into the model. Thus, the model takes into account these variations that alter the machining mechanism from a proper cutting to ploughing and vice versa, and are the main cause of microburr formation. By applying the proposed model, it is possible to estimate more accurately the resulting roughness because the microburr formation dominates the surface generation process during microendmilling of multiphase materials. The proposed model was experimentally validated by machining two different samples of dual-phase steel under a range of chip-loads. The roughness of the resulting surfaces was measured and compared to the predictions of the proposed model under the same cutting conditions. The results show that the proposed model accurately predicts the roughness of the machined surfaces by taking into account the effects of material multiphase microstructure. Also, the developed model successfully elucidates the mechanism of microburr formation at the phase boundaries, and quantitatively describes its contributions to the resulting surface roughness after microendmilling.

A Framework of a Surface Generation Model in Fast Tool Servo (FTS) Machining of Optical Microstructures

2007 ◽  
Vol 364-366 ◽  
pp. 1274-1279
Author(s):  
Tsz Chun Kwok ◽  
Chi Fai Cheung ◽  
Suet To ◽  
Wing Bun Lee
Keyword(s):  
Surface Topography ◽  
Optimization Model ◽  
Tool Path ◽  
Rotational Frequency ◽  
Cutting Conditions ◽  
Surface Generation ◽  
Tool Geometry ◽  
Generation Model ◽  
Fast Tool Servo ◽  
Topography Model

In this paper, a framework of surface generation model in the fast tool servo (FTS) machining of optical microstructures will be described. The integrated model is totally composed of a tool path generator (TPG), a surface topography model (STM) and an optimization model (OM). To develop the tool path generator, two parts should be involved. The first part is the tool path generated based on cutting conditions such as the feed rate and spindle speed, the geometry of optical microstructures, and diamond tool geometry. Another part is the synchronized motion generated by the tool actuation of the FTS at a bandwidth higher than the rotational frequency of the spindle. The surface topography model will be generated based on the TPG and used to predict the technological aspects of FTS machining. It takes into the account the kinematic and dynamic characteristics of the cutting process. The former includes the tool path generated by the tool path generator. The later includes the relative vibration between the tool and the workpiece caused by the axial error motion of the spindle as well as the synchronized motion of the FTS system. The optimization model will be undertaken by an iterative algorithm, which will be developed based on the TPG and STM. The OM will be expected to output the verified tool path, the suggested optimum cutting conditions, and the diagrams with predicted cutting performance characteristic and process parameters being investigated. Eventually, the successful development of this surface generation model can contribute for the knowledge of ultra-precision machining with FTS and the further development of the performance of the machining system.

Model-Based Analysis of the Surface Generation in Microendmilling—Part II: Experimental Validation and Analysis

2006 ◽  
Vol 129 (3) ◽  
pp. 461-469 ◽  
Author(s):  
Xinyu Liu ◽  
Richard E. DeVor ◽  
Shiv G. Kapoor
Keyword(s):  
Surface Roughness ◽  
Stochastic Models ◽  
Feed Rate ◽  
Deterministic Model ◽  
Surface Generation ◽  
Tool Geometry ◽  
Process Conditions ◽  
Deterministic Models ◽  
Floor Surface ◽  
Wide Range

The surface-generation models for the microendmilling process developed in Part I (Liu, DeVor, and Kapoor, 2007, J. Manuf. Sci. Eng., 129(3), pp. 453–460) are experimentally calibrated and validated. Partial immersion peripheral downmilling and full-immersion slotting tests are performed over a wide range of feed rates (0.25–12μm∕flute) using two tools with different edge radii (3μm and 2μm) and runout levels (2μm and 3μm) for the investigation of sidewall and floor surface generation, respectively. The deterministic models are validated using large feed-rate tests with errors within 18% for both sidewall and floor surfaces. For low feed-rate tests, the stochastic portion of the surface roughness data are determined from the observed roughness data and the validated deterministic model. The stochastic models are then calibrated and validated using independent data sets. The combination of the deterministic and stochastic models predicts the total surface roughness within 15% for both the sidewall and floor surface over a range of feed rates. The models are then used to simulate micromachined surfaces under a variety of conditions to gain a deeper understanding of the effects of tool geometry (edge radius and edge serration), process conditions, tool tip runout, process kinematics and dynamics on the machined surface roughness.

Correlating Surface Functionality with Machining Conditions in Precision Machining Processes

2004 ◽  
Vol 471-472 ◽  
pp. 112-116
Author(s):  
X.C. Luo ◽  
K. Cheng ◽  
R. Ward
Keyword(s):  
Surface Topography ◽  
Tool Path ◽  
Surface Generation ◽  
Force Model ◽  
Generation Model ◽  
Machining Processes ◽  
Machined Surface ◽  
Surface Functionality ◽  
Precision Turning ◽  
Machining Conditions

This paper attempts to correlate surface functionality generation with machining conditions by computer simulation and machining trials. The linear and nonlinear machining conditions, such as feed rate, built-up-edge, shear- localized chip formation, regenerative chatter are modelled in the light of their physical features. They are the inputs to the integrated surface topography generation model. The dynamic tool path is calculated through the dynamic cutting force model and surface response model. The surface is generated by transforming the tool profile onto the workpiece surface along the dynamic tool path. All of these models are integrated in a user-friendly Matlab Simulink environment. On the basis of the Simulink model, the dynamic simulation is performed to predict the 3D machined surface topography and its functionality. The simulation results have been validated by precision turning trials. The spectrum analysis of the machining dynamics and surface topography shows that surface generation is highly affected by the nonlinear factors in precision turning process. A case study shows the feasibility of generating some functional surface for some product/component through controlling machining variables.

scholarly journals Milled Surface Generation Model for Chip Thickness Detection in Peripheral Milling

Procedia CIRP ◽  
2013 ◽  
Vol 8 ◽  
pp. 450-455 ◽  
Author(s):  
Antonio Scippa ◽  
Niccolò Grossi ◽  
Gianni Campatelli
Keyword(s):  
Chip Thickness ◽  
Surface Generation ◽  
Generation Model ◽  
Peripheral Milling ◽  
Milled Surface

scholarly journals Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Woldegebriel Assefa Woldegerima ◽  
Aychew Wondifraw
Keyword(s):  
Mathematical Model ◽  
Stochastic Model ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Invariant Solution ◽  
Stochastic Approach ◽  
Disease Dynamics ◽  
Treatment Rate ◽  
Invariant Region ◽  
Contact Transmission

AbstractIn this paper we develop a stochastic mathematical model of cholera disease dynamics by considering direct contact transmission pathway. The model considers four compartments, namely susceptible humans, infectious humans, treated humans, and recovered humans. Firstly, we develop a deterministic mathematical model of cholera. Since the deterministic model does not consider the randomness process or environmental factors, we converted it to a stochastic model. Then, for both types of models, the qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction numbers are obtained for both models and compared. From the comparison, we obtained that the basic reproduction number of the stochastic model is much smaller than that of the deterministic one, which means that the stochastic approach is more realistic. Finally, we performed sensitivity analysis and numerical simulations. The numerical simulation results show that reducing contact rate, improving treatment rate, and environmental sanitation are the most crucial activities to eradicate cholera disease from the community.

STOCHASTIC PREDATION MODEL WITH DEPLETION

1979 ◽  
Vol 111 (4) ◽  
pp. 465-470 ◽  
Author(s):  
Guy L. Curry ◽  
Richard M. Feldman
Keyword(s):  
Stochastic Model ◽  
Deterministic Model ◽  
Expected Number ◽  
Numerical Comparisons ◽  
Prey Depletion

AbstractA stochastic model is developed for the expected number of prey taken by a single predator when prey depletion is apparent. The so-called “random predator equation” with prey exploitation of Royama and Rogers is compared with the stochastic model. The numerical comparisons illustrate situations where the deterministic model provides adequate and inadequate approximations.

Study on Feed Offset in Elliptical Vibration Cutting

2014 ◽  
Vol 490-491 ◽  
pp. 600-606
Author(s):  
Jie Qiong Lin ◽  
Jin Guo Han ◽  
Dan Jing ◽  
Xian Jing
Keyword(s):  
Surface Topography ◽  
Surface Quality ◽  
Simulation Analysis ◽  
Three Dimensional ◽  
Curved Surface ◽  
Elliptical Vibration Cutting ◽  
Vibration Cutting ◽  
Elliptical Vibration ◽  
Tool Edge

Elliptical vibration cutting (EVC) process and three dimensional cutting surfaces are analyzed in this paper to understand the formation of surface topography. The model of EVC surface topography is established based on curved surface remove function under the assumption that the tool edge is sharp enough. And simulation analysis of surface topography is conducted with different feed offset ratios. Results indicate that RMS change with feed offset ratios λ. The range of RMS is larger when feed offset ratio ranges from both 0 to 0.4 and 0.6 to 1, while the range is smaller when feed offset ratio changes from 0.4 to 0.6. Whats more, RMS reaches the minimum when feed offset ratio is 0.5. The present research provides some references for reducing the height of vibration ripples and improving EVC surface quality.

Generation mechanism modeling of surface topography in tangential ultrasonic vibration-assisted grinding with green silicon carbide abrasive wheel

2021 ◽  
pp. 095440542110406
Author(s):  
Yutong Qiu ◽  
Jingfei Yin ◽  
Yang Cao ◽  
Wenfeng Ding
Keyword(s):  
Surface Roughness ◽  
Surface Topography ◽  
Ultrasonic Vibration ◽  
Generation Mechanism ◽  
Surface Generation ◽  
Depth Of Cut ◽  
Abrasive Wheel ◽  
Grinding Parameters ◽  
Conventional Grinding ◽  
Ultrasonic Vibration Assisted Grinding

Tangential ultrasonic vibration-assisted grinding (TUAG) has a wide prospect in machining difficult-to-machine materials. However, the surface generation mechanism in TUAG is not fully recovered. This study proposes an analytical model of the surface topography produced by TUAG. Based on the model, the surface topography and roughness are predicted and experimentally verified. In addition, the influence of the grinding parameters on the surface topography is analyzed. The predicted surface topography well coincides with experimental measurements, and the prediction error in surface roughness Ra by the proposed model is less than 5%. Compared with conventional grinding, TUAG produces a surface with more uniform scratches and surface roughness Ra was reduced by up to 27% with the proper parameters. However, the improvement of surface roughness in TUAG is weakened when grinding speed or depth of cut increases. Moreover, the influence of the ultrasonic vibration amplitude on the surface roughness is not monotonous. With the grinding parameters selected in this study, TUAG with an ultrasonic amplitude of 7.5 μm produces the minimum surface roughness.

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