基于刀具跳动的环形铣刀切削厚度模型的切削力计算

数控铣削过程中,切削变形引起的瞬时切削厚度是影响铣削加工切削力建模的重要参数之一,针对环形铣刀的切削特点,在考虑刀具跳动的情况下,对真实刀刃轨迹运动进行分析。将微细铣削的加工过程用宏观铣削来表示,从而建立了基于宏观铣削过程中刀具跳动下精密加工的瞬时切削厚度。通过仿真模拟和切削力试验来预测切削力,预测结果和试验结果具有一致性,表明该模型可以更好的预测加工过程中的切削力。     

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。     

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。     

径向跳动对球面铣刀切削力的影响研究

研究了径向跳动对刀齿的实际切削半径、切屑形状以及切屑厚度的影响机理。研究了各刀齿沿刀刃螺旋线的切削微元实际切削半径的数学表示和变化规律,实际切削半径的变化改变了刀齿的切削路径,使各刀齿上切屑形状分布不均匀。建立了三维切削下切屑厚度的数学表示,提出了递延累加切屑厚度计算算法。实验验证表明,计算的切削力与测量结果能很好地吻合,瞬时切削力、切削力峰值、平均切削力的预测精度达到85%以上。     

平底立铣刀的切削力尺寸效应研究及其系数估算

检验基于三元切削力机理模型的平底立铣刀尺寸效应,并探索一种简便的切削力系数估算方法。论证了在切削厚度较小时可忽略刀具螺旋角对切削力的影响,据此构建平底立铣刀单个刀齿的三元切削力简化模型。基于该模型,用各齿径向跳动量补偿瞬时切削厚度,用切削试验数据拟合各齿切削力峰值与切削深度及瞬时切削厚度的线性方程式,发现各拟合式的确定系数总体上接近1,表明同一刀齿的切削力系数大体为常数,这意味着平底立铣刀的尺寸效应不显著。据此采用刀具的平均切削力峰值估算切削力系数,该方法不用考虑刀具偏心,且计算比较简便,模拟得到的切削力波形与实测波形相近,表明估算方法比较有效。研究结果可供铣削力尺寸效应机理研究及平底立铣刀应用领域参考。     

铣齿断续切削机理的研究

大模数齿轮铣削具有多刃断续切削和变切屑厚度等特点,属于典型的非自由强力切削.主要从切削力、切屑形态、表面质量等方面对铣齿断续切削的机理进行研究.采用指数经验模型,应用微段切削刃受力积分获得单个刀片瞬时合成转矩,随后考虑刀盘上刀片的分布情况,获得刀盘周期性的载荷,提出铣齿断续切削转矩的计算模型.应用间接测量的试验方法,采集三相异步电动机的主轴输入电流,重构得到切削力,另外通过试验测量出切削变形比,应用理论公式获得切削力.将试验数据和理论计算结果与计算模型进行比较,验证了铣齿加工切削转矩模型的正确性.对切削过程中的残余高度进行几何分析,获得其计算方法.初步完成对铣齿断续切削机理的分析,对铣齿加工精度提供指导作用.     

基于黏结-滑移摩擦模型的304不锈钢切削力仿真研究*

通过预测加工304不锈钢时产生的切削力,从而对切削参数和刀具几何参数进行优化,是提高304不锈钢的加工精度、切屑控制及保障刀具寿命的基础。建立304不锈钢切削仿真模型,为提高模型的精确性,选择Johnson-Cook本构方程和黏结-滑移摩擦模型。结果表明：采用黏结-滑移摩擦模型的切削力预测结果更为准确,表明相对于纯剪切摩擦与库仑摩擦模型,黏结-滑移摩擦模型能更准确地描述刀-屑摩擦特性。展开不同参数下的切削力研究,研究发现：切削力随着刀具前角、后角和切削速度的增大而减小,随切削刃钝圆半径和切削厚度、宽度的增大而增大,其中切削宽度、厚度及前角对切削力大小影响较大。研究结果为304不锈钢切削效率的提高和切削机制的研究提供了理论依据。     

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。     

轴向车铣理论切削力的研究

以瞬时切削面积为主要研究对象建立了瞬时切削力的计算模型,并对瞬时切削力的变化进行了仿真。结果表明,轴向车铣为多参数影响下的变切削力加工,单齿瞬时切削力在整个切削过程中都是一个变化量,且圆周刃为主切削刃,其切削力远大于端面刃。在一次完整的切削过程中,整个刀齿的瞬时切削力产生两次突变。     

球头铣刀多轴铣削加工的切削刃微元点轨迹模型

切削刃微元点轨迹是描述瞬时未变形切削厚度的基础,瞬时未变形切削厚度是铣削力预测的关键.为此,针对球头铣刀多轴铣削加工过程,建立利用位置矢量来准确描述切削刃微元点的轨迹模型.首先,通过建立工件和刀具瞬时坐标系的空间变换模型来描述刀具的位置和位姿;然后,在此基础上结合球头铣刀切削刃的几何特点建立切削刃微元点的空间位置矢量,并进一步推导描述切削刃微元点轨迹的矢量形式;最后,利用C++编程语言和OpenGL图形接口实现切削刃微元点轨迹仿真,并通过对比分析仿真结果与跟踪球头铣刀1∶1三维模型上标记点的位置数据,验证了切削刃微元点轨迹模型的正确性.     

Geometry of chip formation in circular end milling

Machining along continuous circular tool-path trajectories avoids tool stoppage and even feed rate variation. This helps particularly in high-speed milling by reducing the effect of the machine tool mechanical structure and cutting process dynamics. With the increase in popularity of this machining concept, the need for detailed study of a valid chip formation in circular end milling is becoming necessary for accurate kinematic and dynamic modeling of the cutting process. In this paper, chip formation during circular end milling is studied with a major focus on feed per tooth and undeformed chip thickness along with their analytical derivations and numerical solutions. At first, the difference in the feed per tooth formulation for end milling along linear and circular tool-path trajectories is presented. In the next step, valid formulation of the undeformed chip thickness in circular end milling is derived by considering an epitrochoidal tooth trajectory with a wide range of the tool-path radius. The complex transcendental equations encountered in the derivation are dealt with, by a case-based approach to obtain closed-form analytical solutions. The analytical solutions of undeformed chip thickness are validated with results of numerical simulations of tool and tooth trajectories for circular end milling and also compared to the linear end milling. The close resemblance between analytical and numerical calculations of the undeformed chip thickness in circular end milling suggests validity of the proposed analytical formulations. As a case study, the cutting forces in circular end milling are calculated based on the derived chip thickness formulations and an existing mechanistic model. The calculation results reiterate the need of taking into account adjusted feed per tooth and valid chip thickness formulations in circular end milling, especially for small tool-path radii, for more realistic process modeling.     

Instantaneous uncut chip thickness modeling for micro-end milling process

The prediction model of instantaneous uncut chip thickness is critical for micro-end milling process, which can directly affect the cutting forces, surface accuracy, and process stability of the micro-end milling process. This paper presents an instantaneous uncut chip thickness model systematically based on the actual trochoidal trajectory of tooth and the tool run-out in micro-end milling process. The variable entry and exit angles of tool, which are affected by the tool run-out, are concerned in the model. The related instantaneous uncut chip thickness is evaluated by considering the theoretical instantaneous uncut chip thickness and the minimum uncut chip thickness, which is formulated by two types of material removal mechanisms, in the elastic-plastic deformation region and the complete chip formation region, respectively. In comparison with the instantaneous chip thickness obtained from the conventional model, the feasibility of the proposed model can be proved by the related simulation results with variable process parameters including feed per tooth, radial depth of cut, and tool run-out. In addition, the predicted and measured cutting forces are compared with validate the accuracy of the proposed instantaneous uncut chip thickness model for the micro-end milling process.     

A numerical study of the effects of cutter runout on milling process geometry based on true tooth trajectory

Cutter runout is a common phenomenon affecting the cutting performances in milling operations. To date, most of the milling process models considering cutter runout were established based on the circular tooth path approximation, which brought errors into the runout estimation. In this paper, a new approach is presented for modelling the milling process geometry with cutter runout based on the true tooth trajectory of cutter in milling. The mathematical relationship between the trajectories generated by successive cutter teeth with runout is analysed. The milling process geometrical parameters, including the instantaneous undeformed chip thickness, the entry and exit angles of a cutting tooth, and the ideal peripheral machined workpiece surface roughness, are modelled according to the true tooth trajectories. Numerical method is used to solve the derived transcendental equations. A simulation study of the effects of cutter runout on milling process geometry is conducted using the models. It was found that the change of cutter radius for a tooth relative to its preceding one is the most important factor in evaluating the effects of cutter runout.     

基于Z-MAP方法的球头铣刀铣削力的建模

瞬时刚性切削力的建模是铣削加工物理仿真的基础,然而,球头铣刀的刀齿形状复杂,加工过程中姿态多变,瞬时刚性铣削力的建模难度较大。在考虑刀具姿态调整的情况下,通过齐次坐标变换建立了刀齿的运动轨迹,提出了一种识别刀具和工件瞬时接触区的改进Z-MAP算法,通过计算当前刀齿的参考线与工件的边界面或刀齿扫掠面的交点求出瞬时未变形切屑厚度,并采用非线性回归的方法辨识了切削力系数,在此基础上使用微元积分法建立了瞬时切削力的计算模型。为了验证仿真模型的可靠性,分别进行了垂直加工和倾斜加工试验,试验和仿真结果具有较高的一致性,表明该建模仿真方法是有效的,可以为实际加工中参数的选择和优化提供理论依据。     

Mechanistic modeling of cutting forces in micro-end-milling considering tool run out,minimum chip thickness and tooth overlapping effects

This work proposed an improved mechanistic model for prediction of cutting forces in micro-milling process. The combined influences of tool run out, trochoidal trajectory of the tool center, overlapping of tooth, edge radius and minimum chip thickness are incorporated in this model to realize the exact cutting phenomenon. Moreover, an improved undeformed chip thickness algorithm has been presented by considering tool run out, minimum chip thickness and trajectory of all passing teeth for one complete revolution of the tool instead of only the current tooth trajectory. For estimation of tool run out, a model based on the geometry of the two fluted end mill cutter has been developed. Effects of trochoidal trajectory of the tool center and tool run out are found to be significant as each tooth has a different chip load. Further, the effect of minimum chip thickness is found to be significant at lower feed value. The proposed model has been validated by micro-milling experiments on Ti6Al4V-titanium alloys using uncoated flat end mill cutter. The predicted cutting forces were found to be in good agreement with the experimental cutting forces in both feed and cross feed directions.     

Cutting force prediction for ball-end mills with non-horizontal and rotational cutting motions

Accurate cutting force prediction is essential to precision machining operations as cutting force is a process variable that directly relates to machining quality and efficiency. This paper presents an improved mechanistic cutting force model for multi-axis ball-end milling. Multi-axis ball-end milling is mainly used for sculptured surface machining where non-horizontal (upward and downward) and rotational cutting tool motions are common. Unlike the existing research studies, the present work attempts to explicitly consider the effect of the 3D cutting motions of the ball-end mill on the cutting forces. The main feature of the present work is thus the proposed generalized concept of characterizing the undeformed chip thickness for 3D cutter movements. The proposed concept evaluates the undeformed chip thickness of an engaged cutting element in the principal normal direction of its 3D trochoidal trajectory. This concept is unique and it leads to the first cutting force model that specifically applies to non-horizontal and rotational cutting tool motions. The resulting cutting force model has been validated experimentally with extensive verification test cuts consisting of horizontal, non-horizontal, and rotational cutting motions of a ball-end mill.     

Micro slot milling of glass

Micro slot milling micro channels in a single pass vs two step upmilling has the benefit of higher productivity. This problem is approached by showing the theoretical benefits of more than two cutting edges. The acceptable feed per tooth and cutting depth at the maximum undeformed chip thickness for ductile-brittle transition and the benefit of upmilling versus downmilling and other parameters (tool wear, tool trajectory, tool deflection, air pressure/cutting oil) have been assessed by micro and macro-geometrical analyses versus surface finish/transparency, form error of the cross section shape in the micro scale (aspect ratio, tolerances, parallelism, flatness, straightness), chipping and productivity. Quantitative correlation between transparency and roughness is also proposed to estimate the acceptable amount of brittle mode.     

An improved cutting force model for micro milling considering machining dynamics

Micro milling, as a versatile micro machining process, is kinematically similar to conventional milling; however, it is significantly different from conventional milling with respect to chip formation mechanisms and uncut chip thickness modelling, due to the comparable size of the edge radius to the chip thickness, and the small per-tooth feeding. Considering tool runout and dynamic displacement between the tool and the workpiece, the contour of the workpiece left by previous tool paths is typically in a wavy form, and the wavy surface provides a feedback mechanism to cutting force generation because the instantaneous uncut chip thickness changes with both the vibration during the current tool path and the surface left by the previous tool paths. In this study, a more accurate uncut chip thickness model was established including the precise trochoidal trajectory of the cutting edge, tool runout and dynamic modulation caused by the machine tool system vibration. The dynamic regenerative effect is taken into account by considering the influence of all the previous cutting trajectories using numerical iteration; thus, the multiple time delays (MTD) are considered in this model. It is found that transient separation of the tool-workpiece occurring at a low feed per tooth, caused by MTD and the existing cutting force models, is no longer applicable when transient tool-workpiece separation occurs. Based on the proposed uncut chip thickness model, an improved cutting force model of micro milling is developed by full consideration of the ploughing effect and elastic recovery of the workpiece material. The proposed cutting force model is verified by micro end milling experiments, and the results show that the proposed model is capable of producing more accurate cutting force prediction than other existing models, particularly at small feed per tooth.     

A novel chatter stability criterion for the modelling and simulation of the dynamic milling process in the time domain

The modelling of the dynamic processes in milling and the determination of chatter-free cutting conditions are becoming increasingly important in order to facilitate the effective planning of machining operations. In this study, a new chatter stability criterion is proposed, which can be used for a time domain milling process simulation and a model-based milling process control. A predictive time domain model is presented for the simulation and analysis of the dynamic cutting process and chatter in milling. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. The cutting force is determined by using a predictive machining theory. A numerical method is employed to solve the differential equations governing the dynamics of the milling system. The work proposes that the ratio of the predicted maximum dynamic cutting force to the predicted maximum static cutting force can be used as a criterion for the chatter stability. Comparisons between the simulation and experimental results are given to verify the new model.