确定铣削力模型中刀具偏心参数的一种算法

对数控加工中球头铣刀铣削力建模时刀具偏心参数的确定进行了研究。在铣削力模型的建立中考虑了刀具偏心的影响,推导出刀具偏心参数的表达式,考虑到刀具单刃切削条件,提出了刀具偏心参数的确定算法。在通过铣削力试验数据计算铣削力系数的过程中,采用上述算法确定了刀具的偏心参数,用于铣削力的仿真预测中,仿真结果和铣削力试验的结果表明,算法效果良好。     

一种螺旋刃球头铣刀的动态铣削力模型

针对高速铣削中广泛应用的螺旋刃球头铣刀建立刀具微元的铣削力模型,给出了瞬时切削厚度的计算方法,通过积分得出了一种新的整体铣削力模型。该模型考虑了动态铣削时刀杆振动对铣削力的影响,实验数据与仿真结果吻合较好,验证了该模型的正确性。     

球头刀铣削过程动力学模型

建立了考虑刀杆柔性的球头铣刀铣削振动模型,探讨了交变轴向力对刀杆固有频率的影响。考虑刀具动态变形和工件表面波纹对切削厚度的再生反馈,建立了球头刀铣削动力学模型,对铣削中的动态铣削力和刀杆振动进行了仿真,证明了离线仿真可以对铣削过程动特性做出预测。     

一种基于动力学分析的薄壁深腔零件加工变形仿真方法

为了提高薄壁深腔零件侧壁加工变形的预测精度,对铣削力引起的侧壁让刀误差进行了研究,提出一种基于动力学分析的薄壁深腔零件加工变形有限元动态仿真方法。该方法通过建立刀具动力学方程,求解其中关键参数、得到铣削过程中刀具任意点运动状态,并采用生死单元法对被切削材料进行去除。在计算铣削力时考虑刀具/工件挠度变形对铣削力的动态响应,计算获得考虑让刀反馈的铣刀瞬时切削厚度及总体铣削力,最终得到零件加工过程的实时变化规律,以及在此铣削力影响下工件侧壁的变形量。通过实验验证了仿真方法的准确性。     

平头铣刀圆形铣削的切削力预测

针对平头铣刀的圆形铣削,提出一种适用于圆形铣削的切削力预测方法。建立铣刀与工件交点的数学模型,求解工件与铣刀的时变交点进而计算铣削过程中不断变化的切入角与切出角。同时分析了铣刀轨迹曲率效应对瞬时切削厚度的影响。通过槽铣试验来确定切削力系数。基于微分思想,将圆形铣削过程中的瞬时切削厚度运用到切削力模型中计算微元切削力,然后通过积分法获得切削力值。数值仿真与圆形铣削试验结果表明,预测的铣削力和试验结果在幅值和变化趋势上都吻合良好,从而验证了该切削力预测方法的有效性。     

基于单刃铣削力峰值的铣刀偏心辨识

刀具偏心可能导致铣削力的大幅度波动。为辨识铣刀偏心状态,研究偏心作用下的铣削力变化规律。推导出以主轴旋转角和切削刃序号为变量的单刃瞬时铣削力表示式,发现铣削力峰值是切削刃序号的离散正弦函数,其均值为无偏心铣刀的公称力,波动部分为偏心引起的铣削增力。该铣削增力与旋转主轴同频,其初始相位依赖于偏心角,其幅值与偏心距和轴向切深成正比例关系,而与每刃进给量不相关。基于此发现,提出一种估算偏心角和偏心距的数据拟合方法,该方法主要对各刃的铣削力峰值进行正弦函数拟合,算法简单,且只需要做一次铣削测试。铣削试验结果与以上发现一致,且表明该估算方法有效。研究揭示与偏心相关的铣削力峰值特性,提出一种简单直观的偏心尺寸估算方法。研究成果可用于铣削过程状态辨识。     

基于斜角有限元仿真的齿轮铣削力预测研究

针对采用机械力学模型或铣削有限元仿真方法计算齿轮铣削力耗时且繁琐的难题,提出了一种基于斜角有限元仿真的铣削力预测方法。该方法将铣刀的切削刃离散成无限小的微元斜角切削过程,通过一系列斜角切削过程仿真,拟合得出了切削力系数与未变形切削厚度之间的关系;然后通过几何变换,将所求得切削力系数运用于铣削过程,得到了作用在齿轮刀具上的瞬时切削力。通过与实际铣削仿真得到的结果进行对比,结果表明,斜角切削有限元仿真方法可以应用到齿轮轮齿的铣削过程中,并验证了所提出方法的有效性,为齿轮制造过程中力的预测及后续齿轮加工表面完整性研究奠定了较好基础。     

高速面铣加工的动态铣削力和刀具振动研究

基于力学式切削力预测方法建立了面铣刀动态铣削模型,该模型充分考虑切削厚度、刀具前角和刀具后刀面磨损对铣削力的影响.在Matlab/Simulink环境下,进行了动态铣削力和刀具振动仿真及其频谱分析,并根据仿真结果对转速、齿数、刀具磨损量等影响因素进行了分析验证,该模型有利于揭示各切削参数对动态铣削力和刀具振动的影响规律,从而为实现切削加工参数优化提供理论支持.     

基于布尔运算的球头铣刀瞬时切削厚度建模及分析

在五轴球头铣刀的铣削加工中,瞬时切削厚度模型的建立是准确预测切削力的关键步骤之一。目前大部分模型注重刀具和工件接触区域的建模,仅考虑了参与切削的刀刃切削厚度,而忽略了刀刃对工件的影响。本文提出一种基于布尔运算理论的瞬时切削厚度建模方法,从瞬时切削厚度的理论出发,考虑了所有刀刃对工件切削厚度的影响,并引入根据球刃曲线创建的辅助实体模型对瞬时切削厚度进行提取,并经铣削力试验验证了该模型的有效性。     

微径球头铣刀铣削力建模与仿真

以微径球头铣刀铣削力为研究对象,分析了刀具刃线模型.将刀具沿刀轴方向离散为若干切削单元,分别依照单齿切削及两齿切削求得各切削单元的实际瞬时切削厚度.基于实体造型的方法提取了参与切削的切削刃段,并通过实验识别了瞬时切削力系数及主轴径向跳动参数,建立了综合考虑主轴径向跳动、微细铣削所特有的尺度效应的影响及可能出现的单齿切削现象的微径球头铣刀铣削力模型.实验结果验证了所提模型的有效性和可行性.     

An Improved Method for the Determination of 3D Cutting Force Coefficients and Runout Parameters in End Milling

A simple improved method is suggested for determining constant cutting force coefficients, irrespective of the cutting condition and cutter rotation angle. This can be achieved through the combination of experimentally deternimed cutting forces with those from simulation, performed by a mechanistic cutting force model and a geometric uncut chip thickness model. Additionally, this study presents an approach that estimates runout-related parameters, and the runout offset and its location angle, using only one measurement of cutting force. This method of estimating 3D end milling force coefficients was experimentally verified for a wide range of cutting conditions, and gave significantly better predictions of cutting forces than any other methods. The estimated value of the runout offset also agreed well with the measured value.     

A new method for cutting force prediction in peripheral milling of complex curved surface

The instantaneous uncut chip thickness and entry/exit angle of tool/workpiece engagement vary with tool path, workpiece geometry and cutting parameters in peripheral milling of complex curved surface, leading to the strong time-varying characteristic for instantaneous cutting forces. A new method for cutting force prediction in peripheral milling of complex curved surface is proposed in this paper. Considering the tool path, cutter runout, tool type(constant/nonconstant pitch cutter) and tool actual motion, a representation model of instantaneous uncut chip thickness and entry/exit angle of tool/ workpiece engagement is established firstly, which can reach better accuracy than the traditional models. Then, an approach for identifying of cutter runout parameters and calibrating of specific cutting force coefficients is presented. Finally, peripheral milling experiments are carried out with two types of tool, and the results indicate that the predicted cutting forces are highly consistent with the experimental values in the aspect of variation tendency and amplitude.     

A force-model-based approach to estimating cutter axis offset in ball end milling

Cutter runout due to cutter axis offset is quite common in a milling process, yet it is difficult to directly measure the runout geometry of a ball end cutter during the cutting process. This paper presents an analytical method for the estimation of cutter radial offset via forces in ball end milling. Closed form expression for the total milling force in the presence of cutter offset is first obtained. Fourier series coefficients for the offset related force component are shown to be expressed explicitly in terms of the offset geometry and serve as the basis for the identification of the offset geometry from the measured cutting forces. The offset geometry including its magnitude and the phase angle are directly calculated from the measured force component at the spindle frequency through two algebraic expressions. The identification method is finally validated by milling experiments.     

Theoretical modelling of cutting forces in helical end milling with cutter runout

A theoretical cutting force model for helical end milling with cutter runout is developed using a predictive machining theory, which predicts cutting forces from the input data of workpiece material properties, tool geometry and cutting conditions. In the model, a helical end milling cutter is discretized into a number of slices along the cutter axis to account for the helix angle effect. The cutting action for a tooth segment in the first slice is modelled as oblique cutting with end cutting edge effect and tool nose radius effect, whereas the cutting actions of other slices are modelled as oblique cutting without end cutting edge effect and tool nose radius effect. The influence of cutter runout on chip load is considered based on the true tooth trajectories. The total cutting force is the sum of the forces at all the cutting slices of the cutter. The model is verified with experimental milling tests.     

New mathematical method for the determination of cutter runout parameters in flat-end milling

The cutting force prediction is essential to optimize the process parameters of machining such as feed rate optimization, etc. Due to the significant influences of the runout effect on cutting force variation in milling process, it is necessary to incorporate the cutter runout parameters into the prediction model of cutting forces. However, the determination of cutter runout parameters is still a challenge task until now. In this paper, cutting process geometry models, such as uncut chip thickness and pitch angle, are established based on the true trajectory of the cutting edge considering the cutter runout effect. A new algorithm is then presented to compute the cutter runout parameters for flat-end mill utilizing the sampled data of cutting forces and derived process geometry parameters. Further, three-axis and five-axis milling experiments were conducted on a machining centre, and resulting cutting forces were sampled by a three-component dynamometer. After computing the corresponding cutter runout parameters, cutter forces are simulated embracing the cutter runout parameters obtained from the proposed algorithm. The predicted cutting forces show good agreements with the sampled data both in magnitude and shape, which validates the feasibility and effectivity of the proposed new algorithm of determining cutter runout parameters and the new way to accurately predict cutting forces. The proposed method for computing the cutter runout parameters provides the significant references for the cutting force prediction in the cutting process.     

Improved dynamic cutting force model in peripheral milling. Part II: experimental verification and prediction

Cutting trials reveal that a measure of cutter run-out is always unavoidable in peripheral milling. This paper improves and extends the dynamic cutting force model of peripheral milling based on the theoretical analytical model presented in Part I [1], by taking into account the influence of the cutter run-out on the undeformed chip thickness. A set of slot milling tests with a single-fluted helical end-mill was carried out at different feed rates, while the 3D cutting force coefficients were calibrated using the averaged cutting forces. The measured and predicted cutting forces were compared using the experimentally identified force coefficients. The results indicate that the model provides a good prediction when the feed rate is limited to a specified interval, and the recorded cutting force curves give a different trend compared to other published results [8]. Subsequently, a series of peripheral milling tests with different helical end-mill were performed at different cutting parameters to validate the proposed dynamic cutting force model, and the cutting conditions were simulated and compared with the experimental results. The result demonstrates that only when the vibration between the cutter and workpiece is faint, the predicted and measured cutting forces are in good agreement.     

A solid modeler based ball-end milling process simulation

A system for geometric and physical simulation of the ball-end milling process using solid modeling is presented in this paper. A commercially available geometric engine is used to represent the cutting edge, cutter and updated part. The ball-end mill cutter modeled in this study is an insert type ball-end mill and the cutting edge is generated by intersecting an inclined plane with the cutter ball nose. The contact face between cutter and updated part is determined from the solid model of the updated part and cutter solid model. To determine cutting edge engagement for each tool rotational step, the intersections between the cutting edge with boundary of the contact face are determined. The engaged portion of the cutting edge for each tool rotational step is divided into small differential oblique cutting edge segments. Friction, shear angles and shear stresses are identified from orthogonal cutting data base available in the open literature. For each tool rotational position, the cutting force components are calculated by summing up the differential cutting forces. The instantaneous dynamic chip thickness is computed by summing up the rigid chip thickness, the tool deflection and the undulations left from the previous tooth, and then the dynamic cutting forces are obtained. For calculating the ploughing forces, Wu's model is extended to the ball-end milling process [21]. The total forces, including the cutting and ploughing forces, are applied to the structural vibratory model of the system and the dynamic deflections at the tool tip are predicted. The developed system is verified experimentally for various up-hill and down-hill angles.     

球头铣刀切削力计算机预报模型的数值仿真

借助建立的铣刀切削力、扭矩和切削功率的计算机预报模型 ,对平前刀面球头铣刀的切削性能进行了数值仿真研究 ;通过分析各种切削参数对切削性能的影响规律 ,获得了不同切削条件下球头铣刀切削力和扭矩的特征和变化趋势     

Calculations of chip thickness and cutting forces in flexible end milling

In the end milling process of a flexible workpiece, it is well recognized that the precise determination of the instantaneous uncut chip thickness (IUCT) is essential for the cutting force calculation. This paper will present a general method that incorporates simultaneously the cutter/workpiece deflections and the immersion angle variation into the calculation of the IUCT and cutting forces. Contributions are twofold. Firstly, considering the regeneration model, a new scheme for the IUCT calculation is determined based on the relative positions between two adjacent tooth path centers. Secondly, a general approach is established to perform numerical validations. On one hand, the engagement/separation of the cutter from the workpiece is instantaneously identified. On the other hand, the calculation of the IUCT is iteratively performed. To demonstrate the validity of the method, several examples are used to show the convergence history of the cutting force and the IUCT during the flexible end milling process. Both theoretical analyses and numerical results show that the regeneration mechanism is short lived and will disappear after several tooth periods in flexible static end milling process .     

Application of a variable flow stress machining theory to helical end milling

A methodology of modeling chip geometry of flat helical end milling based on a variable flow stress machining theory is presented in this article. The proposed model is concerned with the variation of the width of cut thickness. The nonuniform chip thickness geometry is discretized into several segments based on the radial depth of cut. The chip geometry for each segment is considered to be constant by taking the average value of the maximum and minimum chip thickness. The maximum chip thickness for each chip segment is computed based on the current width of cut, feed per tooth and the cutter diameter. The subsequent radial depth of cut is subtracted from the discretized size of the width of cut to obtain the minimum chip thicknesses. The forces for each segment are summed to obtain the total forces acting on the system of the workpiece and the tool. The cutting forces can be predicted from input data of work material properties, cutter configuration and the cutting conditions used. The validation of the proposed model is achieved by correlating experimental results with the predicted results obtained.