A SIMPLIFIED CUTTING FORCE MODEL FOR LIGHT-CUT BALL-END MILLING APPLICATIONS

In light-cut milling operations, specific correlations have been identified empirically between the maximum cutting force on a cutter and its associated cutting parameters, and a series of ball-end milling tests for P20 tool steel has been conducted to establish the nature of these correlations. The experimental results indicate that the maximum cutting force on a cutter can be expressed as a logarithmic function of the associated cutting parameters. This paper describes the structure and testing of a simplified cutting force model for planar milling based on these results.     

曲面铣削过程加工路径对切削力和磨损的影响研究

针对不同走刀路径下的复杂曲面加工过程进行球头铣刀铣削Cr12MoV加工复杂曲面研究,分析不同走刀路径下铣削力和刀具磨损的变化趋势。试验结果表明:通过对比分析直线铣削和曲面铣削过程中的最大未变形切屑厚度,可以得出单周期内曲面铣削的力大于直线铣削过程的力,铣削相同铣削层时环形走刀测得的切削力普遍大于往复走刀测得的切削力;以最小刀具磨损为优化目标,运用方差分析法分析得出不同走刀路径的影响刀具磨损的主次因素,同时利用残差分析方法建立球头铣刀加工复杂曲面刀具磨损预测模型,并通过试验进行验证。     

凸曲面拼接模具球头铣刀的瞬时铣削力预测

在曲面模具拼接区域球头铣刀铣削过程中,刀具载荷变化大,瞬态铣削力有突变现象,影响模具拼接区域的加工精度和表面质量。为了预测拼接区域球头铣刀的瞬态铣削力,首先,建立考虑冲击振动的球头铣刀三维次摆线轨迹方程,得到瞬时未变形切屑厚度模型;然后,基于铣削微元的思想,建立凸曲面双硬度拼接模具球头铣刀的瞬态铣削力模型,该模型能够综合考虑拼接区冲击振动、硬度变化、刀具工件切触角度变化对瞬态铣削力的影响;最后,进行凸曲面拼接区域球头铣刀铣削加工实验。实验结果表明,预报的瞬态铣削力和实验测量结果在幅值上和变化趋势上具有一致性,在平稳切削时最大铣削力预测误差值基本在15%以内,验证了该模型能有效地预报凸曲面模具拼接区域球头铣刀的瞬态铣削力。     

THE GEOMETRY, SPECIFICATION AND PREDICTIVE FORCE MODELS FOR PLANE FACED BALL-END MILLING CUTTERS AND OPERATIONS

In this paper the geometry and specification of ball-end milling cutters are studied and discussed followed by an outline of the development of computer-aided predictive models for the three force components, torque and power in plane faced ball-end milling operations, based on the 'Unified-Generalised Mechanics of Cutting Approach'. The models allow for six milling modes, namely; slotting, 'on-centre' end-milling and 'off-centre' end-milling, each machining at the cutter ball-end cutting edge only or at the cutter ball-end and cylindrical periphery cutting edges for two or more flute cutters. The models include all the tool and cut geometrical variables and the cutting speed as well as the tool-workpiece material combination (via the database of basic cutting quantities). The models are verified through extensive numerical simulation studies and a comprehensive experimental testing programme. Good qualitative and quantitative correlation has been found between predicted and measured fluctuating and average force components and torque.     

MODELING OF 5-AXIS MILLING PROCESSES

5-axis milling operations are common in several industries such as aerospace, automotive and die/mold for machining of sculptured surfaces. In these operations, productivity, dimensional tolerance integrity and surface quality are of utmost importance. Part and tool deflections under high cutting forces may result in unacceptable part quality whereas using conservative cutting parameters results in decreased material removal rate. Process models can be used to determine the proper or optimal milling parameters for required quality with higher productivity. The majority of the existing milling models are for 3-axis operations, even the ones for ball-end mills. In this article, a complete geometry and force model are presented for 5-axis milling operations using ball-end mills. The effect of lead and tilt angles on the process geometry, cutter and workpiece engagement limits, scallop height, and milling forces are analyzed in detail. In addition, tool deflections and form errors are also formulated for 5-axis ball-end milling. The use of the model for selection of the process parameters such as lead and tilt angles that result in minimum cutting forces are also demonstrated. The model predictions for cutting forces and tool deflections are compared and verified by experimental results.     

MODELING OF 5-AXIS MILLING PROCESSES

5-axis milling operations are common in several industries such as aerospace, automotive and die/mold for machining of sculptured surfaces. In these operations, productivity, dimensional tolerance integrity and surface quality are of utmost importance. Part and tool deflections under high cutting forces may result in unacceptable part quality whereas using conservative cutting parameters results in decreased material removal rate. Process models can be used to determine the proper or optimal milling parameters for required quality with higher productivity. The majority of the existing milling models are for 3-axis operations, even the ones for ball-end mills. In this article, a complete geometry and force model are presented for 5-axis milling operations using ball-end mills. The effect of lead and tilt angles on the process geometry, cutter and workpiece engagement limits, scallop height, and milling forces are analyzed in detail. In addition, tool deflections and form errors are also formulated for 5-axis ball-end milling. The use of the model for selection of the process parameters such as lead and tilt angles that result in minimum cutting forces are also demonstrated. The model predictions for cutting forces and tool deflections are compared and verified by experimental results.     

自由曲面等高加工铣削载荷预报

实际生产过程中球头铣刀主要用于曲面加工,但是关于球头铣刀曲面加工切削力的研究很少.本文针对曲面铣削加工中球头铣刀切削力预报的问题,通过离散近似将动态的切削过程分解为一系列进给方向和刀具与工件接触区不断变化的微小瞬态阶段,将剪切和犁切双重作用的静态球头铣刀切削力模型引入到自由曲面铣削载荷预报中,并选取一自由曲面工件进行铣...     

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。     

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.     

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.     

Cutting Force Model for a Small-diameter Helical Milling Cutter

In the milling process, the major flank wear land area (two-dimensional measurement for the wear) of a small-diameter milling cutter, as wear standard, can reflect actual changes of the wear land of the cutter. By analyzing the wearing characteristics of the cutter, a cutting force model based on the major flank wear land area is established. Characteristic parameters such as pressure parameter and friction parameter are calculated by substituting tested data into their corresponding equations. The cutting force model for the helical milling cutter is validated by experiments. The computational and experimental results show that the cutting force model is almost consistent with the actual cutting conditions. Thus, the cutting force model established in the research can provide a theoretical foundation for monitoring the condition of a milling process that uses a small-diameter helical milling cutter.     

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.     

高速铣削过程铣削力建模及析因试验分析

根据铣削过程和铣刀的几何模型,建立铣削力的瞬时表达式和平均切削力公式,给出基于响应曲面法的切削力系数的二次多项式。综合应用析因试验设计和统计分析理论,计算切削力系数的回归系数模型并分析了切削参数对切削力系数的影响规律。     

面向加工特征的小直径螺旋球头立铣刀切削力模型

在Bayoum i的广义螺旋铣刀几何模型基础上,建立了小直径螺旋球头铣刀的刀具前刀面几何模型和切削力模型;通过将特征概念引入数控加工过程,提出了球头刀加工时的“爬坡”与“下坡”等加工特征的切削力模型求解方法;最后通过实验对比验证了刀具切削力模型的有效性。     

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。     

Prediction of dynamic cutting force and regenerative chatter stability in inserted cutters milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.     

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。     

A High-Precision Surface Grinding Model for General Ball-End Milling Cutters

The paper presents a high-precision manufacturing model for grinding the surface profiles of general ball-end milling (GBEM) cutters. The geometric shape of the grinding wheel is derived with a positive cone angle specifically for grinding the GBEM cutters. The concepts of radial equidistant lines and oblique equidistant surfaces are employed to model the front ball-end profile, the front cutting surface, the rear cutting surface, and the cutting-edge curve of the GBEM cutter. The front cutting surface model is obtained by computing the intersection of the rotating tool surface and the motion enve-ope of the grinder. The cutting-edge curve model is estimated by computing the intersection curve of the front cutting surface and the ball head of the GBEM cutter. A special model of the grinding mechanism is also derived and used to produce the rear surface of the cutter. Both the cutting-edge curve and the surface model are solved simultaneously in order to ensure that the cutting-edge curve leans physically against the rear-cutting surface. The geometry of the full front-end cutter shape and the parameters of the associated manufacturing processes are numerically optimised to ensure best grinding quality is achieved on the surfaces of the GBEM cutter. The concept of oblique equidistant surfaces is applied to produce a family of cutters of similar shapes with an accuracy corresponding to a user-specified allowable tolerance. One numerical example is presented to illustrate the usefulness and effectiveness of the proposed modelling methodology. Numerical results indicate that the proposed manufacturing model and grinding procedure are capable of producing a family of GBEM cutters accurate to a specified tolerance.     

An Enhanced Force Model for Sculptured Surface Machining

The ball-end milling process is used extensively in machining of sculpture surfaces in automotive, die/mold, and aerospace industries. In planning machining operations, the process planner has to be conservative when selecting machining conditions with respect to metal removal rate in order to avoid cutter chipping and breakage, or over-cut due to excessive cutter deflection. These problems are particularly important for machining of sculptured surfaces where axial and radial depths of cut are abruptly changing. This article presents a mathematical model that is developed to predict the cutting forces during ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter path, cutter, and workpiece geometries. In addition to predicting the cutting forces, the model determines the surface topography that can be visualized in solid form. Extensive experiments are performed to validate the theoretical model with measured forces. For complex part geometries, the mathematical model predictions were compared with experimental measurements.     

平头立铣刀铣削力模型中积分限的确定方法

在铣削力预报的研究中 ,通常采用的方法是将铣刀沿其轴线方向逐层划分为很薄的微单元 ,对每一个微单元可认为是一个单刃刀具的斜角切削过程 ,通过建立微单元上的切削力模型并沿轴线方向积分来求得总的切削力 ,轴向积分限通常是通过角度换算获取 ,比较繁琐。本文对刀具的几何特征进行了描述 ,建立了求取平头立铣刀铣削力模型角度积分限的通用方法 ,该方法通过分析刀具几何特征和加工类型 ,直接获取角度积分限 ,避免了繁琐的轴向积分限的计算 ,并通过算例验证了该方法的有效性。