Analytical prediction of part dynamics for machining stability analysis

An analytical procedure is developed to predict workpiece dynamics in a complete machining cycle in order to obtain frequency response functions (FRF) which are needed in chatter stability analyses. For this purpose, a structural modification method which is an efficient tool for updating FRFs is used. The removed mass by machining is considered as a structural modification in order to determine the FRFs at different stages of the process. The method is implemented in a computer code and demonstrated on different geometries. The predictions are compared and verified by FEA. Predicted FRFs are used in chatter stability analyses, and the effect of part dynamics on stability is studied. Different cutting strategies are compared for increased chatter free material removal rates considering part dynamics

Selection of design and operational parameters in spindle-holder-tool assemblies for maximum chatter stability by using a new analytical model

In this paper, using the analytical model developed by the authors, the effects of certain system design and operational parameters on the tool point FRF, thus on the chatter stability are studied. Important conclusions are derived regarding the selection of the system parameters at the stage of machine tool design and during a practical application in order to increase chatter stability. It is demonstrated that the stability diagram for an application can be modified in a predictable manner in order to maximize the chatter-free material removal rate by selecting favorable system parameters using the analytical model developed. The predictions of the model, which are based on the methodology proposed in this study, are also experimentally verified

Investigating dynamics of machine tool spindles under operational conditions

Chatter is one of the major problems in machining and can be avoided by stability diagrams which are generated using frequency response functions (FRF) at the tool tip. During cutting operations, discrepancies between the stability diagrams obtained by using FRFs measured at the idle state and the actual stability of the process are frequently observed. These deviations can be attributed to the changes of machine dynamics under cutting conditions. In this paper, the effects of the cutting process on the spindle dynamics are investigated both experimentally and analytically. The variations in the spindle dynamics are attributed to the changes in the bearing parameters. FRFs under cutting conditions are obtained through the input-output relations of the cutting forces and the vibration response which are measured simultaneously. Experimentally and analytically obtained FRFs are then used in the identification of the bearing parameters under cutting conditions. Thus, bearing properties obtained at idle and cutting conditions are compared and variations in their values are obtained

Experimental Identification of Backbone Curves of Strongly Nonlinear Systems by Using Response-Controlled Stepped-Sine Testing (RCT)

In stepped-sine testing of strongly nonlinear structures with the classical force-control strategy, corrective force perturbations of a standard controller used to capture the reference signal in the proximity of turning points of frequency response curves may often lead to a premature jump before reaching the actual resonance peak. Accordingly, a classical force-control approach is not suitable to identify backbone curves of strongly nonlinear structures. This paper shows that currently available commercial modal test equipment can accurately identify backbone curves of strongly nonlinear structures by using Response-Controlled stepped-sine Testing (RCT) and the Harmonic Force Surface (HFS) concept, both recently proposed by the authors. These methods can be applied to systems where there are many nonlinearities at several different (and even unknown) locations. However, these techniques are not applicable to systems where internal resonances occur. In RCT, the displacement amplitude of the driving point, rather than the amplitude of the applied force, is kept constant during the stepped-sine testing. Spectra of the harmonic excitation force measured at several different displacement amplitude levels are used to build up a smooth HFS. Isocurves of constant amplitude forcing on the HFS lead to constant-force frequency response curves with accurately measured turning points and unstable branches (if there are any), which makes it possible to identify backbone curves of strongly nonlinear structures experimentally. The validation of the proposed approach is demonstrated with numerical and experimental case studies. A five degree-of-freedom (DOF) lumped system with five cubic stiffness elements, which create strong conservative nonlinearity, is used in the numerical example. Experimental case studies consist of a cantilever beam and a control fin actuation mechanism of a real missile structure. The cantilever beam is supported at its free-end by two metal strips constrained at both ends to create strong stiffening nonlinearity. The control fin actuation mechanism exhibits very complex and strong nonlinearity due to backlash and friction

Analysis and compensation of mass loading effect of accelerometers on tool point FRF measurements for chatter stability predictions

Chatter is one of the major problems in machining resulting in poor surface quality and reduced productivity. Stability diagrams can be used to determine chatter-free process conditions yielding high productivity. For generation of stability diagrams, frequency response functions (FRF) at the tool tip are needed to be used in stability models. Impact tests involving accelerometers are commonly used in FRF measurements. Although mass of a typical accelerometer used in these measurements is extremely small compared with the cutting tool, it can have a significant effect on the FRF measurement. In this paper, the effect of accelerometer's mass on tool point FRFs and stability diagrams is demonstrated for several cases with different tool-to-accelerometer mass ratios by using laser velocity sensor measurements In addition, a structural modification method which can be used to compensate this effect is also presented on several cases The structural modification method can be used to correct the FRFs measured with accelerometers, and thus the resulting stability diagrams

Mass loading effect of accelerometers on tool point FRF and stability diagrams

Chatter is one of the major problems in machining resulting in poor surface quality and reduced productivity. Stability diagrams can be used to determine chatter-free process conditions with high productivity. For generation of stability diagrams, frequency re-sponse functions (FRF) at the tool tip is needed to be used in stability model. Impact tests involving accelerometers are commonly used in FRF measurements. Although mass of a typical accelerometer used in these measurements is extremely small com-pared to the cutting tool, it can have a significant effect on the FRF measurement. In this paper, the effect of accelerometer’s on tool point FRFs and stability diagrams will be demonstrated on several cases with different tool-to-accelerometer mass ratios using laser velocity sensor measurement. In addition, a structural modification method which can be used to compensate this effect will also be presented on several cases. The structural modification method can be used to correct the FRFs measured with acceler-ometers, and thus the resulting stability diagram

Analytical modeling of the machine tool spindle dynamics under operational conditions

Chatter is an important problem in machining operations, and can be avoided by utilizing stability diagrams which are generated using frequency response functions (FRF) at the tool tip. In general, tool point FRF is obtained experimentally or analytically for the idle state of the machine. However, during high speed cutting operations, gyroscopic effects and changes of contact stiffness and damping at the interfaces as well as the changes in the bearing properties may lead to variations in the tool point FRF. Thus, stability diagrams obtained using the idle state FRFs may not provide accurate predictions in such cases. Spindle, holder and tool can be modeled analytically; however variations under operational conditions must be included in order to have accurate predictions. In authors previous works Timoshenko beam model was employed and subassembly FRFs were coupled by using receptance coupling method. In this paper, extension of the model to the prediction of operational FRFs is presented. In order to include the rotational effects on the system dynamics, gyroscopic terms are added to the Timoshenko beam model. Variations of the bearing parameters are included by structural modification techniques. Thus, for various spindle speeds, and holder and tool combinations, the tool point FRFs can be predicted and used in stability diagrams