Modeling of three-dimensional numerically controlled end milling operations

A computer-aided cutting simulation system was developed to model three-dimensional numerically controlled (NC) end milling operations. In the developed system, varying axial and radial depths of cut in an NC tool path were identified by a solid modeling system using constructive solid geometry and boundary representation techniques. Once the axial and radial depths of cut were calculated, the dynamic cutting force was calculated from an end milling process model. As a result, the cutting performance in three-dimensional NC end milling operations can be verified and optimized through this approach.     

A neural network approach for force and contour error control in multi-dimensional end milling operations

The problem of controlling the average resultant cutting force together with the contour error in multi-dimensional end milling operations is considered in this study. Two sets of neural networks are used in the control system. The first set is used to specify the feed rate to maintain a desired cutting force. This feed rate is resolved along the feed axes using a parametric interpolation algorithm so that the desired part shape is obtained. The second set is used to make corrections to the feed rate components specified by the parametric interpolation algorithm to minimize the contour error caused by the dynamic lag of the closed-loop servo systems controlling the feed drives. In addition, the control system includes a feedforward input to compensate for static friction effects. Experimental results are presented for machining two-dimensional circular slots and a three-dimensional spherical surface to show the validity of the proposed approach.     

Implementation of pole placement adaptive controller for force control of non-minimum phase end milling operations

The design and implementation of a pole placement adaptive controller are discussed for force control of the end milling process. The end milling process considered is a non-minimum phase system whose computational delay exceeds one half of the control interval. The internal model principle is included in the controller design to ensure a zero steady-state tracking error. Experimental results show that the pole placement adaptive controller is effective for force control of the non-minimum phase end milling operation and the closed-loop control system is stable over a wide range of cutting conditions.     

Direct adaptive control of end milling process

A direct adaptive control algorithm, which is spindle speed and drive dynamics independent, has been developed for machining operations. The combined dynamics of feed motion and cutting process are modelled as a third order system whose parameters may vary with spindle speed and part geometry changes during machining. The algorithm does not use any specific time interval, thus sampling time dependent discrete transfer functions and pole assignments are avoided. The adaptive controller is designed to have a closed loop characteristic function which behaves like an open loop regular and stable machining operation. The proposed direct adaptive controller is practical, can be used in any multi-axes machining, and can be combined with chatter suppression techniques which require spindle speed regulation. The algorithm is applied to the adaptive control of milling. Satisfactory results are obtained in constraining the maximum cutting forces and dimensional surface errors in milling experiments.     

Adaptive control optimization in end milling using neural networks

In this paper, we propose an architecture with two different kinds of neural networks for on-line determination of optimal cutting conditions. A back-propagation network with three inputs and four outputs is used to model the cutting process. A second network, which parallelizes the augmented Lagrange multiplier algorithm, determines the corresponding optimal cutting parameters by maximizing the material removal rate according to appropriate operating constraints. Due to its parallelism, this architecture can greatly reduce processing time and make real-time control possible. Numerical simulations and a series of experiments are conducted on end milling to confirm the feasibility of this architecture.     

数控铣削模糊自适应控制系统

对数控加工中心控制系统进行了分析和建模,提出了一套应用于数控铣削加工设备的模糊自适应控制方案,并进行了系统仿真.该系统可通过实时负载反馈实现主轴电机恒功率控制,达到提高机床加工效率,降低生产成本的目的.     

An in-process surface recognition system based on neural networks in end milling cutting operations

An in-process based surface recognition system to predict the surface roughness of machined parts in the end milling process was developed in this research to assure product quality and increase production rate by predicting the surface finish parameters in real time. In this system, an accelerometer and a proximity sensor are employed as in-process surface recognition sensors during cutting to collect the vibration and rotation data, respectively. Using spindle speed, feed rate, depth of cut, and the vibration average per revolution (VAPR) as four input neurons, an artificial neural networks (ANN) model based on backpropagation was developed to predict the output neuron-surface roughness R_a values. The experimental results show that the proposed ANN surface recognition model has a high accuracy rate (96–99%) for predicting surface roughness under a variety of combinations of cutting conditions. This system is also economical, efficient, and able to be implemented to achieve the goal of in-process surface recognition by retrieving the weightings (which were generated from training and testing by the artificial neural networks), predicting the surface roughness R_a values while the part is being machined, and giving feedback to the operators when the necessary action has to be taken.     

Thermal modelling of end milling

Determination of the temperatures during machining is one of the most important challenges for accurate milling simulations. Coupled with excessive shearing, plastic deformation and friction in a small region of cutting, the temperatures in milling may have very significant impact on parts and tools such as dimensional errors, residual stresses and tool wear. Temperature exhibits a non-linear complex-modelling problem in milling process. In this article, for the first time, a novel thermal modelling is introduced for fast and accurate prediction of temperatures in end milling processes. A theoretical modelling approach and experimental validations are presented for various cutting conditions.     

Geometric adaptive straightness control system for the peripheral end milling process

A relationship between the tool deflection and the feed rate is modelled by a modified Taylor's tool-life equation. An off-line Geometric Adaptive Control (GAC) system to compensate for machining straightness error in the finished surface due to tool deflection and guideway error generated by the peripheral end milling process is proposed.

Without a priori knowledge of the variations of the cutting parameters, the time-varying parameters are estimated by an exponentially windowed recursive least squares method with only post-process measurements of the straightness error through a gap sensor. The location error is compensated by moving the milling bed through a numerical control command before cutting. The waviness error is regulated by using optimal feed rate manipulation as obtained from the proposed GAC method during machining although the parameters do not converge to fixed values.

Experimental results show that the location error is controlled within the range of fixturing error of the milling bed on the guideway, the waviness accuracy can be increased to more than three times that of the case with no control action. A single-pass milling operation can become feasible through practical application of the proposed GAC system for finish cutting conditions.     

Providing stability maps for milling operations

This article presents a new stability prediction tool. The method is based on the dynamic behaviour of both milling tool and workpiece, computed using finite element method. Dynamic behaviour is expressed under the form of transfer functions and used to predict stability lobes at each tool position. The unconditionally stable depth of cut is then stored and displayed on a graphic representation of the machined surface under the form of colour axis, named stability map.An application of the method on a Renault cylinder block is presented as an illustration.     

A predicted milling force model for high-speed end milling operation

In this study, a predicted milling force model for the end milling operation is proposed. The speed of spindle rotation, feed per tooth, and axial and radial depth of cut are considered as the affecting factors. An orthogonal rotatable central composite design and the response surface methodology are used to construct this model. The milling force per spindle revolution period obtained from each treatment is equally divided into suitable sections. The extreme value of the milling force in each section is selected to build the predicted model so as to predict the extreme force in each section for any cutting conditions within the specified range of the design database, including the speed of spindle rotation, feed per tooth, and axial and radial depth of cut. Moreover, the predicted extreme force in each section is applied to reconstruct the milling force waveform by means of the expansion of the Fourier series. The predicted model presented in this paper is adequate for a 95% confidence interval, and shows good correlation between experimental and predicted results.     

In-process prediction of cutting depths in end milling

In geometric adaptive control systems for the end milling process, the surface error is usually predicted from the cutting force owing to the close relationship between them, and the easiness of its measurement. Knowledge of the cutting depth improves the effectiveness of this approach, since different cutting depths result in different surface errors even if the measured cutting forces are the same. This work suggests an algorithm for estimating the cutting depth based on the pattern of cutting force. The cutting force pattern, rather than its magnitude, better reflects the change of the cutting depth, because while the magnitude is influenced by several cutting parameters, the pattern is affected mainly by the cutting depth. The proposed algorithm can be applied to extensive cutting circumstances, such as presence of tool wear, change of work material hardness, etc.     

模糊自适应PID在数控进给伺服系统的应用

数控机床的进给伺服控制是复杂的机电耦合系统,因其存在参数时变、负载扰动以及电机的非线性等缺点,很难为其建立准确的模型。模糊Fuzzy控制具有无需建立被控对象的数学模型、鲁棒性好等优点但稳态精度差,将模糊控制和PID控制相结合,设计了模糊自适应PID控制器,并将此应用于数控伺服系统的控制中,该控制器具有较完善的控制性能。仿真实验的结果表明,采用该模糊自适应PID控制器具有较高的稳定精度,较强的鲁棒性。     

Analysis of chatter vibration in the end milling process

This paper continues the work of a previous paper by the authors. A different approach is applied, which adopts frequency domain analysis by linearizing the nonlinear equations to investigate the dynamic behavior in the milling process. A new relationship among the limiting axial depth of cut, workpiece fundamental natural frequency and spindle speed is constructed, and the obtained stable region is also consistent with that of the previous paper.     

Identification of common sensory features for the control of CNC milling operations under varying cutting conditions

The main focus of this study is to identify the most influential and common sensory features for the process quality characteristics in CNC milling operations—dimensional accuracy (bore size tolerance) and surface roughness—using three different material types (6061-T6 aluminum, 7075-T6 aluminum, and ANSI-4140 steel). The materials were machined on a vertical CNC mill, retrofitted with multiple sensors and data acquisition systems, to investigate the effects of variations in material types and machining parameters. The sensor data include cutting force measurements, spindle quill vibration, and acoustic emission, each of which further divided into measurable components, such as x, y, and z components in cutting force, x and y spindle quill vibration, DC, AC, and Count Rate for acoustic emission signals. Those components were filtered and analyzed to determine the sensory features that best correlate with process quality characteristics. Tool wear rate and machining characteristics appeared differently, depending on the material types, yet some components of the sensory data were found to be significant with relation to the variations in bore size and surface roughness for all three types of materials. This suggests that even under the varying cutting conditions involving different materials, the identified sensory features can be used for the reliable and accurate control of milling operations.     

The shape characteristic detection of tool breakage in milling operations

Detection of tool failure is very important in automated manufacturing. All previously developed tool breakage detection approaches in milling operations have adopted the strategy of parameter detection in which the detection of tool breakage was carried out according to values of specific parameters selected to reflect tool state (with or without tool breakage). In this paper the new concept of shape characteristic detection of tool breakage in milling operations is proposed. The detection of tool breakage is conducted according to the shape characteristics of discrete dyadic wavelet decomposition of cutting force. By means of the proposed method, the influence caused by the variation of cutting parameters and transients is eliminated. The proposed method is conducted in two steps. In the first step, cutting force signals are decomposed by discrete dyadic wavelet, with the shape characteristic vectors then being generated by the proposed shape characteristic vector-generating algorithm. In the second step, the shape characteristic vectors are fast classified by the ART2 neural networks. The accuracy and effectiveness of the proposed method are verified by numerous experiments.     

Chatter suppression in micro end milling with process damping

Micro milling utilizes miniature micro end mills to fabricate complexly sculpted shapes at high rotational speeds. One of the challenges in micro machining is regenerative chatter, which is an unstable vibration that can cause severe tool wear and breakage, especially in the micro scale. In order to predict chatter stability, the tool tip dynamics and cutting coefficients are required. However, in micro milling, the elasto-plastic nature of micro machining operations results in large process damping in the machining process, which affects the chatter. We have used the equivalent volume interface between the tool and the workpiece to determine the process damping parameter. Furthermore, the accurate measurement of the tool tip dynamics is not possible through direct impact hammer testing. The dynamics at the tool tip is indirectly obtained by employing the receptance coupling method, and the mechanistic cutting coefficients are obtained from experimental cutting tests. Chatter stability experiments have been performed to examine the proposed chatter stability model in micro milling.     

Geometric adaptive straightness control system for the peripheral end milling process with large error sources

An off-line Geometric Adaptive Control (GAC) scheme is proposed to compensate for machining straightness errors due to the machine tool's inaccuracy and those arising as a result of the metal cutting process during the finish peripheral end milling process. In the milling process, the workpiece travels along the guideway while the spindle system remains fixed. The scheme is based on the exponential smoothing of post-process measurements of relative machining errors due to the tool and bed deflections. Without a priori knowledge of the variations of the cutting parameters, the time-varying parameters are estimated by an Exponentially Weighted Recursive Least Squares (EWRLS) method. This method is able to incorporate a straightedge which is not necessarily accurate to identify the guideway errors. To reduce the drift of the cutting parameters, a single parameter adaptation method is introduced. Experimental results show that the location error is controlled within the range of the fixing error of the milling bed on the guideway. Further, the waviness error is reduced to less than 10 μm in the machining of a 508-mm long prismatic workpiece regardless of the machining conditions.     

A cutting force model for face milling operations

A procedure for the simulation of the static and dynamic cutting forces in face milling is described. For the static force model, the initial position errors of the inserts and the eccentricity of the spindle are taken into consideration as the major factors affecting the variation of the chip cross-section. The structural dynamics model for the multi-tooth oblique cutting operation is assumed as a multi-degrees of freedom spatial system. From the relative displacement of this system, based on the double modulation principle, the dynamic cutting forces were derived and simulated. The simulated forces were subsequently compared to measured forces in the time and frequency domains.