Variable-step integration method for milling chatter stability prediction with multiple delays

Zhang, XiaoJian; Chen, Xiong; Ding, Ye; Xiong, Yan

doi:10.1007/s11431-011-4599-2

Cited by 46 publications

(30 citation statements)

References 24 publications

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“…In order to ensure the service life and security of constructional works, it is necessary to monitor the constructional work systematically during its building and operating. Due to the diversity, complexity and non-deterministic characters of inducing factors of the building subsidence deformation, the mechanical behavior and deformation trend of building subsidence also reflect non-linear characteristics with the coexistence of the uncertainty and randomness [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Existing methods for building subsidence deformation prediction usually establish the time series analysis model by utilizing monitored data [35][36][37][38][39][40].…”

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confidence: 99%

Dynamic prediction of building subsidence deformation with data-based mechanistic self-memory model

Wang

Hou

et al. 2012

Chin. Sci. Bull.

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This paper describes a building subsidence deformation prediction model with the self-memorization principle. According to the non-linear specificity and monotonic growth characteristics of the time series of building subsidence deformation, a data-based mechanistic self-memory model considering randomness and dynamic features of building subsidence deformation is established based on the dynamic data retrieved method and the self-memorization equation. This model first deduces the differential equation of the building subsidence deformation system using the dynamic retrieved method, which treats the monitored time series data as particular solutions of the nonlinear dynamic system. Then, the differential equation is evolved into a difference-integral equation by the self-memory function to establish the self-memory model of dynamic system for predicting nonlinear building subsidence deformation. As the memory coefficients of the proposed model are calculated with historical data, which contain useful information for the prediction and overcome the shortcomings of the average prediction, the model can predict extreme values of a system and provide higher fitting precision and prediction accuracy than deterministic or random statistical prediction methods. The model was applied to subsidence deformation prediction of a building in Xi'an. It was shown that the model is valid and feasible in predicting building subsidence deformation with good accuracy. The fast development of economics promotes the urbanization of China. More and more high-rises appear in our cities [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In order to ensure the service life and security of constructional works, it is necessary to monitor the constructional work systematically during its building and operating. Due to the diversity, complexity and non-deterministic characters of inducing factors of the building subsidence deformation, the mechanical behavior and deformation trend of building subsidence also reflect non-linear characteristics with the coexistence of the uncertainty and randomness [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Existing methods for building subsidence deformation prediction usually establish the time series analysis model by utilizing monitored data [35][36][37][38][39][40]. However, most of these models are of the "parameter model" class which may not have clear physical meaning of parameters and discard effective parts of monitoring data. On the basis of the retrieved modeling, self-memorization principle has been recently developed based on the mechanism of time series data. As a mathematic realization on integration of deterministic and random theory, the self-memory model is a statistical-dynamical method to solve problems in nonlinear dynamic systems [41][42][43]. The core method of the model is to transform differential equations into difference-integral equations by introduction of the self-memory function. For dynamic systems described by differential equations, pre...

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confidence: 99%

Dynamic prediction of building subsidence deformation with data-based mechanistic self-memory model

Wang

Hou

et al. 2012

Chin. Sci. Bull.

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“…This research does not necessarily conflict with these objectives. Instead, we are trying to define a tool path "pattern", on which there is more room for increasing machining efficiency so that optimization of feedrate and some dynamic factors can be more effective [27][28][29]. On the other hand, for very complicated surface machining, the identified cutting direction can be too twisted to yield effective path.…”

Section: Resultsmentioning

confidence: 99%

Kinematics constrained five-axis tool path planning for high material removal rate

Tao

Chen

Xiong

et al. 2011

Sci. China Technol. Sci.

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Traditional five-axis tool path planning methods mostly focus on differential geometric characteristics between the cutter and the workpiece surface to increase the material removal rate (i.e., by minimizing path length, improving curvature matching, maximizing local cutting width, etc.). However, material removal rate is not only related to geometric conditions such as the local cutting width, but also constrained by feeding speed as well as the motion capacity of the five-axis machine. This research integrates machine tool kinematics and cutter-workpiece contact kinematics to present a general kinematical model for five-axis machining process. Major steps of the proposed method include: (1) to establish the forward kinematical relationship between the motion of the machine tool axes and the cutter contact point; (2) to establish a tool path optimization model for high material removal rate based on both differential geometrical property and the contact kinematics between the cutter and workpiece; (3) to convert cutter orientation and cutting direction optimization problem into a concave quadratic planning (QP) model. Tool path will finally be generated from the underlying optimal cutting direction field. Through solving the time-optimal trajectory generation problem and machining experiment, we demonstrate the validity and effectiveness of the proposed method. tool path, material removal rate, contact motion, quadratic planning Citation:Ye T, Xiong C H, Xiong Y L, et al. Kinematics constrained five-axis tool path planning for high material removal rate.

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“…On this basis, the spectral method with exponential convergence rate [68] and the variable-step integration method suitable for the multiple time delay systems [69] are proposed.…”

Section: Integral Equation Based Methodsmentioning

confidence: 99%

On time-domain methods for milling stability analysis

Ding

Zhu

2012

Chin. Sci. Bull.

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As a basic and advanced machining technique, the high-speed milling process plays an important role in realizing the goal of high performance manufacturing. From the viewpoint of machining dynamics, obtaining chatter-free machining parameters is a prerequisite to guaranteeing machining accuracy and improving machining efficiency. This paper gives an overview on recent progress in time domain semi-analytical methods for chatter stability analysis of milling processes. The state of art methods of milling stability prediction in milling processes and their applications are introduced in detail. The bottlenecks involved are analyzed, and potential solutions are discussed. Finally, a brief prospect on future works is presented. High speed milling is widely utilized in manufacturing of complex surfaces for the fields of aerospace, ship, automotive, dies and molds etc., due to its advantage of obtaining high machining accuracy and high material removal rate with keeping low-amplitude cutting forces. Regarding to modeling of machining processes, the research topics on high speed milling can be categorized as: tool path planning, machining dynamics and machining physical modeling. Tool path planning is to plan the tool path according to the workpiece model, machining strategy and required machined error [1][2][3][4][5]. From the viewpoint of machining dynamics, the relative vibration between the workpiece and cutter in the milling process is the main reason of reducing product surface quality and limiting the production efficiency. To suppress the vibration impact by optimizing the machining parameters, the following two questions need to be addressed.(1) Stability analysis based on the dynamics of milling processes. As far as chatter vibrations are concerned, there are four different mechanisms: regeneration [6], mode coupling [7], friction [8] and thermo-mechanics of chip formation [9]. In milling processes, regenerative chatter is the most common form of self-excited vibration to reduce surface quality and machining efficiency [10,11]. The works on analysis of the stability of milling processes focus on calculating the stability boundary of the machining parameters based on the dynamic models characterizing the milling processes.(2) Machining accuracy analysis on the basis of stability analysis. Due to forced vibrations in milling processes, chatter-free machining parameters cannot ensure high performance machining. Vibration-induced surface errors can be classified as surface location error (SLE) [12] and surface roughness [13]. It is essential to take the stability and dynamical errors into account in machining optimization models to achieve high performance milling.

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Variable-step integration method for milling chatter stability prediction with multiple delays

Cited by 46 publications

References 24 publications

Dynamic prediction of building subsidence deformation with data-based mechanistic self-memory model

Dynamic prediction of building subsidence deformation with data-based mechanistic self-memory model

Kinematics constrained five-axis tool path planning for high material removal rate

On time-domain methods for milling stability analysis

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