scholarly journals Investigating Multiscale Phenomena in Machining: The Effect of Cutting-Force Distribution Along the Tool’s Rake Face on Process Stability

2015 ◽  
Author(s):  
Tamás G. Molnár ◽  
Tamás Insperger ◽  
S. John Hogan ◽  
Gábor Stépán
Keyword(s):  
Cutting Force ◽  
Distributed Delay ◽  
Chip Thickness ◽  
Rake Face ◽  
Center Manifold Reduction ◽  
Force System ◽  
Force Magnitude ◽  
Stability Lobe ◽  
The Stability ◽  
Stability Limits

Regenerative machine tool chatter is investigated in a nonlinear single-degree-of-freedom model of turning processes. The nonlinearity arises from the dependence of the cutting-force magnitude on the chip thickness. The cutting-force is modeled as the resultant of a force system distributed along the rake face of the tool. It introduces a distributed delay in the governing equations of the system in addition to the well-known regenerative delay, which is often referred to as the short regenerative effect. The corresponding stability lobe diagrams are depicted, and it is shown that a subcritical Hopf bifurcation occurs along the stability limits in the case of realistic cutting-force distributions. Due to the subcriticality a so-called unsafe zone exists near the stability limits, where the linearly stable cutting process becomes unstable to large perturbations. Based on center-manifold reduction and normal form calculations analytic formulas are obtained to estimate the size of the unsafe zone.

scholarly journals Estimation of the Bistable Zone for Machining Operations for the Case of a Distributed Cutting-Force Model

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Tamás G. Molnár ◽  
Tamás Insperger ◽  
S. John Hogan ◽  
Gábor Stépán
Keyword(s):  
Cutting Force ◽  
Distributed Delay ◽  
Nonlinear Function ◽  
Force Model ◽  
Center Manifold Reduction ◽  
Stability Boundaries ◽  
Force System ◽  
Bistable Region ◽  
The Stability ◽  
Machining Operations

Regenerative machine tool chatter is investigated for a single-degree-of-freedom model of turning processes. The cutting force is modeled as the resultant of a force system distributed along the rake face of the tool, whose magnitude is a nonlinear function of the chip thickness. Thus, the process is described by a nonlinear delay-differential equation, where a short distributed delay is superimposed on the regenerative point delay. The corresponding stability lobe diagrams are computed and are shown numerically that a subcritical Hopf bifurcation occurs along the stability boundaries for realistic cutting-force distributions. Therefore, a bistable region exists near the stability boundaries, where large-amplitude vibrations (chatter) may arise for large perturbations. Analytical formulas are obtained to estimate the size of the bistable region based on center manifold reduction and normal form calculations for the governing distributed-delay equation. The locally and globally stable parameter regions are computed numerically as well using the continuation algorithm implemented in dde-biftool. The results can be considered as an extension of the bifurcation analysis of machining operations with point delay.

Predictive Modeling of Nonlinear Regenerative Chatter via Measurement, Analysis, and Simulation

1999 ◽  
Author(s):  
J. R. Pratt ◽  
M. A. Davies ◽  
M. D. Kennedy ◽  
T. Kalmár-Nagy
Keyword(s):  
Cutting Force ◽  
Initial Conditions ◽  
Stability Boundary ◽  
Chip Thickness ◽  
Cutting Parameters ◽  
Computational Techniques ◽  
Regenerative Chatter ◽  
Stability Lobe ◽  
Measurement Analysis ◽  
On Chip

Abstract A single-degree-of-freedom active cutting fixture is employed to reveal and analyse the hysteretic nature of the lobed stability boundary in a simple machining experiment. Specifically, the seventh stability lobe of a regenerative cutting process is mapped using experimental, analytical, and computational techniques. Then, taking width of cut as a control parameter, the transition from stable cutting to chatter is observed experimentally. The cutting stability is found to possess a substantial hysteresis so that either stable or chattering tool motions can exist at the same nominal cutting parameters, depending on initial conditions. This behavior is predicted by applying nonlinear regenerative chatter theory to an empirical characterization of the cutting force dependence on chip thickness. Time-domain simulations that incorporate both the nonlinear cutting force dependence on chip thickness and the multiple-regenerative effect due to the tool leaving the cut are shown to agree both qualitatively and quantitatively with experiment.

scholarly journals Approach for multiscale modeling the thermomechanical tool load in gear hobbing

2021 ◽  
Author(s):  
Nico Troß ◽  
Jens Brimmers ◽  
Thomas Bergs
Keyword(s):  
Cutting Force ◽  
Chip Thickness ◽  
Multiscale Model ◽  
Cutting Edge ◽  
Rake Face ◽  
Fe Simulations ◽  
Gear Hobbing ◽  
Input Variables ◽  
The One

AbstractIn this report, an approach is presented how a geometric penetration calculation can be combined with FE simulations to a multiscale model, which allows an efficient determination of the thermomechanical load in gear hobbing. FE simulations of the linear-orthogonal cut are used to derive approximate equations for calculating the cutting force and the rake face temperature. The hobbing process is then simulated with a geometric penetration calculation and uncut chip geometries are determined for each generating position. The uncut chip geometries serve as input variables for the derived equations, which are solved at each point of the cutting edge for each generating position. The cutting force is scaled according to the established procedure of discrete addition of the forces along the cutting edge over all individual cross-section elements. For the calculation of the temperature, an approach is presented how to consider a variable chip thickness profile. Based on this, the temperature distribution on the rake face is calculated. The model is verified on the one hand by cutting force measurements in machining trials and on the other hand by an FE simulation of a full engagement of a hob tooth.

scholarly journals EFFICIENT DETERMINATION OF STABILITY LOBE DIAGRAMS DEPLOYING AN AUTOMATED, DATA-BASED ONLINE NC PROGRAM ADAPTION

2021 ◽  
Vol 2021 (4) ◽  
pp. 4830-4835
Author(s):  
CHRISTIAN BRECHER ◽  
◽  
RALPH KLIMASCHKA ◽  
ALEXANDER STEINERT ◽  
STEPHAN NEUS ◽  
...  
Keyword(s):  
Cutting Parameters ◽  
Cutting Depth ◽  
Fast Detection ◽  
Stability Lobe ◽  
Nc Program ◽  
The Stability ◽  
Machining Operations ◽  
Stability Limits ◽  
Analytical Approaches ◽  
Stability Lobe Diagrams

Process instabilities due to regenerative chatter pose significant limitations on the achievable material removal rates and thus on the profitability of machining operations. Stability lobe diagrams serve to exploit the maximum yet stable cutting depth and can be determined either analytically or experimentally. While analytical approaches suffer from inaccuracies because of the assumptions made for the specific models, experimental stability lobe diagrams require extensive cutting tests. Therefore, this paper introduces a new automated experimental method for determining stability lobe diagrams in milling with reduced effort regarding time. A closed-loop system is designed, containing a sensor-based online chatter detection along with a strategy to set parameters for subsequent cuts based on the stability boundaries known at each iteration. Both cuts with continuously increasing cutting depth and varied spindle speed are deployed to ensure fast detection of stability limits. The method is tested for a slot milling use case and the results are compared to a conventionally obtained stability lobe diagram yielding a significantly reduction in required time (-90 %) and resources (-67 %) whilst maintaining good accuracy. The reduced effort qualifies the proposed method as a tool to rapidly deliver maximum productive yet stable cutting parameters for optimization of existing or enhanced planning of new manufacturing processes.

Integrated Chatter Monitoring Based on Sensorless Cutting Force/Torque Estimation in Parallel Turning

2017 ◽  
Vol 11 (2) ◽  
pp. 215-225 ◽  
Author(s):  
Yuki Yamada ◽  
◽  
Takashi Kadota ◽  
Shinya Sakata ◽  
Junji Tachibana ◽  
...  
Keyword(s):  
Cutting Force ◽  
Disturbance Observer ◽  
Prediction Models ◽  
Estimation Methods ◽  
Torque Estimation ◽  
Frequency Components ◽  
Internal Information ◽  
The Stability ◽  
Stability Limits ◽  
Cutting Point

Parallel turning technology is considerably important in future multi-tasking machine tool because it has the potential to enhance the stability limits, compared to turning operations using a single tool. Although stability prediction models for parallel turning have been developed recently, the technique of in-process monitoring of chatter is almost out of focus. In this study, the monitoring of chatter based on the sensorless cutting force/torque technique was evaluated in the parallel turning and cutting of the same surface of an elongated workpiece. Two cutting force/torque estimation methods were evaluated: a conventional disturbance observer (DOB) using internal information from a servomotor and a multi-encoder-based disturbance observer (MEDOB) using load-side position/angular information as well. In the DOB-based monitoring, chatter frequency components were observable regardless of the guideway type and drive system. However, chatter monitoring may be difficult when the angle of the servomotor is changed slightly because of the damping properties of the sliding guideway. In the MEDOB-based monitoring, the waveform of the estimated cutting force reflected the vibrational state at the cutting point well, and the extraction of chatter frequency components became easier regardless of the guideway type.

scholarly journals Estimates of the bistable region in metal cutting

2008 ◽  
Vol 464 (2100) ◽  
pp. 3255-3271 ◽  
Author(s):  
Zoltan Dombovari ◽  
R. Eddie Wilson ◽  
Gabor Stepan
Keyword(s):  
Cutting Force ◽  
Metal Cutting ◽  
Classical Model ◽  
Orthogonal Cutting ◽  
Chip Thickness ◽  
Stability Limit ◽  
Force Characteristic ◽  
Inflexion Point ◽  
The Stability ◽  
Force Characteristics

The classical model of regenerative vibration is investigated with new kinds of nonlinear cutting force characteristics. The standard nonlinear characteristics are subjected to a critical review from the nonlinear dynamics viewpoint based on the experimental results available in the literature. The proposed nonlinear model includes finite derivatives at zero chip thickness and has an essential inflexion point. In the case of the one degree-of-freedom model of orthogonal cutting, the existence of unstable self-excited vibrations is proven along the stability limits, which is strongly related to the force characteristic at its inflexion point. An analytical estimate is given for a certain area below the stability limit where stable stationary cutting and a chaotic attractor coexist. It is shown how this domain of bistability depends on the theoretical chip thickness. The comparison of these results with the experimental observations and also with the subcritical Hopf bifurcation results obtained for standard nonlinear cutting force characteristics provides relevant information on the nature of the cutting force nonlinearity.

An Improved Tool Path Model Including Periodic Delay for Chatter Prediction in Milling

2006 ◽  
Vol 2 (2) ◽  
pp. 167-179 ◽  
Author(s):  
R. P. H. Faassen ◽  
N. van de Wouw ◽  
H. Nijmeijer ◽  
J. A. J. Oosterling
Keyword(s):  
Periodic Solution ◽  
Cutting Force ◽  
Tool Path ◽  
Chip Thickness ◽  
Milling Process ◽  
Path Model ◽  
Force Model ◽  
Cutting Force Model ◽  
Periodic Delay ◽  
The Stability

The efficiency of the high-speed milling process is often limited by the occurrence of chatter. In order to predict the occurrence of chatter, accurate models are necessary. In most models regarding milling, the cutter is assumed to follow a circular tooth path. However, the real tool path is trochoidal in the ideal case, i.e., without vibrations of the tool. Therefore, models using a circular tool path lead to errors, especially when the cutting angle is close to 0 or π radians. An updated model for the milling process is presented which features a model of the undeformed chip thickness and a time-periodic delay. In combination with this tool path model, a nonlinear cutting force model is used, to include the dependency of the chatter boundary on the feed rate. The stability of the milling system, and hence the occurrence of chatter, is investigated using both the traditional and the trochoidal model by means of the semi-discretization method. Due to the combination of this updated tool path model with a nonlinear cutting force model, the periodic solution of this system, representing a chatter-free process, needs to be computed before the stability can be investigated. This periodic solution is computed using a finite difference method for delay-differential equations. Especially for low immersion cuts, the stability lobes diagram (SLD) using the updated model shows significant differences compared to the SLD using the traditional model. Also the use of the nonlinear cutting force model results in significant differences in the SLD compared to the linear cutting force model.

STABILITY AND HOPF BIFURCATIONS IN A DELAYED PREDATOR–PREY SYSTEM WITH A DISTRIBUTED DELAY

2009 ◽  
Vol 19 (07) ◽  
pp. 2283-2294 ◽  
Author(s):  
CUN-HUA ZHANG ◽  
XIANG-PING YAN
Keyword(s):  
Functional Differential Equations ◽  
Distributed Delay ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Predator Prey ◽  
Prey System ◽  
Functional Differential ◽  
The Stability

This paper is concerned with a delayed Lotka–Volterra two-species predator–prey system with a distributed delay. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of positive equilibrium is investigated and Hopf bifurcations are demonstrated. It is found that the positive equilibrium of the system is always locally asymptotically stable when the delay kernel is the weak kernel while there is a stability switch of positive equilibrium when the delay kernel is the strong kernel and the system can undergo a Hopf bifurcation at the positive equilibrium when the average time delay in the delay kernel crosses certain critical values. In particular, by applying the normal form theory and center manifold reduction to functional differential equations (FDEs), the explicit formula determining the direction of Hopf bifurcations and the stability of bifurcated periodic solutions is given. Finally, some numerical simulations are also included to support the analytical results obtained.

Time Domain Simulation of Milling Chatter Stability

2016 ◽  
Vol 836-837 ◽  
pp. 94-98 ◽  
Author(s):  
Ying Chao Ma ◽  
Min Wan ◽  
Wei Hong Zhang
Keyword(s):  
Time Domain ◽  
Chip Thickness ◽  
Time Algorithm ◽  
Milling Process ◽  
Time Domain Simulation ◽  
Chatter Stability ◽  
Stability Lobe ◽  
Machining System ◽  
The Stability ◽  
Milling Chatter

In this paper, time domain simulation has been carried out to study the chatter stability of milling process. Dynamic chip thickness is calculated by analyzing the kinematics of the cutter, and thus dynamic governing equation revealing the dynamic behaviors between the cutter and workpiece is established. Solving framework is constructed by using the Simulink module and S-Function of Matlab software, and dynamic deflection is achieved with the four-order Runge-Kutta algorithm. With the simulated cutting forces, a criterion for the construction of the stability lobe is suggested. At the same time, algorithm for the prediction of the surface topography involving the dynamic response of the machining system is developed.

Predictions of Cutting Force and Tool Wear in Gear Power Skiving

2021 ◽  
Author(s):  
Zongwei Ren ◽  
Zhenglong Fang ◽  
Takuhiro Arakane ◽  
Toru Kizaki ◽  
Yannan Feng ◽  
...  
Keyword(s):  
Tool Wear ◽  
Cutting Force ◽  
Cutting Tool ◽  
Chip Thickness ◽  
Rake Angle ◽  
Parametric Modeling ◽  
Cutting Conditions ◽  
Cutting Process ◽  
Rake Face ◽  
Power Skiving

Abstract Power skiving is a promising method that can enhance the efficiency of gear machining. The machining mechanism is complicated due to several factors, such as the continuous variation in the rake angle and undeformed chip thickness. The tool wear process is also difficult to be evaluated due to the constantly varying in cutting conditions. Hence, to make a comprehensive understanding of the cutting process, we proposed a parametric modeling process based on the kinematics of power skiving. In this model, the undeformed cutting chip was calculated in each pass and shows the consistency with deformed cutting chip in experiments. The effective rake angle and undeformed cutting chip thickness were defined, calculated, and displayed on undeformed cutting chip for a better understanding of the cutting process. The cutting force and tool crater wear were calculated by estimating the distribution of the stress and temperature on the rake face of the cutting tool. Multiple radial-feed experimental evaluations were conducted with the gears of construction vehicles. In the results, the predicted margin of the absolute error of the normal force on the rake face was under 5% in every pass. The wear distribution on the rake face is consistent with the superimposed tool-chip contact area. The results show high potential for the optimization of the cutting tool or cutting conditions in gear power skiving.

Sign in / Sign up

Export Citation Format

Share Document