汽车运输工业---应用实例

Figure 1: This fixture was developed for Porsche AG. The fixture was designed to handle easy loading and removal of motor part castings. The high precision requirements for loads in the drilling and milling process were verified with Algor FEA.

In this project, KTW used PRO/ENGINEER to create a 3-D CAD solid model of the fixture geometry. They contracted my firm, Speedy Engineering of Germany, to interface the model with Algor finite element analysis (FEA) software to predict the behavior of the fixture design in advance. This analysis work was to take place before the first fixture prototype was produced in order to assure smooth commencement of operation.

Solid Modelers Increase Transparency

Manufacturers of fixtures that secure castings for drilling and milling commonly use a traditional approach in the design cycle -- the design is modeled in a 2-D CAD program based on experience and over-dimensioning. The behavior of a design is discovered much later during the first stage of prototype testing.

Using a 3-D CAD solid modeler such as Pro/ENGINEER leads to a lower error rate during design and construction because 3-D models are easier to understand than 2-D drawings. Design discussions are more efficient and less problematic when the object can be viewed in 3-D, as well as in 2-D drawings. The capability to view and rotate shaded models on a computer adds even more realism to visualization of designs.

FEA Simulation Reduces Prototype Trial and Error Testing

To avoid costly prototypes prior to the casting process, linear static and dynamic (vibration) analyses of the motor component fixture geometry were performed within only a few days of its design to determine displacements and eigenfrequencies of the geometry. FEA can yield precise results, provided that the proper material properties, forces and boundary conditions are applied. I used Algor because of the capability to work with CAD solid geometry and apply an automatic mesh of 8-node brick elements, which is a precise element type.

KTW provided Speedy Engineering a rough draft of the geometry in universal IGES file format, a common method of exchanging geometry when the CAD and Algor FEA system are on separate computers. Reviewing the first IGES file from Pro/ENGINEER revealed that different export parameters needed to be employed in Pro/ENGINEER. Once the final CAD geometry file was received, final meshing and FEA computation were finished in only two days. The results confirmed that the fixture was stiff enough to fulfill all of Porsche's requirements and the casting process could begin.

Figure 2: For the linear static finite element analyses, the loads were applied separately in the X-, Y- and Z-directions. Here we see that a reference load of 1kN in direction +Y at one of the fixing points results in a maximum displacement of 4.0 um. The total displacement of a working load is computed by the equation:

To shorten the operation start-up time, I suggested to KTW that we also analyze the dynamic behavior of the fixture component. Every machined part has to have a high-quality surface. If a vibrating tool causes resonance, the machined part's surface may be unacceptably rough. If the machined part, the fixture, the machine or a combination of these items has resonance frequencies resembling those of the tool frequencies, the surface is destroyed and the part becomes unusable. Therefore, it is important to choose machining frequencies that will not cause resonance.

Typically, trial-and-error tests need to be performed in order to determine resonant frequencies before a new machining component is put into use. The new part is used with varying support and rotational speeds until settings are found that avoid resonant frequencies. Despite considerable costs, this trial-and-error method avoids loss of product and production time later.

Dynamic analysis can cut the need to use the trial-and-error method to test for resonant frequencies. A dynamic analysis can be carried out on the model used for the displacement analysis, provided that the FEA model's mesh is fine enough. A dynamic analysis determines the destructive eigenfrequencies and typical displacements for each mode. This is sufficient to define frequency windows, which the manufacturer can use to properly set up the milling process.

Only the base frequencies and their harmonics are energetically relevant and have to be computed. In our case, the fixture needed to be fully constrained at the six mounting points on the palette (so no rigid body modes were computed) and the first thirty eigenfrequencies were computed. When looking at the displacement produced by each frequency, one needs to consider two factors: whether the displacement is occurring in an area of the model that might cause damage to the surface of the component being milled; and how much energy the mode has (base and low frequencies have more energy than higher frequencies). By considering these two factors for each mode, I determined which frequencies would cause undesirable vibration.

Figure 3: The first three vibration modes are displayed here; they have been exaggerated to facilitate viewing. The red areas represent the highest displacement. The frequencies determined by the software correlate closely with the results of laboratory Fast Fourier Transform tests.

The accuracy of the computation depends on the precision of the material data. Based on the analysis results and accounting for the fact that the stiffness of cast iron often varies more than +/- 10%, we recommended a practical frequency window width between 25Hz to 40Hz. Usually, the weight and stiffness of the parts being machined have to be taken into consideration. However, since only relatively lightweight aluminum motor parts are machined and the fixture is cast iron, the additional mass is less than 5% and would not have a significant effect. A complete analysis would normally include the machined part as well as the fixture since the total assembly could develop local eigenfrequencies which would result in undesirable effects on the surface quality.

To verify the results, we measured the fixture acoustically. We recorded the sound spectrum at different parts of the fixture with a simple microphone and a PC. The resulting Fast Fourier Transform analysis gave us precise frequencies to compare with the computed eigenfrequencies.

The measured frequencies differed with less than 3Hz in the frequency range from 20Hz to 300Hz.

The results of the static and dynamic analyses enabled us to specify maximum working loads for production, which guaranteed success with the first use of this fixture design. Knowledge of behavior and displacement magnitudes of fixtures makes it possible to compute permissible forces for drilling and milling to ensure high efficiency for the creation of machining programs.

Performing static and dynamic analyses typically takes only a few days. This time investment pays off later in the production cycle when the newly developed fixture needs no reworking or even a second prototype -- a process that could delay the project by several weeks.

The process demonstrated in this example represents an advance in construction techniques that opens a new view into the future of machine and fixture development. FEA and cooperation between machine manufacturers, fixture construction companies and end-user companies, like Porsche, will shorten the time to start of production and reduce total costs.

Mr. Mathias C. Landgraf is the managing director of Speedy Engineering, a company offering finite element analysis software and services.

Kurt Wei haupt is the managing director of KTW Konstruktion Technik K.Wei haupt GmbH, a company offering fixture and machine construction services.