Active Vibration Control for Milling Processes

In this paper, a study on the active control of vibration for peripheral milling is presented. Different from the control for the vibrations of cutting tool or workpiece, in this effort, the relative vibration between the workpiece and tool is selected as the control target. To reduce the relative vibration, a two-axis active work-holding stage, which is droved by two piezo-actuators, is designed and the control system synthesis method is used to determine the control gain. By this method, the dynamical stage is considered as plant while the complicated cutting process is treated as disturbance. The cutting vibration control can be considered as a robust disturbance rejection problem (RDRP), and the controller design is based on robust servo-mechanism method. Without the requirement on the model of disturbance, this method simplifies the vibration control problem and only the knowledge of frequencies of disturbance is required. Numerical results indicate the implemented system works well in cutting vibration cancellation.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

Position Domain PD Control for Contour Tracking

For multi-axis motion control applications, contour tracking is one of the most common control problems encountered by industrial manipulators and robots. In this paper, a position domain PD control method is proposed for the purpose of improving the contour tracking performance. To develop the new control method, the multi-axis motion system is viewed as a master-slave motion system where the master motion is sampled equidistantly and used as an independent variable, while the slave motions are described as functions of the master motion according to the contour tracking requirements. The dynamic model of the multi-axis motion system is developed in the position domain based on the master motion by transforming the original system dynamic equations from the time domain to the position domain. In this control methodology, the master motion will yield zero tracking error for the position as it is used as reference, and only the slave motion tracking errors will affect the final contour tracking errors. The proposed position domain PD controller is successfully examined in a Cartesian robotic system for linear motion tracking and circular contour tracking.

A New Nonlinear Higher-Order Shear Deformation Theory for Nonlinear Vibrations of Laminated Shells

A consistent higher-order shear deformation nonlinear theory is developed for shells of generic shape; taking geometric imperfections into account. The geometrically nonlinear strain-displacement relationships are derived retaining full nonlinear terms in the in-plane displacements; they are presented in curvilinear coordinates in a formulation ready to be implemented. Then, large-amplitude forced vibrations of a simply supported, laminated circular cylindrical shell are studied (i) by using the developed theory, and (ii) keeping only nonlinear terms of the von Ka´rma´n type. Results show that inaccurate results are obtained by keeping only nonlinear terms of the von Ka´rma´n type for vibration amplitudes of about two times the shell thickness for the studied case.

Stability of Shear-Thickening Liquids Between Rotating Cylinders

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. It is assumed that shear-thickening fluids behave exactly as opposite of shear thinning ones. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow, however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.

The Internet-Based Teleoperation: Motion and Force Predictions Using the Particle Filter Method

In this paper, we present motion and force predictions in Internet-based teleoperation systems using the particle filter method. The particle filter, also known as the sequential Monte Carlo (SMC) method, is a probabilistic prediction or estimation technique within a sequential Bayesian framework: Data at a current time step are predicted or estimated by recursively generating probability distribution based on previous observations and input states. In this paper, we first formulate the particle filter method using a prediction-based approach. Motion and force data flows, which may be impaired by the Internet delay, are formulated within a sequential Bayesian framework. The true motion and force data are then predicted by employing the prediction-based particle filter method using the impaired observations and previous input states. We performed experiments using a haptic device that interacts with a mechanics-based virtual 3D graphical environment. The haptic device is used as a master controller that provides positioning inputs to a 4-degree of freedom (4-DoF) virtual robotic manipulator while receiving feedback force through interactions with the virtual environment. We simulate the Internet delay with variations typically observed in a user datagram protocol (UDP) transmission between the master controller and the virtual teleoperated robot. In this experimental scenario, the particle filter method is implemented for both motion and force data that experience the Internet delay. The proposed method is compared with the conventional Kalman filter. Experimental results indicate that in nonlinear and non-Gaussian environments the prediction-based particle filter has distinct advantage over other methods.

A Hybrid Approach to Force Balancing of Robotic Mechanisms

A hybrid approach to force balancing of robotic mechanisms which have at least two degrees of freedom is proposed. This hybrid approach is to combine adjusting kinematic parameters (AKP) and counterweights (CW) approaches, and it is called AKP+CW in short. The main motivation of the AKP+CW approach is that CW and AKP each has its own advantage and disadvantage, and thus a combined one may strengthen the both. This paper presents the force balancing principles and equations for the AKP+CW approach. Software called ADAMS is employed as a tool for the simulated experiment to verify the effectiveness of the proposed approach. The implication of the work described in this paper to the balancing of mechanisms in general is that many different force balancing methods may be combined based on the hybridization principle proposed in this paper to become a novel one.

Nonlinear Dynamics of MEMS Arches

In this paper, the dynamic response of electrostatically actuated clamped-clamped arch microbeam is investigated when excited by a DC load superimposed to an AC harmonic load. The dynamic analysis is carried out using a Galerkin-based reduced order model along with a shooting technique to find periodic motions and analyzing its stability using a Floquet theory. Results are presented for the cases of primary and super harmonic resonances. We found several nonlinear dynamic phenomena due to the inherent nonlinear electrostatic force and geometric nonlinearity of the arch. These include frequency-amplitude dependence, jumps, tangent bifurcations, coexistence of solutions, and softening and hardening behaviors. The shooting technique showed high robustness in capturing both the stable and unstable states of the system. Hence, it helped clarify vague behaviors that were previously reported using longtime integration of the equations of motion.

Development of Simplified Spot Weld Models: Stiffness Prediction and Computational Performance Evaluation

Simple spot weld connection models are desirable in huge and complicated finite element models of automotive body-in-white structures which generally contains thousands of spot weld joints. Hence, in this paper six different individual spot weld joint finite element models simplified in terms of their geometric and constitutive representations were developed including the one that is currently used in automotive industries. The stiffness characteristics of these developed models were compared with the experimental results obtained following a simple strategy to design the welded joint based on the desired mode of nugget pull out failure. It was found that the current spot weld modeling practice in automotive industry under predict the maximum joint strength nearly by 50% for different loading conditions. The computational costs incurred by the developed models in different loading conditions were also compared. Hence, a suitable model for spot welded joints is established which is very simple to develop but relatively cheap in terms of computational costs.

Sensorless Simultaneous Rotary-Translational Axis Motion Error Measurement and Trace Based on Virtual Bar

Simultaneous rotary-translational (R-T) axis motion error has significant influence on multi-axis machine tool precision. To improve multi-axis machine tool precision, axis motion error measurement and trace method are investigated in this study. A sensorless R-T axis motion error measurement and trace technology based on virtual bar is proposed. Firstly, the fundamental sensorless test principle is discussed. Then, the virtual-bar-based test path of a circular test though a rotary axis and two translational axes motion is scheduled. The mathematical model of motion error is established. Furthermore, to identify the error source, spatial error charts and some advanced signal processing and feature extraction technologies, such as wavelet transform and frequency analysis, are used. The analysis of experimental results shows that it is practical and efficient to use the virtual bar and the sensorless information to estimate motion error.