Sergey A. Voronov

Modeling Vibratory Drilling Dynamics

The dynamic behavior of deep-hole vibratory drilling is analyzed. The mathematical model presented allows the determination of axial tool and workpiece displacements and cutting forces for significant dynamic system behavior such as the engagement and disengagement of the cutting tool into the workpiece material and tool breakthrough. Model parameters include the actual rigidity of the tool and workpiece holders, time-varying chip thickness, time lag for chip formation due to tool rotation and possible disengagement of drill cutting edges from the workpiece due to tool and/or workpiece axial vibrations. The main features of this model are its nonlinearity and inclusion of time lag differential equations, which require numeric solutions. The specific cutting conditions (feed, tool rotational velocity, amplitude and frequency of forced vibrations) necessary to obtain discontinuous chips and reliable removal are determined. Calculated bifurcation diagrams make it possible to derive the relevant domain of user-specified system parameters along with the determination of optimal cutting conditions.

Nonlinear dynamics of a machining system with two interdependent delays

Abstract The dynamics of turning by a tool head with two rows, each containing several cutters, is considered. A mathematical model of a process with two interdependent delays with the possibility of cutting discontinuity is analyzed. The domains of dynamic instability are derived, and the influence of technological parameters on system response is presented. The numeric analysis show that there exists specific conditions for given regimes in which one row of cutters produces an intermittent chip form while the other row produces continuous chips. It is demonstrated that the contribution of parametric excitation by shape roughness of an imperfect (unmachined) cylindrical workpiece surface is not substantial due to the special filtering properties of cutters that are uniformly distributed circumferentially along the tool head.

Modelling of bore honing

This paper discusses the modelling of deep holes honing. The dynamic model of honing, including the models of tool dynamics, cutting forces calculation, and new surface formation, are presented. The tool frequency characteristics, method of numeric calculation of machined surface and integral criteria of the surface distortion from an ideal cylinder are analysed based on the designed model.

Influence of Torsional Motion on the Axial Vibrations of a Drilling Tool

The nonlinear dynamics of a tool commonly employed in deep hole drilling is analyzed. The tool is modeled as a two-degree of freedom system that vibrates in the axial and torsional directions as a result of the cutting process. The mechanical model of cutting forces is a nonlinear function of cutting tool displacement including state variables with time delay. The equations of new surface formation are constructed as a specific set. These equations naturally include the regeneration effect of oscillations while cutting, and it is possible to analyze continuous and intermittent cutting as stationary and nonstationary processes, respectively. The influence of the axial and torsional dynamics of the tool on chip formation is considered. The Poincare maps of state variables for various sets of operating conditions are presented. The obtained results allow the prediction of conditions for stable continuous cutting and unstable regions. The time domain simulation allows determination of the chip shape most suitable for certain workpiece material and tool geometry. It is also shown that disregarding tool torsional vibrations may significantly change the chip formation process. DOI: 10.1115/1.2389212

Influence of Honing Dynamics on Surface Formation

The dynamics of the rotating tool commonly employed in deep hole honing is considered. The mathematical model of the process including the dynamic model of the tool and the interaction of the workpiece surface and honing sticks is analyzed. The honing tool is modeled as a continuous slender beam with a honing mandrel attached at the intermediate cross section. A single row of stones on the tool rotates and has reciprocational motion in the axial direction. The honing stones are expanded to the machined surface by a special rigid mechanism that provides cutting of workpiece cylindrical surface and which vibrates in the transverse and axial directions. The removal of chip and the tool vibrations cause the variation of expansion pressure and depend on the surface state formed by previous honing stone. The equations of new surface formation are separated as a specific set of the dynamic model. These equations inherently consider the regenerative effect of oscillations during cutting. The expansion pressure, tool stiffness, and technology conditions are considered as varying parameters since their influence on the process are different. The process productivity and precision can be improved by choosing rational conditions evaluated by simulation. The corresponding models and results of numerical simulation are presented. All the results are given in dimensionless form and therefore they are applicable to a wide range of real manufacturing process conditions. The model of new surface formation presented allows the simulation of the machined surface variation in time and to predict workpiece accuracy and possible correction of surface errors.Copyright

Methodic of Rational Cutting Conditions Determination for 3-D Shaped Detail Milling Based on the Process Numerical Simulation

The paper is devoted for the analysis of the dynamics effect on the 5-axis milling process of flexible details. The integrated model of milling dynamics composed by block principle in the paper is presented. The model consist of: 1) dynamical model of tool; 2) dynamical model of machined detail based on Finite Element Method (FEM); 3) phenomenological model of cutting forces and 4) algorithm of geometry modeling for instant machined chip thickness calculation. Regeneration mechanism of cutting and calculation of the machined surface are into this algorithm embedded. The elaborated model is adapted for 5-axis processing of the profiled details with 3-D complex geometry. Alteration of workpiece dynamic characteristics while the allowance removal is considered by the special algorithm of FEM grid changing based on the results of cutting geometry modeling. The results of modeling give us opportunity determine cutting forces, estimate the machined surface quality, calculate the magnitude and the character of tool and detail vibrations under the specified cutting conditions. The conception of increasing the process quality and the machinability for 3-D shaped details machining is offered in the paper. Applying the specified efficient conditions the undesired dynamical effects can be excluded on the base of the results of multi-variant simulation for milling dynamics varying the technological parameters at the different region of the processing route.Copyright

SIMULATION OF MACHINED SURFACE FORMATION WHILE HONING

The dynamics of deep hole honing is considered. The mathematical model of the process including the dynamic model of the tool and the interaction of the workpiece surface and honing sticks is analyzed. The honing tool is modeled as a continuous slender beam with a honing mandrel attached at the intermediate cross section. A single row of stones tool rotates and has reciprocational motion in the axial direction. The honing stones are expanded to the machined surface by a special rigid mechanism that provides cutting of workpiece cylindrical surface. The removal of chip and the tool vibrations cause the variation of expansion pressure and depend on the surface state formed by previous honing stone. The equations of new surface formation are separated as a specific set of the dynamic model. These equations inherently consider the regenerative effect of oscillations during machining. The numerical algorithm of machined surface generation has been developed which facilitates the 3D graphical representation and evaluation of the topography of the generated surface. The simulation model accounts for not only the nominal tool motion but also takes into account errors during machining such as tool components deformations and vibrations, tool runout, as well as initial surface distortions produced by previous operation. Based on the surface formation model software for evaluation of typical surface quality and accuracy criteria such as eccentricity, out-of-round, conicity, barrel, axial waviness, misalignment, faceting has been developed. The expansion pressure, tool stiffness, and technology conditions are considered as varying parameters since their influence on the process are different. The process productivity and accuracy can be improved by choosing rational conditions evaluated by simulation. The corresponding models and results of numerical simulation are presented. All the results are given in dimensionless form and therefore they are applicable to a wide range of real manufacturing process conditions. The model of new surface formation presented allows the simulation of the machined surface topography variation in time and to predict workpiece accuracy and possible correction of surface errors.Copyright

Nonconservative oscillations of a tool for deep hole honing

The dynamics of rotating tool commonly employed in deep hole honing is considered. Mathematical model of a process including the dynamic model of tool and model of workpiece surface and honing sticks interaction is analyzed. It is shown that interaction forces are nonconservative. Honing tool is modeled as a continuous slender beam with honing mandrel attached at intermediate cross section. Multi-stone tool rotates and has reciprocational motion in axial direction. Honing tones are expanded to the machined surface by special rigid mechanism that provides cutting of workpiece cylindrical surface. The tool vibrates in the transverse and axial directions. The transverse oscillations cause the variation of expansion pressure and change the interaction forces on the surface of the workpiece. Hence the vibrating tool shaft is under act of nonconservative forces depending on its position. The expansion pressure is a critical parameter in honing since its influence on process is different. The removal of stock increase linearly with pressure but the lowest expansion pressure and feed rate possible should be used to increase accuracy. The process productivity can be improved by increasing expansion pressure but may in a certain conditions cause a dynamic instability of tool shaft lateral oscillations. Another method of process productivity increasing is applying additional axial vibration of tool. In this case the tool passes more distance along the machined surface at the same time. But this method requires special machine tool with vibration actuator and additional research of system dynamic stability. Methods of vibratory process rational conditions evaluation are considered. The derived partial differential equations of rotating beam motion are reduced to a set of ordinary differential equations by the Galerkin approximation method. The derived differential equations with time periodic functions are numerically analyzed by Floquet method. The system response is studied for different technology and geometric parameters in non-dimensional form. That makes it possible to analyze a set of real processes applying the similarity conditions.

Influence of Torsional Motion on Vibratory Drilling

The nonlinear dynamics of a tool commonly employed in deep hole drilling is analyzed. The tool is modeled as a two-degree of freedom system that vibrates in axial directions and twists caused by the cutting process. The mechanical model of cutting forces is a nonlinear function of cutting tool displacement including state variables with time delay. The equations of new surface formation are separated as a specific set. These equations naturally include the regeneration effect of oscillations under cutting and it is possible to analyze continuous and intermittent cutting involving either stationary or non-stationary processes. The vibratory drilling tool feed consists of a constant as well as a periodic component. The influence of tool axial and torsional dynamics on chip formation is considered. The Poincare maps of state variables for various sets of operating conditions are presented. The obtained results allow prediction of conditions for stable continuous cutting and unstable regions. The conditions of tool axial vibrations synchronized at frequency of external excitation are analyzed. The time domain simulation allows determination of the chip shape most suitable for certain workpiece material and tool geometry. It is also shown that disregarding tool torsional vibrations may significantly change the chip formation process. The suggested model can be applied at the stage of the manufacturing process design.© 2005 ASME

Mathematical modeling of the cylindrical grinding process

This paper proposes a dynamic model of cylindrical grinding with a tool owning specified distribution of abrasive grains. Cutting forces have been calculated, the surface geometry formed after a grinding wheel pass has been determined, the influence of the process dynamics on cutting forces and machined surface geometry has been taken into account, and the effects of cutting condit on vibrations being generated in the process of grinding have been investigated.