球头铣刀高速铣削斜面的三维数值模拟研究

用球头铣刀高速铣削斜面是在三轴加工中心上加工模具时的一种走刀方式。根据球头铣刀高速铣削斜面的特点,建立了在垂直向上和向下、水平向上和向下四种走刀方式下高速铣削45°斜面,以及在垂直向下走刀方式下高速铣削30°、60°、75°斜面的三维有限元模型,以分析不同走刀方式下铣削斜面以及铣削不同角度斜面时切削力和切削温度的变化规律。模拟结果表明,在铣削45°斜面时,采用向上走刀方式较向下走刀方式的切削力幅值小、波动大,且切削温度高;采用垂直向下走刀方式铣削大角度斜面时也出现类似情况。对切削力的实测结果验证了该模型的可靠性。     

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.     

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.     

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.     

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...     

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.     

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.     

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.     

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.     

CALCULATION OF THE SPECIFIC CUTTING COEFFICIENTS AND GEOMETRICAL ASPECTS IN SCULPTURED SURFACE MACHINING

This article presents a method for obtaining the shear and ploughing specific cutting coefficients for a ball-end milling cutting force model. Thus, by using the proposed calculation method, the need for introducing variable shear cutting coefficients has been identified. This fact is due to the dependency among the specific cutting coefficients and the cutting edge inclination angle, which is variable in ball-end mills. Linear, quadratic and cubic polynomial shear cutting coefficients have been calculated, and the degree of adjustment obtained in each approach has been analyzed. At the same time, the expressions of the ploughing specific coefficients have been analyzed. The proposed calculation method has been applied to the following materials: a 7075-T6 aluminum alloy and a 52HRC AISI H13 tool steel. The results obtained from the validation demonstrate how the obtained coefficients are capable of predicting cutting forces over a wide range of cutting conditions. Finally, the results from applying the coefficients calculated in horizontal slot milling tests have been introduced in a model capable of calculating cutting forces in slope milling cases, which validates the calculation method proposed as a generic method for estimation of cutting coefficients.     

Experimental study of the effect of tool orientation in five-axis micro-milling of brass using ball-end mills

The effect of tool orientation on the final surface geometry and quality in five-axis micro-milling of brass using ball-end mills is investigated. Straight grooves with a semicircular cross section are cut with different tool inclination and tilt angles, and the resulting surfaces are characterized using an optical profilometer and microscope. Micro-milling cutting forces are recorded synchronously with spindle electric current and cutting motions in order to investigate the correlation between the tool orientation and the achieved surface quality. Results of various cutting experiments and analysis of the final surface geometry show that varying the tool orientation reduces rubbing of the material at the bottom of the grooves, which often occurs in ball-end milling of brass, and improves the final surface quality. The experimental analysis for surface roughness shows that applying a tool inclination angle of 15° can considerably improve the surface roughness at the bottom of the grooves. Analysis of static and averaged peak-to-valley (P-to-V) values of the cutting forces show that the static cutting force values are reduced by half when the tool inclination was increased from 0 to 15°. P-to-V cutting force values in along-the-feed direction were also decreased in the inclined machining.     

Decoupled chip thickness calculation model for cutting force prediction in five-axis ball-end milling

Cutting force prediction plays very critical roles for machining parameters selection in milling process. Chip thickness calculation supplies the basis for cutting force prediction. However, the chip thickness calculation in five-axis ball-end milling is difficult due to complex geometrical engagements between parts and cutters. In this paper, we present a method to calculate the chip thickness in five-axis ball-end milling. The contributions of lead and tilt angles in five-axis ball-end milling on the chip thickness are studied separately in detail. We prove that the actual chip thickness can be decoupled as the sum of the ones derived from the two individual cutting conditions, i.e., lead and tilt angles. In this model, the calculation of engagement boundaries of tool–workpiece engagement is easy; thus, time consumption is low. In order to verify the proposed chip thickness model, the chip volume predicted based on the proposed chip thickness calculation model is compared with the theoretical results. The comparison results show that the desired accuracy is obtained with the proposed chip thickness calculation model. The validation cutting tests, which are in a constant material removal rate and with only ball part engaged in cutting, are carried out. The optimized lead and tilt angles are analyzed with regard to cutting forces. The geometrical as well as the kinematics meaning of the proposed method is obvious comparing with the existing models.     

Low-frequency chatter genesis during inclined surface copy-milling with ball-end mill: Experimental study

In this study low-frequency chatter during machining of inclined surfaces with ball-end mills is experimentally investigated. An explanation of genesis of low-frequency vibrations have been proposed for various conditions: cutting direction, lead angle values, spindle speed, depth of cut. As a result, it has been proven that low-frequency chatter has more significant effect on machined surface than usual chatter. Low-frequency chatter occurs during downward milling, rather than upward milling, especially when lead angle increases. Furthermore, low-frequency chatter takes place in the beginning of cutting process, thereafter develops into steady state of usual chatter, which has no such significant effect on machined surface, as it has been shown. The results are in line with the supposition that low frequency vibrations are caused by sudden and irregular nature of shearing process, when magnitude is small.     

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。     

Cutter path orientations when high-speed finish milling inclined hardened steel

The use of high-speed milling (HSM) for the production of moulds and dies is becoming more widespread. Critical aspects of the technology include cutting tools, machinability data, cutter path generation and technology. Much published information exists on cutting tools and related data (cutting speeds, feed rates, depths of cut, etc.). However, relatively little information has been published on the evaluation of cutter paths for this application. Most of the research focuses on cutter path generation with the main aim on reducing production time. Work concerning cutter path evaluation and optimisation on tool wear, tool life and relevant workpiece machinability characteristics are scant. This paper investigates and evaluates the different cutter path orientations when high-speed finish milling inclined hardened steel, at a workpiece inclination angle of 75°. The results demonstrate that employing a vertical downward orientation achieved the longest life. However, in terms of workpiece surface roughness, vertical upward orientation is generally preferred.     

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.     

Experimental study on micro electrical discharge machining of porous stainless steel

Various cutter strategies have been developed during milling freeform surface. Proper selection of the cutter path orientation is extremely important in ensuring high productivity rate, meeting the better quality level, and longer tool life. In this work, finish milling of TC17 alloy has been done using carbide ball nose end mill on an incline workpiece angle of 30°. The influence of cutter path orientation was examined, and the cutting forces, tool life, tool wear, and surface integrity were evaluated. The results indicate that horizontal downward orientation produced the highest cutting forces. Vertical downward orientation provided the best tool life with cut lengths 90–380 % longer than for all other orientations. Flank wear and adhesion wear were the primary wear form and wear mechanisms, respectively. The best surface finish was achieved using an upward orientation, in particular, the vertical upward orientation. Compressive residual stresses were detected on all the machined surfaces, and vertical upward orientation provided the minimum surface compressive residual stress. In the aspect of tool wear reduction and improvement of surface integrity, horizontal upward cutter path orientation was a suitable choice, which provided a tool life of 270 m, surface roughness (R _a ) of 1.46 μm, and surface compressive residual stress of ?300 MPa.     

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.