Uncertainty propagation through an empirical model of cutting forces in end milling

2021 ◽  
pp. 1-14
Author(s):  
Abhijit Bhattacharyya ◽  
John Schueller ◽  
Brian Mann ◽  
Tony Schmitz ◽  
Michael Gomez
Keyword(s):  
Monte Carlo ◽  
Uncertainty Analysis ◽  
Cutting Forces ◽  
Prediction Models ◽  
End Milling ◽  
Input Parameter ◽  
Parameter Uncertainties ◽  
Machining Processes ◽  
Systematic Effects ◽  
The Impact

Abstract Empirical mathematical models of cutting forces in machining processes use experimentally determined input parameters to make predictions. A general method for propagation of input parameter uncertainties through such predictive models is developed. Sources of uncertainty are identified and classified. First, a classical uncertainty procedure is employed to estimate uncertainties associated with the data reduction equation using a first order Taylor series expansion. Small values of input parameter uncertainties justify this local linearization. Coverage factors required to estimate confidence intervals are computed based on appropriate underlying statistical distributions. A root sum of squares method yields the overall expanded uncertainty in force predictions. A popular model used for predicting cutting forces in end milling is selected to demonstrate the procedure, but the demonstrated approach is general. The analysis is applied to experimental data. Force predictions are quoted along with a confidence interval attached to them. An alternative analysis based on Monte Carlo simulations is also presented. This procedure yields different insights compared with the classical uncertainty analysis and complements it. Monte Carlo simulation provides combined uncertainties directly without sensitivity calculations. Classical uncertainty analysis reveals the impacts of random effects and systematic effects separately. This information can prompt the user to improve the experimental setup if the impact of systematic effects is observed to be comparatively large. The method of quoting an estimate of the uncertainty in force predictions presented in this paper will permit users to assess the suitability of given empirical force prediction models in specific applications.

scholarly journals Modified Mechanistic Model Based on Gaussian Process Adjusting Technique for Cutting Force Prediction in Micro-End Milling

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Xiaoping Liao ◽  
Zhenkun Zhang ◽  
Kai Chen ◽  
Kang Li ◽  
Junyan Ma ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Cutting Force ◽  
Cutting Forces ◽  
End Milling ◽  
Mechanistic Model ◽  
Machining Process ◽  
Mechanistic Models ◽  
Machining Processes ◽  
Model Based ◽  
Micro End Milling

Micro-end milling is in common use of machining micro- and mesoscale products and is superior to other micro-machining processes in the manufacture of complex structures. Cutting force is the most direct factor reflecting the processing state, the change of which is related to the workpiece surface quality, tool wear and machine vibration, and so on, which indicates that it is important to analyze and predict cutting forces during machining process. In such problems, mechanistic models are frequently used for predicting machining forces and studying the effects of various process variables. However, these mechanistic models are derived based on various engineering assumptions and approximations (such as the slip-line field theory). As a result, the mechanistic models are generally less accurate. To accurately predict cutting forces, the paper proposes two modified mechanistic models, modified mechanistic models I and II. The modified mechanistic models are the integration of mathematical model based on Gaussian process (GP) adjustment model and mechanical model. Two different models have been validated on micro-end-milling experimental measurement. The mean absolute percentage errors of models I and II are 7.76% and 6.73%, respectively, while the original mechanistic model’s is 15.14%. It is obvious that the modified models are in better agreement with experiment. And model II performs better between the two modified mechanistic models.

Monte-Carlo Simulation of the Theoretical Site Response Variability at Turkey Flat, California, Given the Uncertainty in the Geotechnically Derived Input Parameters

1993 ◽  
Vol 9 (4) ◽  
pp. 669-701 ◽  
Author(s):  
Edward H. Field ◽  
Klaus H. Jacob
Keyword(s):  
Monte Carlo ◽  
Physical Model ◽  
Site Response ◽  
Input Parameter ◽  
Model Parameters ◽  
Spectral Ratios ◽  
Parameter Uncertainties ◽  
Theoretical Predictions ◽  
High Degree ◽  
Geotechnical Studies

In the weak-motion phase of the Turkey Flat blind-prediction effort, it was found that given a particular physical model of each sediment site, various theoretical techniques give similar estimates of the site response. However, it remained to be determined how uncertainties in the physical model parameters influence the theoretical predictions. We have studied this question by propagating the physical parameter uncertainties into the theoretical site-response predictions using monte-carlo simulations. The input-parameter uncertainties were estimated directly from the results of several independent geotechnical studies performed at Turkey Flat. While the computed results generally agree with empirical site-response estimates (average spectral ratios of earthquake recordings), we found that the uncertainties lead to a high degree of variability in the theoretical predictions. Most of this variability comes from poor constraints on the shear-wave velocity and thickness of a thin (∼2m) surface layer, and on the attenuation of the sediments. Our results suggest that in site-response studies which rely exclusively on geotechnically based theoretical predictions, it will be important that the variability resulting from input-parameter uncertainties is recognized and accounted for.

scholarly journals Evaluation of Ball End Micromilling for Ti6Al4V ELI Microneedles Using a Nanoadditive Under MQL Condition

2021 ◽  
Author(s):  
Pavel Celis ◽  
Elisa Vazquez ◽  
Cintya G. Soria-Hernández ◽  
Diego Bargnani ◽  
Ciro A. Rodriguez ◽  
...  
Keyword(s):  
Cutting Forces ◽  
End Milling ◽  
Experimental Tests ◽  
Burr Formation ◽  
Tool Performance ◽  
Micro End Milling ◽  
Product Surface ◽  
Microneedle Arrays ◽  
The Impact ◽  
Minimum Quantity Of Lubrication

AbstractThe use of nanoadditives in lubricants has gained much attention to the research community due to the enhancement of tribological properties and cooling capabilities. This paper studies the advantages of using a MQL (Minimum Quantity of Lubrication) system and nanoadditive in the manufacture of microneedle arrays in Ti6Al4V ELI alloy. Tungsten carbide ball nose tools with a cutting diameter of 200 µm were used in experimental tests. Surface and dimensional characterization was performed to evaluate the impact of a nanoadditive to a vegetable-based oil. Additionally, cutting forces and cutting edge radius (CER) were measured while needles were machined. Experimental tests confirmed that micro end milling with nanoadditives provide slightly better dimensional features and low cutting forces compared to oil. The performance of nanoadditives resulted in a reduction of surface roughness (~ 0.3 μm). Qualitative study of microneedles illustrated burr formation on needle surface manufactured without a nanoadditive solution. Results reveal an increment of CER using low feed rate values (2.0 µm/flute) while a reduction of CER was observed with feed rates up to 2.5 µm/flute. Our results indicated that the addition of nanoadditives to vegetable oil promotes a better product surface topography and cutting tool performance.

Human Exposure Assessment I: Understanding the Uncertainties

1992 ◽  
Vol 8 (5) ◽  
pp. 297-320 ◽  
Author(s):  
Gary K. Whitmyre ◽  
Jeffrey H. Driver ◽  
Michael E. Ginevan ◽  
Robert G. Tardiff ◽  
Scott R. Baker
Keyword(s):  
Monte Carlo ◽  
Exposure Assessment ◽  
Ingestion Rate ◽  
Input Parameter ◽  
Quantitative Aspect ◽  
Worst Case ◽  
Exposed Population ◽  
Total Variability ◽  
Human Exposure Assessment ◽  
The Impact

Exposure estimates produced using predictive exposure assessment methods are associated with a number of uncertainties that relate to the inherent variability of the values for a given input parameter (e.g., body weight, ingestion rate, inhalation rate) and to unknowns concerning the representativeness of the assumptions and methods used. Despite recent or ongoing consensus-building efforts that have made significant strides forward in promoting consistency in methodologies and parameter default values, the potential variability in the output exposure estimates has not been adequately addressed from a quantitative aspect. This is exemplified by remaining tendencies within federal and state agencies to use worst-case approaches for exposure assessment. In this study, range-sensitivity and Monte Carlo analyses were performed on several different exposure scenarios in order to illustrate the impact of the variability in input parameters on the total variability of the exposure output. The results of this study indicate that the variability associated with the example scenarios range up to more than four orders of magnitude when just some of the parameters are allowed to vary. Comparison of exposure estimates obtained using Monte Carlo simulations (in which selected parameters were allowed to vary over their observed ranges) to exposure estimates obtained using standard parameter default assumptions demonstrate that a default value approach can produce an exposure estimate that exceeds the 95th percentile exposure in an exposed population.

Uncertainty analysis of calibrated parameter values of an urban storm water quality model using metropolis monte carlo algorithm

1997 ◽  
Vol 36 (5) ◽  
pp. 141-148 ◽  
Author(s):  
A. Mailhot ◽  
É. Gaume ◽  
J.-P. Villeneuve
Keyword(s):  
Monte Carlo ◽  
Uncertainty Analysis ◽  
Model Calibration ◽  
Monte Carlo Algorithm ◽  
Storm Water ◽  
Model Parameters ◽  
Calibration Data ◽  
Parameter Uncertainties ◽  
Metropolis Monte Carlo ◽  
Parameter Values

The Storm Water Management Model's quality module is calibrated for a section of Québec City's sewer system using data collected during five rain events. It is shown that even for this simple model, calibration can fail: similarly a good fit between recorded data and simulation results can be obtained with quite different sets of model parameters, leading to great uncertainty on calibrated parameter values. In order to further investigate the lack of data and data uncertainty impacts on calibration, we used a new methodology based on the Metropolis Monte Carlo algorithm. This analysis shows that for a large amount of calibration data generated by the model itself, small data uncertainties are necessary to significantly decrease calibrated parameter uncertainties. This also confirms the usefulness of the Metropolis algorithm as a tool for uncertainty analysis in the context of model calibration.

scholarly journals DYNAMOMETER CHOICE FOR CUTTING FORCE MEASUREMENT AT END MILLING

2019 ◽  
Vol 2019 (5) ◽  
pp. 15-24
Author(s):  
Борис Пономарев ◽  
Boris Ponomarev ◽  
Ши Нгуен ◽  
Shi Nguen
Keyword(s):  
Cutting Forces ◽  
Force Measurement ◽  
End Milling ◽  
Dynamics Modeling ◽  
Cutting Force Measurement ◽  
Theoretical Investigations ◽  
Measurement Series ◽  
Definition Of ◽  
Tool Position ◽  
The Impact

In the paper there are presented results of the comparison of dynamometers of three types with reference to measurements connected with the definition of values making cutting forces in the course of blank finish five-coordinate milling with spherical-cylindrical mill cutters with the diameter from 5 to 10 mm. At that a particular attention is paid to the protection of these devices against external influences, to the processing possibility of data obtained in measuring equipment with the use of program applications. The measurement series of cutting forces with the aid of a stationary dynamometer and a rotary one allowed revealing basic advantages and drawbacks of both of them. The assessment results of forces measured at tool idling and in the course of machining allowed drawing a conclusion of that the use of the stationary dynamometer of Kistler Type 9129AA is most preferable. The measurement series carried out allowed confirming the results of theoretical investigations and machining dynamics modeling, and also defining the impact of a tool position regarding a normal upon measurement processes and data reliability.

Prediction of Cutting Forces during End Milling using 3D FEM based Simulation Analysis

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
T. Mugilan ◽  
T. Alwarsamy
Keyword(s):  
Cutting Forces ◽  
High Speed ◽  
Metal Removal ◽  
End Milling ◽  
Cutting Parameters ◽  
Simulation Software ◽  
3D Fem ◽  
Cutting Force Prediction ◽  
The Impact ◽  
Deform 3D

Material removal process for dies, moulds and additionally diverse aircraft parts can be made possible by the highspeed end milling operation. Devious cutting forces are created by the impact of various cutting parameters in course with high speed milling process. Due to this phenomenon the wear and chatter of tool can occur. Cutting force prediction is useful method to reduce the chatter occurrence during the machining of hardest materials. DEFORM 3D is an important simulation software which is used for the analysis of complicated metal removal processes. In this work, the tool insert was designed by Solid Works modelling software. The FEM simulation of high-speed end milling of Titanium-Vanadium based alloy was carried out in Deform 3D simulation software to obtain the cutting forces. The material behaviour was modelled with a classical constitutive material equation and was applied in the FEM code to predict the effective stress, strain, temperature and cutting forces towards the impact of cutting parameters. Analysis of variance is achieved to determine the impact of cutting forces with help of Taguchi method in Minitab-17. L16 orthogonal array was used to conduct the analysis of high speed end milling.

Cutting Force Model for Heat Assisted Titanium Alloy Milling

2014 ◽  
Vol 887-888 ◽  
pp. 1191-1194 ◽  
Author(s):  
Chang Yi Liu
Keyword(s):  
Titanium Alloy ◽  
Cutting Forces ◽  
Orthogonal Cutting ◽  
Shear Banding ◽  
Cutting Speed ◽  
Constitutive Law ◽  
Force Model ◽  
Machining Processes ◽  
Machine Material ◽  
The Impact

Thermal energy sources have been applied for softening the difficult-to-machine material when it is combined with conventional machining processes. Cutting forces has been reduced during the process. To investigate the plastic deformation property of workpiece materials heated by thermal sources, and its influence to the cutting forces, the analytical model of orthogonal cutting is established. The impact of cutting speed and initial temperature of the shear banding to the cutting forces are taken account of, based on adiabatic shear banding model and Johnson-Cook material constitutive law. The shear banding average shear stress failure criteria has been proposed to decide the fracture between workpiece and chip. Simulation has been carried out and compared with experimental data of laser-heat assisted titanium alloy milling, showing good agreement.

scholarly journals An Experimental Evaluation of Particle Impact Dampers Applied on the Tool for Milling of Hardened Steel Complex Surface

2021 ◽  
Author(s):  
Victor Rossi Saciotto ◽  
Anselmo Eduardo Diniz
Keyword(s):  
Complex Geometry ◽  
End Milling ◽  
Removal Rate ◽  
Complex Surface ◽  
Momentum Exchange ◽  
Machining Processes ◽  
Milling Tool ◽  
Highly Nonlinear ◽  
The Impact ◽  
Finishing Tool

Abstract In the manufacturing of dies and molds, vibrations may represent serious problems, since the finishing tool used is usually slender (high Length / Diameter ratio) in order to machine deep cavities with complex geometry, typical of these products. Vibration is an undesirable phenomenon in any machining operation as it can lead to poor surface finish, lower material removal rate and increased tool wear. The use of impact dampers in the tool has proven to be an effective method for reducing vibration in machining processes. Damping occurs through energy dissipation and linear momentum exchange during intermittent collisions between the main structure (in this case the milling tool) and a free mass (spheres or cylinders placed within a tool cavity). Although efficient, these types of dampers are highly nonlinear. Thus, the aim of this work is to analyze the effect of different materials and geometries (steel spheres, tungsten spheres and steel cylinders) acting as impact dampers inside a ball nose end milling tool. To do so, milling of a convex D6 steel surface was performed, comparing commercial tool holders with dampened ones. The results showed that the tools with impact dampers generated lower values of roughness in the workpiece (around 30% of the value observed in the conventional steel tool holder for the case of steel cylinders and around 40% for both spheres) and presented lower levels of vibration when compared to the same tool without the impact damper, mainly in the machining of workpiece regions where radial and tangential forces are predominant. The tool which used tungsten spheres generated roughness surfaces similar to those obtained with steel spheres, while the tool that used steel cylinders only generated lower roughness in the regions where the axial force component is not predominant, which shows that their performance is highly dependent on the resulting force direction.

Surface Topography Predication in High-Speed End Milling of Flexible Milling System

2010 ◽  
Vol 29-32 ◽  
pp. 1832-1837
Author(s):  
Zhong Qun Li ◽  
Shuo Li ◽  
Ming Zhou
Keyword(s):  
Surface Topography ◽  
Cutting Forces ◽  
High Speed ◽  
End Milling ◽  
Cutting Parameters ◽  
Numerical Approach ◽  
Depth Of Cut ◽  
Machined Surface ◽  
Milling Operation ◽  
The Impact

During milling operation, the cutting forces will induce vibrations on both the cutting tool and the workpiece, which will affect the topography of the machined surface. Based on the Z-map representation of the workpiece, an improved model is presented to predicate the 3D surface topography along with the dynamic cutting forces during an end milling operation. A numerical approach is employed to solve the differential equations governing the dynamics of the milling system. The impact of cutting parameters such as the feedrate, the axial depth of cut and the dynamic characteristic of milling system on the surface topography is investigated by simulation. The all above can provide some instructive directions to the manufacturing engineers in determining the optimal cutting conditions of an end milling operation.

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