Parametrically automated 3D design and manufacturing for spiral-type free-form models in an interactive CAD/CAM environment

Abstract

For product lifecycle management reasons, research trends impose the need of automated engineering tasks, such as computer-aided design and manufacturing. This paper proposes a novel approach of automating both the design and manufacturing processes of impeller-type geometries, when CAD/CAM technology is employed. To do so, a newly developed application was built; exploiting application programming interface objects of parametric instances, in order to automate time-consuming repetitive tasks for the preparation of 3D models and their direct manufacturing process. The developed application incorporates Simpson’s method, Bezier-Bernstein equation and Non-Uniform Rational B-Spline for curve approximation describing blades of centrifugal impellers, as a representative case study. The machining technology is that of 3-axis CNC, thereby; each curve extends along a constant x-y plane. In the first step of the application, the entire 3D model of the impeller-type model is automatically generated according to variable values taken as user-defined entities from the interface. The application then carries on by automatically modeling the manufacturing process and ultimately generating the NC program from the cutter location data for a given CNC machine tool.

Introduction

Research on design and manufacturing of spiral-curved parts like cam followers, turbine blades, gears and impellers, requires good mathematical background, as well as flexibility in the usage of CAD/CAM systems. Even though the current level of CAD/CAM automation is quite high, time-consuming operations are still needed to define complex geometries and particular design features that are described mathematically through equations or parametric relations. To capture such needs, engineering software suppliers provide access to their software through the establishment of open application program interfaces (APIs). That is, users and software developers can create their own macros and add-in application, taking advantage of available automation objects and routines through programming languages, such as C++, Visual Basic and JavaScript.

To make use of this beneficial technology, several researchers have already presented their high-quality contribution, which concerns the automated handling of specialized functions found in most commercially available CAD/CAM systems. Up to this day, research conducted deals with the development of novel and sophisticated applications to automate design of cutting tool profiles [1], part holding or fixturing devices [2] and product geometries along with their special features [3–5]. On their efforts to predict surface errors when machining thin-walled parts, Izamshah et al. [6] needed to automate simulations for modeling solids, material removal processes and structural analysis operation, through the use of macros and Microsoft Visual Basic. Reddy and Brioso [7] developed a methodology where tedious and repetitive processes are automated while designing an industrial robot lower arm. Further on, their model is structurally evaluated in ANSYS${}^{\circledR }$. Finite element analysis process is automated by the use of the programming languages Python and JavaScript. Furthermore, a user interface is created using Microsoft Excel with Visual Basic.

Aiming at rapidly producing setup sheets for the CNC machining of industrial products research efforts have also been conducted to automate the process planning stage. Harik et al. [8], developed an entire platform to facilitate process planning for aeronautical parts using the main application development framework namely CAA-RADE${}^{\circledR }$ of Dassault Systèmes CATIA${}^{\circledR }$. CAA-RADE${}^{\circledR }$ is a C++ based development environment native for CATIA and provides a low-level access to most of CATIA’s features, thus allowing the creation of embedded commands, toolbars, dialogs etc. To overcome limitations found by employing this development platform, Fountas [9] moved towards the automated process planning. This was carried out by creating support functions, with the use of Visual Basic as the main programming application. Jeba Singh and Jebaraj [10] presented an automatic environment within CAD/CAM software to generate optimal process plans for pre-determined objectives with respect to factory environment for modelled components. In their work, data exchange is achieved between a feature-based design system and spreadsheet software applications through Visual Basic programming. Dupe and Briand [11] proposed a a multidisciplinary and interactive approach for the design of autonomous microsystems. Raffaeli and Germani [12] proposed an approach capable of using special tools to automatically perform design of footwear shape models whilst flattening shoe styling curves represented in virtual prototypes. Buzzi et al.  [13] studied the technology of femoral components and contributed by presenting an innovative infrastructure targeted on virtual models of the human body so as tp design and configure transfemoral and transbial lower limp prosthesis parts. Hincapié et al. [14] utilized product lifecycle management properties to establish a novel framework for automated manufacturing systems. Their work takes advantage of actual results taken from experiments conducted, as well as virtual attributes necessary for customizing the environment. A work focused on exploiting the performance in a human–computer numerically controlled (CNC) machine interface (HCMI) environment was forwarded by Khan [15].

Deb et al. [16] developed a methodology for selecting machining operations using artificial neural networks (ANNs). Process planning is conducted by a modular expert system fully integrated with an automated data extraction system, which obtains data from CAD and feeds process planning modules in a fully automated environment. Krimpenis [17] conducted an extensive research in the area of machining optimization using artificial intelligence (AI). In his work, a special programming module was developed to automate tasks needed for argument passing and parameter evaluations among a CAM system and a genetic algorithm (GA). Remaining volume, machining time and material uniformity left for finishing were treated as quality objectives for a rough machining optimization problem. With reference to the state of-the-art presented so far, no research effort seems to cope with more than two of the aforementioned components in terms of the automated functionality of specialized tools to come up with an integrated CAD/CAM infrastructure.

This paper’s structure is as follows: The first section deals with the mathematical relations and respective computations for curves that are used by CAD environment to produce the parametric 3D models. Simpson’s rule, Bezier’s equation and NURBS spline are discussed regarding their contribution to the problem formulation of the current study’s objectives. In the second section, the automated design module in CAD environment is presented. The last section gives an overview of the methodology that leads to the automatic tool path generation for the designed part. Impeller-type 3D CAD models were employed as case studies.

As it is presented in the following sections, this study offers a useful, hands-on tool that automatically: (a) drives a parametric CAD modeler to create a high consistency 3D model of a spiral-type free-form part and (b) exploits CAM software and its post-processor in obtaining an efficient G-code to mill this part in an appropriate 3-axis CNC machine tool. The user interacts with the application in order to choose all involved design and manufacturing specifics; part design characteristics along with design parameter values, machining strategy and cutting parameter values are given by simple keystrokes. If the model does not meet the user’s design or machining standards, just a few more moments are needed to produce a new, different part; or machining strategy. This is a novel approach in decision-making in the field of spiral-type free-form part design and manufacturing, as most relevant literature focuses on either optimal design or optimal manufacturing and usually oversees that these two are both links of the same production chain.

Mathematical background of high-order curves

Complex-shaped features found in modern functional and aesthetic parts belong to a broader family of curves and surfaces, which are mathematically described through higher degree special functions and computational relations. Various types of mathematical definitions may be applied according to the nature of the curved segment or surface. For example, the design of helical or straight-tooth gears is based on the involute curve. The main goal here is to evaluate all variables involved in the engineering design of a specific part and thus to choose the most convenient approach, that will optimize its performance. In any case, a text file that holds x-y-z point coordinates is generated for the desired curve. Variables that are taking part in the mathematical calculations are inserted by the end-user. These variables are different for each design approach.

Model definition using Simpson’s rule

In a centrifugal impeller design, the blade’s orbit may be described by Simpson’s differential equation as,

1

$$\begin{array}{c}\hfill d\mathit{\phi }=\frac{dr}{rtan(\mathit{\beta }(r))}\end{array}$$or in an integral form as,

2

$$\begin{array}{c}\hfill \mathit{\phi }(r)=\frac{180}{\mathit{\pi }}\left(\underset{r_1}{\overset{r_2}{\int }}\frac{1}{rtan\left(\mathit{\beta }(r)\right)}\right)\end{array}$$where,

3

$$\begin{array}{c}\hfill \mathit{\beta }(r)={\mathit{\beta }}_1+(r_2-r_1)\frac{{\mathit{\beta }}_2-{\mathit{\beta }}_1}{r_2-r_1}\end{array}$$‘$\mathit{\beta }(r)$’ is a linear distribution of the outer (pressure) angle of fluid flow $({\mathit{\beta }}_2)$ [18] and $({\mathit{\beta }}_1)$ is the inlet angle at the suction portion (Fig. 1). The values of $\mathit{\beta }(r)$ are calculated for each value of $r$, depending on the partitioning provided by the user via a loop statement. A similar loop statement computes the values of polar angle $\mathit{\phi }(r)$ for each r value by applying the trapezoidal rule for computing definite integrals. Finally, every point of the curve is described through its general parametric form as,

4

$$\begin{array}{c}\hfill \mathit{\gamma }(r)=[cos\mathit{\phi }(r),sin\mathit{\phi }(r)]\end{array}$$After all iterations, resulting point coordinates are saved in a text file. It is mentioned that all technical data presented above are products of mathematical computations conducted prior to the development of this study. Figure 1 depicts the main variables needed to perform the respective calculations and extract data, in terms of points and their coordinates which will facilitate the design process later on. Moreover, velocity triangles drawn for inlet and outlet sections are also depicted. The blades are curved between the inlet and outlet diameters.

Fig. 1 [Images not available. See PDF.]

Main parameters and velocity triangles for a typical centrifugal impeller

Model definition using Bezier curves

This alternative modeling suggests that the blade’s orbit may be described by cubic Bezier’s equation (Eq. 5).

5

$$\begin{array}{cc}\hfill B(t)& ={(1-t)}^3{P}_0+3{(1-t)}^{2}t{P}_1\hfill \\ \hfill & +3(1-t)t^2{P}_2+t^3{P}_3,t\in [0,1]\hfill \end{array}$$where $P_0$ and $P_3$ are points on the curve whilst $P_1$ and $P_2$ are two control points needed for curve approximation (Fig. 2). $P_1$ and $P_2$ are calculated using angles in pressure and suction regions as variables. Even though these points can be arbitrary determined, they directly affect the impeller’s performance. Thereby, the angles ought to be inserted either as ‘fixed’ values from an existing impeller, or by considering relation to an individual impeller model.

Fig. 2 [Images not available. See PDF.]

Typical Bezier curve with two control points

It is of paramount importance to refer to the ‘independence’ and ‘similarity’ of the functions that will generate x, y and z values in the 3 dimensional space. However this paper concerns only 2D curves extended along a constant x-y plane. The functions that represent x and y coordinates are shown in Eqs. (6) and (7) respectively.

6

$$\begin{array}{cc}\hfill B_x(t)& ={(1-t)}^3{P}_{0x}+3{(1-t)}^{2}t{P}_{1x}\hfill \\ \hfill & +3(1-t)t^2{P}_{2x}+t^3{P}_{3x},t\in [0,1]\hfill \end{array}$$

7

$$\begin{array}{cc}\hfill B_y(t)& ={(1-t)}^3{P}_{0y}+3{(1-t)}^{2}t{P}_{1y}\hfill \\ \hfill & +3(1-t)t^2{P}_{2y}+t^3{P}_{3y},t\in [0,1]\hfill \end{array}$$Looping variable t in the space [0, 1] and calculating the value of $B$ function for $x$ and $y$ values of the curve in question respectively generates the coordinates of the Bezier curve which are saved on a text file.

Model definition using NURBS curves

Should NURBS curves be adopted to develop the blade’s orbit, weight values of control points should be specified. In this particular case, four control points were assigned to determine the orbit of impeller’s blade. 1st and 4th control point can change the starting and ending points of the curve, consequently it is highly recommended to use 1 for both values to avoid design errors. The blade’s orbit is described by a 3rd degree equation of the NURBS spline, as seen in Eq. 8.

8

$$\begin{array}{c}\hfill C(u)=\sum _{i-0}^2{B}_i(u)\times P_i\times w_i\end{array}$$Bernstein polynomials [19, 20] were adopted for this case as a basic NURBS spline-type. Yet again, the process executes looping operations with variable $(t)$ in space [0, 1] whilst considering the determined weights. Finally, the coordinates of the NURBS curve are computed and saved on a text file.

Automation of 3D parametric CAD modeling

When the developed application starts, it allows the user to create the 3D model of the part and to model the manufacturing process. Execution of the manufacturing process is only possible when a 3D impeller part has been designed in advance. Otherwise, the application form notifies the user to create the part first.

The application’s design section is directly coupled with the automation process of a typical CAD system [21] through macros using its application programming interface (API). In most CAD systems, when recording a macro, the majority of performed actions in the CAD environment is translated to subroutine or function coding modules of Visual Basic, Visual Basic. NET or C#.NET language. Automating the design process involves external programming in Visual Basic.NET${}^{\circledR }$. The application’s commands are parametrically defined and in each execution the design operation uses different values according to the user’s choices (see Fig. 3).

Fig. 3 [Images not available. See PDF.]

The automatic design form

The tasks of executing the CAD session, opening a new part, saving the 3D model and exiting from the application are totally automated. All necessary attributes are asked from the user, inserted properly in the application and thoroughly taken under consideration during execution of the design process. It is also up to the user to either watch the design procedure or allow it to run in “ghost” mode. The latter drastically reduces CPU time and memory usage. Actions written in VB.NET environment are listed below:

• New session document and new part creation.

• Importing coordinate files generated from computations via 3D sketching tools.

• Curve fitting according to the reference points calculated using start and end point values of suction and pressure diameters.

• Bi-directional offsetting using blade’s thickness as the major offset parameter.

• Feature operations execution to extrude the sketch regarding the blade’s height.

• Insertion of a second sketch segment in which 2 circles are designed to formulate the impeller’s base.

• Selection and backwards extrusion of a specified height for the sketch region representing the base.

• Insertion of a thin feature for hub creation utilizing the hub diameter as a variable.

• Filleting using a radius determined equal to a percentage of blade thickness.

• Outwards cut extrusion to remove unnecessary solid regions that lie inside and outside the basic model of the impeller.

• Part storage as *.STP file and exiting.

Figure 4 shows three impeller-type models for each design category; Simpson, Bezier and NURBS. All their characteristics, for both design and manufacturing, are mentioned in Table 1. Design process lasts about 2 min in visible mode and a couple of seconds in “ghost” mode in a Quad-core CPU, 4 GB RAM with 512 MB graphics card.

Fig. 4 [Images not available. See PDF.]

Impeller models approximated with: a Simpson’s method-case 1, b Simpson’s method-case 2, c Bezier curves-case 1, d Bezier curves-case 2, e NURBS curves-case 1, f NURBS curves-case 2

Table 1. Design and manufacturing parameters applied to impeller-type test cases for Simpson (Sim.1 and Sim.2), Bezier (Bez.1 and Bez.2), and NURBS (NURBS.1 and NURBS.2) with respect to Fig. 5a–f

Design variables	Sim.1	Sim.2	Bez.1	Bez.2	NURBS.1	W.1	NURBS.2	W.2
Entities
Suction radius (mm)	100	100	110	100	80	1	60	1
Pressure radius (mm)	120	300	250	350	220	9	220	0.3
Suction angle (deg)	14	11	86	5	2	0.7	20	0.9
Pressure angle (deg)	30	25	10	70	70	1	80	1
Blade thickness (mm)	4	5	6	5	12		5
Blades height (mm)	20	30	12	15	30		20
Hub plate width (mm)	25	30	50	25	25		25
Hub radius (mm)	35	30	40	30	50		35
Number of blades (Integer)	6	6	5	10	7		13
Curve partition (Integer)	100	100	100	100	100		100

Automated CAM

The second section of the developed application makes use of the main entities for machining modeling and strategy definition properties. Thus, variables such as cutting feed $V_f$ (mm/min), spindle speed $n$ (rpm), tool diameter (Ø), step-over $a_e$(mm) and step-down $a_p$ (mm) are inserted by user (Fig. 5).

Fig. 5 [Images not available. See PDF.]

The automatic machining form

In order to automatically produce tool-paths for both roughing and finishing procedure, these have been fully automated using the corresponding programming objects via the API of a typical CAM system, specifically DelCAM’s PowerMill${}^{\circledR }$ [22]. During this module’s execution, the following actions are performed:

• Opening a new machining modeling document and importing part model previously created in the CAD module.

• Block definition to formulate the raw stock according the part’s outer dimensions and cutting tool definition according to design features and technological constraints.

• Work-plane definition and specification of machining parameters regarding the material type, machine tool configurations, cutting tool geometry and material, etc.

• Definition of rapid move heights and safety plane - automatic tool-path computation, post-processing and NC code creation.

• Project storage and exiting.

Particularly, for producing NC code depending on the type of NC controller, an independent module that interacts with the rest of the application’s components was developed [23]. The specific function produces ISO G-codes to enable CNC machine tool handling by almost all kinds of NC controllers found in industry. If the end-user desires to manually produce the NC code, the application has the ability to only extract the cutter location (CL) data, for a later post-processing. Figure 6 illustrates several machined models generated from machining simulations in the CAM environment. Manufacturing variables with sample values are tabulated in Table 2 along with the resulting manufacturing time, as it was calculated from the CAM system.

Fig. 6 [Images not available. See PDF.]

Impeller clearance and finishing tool-paths for the impeller-type models of Fig. 5: a Sim.1, b Sim.2, c Bez.1, d Bez.2, e NURBS.1, f NURBS.2

Table 2. Manufacturing parameters applied to impeller-type test cases for Simpson (Sim.1 and Sim.2), Bezier (Bez.1 and Bez.2), and NURBS (NURBS.1 and NURBS.2) with respect to Fig. 5a–f

Manufacturing variables	Sim.1	Sim.2	Bez.1	Bez.2	NURBS.1	W.1	NURBS.2	W.2
Entities
Cutting speed (mm/min)	3,000	2,500	3,000	2,500	500	1	1,000	1
Spindle speed (rev/min)	1,000	1,000	1,500	1,000	500	9	500	0.3
Passes (mm)	2	2	3	3	2	0.7	2	0.9
Tool diameter (mm)	10	8	8	7	6	1	6	1
Roughing time (s)${}^{\mathrm{a}}$	41,449	96,424	21,835	157,898	124,970		29,660
Finishing time (s)${}^{\mathrm{a}}$	33,519	79,605	10,033	60,579	24,448		15,207

${}^{\mathrm{a}}$ Roughing and finishing time are calculated through PowerMill${}^{\circledR }$

Statistical results that are generated from machining simulations refer to both roughing and finishing stages and include machining times, number of tool lifts, tool movement length etc. The ability to automatically handle the CAM environment, so as to test manufacturing operation sequences is of paramount importance, since it contributes to decision-making when generating NC programs. What is more, all outputs extracted from the developed application may be further evaluated using specialized systems to verify NC codes. Figure 7 illustrates an NC verification in such environment by utilizing the extracted G-code from one of the experimental scenarios. It was shown that this G-code not only satisfies production indicators (machining time), but it also offered optimal and collision-free tool paths.

Fig. 7 [Images not available. See PDF.]

Machining setup for a typical centrifugal impeller-type model: a fixturing and setup, b roughing-finishing simulation, c resulting part

Discussion

The process of designing impeller-type models is a time-consuming and tedious task mainly because such models require an excellent curve description through extensive series or vast clouds of points. In general, technical computing software is employed, so as to solve the mathematical equations that generate the point coordinates that are further utilized for the design of the generative curve. Usually, points obtained from such a procedure are explicitly created, that is; they do not hold coordinates when loaded as instances in CAD platform. Should these points be utilized for curve design, their transformation to coordinate points is an imperative action. To tackle with this issue, design engineers are forced to develop their own macros and modules that summon the points and change their coordinate values. Even though this is a quite efficient approach, objects that automate the corresponding functions are not always provided. The problem becomes even tougher when the environment for these actions is totally windows-based. A representative example of the above is the need to change explicit points to coordinates through selections available in forms or combo boxes. To automate these entities special WinAPI${}^{\circledR }$ programming knowledge is required.

The application presented in this study does not only overcome this problem, but proceeds with the design of the rest of the features for impeller-type models as well. Nevertheless, it is to be noted that there is no guaranteed information regarding the efficiency of the final impeller model, as this lies entirely on the user mainly in terms of specialized knowledge concerning fluid mechanics and engineering design. As a result, even though the obtained 3D models are geometrically consistent, the same cannot be assumed for their operational behavior. It is, however, the goal of a following study to include such operational and qualitative properties in the application, thus make the application a robust tool for the overall optimal design and manufacture of impellers. The capability of automatically preparing the model for machining simulation is another novel technique, which satisfies such demands as high productivity and machining modeling acceleration. At its current state, the application directly passes the 3D model to CAM environment and important entity values, such as strategy and tool selection, feeds and speeds selection, etc, are automatically determined. However, the proposed application does not investigate specialized setups and work holding. Moreover an automated feature recognition activity is yet to be developed that assists machining modeling towards a more reliable and sophisticated way of process planning. Nevertheless the application presented in this work will help end-users to avoid repetitive and routine tasks concerning the design and machining modeling leaving this way considerable time to validate impeller-type models, in terms of engineering design and functionality. For the time being, these are yet to be integrated into the application.

Conclusion

In the light of ongoing pursuit for accelerated product design and manufacturing, a programming interface, that integrates both CAD and CAM environments for impeller-type parts, was presented in this paper. The application automates the time-consuming repetitive tasks concerning CAD and CAM by manipulating objects dedicated for customization and programming. It was indicated that the approach yields significant benefits since the overall time of CAD model preparation and process planning can be reduced to 85–90 %. This was verified by manually producing several impeller-type models and feeding them to CAM environment. Moreover the approach is able to produce CAD models and manufacturing programs with great efficiency and accuracy. Experiments conducted to various CAD models of centrifugal impeller-type parts revealed that time-consuming actions can be easily automated provided that openness of architecture exists, in terms of applications programming interface. Since almost all modern CAD/CAM packages offer such functionality, the philosophy presented in this study can easily be adopted to any such system. In addition, modern central processing units that are equipped in current industrial hardware may reduce even more the computational cost, when a large number of trial and error experiments is to be performed, so as to arrive at an optimal solution. The authors plan to further extend the capabilities of the approach to other types of complex sculptured surfaces, as well as incorporate functional characteristics of resulting impellers.

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