The Effect of Geometry on Harmonically Varied Helix Milling Tools

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Markel Sanz ◽  
Alex Iglesias ◽  
Jokin Munoa ◽  
Zoltan Dombovari
Keyword(s):  
Algebraic System ◽  
Point Of View ◽  
Geometrical Parameters ◽  
Stability Properties ◽  
Edge Geometry ◽  
Variable Helix ◽  
Nonlinear Algebraic System ◽  
The Stability ◽  
Milling Tools ◽  
Equivalent Description

Abstract Two different kinds of descriptions for edge geometry of harmonically varied helix tools are studied in this work. The edge geometries of the so-called lag and helix variations are used in this paper, and their equivalency is established from engineering point of view. The equivalent relation is derived analytically and the nonlinear algebraic system is described, with which the numerical equivalency properties can be determined. The equivalent description can be utilized in variable helix tool production to determine an optimized set of geometrical parameters of the edge geometry. The stability properties are shown and compared for a simple one degree-of-freedom case with the nonuniform constant helix tools. The robustness of the results related to the harmonically varied tools is critically discussed in this paper showing advantages compared to the nonuniform constant helix case. The results suggest that the more extreme the edge variation is, the more stable the process performed with the corresponding harmonically varied tool becomes.

Numerical Nonlinear Analysis for Dynamic Stability of an Ankle-Hip Model of Balance on a Balance Board

2019 ◽  
Vol 14 (10) ◽  
Author(s):  
Erik Chumacero-Polanco ◽  
James Yang ◽  
James Chagdes
Keyword(s):  
Dynamical System ◽  
Dynamic Stability ◽  
Point Of View ◽  
Local Dynamic ◽  
Stability Properties ◽  
Dynamical Behaviors ◽  
Local Dynamic Stability ◽  
The Stability ◽  
Delay Differential ◽  
Balance Board

Abstract Study of human upright posture (UP) stability is of great relevance to fall prevention and rehabilitation, especially for those with balance deficits for whom a balance board (BB) is a widely used mechanism to improve balance. The stability of the human-BB system has been widely investigated from a dynamical system point of view. However, most studies assume small disturbances, which allow to linearize the nonlinear human-BB dynamical system, neglecting the effect of the nonlinear terms on the stability. Such assumption has been useful to simplify the system and use bifurcation analyses to determine local dynamic stability properties. However, dynamic stability analysis results through such linearization of the system have not been verified. Moreover, bifurcation analyses cannot provide insight on dynamical behaviors for different points within the stable and unstable regions. In this study, we numerically solve the nonlinear delay differential equation that describes the human-BB dynamics for a range of selected parameters (proprioceptive feedback and time-delays). The resulting solutions in time domain are used to verify the stability properties given by the bifurcation analyses and to compare different dynamical behaviors within the regions. Results show that the selected bifurcation parameters have significant impacts not only on UP stability but also on the amplitude, frequency, and increasing or decaying rate of the resulting trajectory solutions.

scholarly journals Fast chatter stability prediction for variable helix milling tools

2015 ◽  
Vol 230 (1) ◽  
pp. 133-144 ◽  
Author(s):  
Neil D Sims
Keyword(s):  
Regenerative Chatter ◽  
Frequency Effects ◽  
Excited Vibration ◽  
Model Predictions ◽  
The Laplace Transform ◽  
Variable Helix ◽  
Observed Behaviour ◽  
The Stability ◽  
Machining Operations ◽  
Milling Tools

Regenerative chatter is a well-known form of self-excited vibration that limits the productivity of machining operations, in particular for milling. Variable helix tools have been previously proposed as a means of avoiding regenerative chatter, and although recent work has analysed the stability of such tools there has not always been a strong agreement with experimentally observed behaviour. Furthermore, the analysis of variable helix tool stability can be tedious and numerically slow, compared to standard tools. Consequently it has been difficult to gain insight into the potential advantages of variable helix tools. The present work attempts to address these issues, by first developing an efficient approach to variable helix tool stability based upon the Laplace transform. Then, this new analysis method is used to demonstrate the importance of multi-frequency effects and nonlinear cutting stiffness. The work suggests that whilst variable-helix tools can have more operating regions that are stable, un-modelled behaviour (such as nonlinearity and multi-frequency effects) can have a critical influence on the accuracy of model predictions.

scholarly journals A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Issam El Hantati ◽  
Ahmed Adri ◽  
Hatim Fakhreddine ◽  
Said Rifai ◽  
Rhali Benamar
Keyword(s):  
Approximate Method ◽  
Forced Vibration ◽  
Algebraic System ◽  
Strain Energy ◽  
Dynamic Behaviour ◽  
Forced Vibrations ◽  
Geometrical Parameters ◽  
Geometrically Nonlinear ◽  
Free And Forced Vibrations ◽  
Nonlinear Algebraic System

The scope of this study is to present a contribution to the geometrically nonlinear free and forced vibration of multiple-stepped beams, based on the theories of Euler–Bernoulli and von Karman, in order to calculate their corresponding amplitude-dependent modes and frequencies. Discrete expressions of the strain energy and kinetic energies are derived, and Hamilton’s principle is applied to reduce the problem to a solution of a nonlinear algebraic system and then solved by an approximate method. The forced vibration is then studied based on a multimode approach. The effect of nonlinearity on the dynamic behaviour of multistepped beams in the free and forced vibration is demonstrated and discussed. The effect of varying some geometrical parameters of the stepped beams in the free and forced cases is investigated and illustrated, among which is the variation in the level of excitation.

A Class of Methods with Optimal Stability Properties for the Numerical Solution of IVPs: Construction and Implementation

2017 ◽  
Vol 14 (01) ◽  
pp. 1750007
Author(s):  
Masoumeh Hosseini Nasab ◽  
Gholamreza Hojjati ◽  
Ali Abdi
Keyword(s):  
Numerical Solution ◽  
Numerical Experiments ◽  
Point Of View ◽  
Variable Step Size ◽  
Second Derivative ◽  
Step Size ◽  
Stability Properties ◽  
Variable Step ◽  
The Stability ◽  
Size Mode

Considering the methods with future points technique from second derivative general linear methods (SGLMs) point of view, makes it possible to improve their stability properties. In this paper, we extend the stability regions of a modified version of E2BD formulas to optimal one and show its effectiveness by numerical verifications. Also, implementation issues, with numerical experiments, of these methods are investigated in a variable step-size mode.

Dynamics of Drill Bits With Cutting Edges of Varying Parameters

2013 ◽  
Author(s):  
Zoltan Dombovari ◽  
Gabor Stepan
Keyword(s):  
Metal Cutting ◽  
Helix Angle ◽  
Milling Process ◽  
Drilling Process ◽  
Deep Drilling ◽  
Stability Properties ◽  
Stability Diagrams ◽  
Drill Bits ◽  
Variable Helix ◽  
The Stability

In the metal cutting industry it is well known that milling processes can be stabilized by applying different strategies in order to destroy the pure single delay regeneration that arise in case of conventional milling tools when high material removal rates are used either at low or at high cutting speeds. To achieve this goal, variable pitch angle, variable helix angle and serrated tools are already available in the market and serve alternative solutions for process designers to enhance milling process stability. Regeneration can occur and can cause instability on the tip of the deep drilling equipment when the drill bit is driven across hard earth crust materials. This work shows that theories introduced for milling processes can be implemented to improve the stability properties of deep drilling processes, too. Unlike in case of most milling processes, however, the stability properties of deep drilling are affected by the longitudinal and the torsional vibration modes. In this paper, the geometrical and mechanical models are derived for drill bits with general shapes of cutting edges and it is shown that the two DOF dynamics can be described by distributed state dependent delay differential equations. The stability properties are characterized in stability diagrams that can help to select the optimal drilling process parameters.

Parametric Optimization of Dental Implants

2020 ◽  
Vol 22 (4) ◽  
pp. 1061-1076
Author(s):  
Wafa Bensmain ◽  
Mohammed Benlebna ◽  
Boualem Serier ◽  
Bel Abbes ◽  
Bachir Bouiadjra
Keyword(s):  
Dental Implants ◽  
Clinical Success ◽  
Equivalent Stress ◽  
Radius Of Curvature ◽  
Geometrical Parameters ◽  
Neck Size ◽  
Biomechanical Behavior ◽  
Dynamic Charging ◽  
The Stability ◽  
Masticatory Process

AbstractOsseointegration is a fundamental phenomenon of dental implantology. It ensures the stability, the safety and the durability of dental implants and predictable clinical success in long-term. The geometric form of the implant is a defining parameter of osseointegration and implant-bone charge transfer. This is the essential constitutes of this study. In fact, we demonstrate using the finite elements method with tridimensional numerical computations, that the geometrical parameters of the implant conditionate the level and the repartition of the stresses, induced in the cortical bone and the spongy bone during the masticatory process, simulated here by dynamic charging. The effect of several parameters [size and conicity of the implant neck, size and radius of curvature of the implant apex] and the shape of the implant corps on the biomechanical behavior of the bone. The latest was analyzed in terms of variation of the equivalent stress induced in the bone. The purpose of this analysis was the developing of an implant form allowing stress relaxation, during the mastication process, in the living tissue.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

scholarly journals Suboptimal Disturbance Observer Design Using All Stabilizing Q Filter for Precise Tracking Control

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1434 ◽  
Author(s):  
Wonhee Kim ◽  
Sangmin Suh
Keyword(s):  
Design Method ◽  
Industrial Applications ◽  
Point Of View ◽  
Observer Design ◽  
Linear Matrix ◽  
External Disturbances ◽  
Closed Loop Systems ◽  
Control Target ◽  
The Stability ◽  
Unified Index

For several decades, disturbance observers (DOs) have been widely utilized to enhance tracking performance by reducing external disturbances in different industrial applications. However, although a DO is a verified control structure, a conventional DO does not guarantee stability. This paper proposes a stability-guaranteed design method, while maintaining the DO structure. The proposed design method uses a linear matrix inequality (LMI)-based H∞ control because the LMI-based control guarantees the stability of closed loop systems. However, applying the DO design to the LMI framework is not trivial because there are two control targets, whereas the standard LMI stabilizes a single control target. In this study, the problem is first resolved by building a single fictitious model because the two models are serial and can be considered as a single model from the Q-filter point of view. Using the proposed design framework, all-stabilizing Q filters are calculated. In addition, for the stability and robustness of the DO, two metrics are proposed to quantify the stability and robustness and combined into a single unified index to satisfy both metrics. Based on an application example, it is verified that the proposed method is effective, with a performance improvement of 10.8%.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

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