# CAD system for calculating orientation errors.

1. INTRODUCTION

In most cases, the determination of errors that appear to orientation process of parts in devices for processing presumes laborious calculations and assumes a good experience for designers. This process is often made by approximation, reffering at samples existing in literature which are more or less appropriate with the concrete design case.

We started from the typology of real surfaces from the workpiece and from the locator element. We analyzed the relative position of bases (geometrical elements defined as plans, lines and points associated with the surfaces). Following these, we built a database containing graphic patterns used as a library schemes targeting, by encoding the information.

The library scheme presented in this work is built using a mathematical model based on the theory of transformation of coordinates (Simion, 1995). The results from our earlier work show that the proposed math model is compatible with the standards and that it provides three-dimensional relations for orientation error. The project includes the implementation of the error analysis system into a CAD system.

2 LITERATURE REVIEW

Various computer-aided fixture design methods have been developed through the years to assist the fixture designer. One of the approaches consists in using relevant design experience from a design library and adapting it to provide a new fixture design solution. Another approach is based on simulating the orientation process, in order to select the optimal scheme.

From another point of view, some of the approaches can be based on geometric patterns. Other approaches are based on cinematic models. Asada and By (1985) created the Jacobian Matrix to model the 3D fixture-workpiece relationship. Xiong (1993) applied the kinetic model from multi-fingered robot hand grasping problem to the fixture configuration. Rong et al. (1996) have a series of studies on tolerance and stability analysis. Zhang et al. (2001) analyzed the locating error and tolerance assignment for computer-aided fixture design. Bragaru (1998) introduced a formula for calculating the vector error guidance, based on the relative position of bases.

3 THE BASIC MODEL

In order to cover possible situations, the database has been structured for the following levels of diversification:

* level 1--depending on the number of orientation surfaces;

* level 2--depending on the orientation surfaces type: plane, cylinder, cone, sphere;

* level 3--according to the typology and the relative position of associated bases: plane ([GAMMA]), line (D), point (P); for example, Fig.1 shows the analysis of the case of three bases of the same type (line);

* level 4-in a graphic model there are more technically possible oriented schemes, differentiated by the type of the dimension that is analyzed in order to determine the orientation error and by the symbols of locators.

[FIGURE 1 OMITTED]

In Fig. 2 there is presented a sample model from a database built as such.. The orientation schemes shown in this figure is modelled on an inside or outside cylinder surface (the orientation base is an axis, meaning a fictional line ) and on a flat surface (the orientation base is a plane which can be real or fictional).

Table 1 is associated to the model in Fig. 2. The components of error orientation are defined as variations of the relative positions between the dimension bases (DB) and the active bases (AB), projected on the direction of the dimension for which the orientation error is determined (Simion, 1995).

We used the following notations: TDp is the tolerance for the diameter of the dimension surface; TA is the tolerance for dimension A; Ai is the minimum effective dimension A; J1max is the maximum clearance between the workpiece and the locator; [gamma] is the half-angle of the V-block; [delta] is the angle between measuring direction and the bisector plane of the V-block.

[FIGURE 2 OMITTED]

The original ERCAD software for automate determination of the orientation error is designed for schemes involving one, two or three orientation surfaces and includes a database comprising over 5000 orientation schemes type.

The program operates for dimensions of parts between 0 and 500 mm and for precision between IT5 and IT12. The system operates in an AutoCAD environment and has its own menus, which are based on the types of schemes. Depending on the data explicitly introduced by the user or taken from the formal description of the workpiece (dimensions, tolerances etc.), the system automatically calculates and displays the specific orientation error.

Logical sequence of steps is shown for the model in Fig. 3, referring to the determination of orientation error for dimension t = 90[degrees] (the workpiece is oriented on two cylindrical surfaces).

[FIGURE 3 OMITTED]

Step 1: The user decides the number of surfaces on which the workpiece is oriented, by selecting the "2 SURFACES" menu.

Step 2: The user decides the type of orientation surfaces. In this case the appropriate option couple "CYILINDER-CYLINDER" must be selected.

Step 3: Depending on the relative position of the two orientation surfaces (parallelism in this case) the user chooses the appropriate graphical model. As a result, the model is displayed, as in Fig. 3.

Step 4: The user is required to confirm the choice of the appropriate model. Assuming an affirmative answer the user will proceed to the next step.

Step 5: As the model usually contains several possible schemes, the user is required to choose the scheme for which the error is calculated. The prompter indicates possible schemes to avoid choosing an impossible scheme: "Choose scheme targeting (1 + 7/2+7/3+7/4+7):". In this case, "3 +7" is to be written usig the keyboard.

Step 6: It is required to choose the dimension type (linear or angular and the direction) for which the error is determined. For the presented case, as a response to the prompter "Choose dimension (a1/a2/a3/ = /1):" the option "t" is to be typed.

Step 7: The system requires the introduction of user data regarding size, shape and relative position, needed for calculating the specific orientation error, according to the associated database.

Step 8: The prompter displays the calculated value of orientation error: "The error is 0.1215 degrees".

5. CONCLUSION

This paper presents an original system for computer aided determination of the orientation error. Note that if the presented system is integrated within a comprehensive fixtures design system, all the values introduced by the user (the type of orientation scheme, the nominal size, precision etc.) are automatically taken from previous design activities.

A second remark refers to the correctness of values calculated using the described software. Relations obtained by the method of coordinates processing and placed in the database were verified by data from literature, where they existed, or by applying other methods of calculating the orientation errors. The results were validated.

We anticipate that successful completion of the project will provide the designers a helpful tool for making better decisions about optimizing the fixture design.

6. REFERENCES

Asada, H. & By, A. (1985). Kinematic Analysis of Workpart Fixturing for Flexible Assembly with Automatically Reconfigurable Fixtures, IEEE J. of Robotics and Automation, Vol. 1, pp. 86-94.

Bragaru, A. (1998). Proiectarea dispozitivelor (Fixture Design), Editura Tehnica, ISBN 973-31-0717-4, Bucharest.

Rong, Y. & Bai, Y. (1996). Machining Accuracy Analysis for Computer- Aided Fixture Design, J. of Manufacturing Science and Engineering, Vol. 118, pp. 289-300.

Simion, I. (1995). Research concerning the precision of the orientation schemes, Ph.D.Thesis, University "Politehnica" from Bucharest.

Xiong, Y. L. (1993). Theory and Methodology for Concurrent Design and Planning of Reconfiguration Fixture, Proceedings--IEEE International Conference on Robotics and Automation, Vol. 3, May 2-6, pp. 305-311.

Zhang,Y.; Hu, W.; Kang, Y.; Rong, Y. & Yen, D. W. (2001). Locating error analysis and tolerance assignment for computer-aided fixture design, International Journal of Production Research, Vol. 39, No. 15, pp. 3529-3545.
```Tab. 1. The orientation error components associated to the
model in Fig. 2.

Orientation DB AB component
schemes component

Dimension type: a1, a2, a3

+,,; 0 for J1 max cos [epsilon]
+,, dimension
a1, TDp/2 TDp cos d / 2 sin [gamma] -
+,, for Dp cos d cos gT[gamma] /
dimensions 2 [sin.sup.2] [gamma]
+,, a2, a3 0

Dimension type: [epsilon]

+; + TA/R + Ai J1max/R + Ai

+,; 0 J1max/R + Ai
+,

+ TA/R + Ai arctg(TDp cos [delta]/
2 [sin.sup.2][gamma]R

Dp cos gT[gamma]/
2 [sin.sup.2] [gamma]R)

+ TA/R + Ai 0

+,; 0 0
+,

Dimension type: =

,+,, 0 J1 max cos [epsilon]

,+,, 0 0
```