Analysis of Vibration Damping in Machine Tools

AbstractThe dynamic behavior of a machine tool structure directly influences key metal cutting performance like being able to quickly remove hard workpiece material during roughing or minimize unwanted oscillations during high speed movements in finishing. While structure conception is still funded on designer experience and inventiveness, Finite Element models are very effective in analyzing the conceived structure, allowing its optimization, in term of stiffness increase and/or mass reduction.While today FE models provide a satisfying description of structure distributed stiffness and inertia, machine damping is usually not represented or is approximated as a uniform viscous damping, with no precise reference to the actual dissipation phenomena occurring in the structure. The corresponding incertitude in the estimation of the overall dynamic behavior often strongly limits the possibility of delivering accurate absolute estimations of machine performance. In order to overcome this limitation, this work aims at adding key energy dissipation mechanisms into numerical structural models: the velocity loop of the axis position controller, the frictional forces acting on the axis kinematic chain and guide ways and a distributed modal damping. Experimental tests have been performed on a machine tool axis equipped with tunable roller plus plain friction guide ways. The proposed model shows how different components and phenomena contribute into increasing machine performance, in term of material removal capacity. Given that the resulting models are essentially non-linear, appropriate methodologies are also suggested to integrate the proposed analysis into the usual machine development design cycle

Constructive interconnection and damping assignment passivity-based control with applications

Energy-based modeling and control of dynamical systems is crucial since energy is a fundamental concept in Science and Engineering theory and practice. While Interconnection and Damping Assignment Passivity-based Control (IDA-PBC) is a powerful theoretical tool to control port-controlled Hamiltonian (PCH) systems that arise from energy balancing principles, sensorless operation of energy harvesters is a promising practical solution for low-power energy generation. The thesis addresses these two problems of energy-based control and efficient energy generation. The design via IDA-PBC hinges on the solution of the so-called matching equation which is the stumbling block in making this method widely applicable. In the first part of the thesis, a constructive approach for IDA-PBC for PCH systems that circumvents the solution of the matching equation is presented. A new notion of solution for the matching equation, called algebraic solution, is introduced. This notion is instrumental for the construction of an energy function defined on an extended state-space. This yields, differently from the classical solution, a dynamic state-feedback that stabilizes a desired equilibrium point. In addition, conditions that preserve the PCH structure in the extended closed-loop system have been provided. The theory is validated on four examples: a two-dimensional nonlinear system, a magnetic levitated ball, an electrostatic microactuator and a third order food-chain system. For these systems damping structures that cannot be imposed with the standard approach are assigned. In the second part of the thesis, the design of a nonlinear observer and of an energy-based controller for sensorless operation of a rotational energy harvester is presented. A mathematical model of the harvester with its power electronic interface is developed. This model is used to design an observer that estimates the mechanical quantities from the measured electrical quantities. The gains of the observer depend on the solution of a modified Riccati equation. The estimated mechanical quantities are used in a feedback control law that sustains energy generation across a range of source rotation speeds. The proposed observer-controller scheme is assessed through simulations and experiments.Open Acces

Steering control for haptic feedback and active safety functions

Steering feedback is an important element that defines driver–vehicle interaction. It strongly affects driving performance and is primarily dependent on the steering actuator\u27s control strategy. Typically, the control method is open loop, that is without any reference tracking; and its drawbacks are hardware dependent steering feedback response and attenuated driver–environment transparency. This thesis investigates a closed-loop control method for electric power assisted steering and steer-by-wire systems. The advantages of this method, compared to open loop, are better hardware impedance compensation, system independent response, explicit transparency control and direct interface to active safety functions.The closed-loop architecture, outlined in this thesis, includes a reference model, a feedback controller and a disturbance observer. The feedback controller forms the inner loop and it ensures: reference tracking, hardware impedance compensation and robustness against the coupling uncertainties. Two different causalities are studied: torque and position control. The two are objectively compared from the perspective of (uncoupled and coupled) stability, tracking performance, robustness, and transparency.The reference model forms the outer loop and defines a torque or position reference variable, depending on the causality. Different haptic feedback functions are implemented to control the following parameters: inertia, damping, Coulomb friction and transparency. Transparency control in this application is particularly novel, which is sequentially achieved. For non-transparent steering feedback, an environment model is developed such that the reference variable is a function of virtual dynamics. Consequently, the driver–steering interaction is independent from the actual environment. Whereas, for the driver–environment transparency, the environment interaction is estimated using an observer; and then the estimated signal is fed back to the reference model. Furthermore, an optimization-based transparency algorithm is proposed. This renders the closed-loop system transparent in case of environmental uncertainty, even if the initial condition is non-transparent.The steering related active safety functions can be directly realized using the closed-loop steering feedback controller. This implies, but is not limited to, an angle overlay from the vehicle motion control functions and a torque overlay from the haptic support functions.Throughout the thesis, both experimental and the theoretical findings are corroborated. This includes a real-time implementation of the torque and position control strategies. In general, it can be concluded that position control lacks performance and robustness due to high and/or varying system inertia. Though the problem is somewhat mitigated by a robust H-infinity controller, the high frequency haptic performance remains compromised. Whereas, the required objectives are simultaneously achieved using a torque controller