Enhanced virtual machining for sculptured surfaces by integrating machine tool error models into NC machining simulation

Sculptured surface machining is a time-consuming and costly process. It requires simultaneously controlled motion of the machine axes. However, positioning inaccuracies or errors exist in machine tools. The combination of error motions of the machine axes will result in a complicated pattern of part geometry errors. In order to quantitatively predict these part geometry errors, a new application framework ‘enhanced virtual machining’ is developed. It integrates machine tool error models into NC machining simulation. The ideal cutter path in the NC program for surface machining is discretized into sub-paths. For each interpolated cutter location, the machine geometric errors are predicted from the machine tool error model. Both the solid modeling approach and the surface modeling approach are used to translate machine geometric errors into part geometry errors for sculptured surface machining. The solid modeling approach obtains the final part geometry by subtracting the tool swept volume from the stock geometric model. The surface modeling approach approximates the actual cutter contact points by calculating the cutting tool motion and geometry. The simulation results show that the machine tool error model can be effectively integrated into sculptured surface machining to predict part geometry errors before the real cutting begins.     

A CAD approach to helical groove machining-I. mathematical model and model solution

The problem of helical groove machining in practice is still predominantly approached from an empirical trial and error standpoint. For the analytical resolution of this problem through a CAD approach, a generalized helical groove machining model, utilizing the principles of differential geometry and kinematics, has been formulated. The approach is based on the establishment of the fundamental analytical conditions of engagement between the generating tool surface and generated helical groove surface. The general mathematical relationships established facilitate the determination of the resulting tool or helical groove profile for a given helical groove or cutting tool profile, respectively.     

Simulation of flank milling processes

The paper presents prediction of cutting forces when flank milling ruled surfaces with tapered, helical, ball end mills. The geometric model of the workpiece is imported from standard CAD systems, and the tapered helical ball end mill is modeled as the combination of sphere and cone primitives in ACIS^© solid modeling environment. The intersection of cutter and part with a ruled surface is evaluated, and the cutter entry into and exit angles from the work material are modeled, and stored as a function of tool center coordinates along the path. The cutter entry and exit angles, the immersion angles, are used as boundary conditions in predicting the cutting forces along the path. The methodology allows prediction of cutting load distribution on the tool and part, as well optimization of machining cycle times by scheduling the feedrate in such a way that torque, power and static deflections can be maintained at safe levels.     

基于Pro/E的斜齿轮参数化建模及仿真加工

文章以渐开线斜齿圆柱齿轮为例,介绍了斜齿轮CAD参数化模型的构建方法,并在Pro/E系统中将其实现,解决了参数不同的同类齿轮反复建造的问题.并基于Pro/NC实现了斜齿轮的仿真加工,且通过后置处理器生成了加工斜齿轮的数控程序.对异型曲面零件的CAD/CAM一体化研究很有参考价值.     

Process geometry modeling with cutter runout for milling of curved surfaces

Prediction of cutting forces and machined surface error in peripheral milling of curved geometries is non-trivial due to varying workpiece curvature along tool path. The complexity in this case, arises due to continuously changing process geometry as workpiece curvature varies along tool path. In the presence of cutter runout, the situation is further complicated owing to changing radii of cutting points. The present work attempts to model process geometry in machining of curved geometries and in the presence of cutter runout. A mathematical model computing process geometry parameters which include cutter/workpiece engagements and instantaneous uncut chip thickness in the presence of cutter runout is presented. The developed model is more realistic as it accounts for interaction of cutting tooth trajectory with that of preceding teeth trajectories in computing process geometry. Computer simulation studies carried for this purpose has shown that it is essential to account for teeth trajectory interactions for accurate prediction of process geometry parameters. This aspect is further confirmed with machining experiments, which were conducted to validate this aspect. From the outcomes of present work, it is clearly seen that the computation of process geometry during machining of curved geometries and in presence of cutter runout is not straightforward and requires a systematic approach as presented in this paper.     

An image detection approach to NC rough-cut milling from solid models

This paper presents a method of converting information from a CAD solid model into a form suitable for CAM operation. The rough machining of a cavity into a block is used to illustrate the working of the system. This example was chosen because the machining of cavities presents difficulties as outlined below and rough machining involves the removal of more material than finish machining and therefore is of more economic significance in a production process. A three-axis NC miller is used to cut the cavity which has depth, requiring material to be removed in layers. A computer-based image detection method is used for cutter-path generation and models that contain planar surfaces, general quadratic surfaces, B-spline surfaces and compound surfaces can be treated. The B-rep solid object is transformed into an image as a grid-height model, allowing a three-dimensional object to be approximated by a two-dimensional spatial array. The cutter location (CL) data file is automatically generated from this spatial array. The height change of stock material in each grid is recorded in a two-dimensional array during the machining process and is utilized as an image for further roughing and verification. Efficient machining procedures are obtained by an analysis of cutting simulation, utilizing large cutter sizes for simple shaped portions in the first stage of roughing and then using small cutter sizes for complex portions and to remove uncut material left by the large cutters in a fine roughing operation. This approach allows a three-dimensional cutter path problem to be reduced to one of two dimensions which is solved by image detection of cutting attributes.     

Optimization of CNC isoscallop free form surface machining using a genetic algorithm

Isoscallop machining with edge-based master cutter path (MCP) essentially ensures uniformity of surface roughness over entire surface of part but may not necessarily ensure minimization of machining time. In the present work, it has been shown that there is a provision for minimizing machining time while implementing Isoscallop machining, by optimizing the orientation of the primary or Master Cutter path (MCP) through application of a GA. The results indicate a substantial reduction in total machining time for the proposed approach compared to those obtained through previously reported cutter path generation strategies.     

Mechanics and dynamics of general milling cutters.: Part I: helical end mills

A variety of helical end mill geometry is used in the industry. Helical cylindrical, helical ball, taper helical ball, bull nosed and special purpose end mills are widely used in aerospace, automotive and die machining industry. While the geometry of each cutter may be different, the mechanics and dynamics of the milling process at each cutting edge point are common. This paper presents a generalized mathematical model of most helical end mills used in the industry. The end mill geometry is modeled by helical flutes wrapped around a parametric envelope. The coordinates of a cutting edge point along the parametric helical flute are mathematically expressed. The chip thickness at each cutting point is evaluated by using the true kinematics of milling including the structural vibrations of both cutter and workpiece. By integrating the process along each cutting edge, which is in contact with the workpiece, the cutting forces, vibrations, dimensional surface finish and chatter stability lobes for an arbitrary end mill can be predicted. The predicted and measured cutting forces, surface roughness and stability lobes for ball, helical tapered ball, and bull nosed end mills are provided to illustrate the viability of the proposed generalized end mill analysis.     

基于UG/Open API的齿面侧铣精加工方法研究

将自由曲面的数控加工方法应用于大模数齿面加工中,采用多轴联动侧铣完成最终齿轮表面的精加工。为了使加工中刀具切触点能够与齿面相适应、减小刀具的磨损,利用UG NX的二次开发环境,对齿面加工的走刀轨迹进行控制。仿真结果表明:该方法能够较好地解决齿面加工中切触点固定的问题,有利于延长刀具寿命,提高加工效率。     

薄壁件铣削加工刀具几何参数优化

针对汽车检具薄壁件铣削变形问题,通过改变铣刀的几何参数建立铣削单因素和三因素四水平的正交实验。利用有限元软件AdvantEdge和ABAQUS分别对铣削加工过程和加工残余应力引起的变形进行仿真,研究不同的刀具几何参数对工件变形的影响。采用田口法分析了刀具几何参数对加工变形的综合影响程度。结果表明:刀具后角对工件加工变形影响的最为显著,螺旋角次之,前角最不显著;获得AA5083铣削的铣刀刀具几何参数组合。通过实验对优化后的刀具几何参数的正确性进行验证,证明该方法是检具薄壁件加工中刀具几何参数优化选择的一种有效的方法。     

Effects of the hob cutter regrinding and setting on ZE-type worm gear manufacture

A mathematical model for a ZE-type worm gear set is proposed. The characteristics of a ZE-type worm gear cut with an oversize hob cutter are investigated. Bearing contacts and kinematic errors in the ZE-type worm gear set due to regrinding of oversize hob cutters are also studied. Bearing contacts in the worm gear set were obtained using surface separation topology techniques and tooth contact analysis. It was found that bearing contact locations are sensitive to the hob cutter setting angle and setting distance. Kinematic error minimization was achieved modifying worm normal tooth angle. By applying the optimization theorem and computer simulation programs, optimum hob cutter settings and worm normal tooth angle were determined to improve bearing contact location and minimize the worm gear set kinematic errors. A numerical example is given to demonstrate the results of the investigation. The developed computer-aided manufacture program has successfully been applied to the worm gear manufacture and hob cutter design.     

An accurate,efficient envelope approach to modeling the geometric deviation of the machined surface for a specific five-axis CNC machine tool

Geometric deviation, defined as the difference between the nominal surface and the simulation model of the machined surface, is the fundamental concern of five-axis tool path planning. Since the machined surface is part of the cutter envelope surface generated by the cutter motion, it is necessary to calculate the envelope surface in order to obtain the geometric deviation. In the stage of tool path planning, current approaches calculate the cutter envelope surface by using the cutter motion along the given tool path. However, the cutter motion of practical machining on a specific five-axis CNC machine tool is different from the given tool path. Moreover, the computation is very challenging when the accurate cutter motion of practical machining is applied to calculate the envelope surface. To overcome these two problems, a geometric envelope approach with two major distinctions is proposed in this paper. First, the envelope surface of the cutter undergoing a general motion is efficiently obtained as a closed-form vector expression. Second, the accurate cutter motion, which is determined by machine kinematic and interpolation scheme in practical machining, can be easily applied to calculate the accurate envelope surface. With the envelope surface, the geometric deviation is calculated to estimate the overcut or undercut in five-axis milling. An example is given to demonstrate the validity of the proposed method.     

数控双盘铣刀铣削斜齿轮模型分析及加工仿真

根据斜齿轮加工原理,对双盘铣刀斜齿轮加工过程进行分析,推导出被加工齿轮的螺旋面方程,分析了双盘铣刀中心间距与齿数、模数以及齿廓各部分余量的关系,并在AutoLisp二次开发语言环境下,编制仿真加工程序,对双盘铣刀斜齿轮加工过程进行了仿真验证.     

Chip geometry and cutting forces in gear power skiving

This paper describes a new virtual model for predicting the uncut chip geometry and cutting forces in power skiving, which is a high-speed, versatile gear cutting process. The developed kinematic model is applied in a dexel-based solid modeling engine to extract three-dimensional uncut chip geometry, from which the two-dimensional cross section is obtained via Delaunay triangulation. Cutting velocities along discretized cutter edges are calculated and used to determine the effective rake and oblique angles. Then, force predictions are made using the oblique cutting model and validated using measurements from power skiving trials performed on a DMG MORI NT5400DCG mill-turn machine.     

内斜齿轮车齿加工数学模型及实验研究

为了解决内齿轮高效加工的问题,提出内齿轮车齿加工方法。根据内齿轮车齿加工原理构建数学模型,建立车齿刀具齿面方程并完成内齿轮齿面方程推导,随后在Vericut中对内齿圈进行模拟加工,验证理论模型的正确性,最后进行了切齿加工实验及检测,测量结果满足工程要求。实验结果表明：所提出的车齿加工方法能够完成内齿圈的高效加工,具有重要的理论意义和工程应用价值。     

基于ARM9的齿轮加工数控系统的研究

为了提高齿轮的加工精度、嵌入自主研发的控制算法,提出一种基于嵌入式系统的齿轮加工数控系统。对系统进行了硬件设计和软件设计,并对系统进行了功能模块划分;分析插齿刀加工运动轨迹以及插齿刀和工件的运动关系,计算出关键点坐标值,构建出插齿加工自动编程的数学模型,并实现了插齿加工自动编程功能模块。研究内容为今后齿轮数控加工控制精度的提高提供了参考。     

Surface finish visualisation in high speed, ball nose milling applications

High speed milling systems are capable of producing complex parts that require little or no hand finishing operations. The machined surfaces are smooth to the touch and they are within the required machining tolerances. However, the visual surface appearance of the parts can be a quality issue because the surface patina is generated by a rotating, multi-flute, ball nose milling cutter as it moves over the surface of the part. Current CAM systems provide good simulating procedures to view the overall surface geometry with swept volume procedures, but they do not consider the micro pattern pertaining to the cutting action of individual cutter flutes. The work presented in this paper addresses this consideration and assesses two new methods to satisfy the need to account for, and predict, the surface machining effects from a ball nose milling cutter.     

Modelling the machining dynamics of peripheral milling

The machining dynamics involves the dynamic cutting forces, the structural modal analysis of a cutting system, the vibrations of the cutter and workpiece, and their correlation. This paper presents a new approach modelling and predicting the machining dynamics for peripheral milling. First, a machining dynamics model is developed based on the regenerative vibrations of the cutter and workpiece excited by the dynamic cutting forces, which are mathematically modelled and experimentally verified by the authors [Liu, X., Cheng, K., Webb, D., Luo, X.-C. Improved dynamic cutting force model in peripheral milling—Part 1: Theoretical model and simulation. Int. J. Adv Manufact Tech, 2002, 20, 631–638; Liu, X., Cheng, K., Webb, D., Longstaff, A. P., Widiyarto, H. M., Jiang, X.-Q., Blunt, L., Ford, D. Improved dynamic cutting force model in peripheral milling—Part 2: Experimental verification and prediction. Int. J. Adv Manufact Tech, 2004, 24, 794–805]. Then, the mechanism of surface generation is analysed and formulated based on the geometry and kinematics of the cutter. Thereafter a simulation model of the machining dynamics is implemented using Simulink. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machine centre were measured in both normal and feed directions by an instrumented hammer and accelerometers. Then a set of well-designed cutting trials was carried out to record and analyse the dynamic cutting forces, the vibrations of the spindle head and workpiece, and the surface roughness and waviness. Corresponding simulations of the machining processes of these cutting trials based on the machining dynamics model are investigated and the simulation results are analysed and compared to the measurements. It is shown that the proposed machining dynamics model can well predict the dynamic cutting forces, the vibrations of the cutter and workpiece. There is a reasonable agreement between the measured and predicted roughness/waviness of the machined surface. Therefore the proposed approach is proven to be a feasible and practical approach analysing machining dynamics and surface roughness/waviness for shop floor applications.     

High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation

Reference trajectory generation plays a key role in the computer control of machine tools. Generated trajectories must not only describe the desired tool path accurately, but must also have smooth kinematic profiles in order to maintain high tracking accuracy, and avoid exciting the natural modes of the mechanical structure or servo control system. Spline trajectory generation techniques have become widely adopted in machining aerospace parts, dies, and molds for this reason; they provide a more continuous feed motion compared to multiple linear or circular segments and result in shorter machining time, as well as better surface geometry. This paper presents a quintic spline trajectory generation algorithm that produces continuous position, velocity, and acceleration profiles. The spline interpolation is realized with a novel approach that eliminates feedrate fluctuations due to parametrization errors. Smooth accelerations and decelerations are obtained by imposing limits on the first and second time derivatives of feedrate, resulting in trapezoidal acceleration profiles along the toolpath. Finally, the reference trajectory generated with varying interpolation period is re-sampled at the servo loop closure period using fifth order polynomials, which enable the original kinematic profiles to be preserved. The proposed trajectory generation algorithm has been tested in machining a wing surface on a three axis milling machine, controlled with an in house developed open architecture CNC.     

复杂螺旋曲面加工刀具参数的优化设计

在螺旋曲面铣削加工过程中,刀具参数对所形成的螺旋面精度有很大的影响,为了满足其精度的需要,文章针对双螺杆混输泵转子截面廓形的几何特点,依据空间圆弧逼近原理,对转子螺旋曲面的加工刀具进行了参数优化设计,并通过计算实例验证了该优化方法的可行性。