A study on calibration of coefficients in end milling forces model

This paper presents an improved approach to calibrate the cutting coefficients in an end-milling model. In order to predict end-milling forces, lots of simulative models are established. In order to use them, coefficients in the models, for example, cutting pressure constants etc., must firstly be calibrated experimentally, and simulative precision and applicability of the models are influenced by them. For simplicity, using average forces to calibrate cutting parameters are widely adopted by lots of researchers. However, the existence of an instruments zero-drift, noise, etc., will have effect on the precision of experimental data, so, it is difficult to directly obtain exact average-cutting forces through experimental data. Aiming at the above problem, the paper investigates milling forces in the frequency domain, discusses the impact of experimental data at different frequencies on cutting force coefficients and the influence of sensitivity of error on experimental data at different frequencies on coefficients is studied. Based on the research, an improved method to calibrate the cutting coefficients is provided. Based on a series of experiments and numerical simulations, the validity of the method is confirmed. At the end of the paper, some useful conclusions are drawn.     

Prediction and analysis of size tolerances achievable in peripheral end milling

Size tolerance is the most critical parameter requiring attention for ensuring dimensional repeatability of manufactured component parts, yet very little research has been reported on this important topic. This paper presents a method for predicting size tolerances of component parts machined through peripheral end milling. The method makes use of prototype software based on previously reported cutting-force and surface-generation models in which the end mill is modelled as a cantilever beam rigidly gripped by the tool holder. It also takes into account the effect of size variation for the cutting tool. The method is validated through several cutting experiments. For further analysis, the method is employed for predicting the size tolerances of a prismatic component by varying one controllable variable at a time and then monitoring the relationship between size tolerance and the variable. When a distinct relationship is noted it is verified both analytically and experimentally. The results indicated that whilst the average size variation, which contributed to the variation of the basic size of component parts, is always proportional to the metal removal rate, the range of size variations that contributed to the size tolerance is not. Therefore, there is scope for increasing the metal removal rate without sacrificing the size tolerance. The knowledge acquired through this research can be applied for selecting an optimum cutting condition using the developed method when the size tolerances of component parts are specified.     

Cutting force model considering tool edge geometry for micro end milling process

The analysis of the cutting force in micro end milling plays an important role in characterizing the cutting process, as the tool wear and surface texture depend on the cutting forces. Because the depth of cut is larger than the tool edge radius in conventional cutting, the effect of the tool edge radius can be ignored. However, in micro cutting, this radius has an influence on the cutting mechanism. In this study, an analytical cutting force model for micro end milling is proposed for predicting the cutting forces. The cutting force model, which considers the edge radius of the micro end mill, is simulated. The validity is investigated through the newly developed tool dynamometer for the micro end milling process. The predicted cutting forces were consistent with the experimental results.     

A study on the five-axis end milling for sculptured surfaces

The direction vector of milling cutter for CL-data of five-axis milling is obtained by the fact that the bottom part of the milling cutter rides on free-form surfaces using the z-map method. Since the direction vector is known, CL-data can be transformed to the NC-code with regard to the geometry of the five-axis machine and post-processing. For uniform surfaces, the tool path is created from the prediction of cusp heights. After generating the NC-code, a sculptured surface was machined by five-axis end milling and cusp heights on the machined surface were measured by a three-dimensional CMM with laser scanner. From this machining test, it was found that this machining method is effective.     

数控铣床加工端面螺纹的方法

利用数控铣床的宏程序功能与端面螺纹的阿基米德螺旋线特性来加工端面螺纹,具有工艺设计简单,程序编制简单,经济性好的特点;通过对端面螺纹加工的工艺分析和宏程序编制方法的详细论述,介绍了端面螺纹在数控铣床上的加工过程。     

Programmable end milling of thermoplastics

The end milling of industrial and engineering thermoplastics on numerically controlled machine tools is considered. Specifically, attention focuses on the sources and prevention of machining defects. Recommendations are made regarding the selection of the tool geometry, the cutting conditions, and the mill trajectory.     

A simulation shape error for end milling AL6061-T6

A simulation system for shape error in end milling is developed and tested experimentally. The flexural rigidity of a rotated end mill was derived from its cross-section. The tool deflections due to the bending, the twist and the deformation of a tooth were studied individually. The resulting twist, due to the uniform and nonuniform torsions, was proposed for a nonprismatic tool. The adequacy of the simulation system was established by a set of tests. The results show that the deflections in the X and Y directions produced by torsion were larger than those due to bending in the cutting process.     

球头铣刀数控加工表面形貌几何仿真的研究

几何仿真是建立铣削力预测模型的基础,而传统的几何仿真只考虑刀具的平动而忽略其转动。本文在同时考虑刀具平动和转动的基础上,利用工件Z-Map表示模型和刀刃离散表示法,提出了一种球头铣刀三轴数控铣削的微观几何仿真算法。该算法鲁棒性好、适用范围广,不仅能高效而准确地仿真铣削表面形貌,而且能准确提供切屑的轮廓,为建立精确的切削力预测模型提供了重要的几何参数。     

A microcontroller-based end milling cutter monitoring and management system

The monitoring of end milling cutting operations for tool breakage is achieved using a low-cost microcontroller-based system. The system is based upon acquiring and analysing machine tool-based signals for characteristic responses to tool breakage. Spindle speed and load signals are shown to be responsive to tool condition and thus capable of supporting the deployed approach. The resulting system operates in real time with tool breakage detection consistently diagnosed within two revolutions. The monitoring function is extended to consider tool wear using analysis methods applied in the time and frequency domains. Decisions about tool condition are made by integrating all relevant information into a rule base. Higher-level tool management functions supported by the deployed system are identified.     

A non-contact method for part-based process performance monitoring in end milling operations

Surface response to excitation (SuRE) method was originally developed for structural health monitoring (SHM) applications. SuRE was used to evaluate the performance of completed milling operations. The method generates surface waves on the plate and studies the spectrum changes at selected points to detect defects and change of compressive forces. In this study, the length, depth, and width of a slot were changed step by step. The surface of the aluminum plate was excited in the 20–400 kHz range with a piezoelectric element. A laser scanning vibrometer was used to monitor the vibrations at the predetermined grid points after the dimensions of the slot were changed methodically. The frequency spectrums of measured vibrations were calculated by using the Fast Fourier Transformation (FFT). The sums of the squares of the differences (SSD) of the spectrums were calculated to evaluate the change of the spectrums. The SuRE method was able to determine if the dimensions were changed in each case at all the selected points. The scanning laser vibrometer is not feasible to be used at the shop floor. However, the study demonstrated that a piezoelectric element attached to any of the grid points would be able to evaluate the completed machining process.     

基于多项式拟合的EMD端点效应处理方法研究

EMD经验模态分解方法在非平稳信号的分析和处理中起着重要的作用,但是在利用样条插值获得上下包络过程中存在着棘手的端点问题.多项式拟合极值延拓是一种抑制端点效应的方法,但是在应用过程中也有其不足的地方,针对其不足之处进行了深入研究,并提出了一种新的解决方法.将其应用于烟机的信号分析中,结果证明该方法能有效抑制EMD方法的端点效应,可以得到较好的结果.     

A model-based approach for monitoring of shape deviations in peripheral milling

This paper presents a model-based approach for monitoring of shape deviations for milling operations. In order to detect occurring shape deviations of the machined workpiece during the milling process, different kinds of process models are presented and discussed for their application on manufacturing quality monitoring. Thereby, a model-based system was presented for the monitoring of shape deviations based on measured cutting forces. For the transformation of cutting forces into shape deviations, a tool deflection model and material removal model were designed and applied to a monitoring system. The presented model-based monitoring approach delivers accurate quality information, like geometric shape deviations, which can be monitored against geometric tolerances, providing a quality monitoring of manufacturing processes. The reconstruction of shape deviations from measured cutting forces is verified experimentally by comparing measured and reconstructed shape contours.     

A dynamic surface roughness model for face milling

This paper presents a newly developed mathematical model for surface roughness prediction in a face-milling operation. The model considers the static and the dynamic components of the cutting process. The former includes of cutting conditions as well as the edge profile and the amount of runout of each insert set into a cutter body. The latter introduces the dynamic characteristics of the milling process. It is verified that such a model predicts the maximum or the arithmetic mean surface roughness value through the cutting experiments. The model can evaluate the surface texture of the precision parts machined with face milling.     

基于数据拟合的机械参数测量模型研究

以机械工程中无法用传感器直接测量或测量十分困难的动态参数为研究对象,根据已知离散数据样本,采用数据拟合理论建立测量模型,解决了2个具有因果性质被测物理量之间函数关系的计算问题,为不易直接监测的机械参数提供了一种间接测量方法。液压打桩锤冲击力和塔式起重机力矩实测研究证明该方法可行、可靠、可移植性好。     

A generalised model of milling forces

This paper presents the development of a generalised cutting force model for both end-milling and face-milling operations. The model specifies the interaction between workpiece and multiple cutter flutes by the convolution of cutting-edge geometry function with a train of impulses having the period equivalent to tooth spacing. Meanwhile, the effect of radial and axial depths of cut are represented by the modulation of the cutting-edge geometry function with a rectangular window function. This formulation leads to the development of an expression of end/face-milling forces in explicit terms of material properties, tool geometry, cutting parameters and process configuration. The explicitness of the resulting model provides a unique alternative to other studies in the literature commonly based on numerical integrations. The closed-form nature of the cutting force expression can facilitate the planning, optimisation, monitoring, and control of milling operations with complicated tool—work interactions. Experiments were performed over various cutting conditions and results are presented, in verification of the model fidelity, in both the angle and frequency domains.Notation * convolution operator - helix angle of an end mill - _A,_R axial and radial angles of a face mill - angular position of any cutting point in the cylindrical coordinate system - unit area impulse function - ^(i–1)(–T _o) (i–1)th derivative of (–T _o) with respect to - angular position of cutter in the negative Y-direction - _L, lead and inclination angles of a face mill - angular position of any cutting point in the negative Y-direction - ₁, ₂ entry and exit angles - upper limit of cutting edge function in terms of - as defined in equation (10) - A _xk ,A _yk ,A _zk kth harmonics of cutting forces in the X-, Y-, and Z-directions - d _a,d _r axial and radial depth of cut - dA instantaneous cut area - D diameter of cutter - f _o frequency of spindle - f _t,f _r,f _a local cutting forces in the tangential, radial, and axial directions - f _x ,f _y ,f _z local cutting forces in the X-, Y-, and Z-directions - F _x ,F _y ,F _z resultant cutting forces in the angle domain in the X-, Y-, and Z-directions - F as defined in equation (5) - h derivative of height function of cutting edge with respect to - h() height function of one cutting edge with respect to - H height of any cutting point - K _r,K _a radial-to-tangential and axial-to-tangential cutting force ratios - K _t tangential cutting pressure constant - K as defined in equation (6) - p as defined in equation (6) - N number of cutting edges - r() radius function of one cutting edge with respect to - R radius of any cutting point - T cutting engagement time function of any cutting point - T _o cutting engagement time of the cutting point at =0 - T th() tooth sequence function - t _c average cut thickness - t _x feed per tooth - W _A,W _W,W _C amplitude, width and centre of a window function - W(,) unit rectangular window function - y _min,y _max minimum and maximum positions of workpiece in the Y-direction - Z _min,Z _max integration limits in the Z-direction     

Chatter stability analysis for end milling via convolution modelling

This research discusses the methodology of developing a symbolic closed form solution that describes the dynamic stability of multiflute end milling. A solution of this nature facilitates machine tool design, machining parameter planning, process monitoring, diagnostics, and control. This study establishes a compliance feedback model that describes the dynamic behavior of regenerative chatter for multiflute tool-work interaction. The model formulates the machining dynamics based upon the interconnecting relationship of the tool geometry and the machining system compliance. The tool geometry characterises the cutting forces as a function of the process parameters and the material properties, while two independent vibratory modules, the milling tool and the workpiece, represent the machining system compliance. The compliance feedback model allows the development of a corresponding characteristic equation. By investigating the roots of the characteristic equation, this research symbolically expresses the stability of the system as a function of the cutting parameters, the tool geometry, the workpiece geometry, and the vibrational characteristics of the machine tool. Machining experimentation examining the fidelity of the regenerative chatter model is discussed. The dynamic cutting forces, cutting vibration, and surface finish of the machining process confirm the validity of the analytical prediction.Nomenclature b damping coefficient: mass-spring-damper representation - b _e equivalent damping coefficient: mass-spring-damper representation - C compliance element - CWD chip with density function - D diameter of cutter - d _a axial depth of cut - d _r radial depth of cut - average total cutting force - K _r radial specific cutting pressure constant - K _t tangential specific cutting pressure constant - k spring constant - k _e equivalent spring constant - m mass: mass-spring-damper representation - m _e equivalent mass: mass-spring-damper representation - n number of flutes on the cutter - p _x,y elemental cutting forces - P _1,2 elemental cutting force functions - R cutter radius - s Laplace variable - TS tooth sequencing function - chip thickness - t _c average chip thickness - t _x feed per tooth - helix angle - _x actual displacement of cutter tip - unit impulse function - _d damped circular frequency of vibration - damping ratio - spindle speed