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A semi-analytical method is presented in this paper for stability analysis of milling with a variable spindle speed (VSS), periodically modulated around a nominal spindle speed. Taking the regenerative effect into account, the dynamics of the VSS milling is governed by a delay-differential equation (DDE) with time-periodic coefficients and a time-varying delay. By reformulating the original DDE in an integral-equation form, one time period is divided into a series of subintervals. With the aid of numerical integrations, the transition matrix over one time period is then obtained to determine the milling stability by using Floquet theory. On this basis, the stability lobes consisting of critical machining parameters can be calculated. Unlike the constant spindle speed (CSS) milling, the time delay for the VSS is determined by an integral transcendental equation which is accurately calculated with an ordinary differential equation (ODE) based method instead of the formerly adopted approximation expressions. The proposed numerical integration method is verified with high computational efficiency and accuracy by comparing with other methods via a two-degree-of-freedom milling example. With the proposed method, this paper details the influence of modulation parameters on stability diagrams for the VSS milling. [ABSTRACT FROM AUTHOR]

This paper proposes a semi-analytical solution via the differential quadrature method (DQM) for stability analysis of linear multide gre e-of-freedom second-order systems with multiple delays. The vibration systems are reformulated as a delayed differential equation (DDE) in state-space form. With the derivative of the state vector with respect to time at an arbitrary discrete-time point being expressed as a linear weighted sum of the values of the state vector, the original DDE is approximated by a set of algebraic equations, leading to the Floquet transition matrix. Based on Floquet theory, the stability of the systems is then determined by checking the eigenvalues of the transition matrix. The computational accuracy and efficiency are demonstrated through comparison with existing methods via numerical examples. As an application, the proposed method is employed to predict chattelstability in simultaneous machining operations, providing a reference for the choice of machining parameters. [ABSTRACT FROM AUTHOR]

This paper presents a time-domain semi-analytical method for stability analysis of milling in the framework of the differential quadrature method. The governing equation of milling processes taking into account the regenerative effect is formulated as a linear periodic delayed differential equation (DDE) in state space form. The tooth passing period is first separated as the free vibration duration and the forced vibration duration. As for the free vibration duration, the analytical solution is available. As for the forced vibration duration, this time interval is discretized by sampling grid points. Then, the differential quadrature method is employed to approximate the time derivative of the state function at a sampling grid point within the forced vibration duration by a weighted linear sum of the function values over the whole sampling grid points. The Lagrange polynomial based algorithm (LPBA) and trigonometric functions based algorithm (TFBA) are employed to obtain the weight coefficients. Thereafter, the DDE on the forced vibration duration is discretized as a series of algebraic equations. By combining the analytical solution of the free vibration duration and the algebraic equations of the forced vibration duration, Floquet transition matrix can be constructed to determine the milling stability according to Floquet theory. Simulation results and experimentally validated examples are utilized to demonstrate the effectiveness and accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a numerical scheme to predict the milling stability based on the integral equation and numerical integration formulas. First, the milling dynamics taking the regenerative effect into account is represented in the form of integral equation. Then, the tooth passing period is precisely divided into the free vibration phase during which the analytical solution is available and the forced vibration phase during which an approximate solution is needed. To obtain the numerical solution of the integral equation during the forced vibration phase, the time interval of interest is equally discretized. Over each small time interval, Newton-Cotes integration formulas or Gauss integration formulas are employed to approximate the integral term in the integral equation. After establishing the state transition matrix of the system in one period, the milling stability is predicted by using Floquet theory. The benchmark examples are utilized to verify the proposed approach. The results demonstrate that it is highly efficient and accurate. [ABSTRACT FROM AUTHOR]

This paper presents a novel model for workpiece positioning analysis. Existing fixturing models may underestimate the positioning error due to neglect of the curvature of one or both contacting bodies. By using surface-to-surface signed distance function, a two-sided quadratic model for fixture locating analysis is developed. A system of quadratic sensitivity equations, which relate locators' source errors to the resulting workpiece localization error, are derived. The second-order geometric properties of both workpiece and locators are taken fully into account. The present model is more accurate than the existing linear model and one-sided quadratic model, which is verified through numerical examples. It has potential applications in fixture design, fault diagnosis, and tolerance analysis. [ABSTRACT FROM AUTHOR]

This brief proposes a numerical approach for simultaneous prediction of stability lobe diagrams and surface location error in low radial immersion milling based on the direct integration scheme and the precise time-integration method. First, the mathematical model of the milling dynamics considering the regenerative effect is presented in a state space form. With the cutter tooth passing period being divided equally into a finite number of elements, the response of the system is formulated on the basis of the direct integration scheme. Then, the four involved time-variant items, i.e., the time-periodic coefficient item, system .state item, time delay item, and static force item in the integration terms of the response, are discretized via linear approximations, respectively. The corresponding matrix exponential related functions are all calculated by using the precise time-integration method. After the state transition expression on one small time interval being constructed, an explicit form for the discrete dynamic map of the system on one tooth passing period is established. Thereafter, the milling stability is predicted via Floquet theory and the surface location error is calculated from the fixed point of the dynamic map. The proposed method is verified by the benchmark theoretical and experimental results in published literature. The high efficiency of the algorithm is also demonstrated. [ABSTRACT FROM AUTHOR]

Based on the observation that many surfaces of revolution can be treated as a canal surface, i.e., the envelope surface of a one-parameter family of spheres, the analytical expressions of the envelopes of the swept volumes generated by the commonly used rotary cutters undergoing general spatial motions are derived by using the envelope theory of sphere congruence. For the toroidal cutter two methods for determining the effective patch of the envelope surface are proposed. With the present model, it is shown that the swept surfaces of a torus and a cylinder can be easily constructed without complicated calculations, and that the minimum distance (between the swept surface and a simple surface) and the signed distance (between the swept surface and a point in space) can be easily computed without constructing the swept surface itself An example of global tool path optimization for flank milling of ruled surface with a conical tool, which requires to approximate the tool envelope surface to the point cloud on the design surface, is given to confirm the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for the optimal design. of the measurement point layout for 3D workpiece localization in the presence of part surface errors and measurement errors. A number of frame-invariant norms of the infinitesimal rigid body displacement, two of which give Riemann metrics on the Euclidean group, are defined to quantify the localization accuracy required by manufacturing processes. Then, two types of indices, both frame invariant and scale invariant, are derived to characterize the sensitivities of the accuracy measures to the sampling errors at the measurement points. With a dense set of discrete points on the workpiece datum surfaces predefined as candidates for measurement, planning of probing points to accurately recover part location is modeled as a combinatorial problem focusing on minimizing the accuracy sensitivity index. It is shown that if the number of measurement points is large enough, there is no need to optimize their positions, and that if the systematic error component of the sampled geometric errors is not negligible as compared with the random error component, addition of measurement points offers no guarantee of a smaller upper bound of the localization error. A heuristic floating forward search algorithm is employed to efficiently find a near-optimal solution. Two relevant problems of sensor placement optimization for geometric imperfection diagnosis and fixture fault diagnosis are also briefly revisited in the same framework. Examples are given to illustrate the effectiveness of the proposed design criteria and algorithm. [ABSTRACT FROM AUTHOR]

The article presents several papers on vibration and acoustics. One paper describes a method for designing and fabricating broadband vibration absorbers for structural noise control. Another paper investigates the pressure pulsations caused by each mass flow rate through suction valves and ports of a compressor to attribute high-pressure pulsations responses to certain valves. In one paper, vibration behavior of engine on the nonlinear hydraulic engine mount is studied. Another one proposes a mechanical model describing finite motions of nonshallow cables around the initial catenary configurations.

This paper presents a novel methodology for evaluating spatial straightness error based on the minimum zone criterion. Spatial straightness evaluation is formulated as a linear complex Chebyshev approximation problem, and then reformulated as a semi-infinite linear programming problem. Both models for the primal and dual programs are developed. An efficient simplex-based algorithm is employed to solve the dual linear program to yield the straightness value. Also a general algebraic criterion for checking the optimality of the solution is proposed. Numerical experiments are given to verify the effectiveness and efficiency of the presented algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a unified framework for best-fitting of complex rigid surface to measured 3-D coordinate data by adjusting its location (position/orientation). For a point expressed in the machine reference frame and a nominal surface represented in its own model frame, a signed point-to-surface distance function is defined, and its properties are investigated, especially, its increment with respect to the differential motion of the surface, up to the second order, is derived. On this basis, localization and profile error evaluation of complex surface are formulated as a nonlinear least-squares problem and nonlinear constrained optimization problem respectively, and sequential approximation algorithms are developed to solve them. The two algorithms have the advantages of implementational simplicity, computational efficiency and robustness. Also strategies for estimating initial solution and compensating probe radius are presented. Examples confirm the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Blisks suffer from flutter, a self-sustained vibration caused by aerodynamic coupled forces. This instability could cause serious damage to the blades and the machine. Flutter stability is usually analyzed based on the eigenvalue method in the aspect of the linear structural dynamic system, which transforms a dynamics stability analysis into a point of equilibrium in an infinite time scale. However, in reality, most of the blisk vibrations arise on a finite time horizon. The transient vibration amplification may cause serious damage. This paper proposes a transient flutter stability analysis method in a finite time for structural mistuned blisk based on the energy growth method. First, two common blisk models coupled aerodynamic force with different complexity are built and are all expressed in the state space representation. A novel energy growth method is then employed to analyze the transient stability and to find the maximum energy growth of the models. The optimal initial condition which leads to the maximum energy growth is obtained. A new flutter stability criterion is developed to consider the transient stability based on the energy growth method and the infinite time stability based on the eigenvalue method. The new transient stability method is verified by two numerical studies. It is found that the structural mistuned blisk model which is traditionally predicted stable still has a transient instability in a finite time due to the non-normal property of the dynamic state matrix. [ABSTRACT FROM AUTHOR]