Improved dynamic cutting force model in ball-end milling. Part I: theoretical modelling and experimental calibration

An accurate cutting force model of ball-end milling is essential for precision prediction and compensation of tool deflection that dominantly determines the dimensional accuracy of the machined surface. This paper presents an improved theoretical dynamic cutting force model for ball-end milling. The three-dimensional instantaneous cutting forces acting on a single flute of a helical ball-end mill are integrated from the differential cutting force components on sliced elements of the flute along the cutter-axis direction. The size effect of undeformed chip thickness and the influence of the effective rake angle are considered in the formulation of the differential cutting forces based on the theory of oblique cutting. A set of half immersion slot milling tests is performed with a one-tooth solid carbide helical ball-end mill for the calibration of the cutting force coefficients. The recorded dynamic cutting forces are averaged to fit the theoretical model and yield the cutting force coefficients. The measured and simulated dynamic cutting forces are compared using the experimental calibrated cutting force coefficients, and there is a reasonable agreement. A further experimental verification of the dynamic cutting force model will be presented in a follow-up paper.     

Geometric error compensation for five-axis ball-end milling by considering machined surface textures

Arbitrarily adjusting tool poses during error compensation may affect the quality of surface textures. This paper presents one tool center limitation-based geometric error compensation for five-axis ball-end milling to avoid the unexpected machined textures. Firstly, the mechanism of cutter location generation with cuter contact (CC) trajectory is analyzed. Due to zero bottom radius of ball-end cutter, CC points of the surface are only related to the tool center of the cutter. Realizing that, tool center limitation method of ball-end milling is established based on the generation of movements of all axes in order to ensure the machined textures. Then, geometric error compensation of ball-end milling is expressed as optimizing rotation angles of rotary axes by limiting tool centers of cutter locations. Next, particle swarm optimization (PSO) is intergraded into the geometric error compensation to obtain the compensated numerical control (NC) code. The limited region for particles of rotation angles is established, and moving criterion with a mutation operation is presented. With the help of the tool center limitation method, fitnesses of all particles are calculated with the integrated geometric error model. In this way, surface textures are considered and geometric errors of the machine tool are reduced. At last, cutting experiments on five-axis ball-end milling are carried out to testify the effectiveness of the proposed geometric error compensation.     

Cutter workpiece engagement region and surface topography prediction in five-axis ball-end milling

Based on the machining tool path and the true trajectory equation of the cutting edge relative to the workpiece, the engagement region between the cutter and workpiece is analyzed and a new model is developed for the numerical simulation of the machined surface topography in a multiaxis ball-end milling process. The influence of machining parameters such as the feed per tooth, the radial depth of cut, the angle orientation tool, the cutter runout, and the tool deflection upon the topography are taken into account in the model. Based on the cutter workpiece engagement, the cutting force model is established. The tool deflections are extracted and used in the surface topography model for simulation. The predicted force profiles were compared to the measured ones. A reasonable agreement between the experimental and the predicted results was found.     

Improving the high-speed finishing of forming tools for advanced high-strength steels (AHSS)

Forming tools manufacturers have extensively incorporated high-speed milling technology for the finishing of large punch or die tools. The main objective is to achieve a good surface quality directly form machining, without any additional, tedious, manual work. Currently, new advanced high-strength steels (AHSS) are being used for car body parts. In this case, there are two special changes related to the forming tools: a higher proportion of harder surfaces on the working area, and long try-out iterations, due to their great springback. Tempered surfaces and insert blocks harder than 60 HRC are needed to withstand the forming charges with a good working life expectancy. From this, two problems arise with regards to high-speed finishing: first, the deflection of the tool due to the cutting forces, which can produce unacceptable dimensional errors; and second, in the same finishing operation, zones with sharp changes in hardness must be machined with the same CNC program and cutting tool. The key to solving both problems will be the use of newly developed utilities in the preparation stage, and the elaboration of CNC programs using CAM software. In the first case, the deflection of tool is dealt with by a milling model which obtains the values of cutting forces. This model characterises the couple tool/material with six coefficients, which are previously obtained for ball-end milling tools and base die materials. Inputs provided by the CAM user include feed per tooth, and radial and axial depths of cut. The problem of surfaces with areas of different hardness and poorly defined boundaries is solved with a special postprocessor coded in C language. Once the CAM user has defined (on the CAD model) the theoretical boundaries of the tempered areas, the insert blocks or the deposition material areas, this utility includes changes of the programmed feed function in the CNC program. In this paper, these approaches are applied to medium size workpieces with the same features of the actual punch and die for AHSS forming. Results are provided to die manufacturers for application in real forming tools. This technological model of the milling process estimates values of cutting forces and offers manufacturers a reduction of production and lead times.     

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.     

Chatter stability of micro end milling by considering process nonlinearities and process damping

The micro end milling uses the miniature tools to fabricate complexity microstructures at high rotational speeds. The regenerative chatter, which causes tool wear and poor machining quality, is one of the challenges needed to be solved in the micro end milling process. In order to predict the chatter stability of micro end milling, this paper proposes a cutting forces model taking into account the process nonlinearities caused by tool run-out, trajectory of tool tip and intermittency of chip formation, and the process damping effect in the ploughing-dominant and shearing-dominant regimes. Since the elasto-plastic deformation of micro end milling leads to large process damping which will affect the process stability, the process damping is also included in the cutting forces model. The micro end milling process is modeled as a two degrees of freedom system with the dynamic parameters of tool-machine system obtained by the receptance coupling method. According to the calculated cutting forces, the time-domain simulation method is extended to predict the chatter stability lobes diagrams. Finally, the micro end milling experiments of cutting forces and machined surface quality have been investigated to validate the accuracy of the proposed model.     

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.     

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.     

Form error estimation in ball-end milling of sculptured surface with z-level contouring tool path

This paper presents a flexible model for estimating the form error in three-axis ball-end milling of sculptured surface with z-level contouring tool path. At an interval of feed per tooth, the whole process of sculptured surface machining is treated as a combination of sequential small inclined surface milling. For ball-end milling of the inclined surface with z-level contouring tool path, at surface generation position, an analytical model is proposed to identify the feedback effect of tool deflection on cutting edge engagement. The deflection-dependent cutting edge engagement is determined by using an iterative procedure. And ultimately, the form error is obtained from the balanced tool deflection and associated surface inclination angle. In a validation experiment, the estimated form errors are compared with both the measurements and the predictions of a rigid model. It is shown that the proposed flexible model gives significant better predictions of the form error than rigid model. Good agreement between the predicted and measured form errors is demonstrated for the ball-end milling of sculptured surface with z-level contouring tool path.     

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.     

Form error compensation in ball-end milling of sculptured surface with z-level contouring tool path

This paper presents an integrated form error compensation approach for ball-end milling of sculptured surface with z-level contouring tool path. From the analysis of local cutting equilibrium in general milling, an integrated form error compensation strategy is derived. In this strategy, the tool deflection is adopted as compensation value. The compensation value and local cutting equilibrium can be directly obtained from nominal cutting conditions; moreover, the time-consuming iterative process is no longer needed. The integrated strategy is then expanded to ball-end milling of sculptured surface based on the differential idea. A tool path modification model is also suggested to record the compensation value into tool path. A numerical example of comparing the calculation process of traditional multilevel compensation strategy and that of the integrated compensation strategy is described. The results of numerical examples show that the essentials of proposed integrated strategy and multilevel strategy are consistent, but the needed calculation steps of the two strategies are about 1 vs. 30. In the validation experiment, two practical sculptured surfaces are machined. Experimental results reveal that the integrated form error compensation approach can significantly reduce form error in ball-end milling of sculptured surface.     

A new approach to analysing machined surfaces by ball-end milling, part I:

Since productivity and product quality are always regarded as important issues in manufacturing technologies, a reliable method for predicting machining errors is essential to meeting these two conflicting requirements. However, the conventional roughness model is not suitable for the evaluation of machining errors for highly efficient machining conditions. Therefore, a different approach is needed for a more accurate calculation of machining errors. This study deals with the geometrical surface roughness in ball-end milling. In this work, a new method, called the ridge method, is proposed for the prediction of the machined surface roughness in the ball-end milling process. In Part I of this two-part paper, a theoretical analysis for the prediction of the characteristic lines of the cut remainder are generated from a surface generation mechanism of a ball-end milling process, and three types of ridges are defined. The trochoidal trajectories of cutting edges are considered in the evaluation of the cut remainder. The predicted results are compared with the results of a conventional roughness model.     

Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.     

Dispatching rules for unrelated parallel machine scheduling with release dates

A simplified procedure is proposed to predict the surface integrity of complex-shape parts generated by ball-end finishing milling. Along a complex cutting path, the tool inclination may vary within a large range. A geometrical study is performed to predict the effect of the tool inclination (lead angle) on the micro-geometry of the machined surface and on the effective cutting speed. This geometrical study brings out a range of values of the lead angle for which the machined surface is damaged by cutting pull-outs. This geometrical study also brings out a range of values of the lead angle for which the effective cutting speed is null. This case corresponds to extreme values of the cutting forces and to high compressive residual stresses. These predictions are verified for a selection of tool inclinations and other cutting parameters such as cutting speed, feed per tooth and cusp height. These machining tests are performed on a high-strength bainitic steel. The experimental campaign includes milling tests with cutting forces measurements, 2-D optical micro-geometry measurements and X-ray diffraction measurements.     

Process modeling and toolpath optimization for five-axis ball-end milling based on tool motion analysis

In free-form surface machining, the prediction of five-axis ball-end milling forces is quite a challenge due to difficulties of determining the underformed chip thickness and engaged cutting edge. Part and tool deflections under high cutting forces may result in poor part quality. To solve these concerns, this paper presents process modeling and optimization method for five-axis milling based on tool motion analysis. The method selected for geometric stock modeling is the dexel approach, and the extracted cutter workpiece engagements are used as input to a force prediction. The cutter entry?Cexit angles and depth of cuts are found and used to calculate the instantaneous cutting forces. The process is optimized by varying the feed as the tool?Cworkpiece engagements vary along the toolpath, and the unified model provides a powerful tool for analyzing five-axis milling. The new feedrate profiles are shown to considerably reduce the machining time while avoiding process faults.     

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。     

高速铣削半圆弧工件表面形貌的仿真

在高速铣削情况下,利用平面刃球头铣刀沿半圆弧路线进行加工,对加工后的表面形貌进行理论建模与仿真。给出在空间三维切削时刀具切削刃的运动轨迹数学模型,并借助该模型给出球头刀切削半圆弧工件表面形貌的仿真算法。     

钼钒铸铁汽车覆盖件模具数控高效切削加工稳定性研究

针对汽车覆盖件模具型面特点,进行了球头铣刀高效加工自由曲面铣削方式与切削层参数的研究,获得了被加工曲面曲率和铣削参数对切削层参数的影响规律,提出了控制模具型面切削过程稳定性的方法。结果表明:在汽车覆盖件模具型面粗加工阶段通过选择合理的刀路使被加工表面的曲率连续变化,有助于控制切削过程的稳定性,而在半精加工和精加工阶段通过减小行距能够降低切削层参数的变化幅度,获得较高的模具加工质量。     

The effect of characteristics of free<Emphasis Type="Bold">-</Emphasis>form surface on the machined surface topography in milling of panel mold

In the milling process of automobile panel mold of hardened steel, the characteristic of free-form surface is one of the dominant factors for surface topography. In this paper, the trajectory of cutting edge is firstly modeled to analyze the residual height of the free-form surface in ball-end milling of hardened steel. Furthermore, the non-uniform rational B-splines (NURBS) surface reconstruction is utilized to generate the surface topography. Subsequently, the influences of surface curvature, lead angle, milling vibrations on the machined surface topography, and residual height are investigated, respectively. Finally, the accuracy of the surface topography and the roughness prediction model are validated by the milling experiments of free-form surface, where two-dimensional contour maps could be obtained. The simulation and experimental results demonstrate that the machined surface topography of hardened steel is fitted by means of NURBS surface reconstruction. In that manner, the effects of surface characteristics on the machined surface topography can be accurately predicted.     

变密度微织构球头铣刀切削性能多目标优化

为深入研究微织构排列形式对微织构理刀具的抗磨减摩机理的影响,分别从理论、仿真及试验等方面对最优的微织构排布形式进行研究。首先,建立微织构在刀具前刀面的数学模型及仿真模型。其次,通过试验验证仿真结果的准确性。仿真及试验研究均发现,变密度微织构球头铣刀的铣削性能优于均匀分布密度的微织构球头铣刀。最后,运用模糊评价法优选最优的铣削性能的微织构球头铣刀,优化结果表明,两排织构间距先为200 μm,再为150 μm,最后为175 μm的微织构球头铣刀的铣削性能最好。该项研究使刀具具有良好的抗磨减磨性,提高加工效率及被加工工件的表面质量。