CAD system for calculating orientation errors.
Simion, Ionel ; Dobre, Daniel ; Marin, Dumitru 等
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]
4. THE ERCAD SYSTEM
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
[1]+[5],[6],[7]; 0 for J1 max cos [epsilon]
[2]+[5],[6],[7] dimension
a1, TDp/2 TDp cos d / 2 sin [gamma] -
[3]+[5],[6],[7] for Dp cos d cos gT[gamma] /
dimensions 2 [sin.sup.2] [gamma]
[4]+[5],[6],[7] a2, a3 0
Dimension type: [epsilon]
[1]+[5]; [2]+[5] TA/R + Ai J1max/R + Ai
[1]+[6],[9]; 0 J1max/R + Ai
[2]+[6],[7]
[3]+[5] TA/R + Ai arctg(TDp cos [delta]/
2 [sin.sup.2][gamma]R
Dp cos gT[gamma]/
2 [sin.sup.2] [gamma]R)
[4]+[5] TA/R + Ai 0
[3]+[6],[7]; 0 0
[3]+[6],[7]
Dimension type: =
[1],[2]+[5],[6],[7] 0 J1 max cos [epsilon]
[3],[4]+[5],[6],[7] 0 0