铣削力的傅立叶级数建模与实验

建立了一种采用傅立叶级数的铣削力模型用以描述铣削加工过程的物理状态,考虑了铣削过程的剪切机制与犁切机制,建立了沿刀具轴向的微元刀刃的铣削力模型,通过傅立叶变换将刀具总的铣削力表示为傅立叶级数形式。给出了通过槽铣实验的平均铣削力回归切削力系数的方法,采用测力仪在数控机床上进行了铣削实验,通过实验数据回归出了立铣刀的切削系数,对比了模型预测值和实验实测值,结果吻合良好,从而验证了铣削力模型。     

铣削加工力-位误差的综合建模与补偿

基于铣削加工特点,建立铣削加工过程中的力-位综合误差模型,并基于原点偏移法建立了力-位综合误差在线补偿系统。根据铣削过程中的剪切和犁切机制,建立刀具微元切削力模型,通过积分得到切削力模型。依据变形理论,提出刀具及工件的切削力所致误差模型,并结合机床几何误差模型,利用齐次坐标变换,建立力-位综合误差模型。基于Fanuc数控系统的原点偏置功能开发误差在线补偿系统,实现力-位综合误差的在线补偿。利用立式加工中心对工件进行铣削加工实验,并对无误差补偿、仅补偿机床几何误差、仅补偿切削力所致变形误差、补偿力-位综合误差四种加工方式的加工精度进行对比,结果表明,力-位综合误差补偿的加工精度大大优于各单项误差补偿及无补偿的加工精度。     

脆性材料微铣削理论及微铣削力模型研究

从脆性材料塑性域铣削机理和特点出发,建立了微径球头铣刀几何模型,改进了瞬时切厚模型,利用合理的切削力微元模型建立了脆性材料铣削瞬时的铣削力解析模型;以石英玻璃为工件材料,基于改进的实验平台进行球头铣刀微铣削试验,并获取了铣削力实验数据,回归出了所建模型中的切削力系数。利用试验对模型进行验证分析,结果表明所建模型具有良好的适用性。     

球头铣刀加工倾角对切削力的影响

对球头铣刀刀具轴线和工件加工表面之间的加工倾角进行了理论研究,建立了加工曲面时刀具倾角的数学模型,并通过试验研究了高速铣削铝合金时刀具倾角对切削力的影响规律。随着刀具轴线相对于进给方向倾斜角度β的增大,切削力变化的趋势是减小;编制多轴数控加工程序时可以通过设置合理的刀具倾角来改善切削条件。     

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.     

钛合金TC11铣削力分析与建模

基于单位切削力系数法,建立了侧铣钛合金时的切削力预报模型。文中将微元切向分力、微元径向分力、微元轴向分力分别用刀面单位剪力系数和刀腹单位犁入力系数的组合来描述,切削合力则通过沿切削刃进行积分而获得。实验结果表明,仿真的铣削力曲线无论在形状上还是幅值大小以及波形变化趋势等方面都与实际测得的铣削力吻合一致。     

基于切削层形状的动态铣削力试验研究及建模

选取轴向切深、每齿进给量、径向切深和主轴转速为试验因素,采用YDX-Ⅲ9702型压电式铣削测力仪,进行了动态铣削力正交实验。针对立铣刀侧铣加工,研究了单刃铣削的临界条件,为设计试验方案提供了理论依据。结合铣削过程,采用角度积分方法求解铣削力模型,避免了轴向积分的繁琐计算。精确地建立了简捷且适应性强的基于切削层形状的动态铣削力预测模型,模型的仿真结果和试验数据相吻合。     

SiCp/Al轴向超声振动微铣削的切削特性试验研究

针对SiCp/Al复合材料微铣削刀具易磨损、难以获得高质量加工表面的问题,对40%体积分数的SiCp/Al复合材料采用轴向超声振动进行辅助微铣削,根据轴向超声振动微铣削的切削特点,通过试验研究铣削力信号的幅频特性,三向切削力随主轴转速、切削深度和每齿进给量的变化规律,并与普通微铣削进行和对比。结果表明:采用轴向超声振动辅助微铣削,三向铣削分力都呈现出随主轴转速先增大再缓慢减小的趋势,可使3个方向的铣削力减小10%～50%。     

内螺纹铣削力预测模型及试验研究

通过分析内螺纹铣刀的铣削机理和切屑厚度,确定内螺纹加工的主轴转速、进给率、刀具几何参数,提出了一种通用的内螺纹铣削力数学预测模型,研究内螺纹铣削力的变化规律。结合具体的铝合金7075内螺纹加工试验来验证本数学预测模型。试验研究表明,切削力在X方向,其分量力最大,对铣刀旋转角度的变化也最为敏感,力分量最小为Y方向分量,对铣刀旋转角度的变化最不敏感。试验结果与所建立切削力预测模型在力变化趋势上以及分力数值上都很好的匹配。数学模型所预测切削力与试验所测数据平均误差控制在10%以内,从而验证了所建数学模型的精确性。     

切削参数对钛合金叶片铣削力的影响分析

进行钛合金叶片加工时,切削力易导致加工变形,影响加工精度和表面质量。因此利用UG软件建立钛合金叶片和切削刀具的三维模型,采用仿真软件建立铣削仿真模型,研究分析了切削参数的变化对铣削力产生的影响。对仿真所得铣削力进行极差分析,判断切削参数对铣削力的影响情况,并通过实际铣削加工试验对比仿真数据验证其准确性和可行性,基于此仿真模型对切削参数对轴向力的影响程度进行了单因素分析。研究结果表明：铣削钛合金叶片时,切削参数对切削力的影响程度从大到小依次为切削速度、背吃刀量和每齿进给量;切削速度与轴向力成反比,每齿进给量和背吃刀量与轴向力成正比。     

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.     

Three dimensional cutting force analysis in end milling

The analysis of cutting forces plays an important part in the design of machine tool systems as well as in the planning, optimization, and control of machining processes. This paper presents a three-dimensional model of cutting forces in peripheral end milling in terms of material properties, cutting parameters, machining configuration, and tool/work geometry. Based on the relationship of the local cutting force and the chip load, the total cutting force model is established via the angle domain convolution integration of the local forces in the feed, cross feed, and axial directions. The integration is taken along the cutter axis and summarized across the cutting flutes. The convolution integral leads to a periodic function of cutting forces in the angle domain and an explicit expression of the dynamic cutting force components in the frequency domain. The closed-form nature of the expressions allows the prediction and optimization of cutting forces to be performed without the need of numerical iterations. To assess the fidelity of the analytical model, experimental data from end milling tests are presented in the context of three dimensional time waveforms, power spectra, and phase angles, in comparison to the values predicted by the model.     

基于斜角切削的曲线端铣切削力建模

切削力预测是制定与优化加工工艺的重要环节。针对曲线端铣加工过程,提出一种基于斜角切削的切削力建模方法。将刀具沿轴向微分,以曲线微分几何计算微元刃上的工作基面。在微元刃的工作法平面参考系中,应用最小能量原理,构建微元刃中力矢量、速度矢量、流屑角、法向摩擦角、法向剪切角及剪应力等切削参数之间的约束。以单齿直线铣削试验对切削参数进行标定,其中法向摩擦角、法向剪切角及剪应力等可表示为瞬时未变形切屑厚度的函数。选取高强度钢PCrNi3MoVA试件,分别进行圆弧和Bézier曲线端铣加工试验。试验结果表明,曲线端铣时切削力的变化与瞬时进给方向和曲线曲率相关。切削力预测值的幅值大小和变化趋势与试验值一致,验证了该切削力建模方法的有效性。     

Extracting cutting constants via harmonic force components for a general helical end mill

Mechanistic cutting constants serve well in predicting milling forces, monitoring the milling process as well as in helping to understand the mechanistic phenomena of a machining process for a unique pair of workpiece and cutter materials under various types of cutting edge geometry. This paper presents a unified approach in identifying the six shearing and ploughing cutting constants for a general helical end mill from the dynamic components of the measured milling forces in a single cutting test. The identification model is first presented assuming the milling force is measured with a known phase angle of the cutter spindle. When the phase angle of the cutter rotation is not available, as is the case for most milling machines, it is shown that the true phase angle can be identified through the theoretical phase relationship between the different harmonic components of the milling forces measured with an arbitrary phase angle. The numerical simulation and the experimental results for ball and cylindrical end mills are presented to demonstrate and validate the identification methods.     

Dynamic Force Modelling for a Ball-End Milling Cutter Based on the Merchant Oblique Cutting Theory

A new dynamic force model for a ball-end milling cutter is presented in this paper. Based on the principle of the power remaining constant in cuts, the Merchant oblique cutting theory has been successfully used for the differential cutting edge segment of a ball-end milling cutter. A concise method for characterising the relationship of the complex geometry of a ball-end milling cutter and the milling process variables is determined, so that the force coefficients can be decomposed. The geometric property of a ball-end milling cutter and the dynamics of the milling process are integrated into the general model to eliminate the need for the experimental calibration of each cutter geometry and milling process variable. The milling experiments prove that this model can predict accurately the cutting forces in three Cartesian directions.     

Parametric instability of a spinning pretwisted beam under periodic axial force

This paper addresses the parametric instability of a cantilever pretwisted beam rotating around its longitudinal axis under a time-dependent conservative end axial force which contains a steady-state part and a small periodically fluctuating component. This structural element can be used to model fluted cutting tools such as the twist drill bit and the end milling cutter, etc. Using the Euler—Bernoulli beam theory and Hamilton's principle, the present study derives the equation of motion which governs the lateral vibration of a spinning pretwisted beam. Rotary inertia, structural viscous damping and conservative end axial force are included. The Galerkin method is then applied to obtain the associated finite element equations of motion. Due to the existence of the Coriolis force, the resulting finite element equations of motion are transformed into a set of first-order simultaneous differential equations by a special modal analysis procedure. This set of simultaneous differential equations is solved by the method of multiple scales, yielding the system response and expressions for the boundaries of the unstable regions. Numerical results are presented to demonstrate the effects of pretwist angle, spinning speed and steady-state part of the end axial force on the parametric instability regions of the present problem.     

球头铣刀余摆线加工表面形貌的建模与仿真研究

余摆线铣削因切削力小、表面质量和生产率高,而广泛应用于高速加工中。球头铣刀因适应性好,且姿态可灵活调整,而成为多轴加工复杂表面的常用刀具。然而,球头铣刀齿形复杂,余摆线铣削的运动轨迹方向不断变化,工件的材料去除和表面形貌的创成过程异常复杂,传统方法建模困难。提出一种球头铣刀余摆线加工表面形貌的数值仿真方法,根据齐次坐标矩阵变换原理建立刀齿的运动轨迹方程,通过改进Z-MAP算法完成了加工表面形貌的仿真。该算法通过建立刀齿微元的随动矩形包围圈和瞬时扫掠四边形,使用角度累加法快速地获取刀齿微元在单位时间步长内扫掠到的工件网格点,根据多元函数的泰勒公式,用线性插值的方法求出该网格点的高度坐标。仿真结果表明球头铣刀余摆线铣削的表面形貌整体上优于普通直线铣削。试验结果表明,在垂直和倾斜加工条件下,球头铣刀余摆线铣削获得的表面形貌与仿真结果具有较高的一致性,说明所提出的方法可以预测球头铣刀余摆线的加工表面形貌。     

一种新型的广义铣削力模型

基于微分几何理论建立了任意形状铣刀的数学模型,给出适用于任意形状铣刀的三维单元铣削力模型。该铣削力模型考虑了铣刀的法向前角,认为作用单元体上的铣削力由作用于前后刀面上的正压力和摩擦力组成,并表示为与瞬时切厚有关的非线性函数。