Design criteria for grinding machine dynamic stability

Abstract Surface grinding is one of the oldest and most widely used machining process: to date, there are still few alternatives available for producing smooth and flat surfaces, satisfying both technical and economic constraints. The quality of a workpiece resulting from a grinding process is strongly influenced by the static and dynamic behavior of the mechanical system, composed by machine tool, wheel, fixture and workpiece. In particular, the dynamic compliance of the machine at wheel-workpiece interface may cause vibrations leading to poor surface quality. Starting from the analysis of process-machine interaction according to self-excited vibrations theories (the most relevant), this paper outlines a path for surface grinding machines design, focused on the identification of the most critical dynamic eigenmodes both in terms of dynamical parameters and geometry (vibration direction). The methodology is based on the application of Nyquist stability criterion for MIMO systems. Firstly, the methodology distinguishes between a limitation mainly ascribable to regenerative chatter and one ascribable to closed-loop eigenmodes properties. In this latter case, it will be shown that stability properties are strongly influenced by the shape and orientation of the elliptical movement of the wheel entailed by the limiting eigenmode (that, in general, is complex). Such an analysis can be also exploited to provide some indications guiding machine structural modifications. Finally, the approach is demonstrated on a couple of grinding machine variants via FE modeling

Energy Driven Process Planning and Machine Tool Dynamic Behavior Assessment

AbstractThe current work outlines an approach to close the loop between process planning and machine tool dynamic modeling by addressing the problem of energy efficiency across the process design and realization chains, from the process settings and pallet configuration to the machine tool design and usage phases. The proposed closed loop approach consists of an off-line and on-line component enabling the process and equipment dynamic and energy assessment over time. The benefits of the approach have been evaluated against an industrial case study related to the automotive industry

A meta-model framework for grinding simulation

When considering the mechanics of grinding, several physical phenomena have to be modeled, each one having effect on the resulting grinding forces, wheel and workpiece geometry. Depending on the analyzed problem, some dependencies can be neglected to privilege some aspects instead of others. Nevertheless, all models essentially start considering wheel-workpiece engagement and the corresponding material removal (both wheel and workpiece side), deriving the forces by means of energy balances and/or shear mechanics. The meta-model proposed in this paper represents a general framework conceived for providing a time-domain simulation engine based on a dexel representation of wheel and workpiece, capable to “host” all the semi-empirical models existing in literature, where the overall grinding force is the result of the integration of the force contributions associated to the local removal along wheel-workpiece engagement arc. A cascade approach is adopted to solve for forces and displacements the DAEs set describing the dynamic interactions between wheel and workpiece, whereas all the algebraic relationships pertaining to the various specific models are solved in a pre-processing phase, yielding a set of response surfaces that are queried during time integration. Finally, the meta-model framework is instantiated for a model of traverse roll grinding with force-dependent wheel wear

Tripod_function

Representation of Tripod function, used as benchmark for global optimization.</p

Roundness prediction in centreless grinding using physics-enhanced machine learning techniques

This work proposes a model for suggesting optimal process configuration in plunge centreless grinding operations. Seven different approaches were implemented and compared: first principles model, neural network model with one hidden layer, support vector regression model with polynomial kernel function, Gaussian process regression model and hybrid versions of those three models. The first approach is based on an enhancement of the well-known numerical process simulation of geometrical instability. The model takes into account raw workpiece profile and possible wheel-workpiece loss of contact, which introduces an inherent limitation on the resulting profile waviness. Physical models, because of epistemic errors due to neglected or oversimplified functional relationships, can be too approximated for being considered in industrial applications. Moreover, in deterministic models, uncertainties affecting the various parameters are not explicitly considered. Complexity in centreless grinding models arises from phenomena like contact length dependency on local compliance, contact force and grinding wheel roughness, unpredicted material properties of the grinding wheel and workpiece, precision of the manual setup done by the operator, wheel wear and nature of wheel wear. In order to improve the overall model prediction accuracy and allow automated continuous learning, several machine learning techniques have been investigated: a Bayesian regularized neural network, an SVR model and a GPR model. To exploit the a priori knowledge embedded in physical models, hybrid models are proposed, where neural network, SVR and GPR models are fed by the nominal process parameters enriched with the roundness predicted by the first principle model. Those hybrid models result in an improved prediction capability

Self-locking analysis in closed kinematic chains

Self-locking analysis in closed kinematic chains is sometimes likened to kinematic singularity analysis, especially when mechanisms are characterized by more than one degree of freedom. Although in singular configurations a mechanism is obviously locked-up since joint constraint reactions and friction forces rise to infinity, this approach identifies only a condition sufficient for self-locking, while the phenomenon actually occurs in a larger domain, the size of which depends on the values of friction coefficients. The paper proposes a definition of self-locking for multi degrees of freedom mechanisms and presents an algorithm for computing the geometrical locus that corresponds to a specific self-locking configuration. This methodology is then demonstrated on a simple parallel kinematic mechanism with two degrees of freedom

Stability Analysis of Centerless Grinding with Loss of Contact Nonlinearity

The paper presents a novel geometrical stability analysis of centerless grinding that takes into account the nonlinearity associated to wheel-workpiece detachment during lobes formation. Even though the rounding mechanism in centerless grinding has been studied since more than fifty years, stability analysis has been carried out applying stability criteria for linear systems (e.g., Nyquist) on a process model that neglects actual removal “clipping” due to wheel-workpiece detachment. This model limitation is usually overcome by considering only an integer number of lobes, supporting the restriction by the claim that a non-integral number of waves is less likely to build up since the waviness must be constantly removed and replaced by a succeeding wave, which is constantly moving around the workpiece. In this work, the nonlinearity entailed by removal clipping is explicitly taken into account and, by harmonic linearization, represented by a double input describing function (DIDF). Applying the Nyquist criterion on the resulting equivalent delayed system, the paramount instability associated to a quasi-integer number of lobes emerges naturally, without requiring additional assumptions. Moreover, it is shown that the nonlinearity due to wheel-workpiece detachment does not produce a limit cycle in a reasonable operation time. The results delivered by the proposed approach are verified by numeric simulations and positively compared to the relevant literature. The proposed formulation can be easily extended to consider also machine structure dynamics, thus increasing, even in this case, the accuracy of the stability analysis provided by the standard approach

A model-based approach for online estimation of surface waviness in roll grinding

Vibrations onset represents a paramount issue in all grinding processes. The related surface defects appear in the form of micrometric waviness that decreases the finishing quality and in some cases the functionality of the ground workpieces: sometimes, these defects can be also marked on the grinding wheel surface. This paper presents an online model-based approach to identify and quantify the level of waviness starting from multiple acceleration measurements, allowing a continuous monitoring of wheel and/or workpiece defects. The identification algorithm, that exploits a linear model of machine and process dynamics, is based on the application of Least Squares method in the frequency domain. Experiments confirm the good performance of the algorithm that, hence, can be exploited for developing advanced control schemes of the grinding process

Stability Analysis of Centerless Grinding with Loss of Contact Nonlinearity

The paper presents a novel geometrical stability analysis of centerless grinding that takes into account the nonlinearity associated to wheel-workpiece detachment during lobes formation. Even though the rounding mechanism in centerless grinding has been studied since more than fifty years, stability analysis has been carried out applying stability criteria for linear systems (e.g., Nyquist) on a process model that neglects actual removal “clipping” due to wheel-workpiece detachment. This model limitation is usually overcome by considering only an integer number of lobes, supporting the restriction by the claim that a non-integral number of waves is less likely to build up since the waviness must be constantly removed and replaced by a succeeding wave, which is constantly moving around the workpiece. In this work, the nonlinearity entailed by removal clipping is explicitly taken into account and, by harmonic linearization, represented by a double input describing function (DIDF). Applying the Nyquist criterion on the resulting equivalent delayed system, the paramount instability associated to a quasi-integer number of lobes emerges naturally, without requiring additional assumptions. Moreover, it is shown that the nonlinearity due to wheel-workpiece detachment does not produce a limit cycle in a reasonable operation time. The results delivered by the proposed approach are verified by numeric simulations and positively compared to the relevant literature. The proposed formulation can be easily extended to consider also machine structure dynamics, thus increasing, even in this case, the accuracy of the stability analysis provided by the standard approach

Frequency domain identification of grinding stiffness and damping

As equivalent stiffness and damping of the grinding process dominate cutting stability, their identification is essential to predict and avoid detrimental chatter occurrence. The identification of these process constants is not easy in large cylindrical grinding machines, e.g. roll grinders, since there are no practical ways to measure cutting force normal component. This paper presents a novel frequency domain approach for identifying these process parameters, exploiting in-process system response, measured via impact testing. This method adopts a sub-structuring approach to couple the wheel-workpiece relative dynamic compliance with a two-dimensional grinding force model that entails both normal and tangential directions. The grinding specific energy and normal force ratio, that determine grinding stiffness and damping, are identified by fitting the closed loop FRF (Frequency Response Function) measured during specific plunge-grinding tests. The fitting quality supports the predictive capability of the model. Eventually, the soundness of the proposed identification procedure is further assessed by comparing the grinding specific energy identified through standard cutting power measurements