# Alignment appropriate machinery of measure for coordinates

**INTRODUCTION**

This type of inspection occurs in general machinery of measure for coordinates (MMC). The activity set piece in the field of work is hold with useful dedicated (sizes) or general use fixing elements, annulling its six degrees of freedom of movement. The alignment is performed on the set piece, which It consists of defining the ideal piece through their representative features reference system.

In other words: *
align* means put the piece in position and orientation
"privileged", in accordance with the wish of the author of its design, expressed
at the level of the piece or on your computer model. The results of the
inspection depends on the quality of the process of alignment, and
It derives from the importance of this phase of metrological work.

For the correct development of the phase of alignment and inspection is generally needed before a study of the piece.

**1. STUDY OF THE PIECE**

In an analytical process, using the sample as a real model and its level as virtual model, the metrólogo will try to understand the composition of forms that constitutes the piece.

*Form
feature *(FC).

fundamental attribute of each piece, is the rational combination of elementary forms which allows us to distinguish the parts, which ensures the functionality of the piece in a set.

*Form
technological* (FT).

Is that arises after the development process of the
manufacturing technology, and which enclosed the functionality requirements and
feasibility. In this simple basic forms are combined with
complex elementary forms to avoid collecting *critical areas*
tension (generated by difficulties of expulsion, temperatures,)
(pressure, load, etc.) during the manufacturing process or in
operation. Failure to comply with any of these requirements leads to
*atecnológicas*forms.

Fig. 1 Forms atecnológicas |
Technological form |

*Elementary forms
simple* (FELSEN).

They are those parts of the piece that materialize on primitive geometric elements such as prisms, pyramids, cylinders, cones, areas, Bulls. These are the most common ways to align.

*Elementary forms
complex* (FELCOM).

The areas bounded by three-dimensional curves complex or definable only by high degree equations. By the General are not useful to align, but if you are predominant and importance functional (helical, paraboloids, etc.). Can also be used for align with the help of an appropriate measurement programme (PC-DMIS, LIMA) HOLOS etc.).

Fig. 2. Simple elementary forms (FELSEN) and elementary forms comlejas (FELCOM) |

**2 EVALUATION OF FORMS**

In a analytical process, any piece can be decomposed into elementary forms simple and/or complex elementary forms, such that:

FT = S FELSEN (i) + S FELCOM (j)

Know the piece as a way to technological means to describe, locate and orient the present forms in the composition. In other words, be able to answer for each of its elements to the questions: what is? Where is it located? Which one It is its orientation?

The FELSEN can describe with specific dimensions, locate using the coordinates of any representative point and orient using angles.

In the virtual model of the
piece - expression of its technological form as flat on paper or model
computer 3D - this defining information is expressed through levels.
Both coordinates and angles are derivatives of the
size of type long, understood as the distance between two points
Representative, of the same or different characteristics
(the use of the generic term * feature* is common to name forms)
(primitives, without more details).

In the evaluation of many levels with the MMC is item is simply reading coordinates and, given that they are evaluated at the long from the axis of the system, it is essential that the system of reference is the appropriate. The same is true in the inspection of the FELCOM, where it She practices a discrete evaluation by means of coordinates of points taken on these areas. The problem is even more complex due to the collection of discrete points can not get compensation correct the radius of the tip of exploration if the movement's approach not held in perpendicular direction to the surface

**3 METHODS TO ALIGN**

There are standards such as ISO 5459 or ANSI Y14.5.1, indicating how the industrial pieces must align. The correct application of these rules greatly facilitates the process of inspection. These rules assigned to the designer of the piece the responsibility for defining the system of reference, through representative characteristics and restrictions on them, to be reflected in the level through a symbology reading and interpreting allow the metrólogo to reproduce the reasoning of the designer.

Fig. 4 Symbolism related to the alignment |

Often the alignment of the piece is derived from the set that belongs to ensure easy to assemble, avoid interference or secure functionality. Some components or subsets of the car are inspected in a frame of reference that You can have the origin out of the workload of the MMC.

Provided that in the flat some information about the alignment is to align respecting the marked demands. If in the plain lack the information relating to the alignment, we recommend using one of the methods presented below.

**3.1 Flat method, line, point**

- Choose the most representative piece feature to define the
*Datum primarium*[A]. Flat defined can be used for this purpose by number of points or axes of cylinders. To obtain the first axis (Z) and the piece loses three degrees of freedom: two turns (Rx, Ry) and a translation (Tz). Please note that failure to comply with the requirement of form (flatness), (cylindricity) disqualifies the feature for use in alignment. This occurrence should be commented on, with the beneficiary of the piece before we continue, in order to find an alternative solution - Define an address several points projected onto the plane
perpendicular to the first axis. This will be
*datum secundarium*[B]. The imposition of this address as the second axis (X) determines the loss of other two degrees of freedom (Rz and Ty) of the piece. The failure of the requirement of form (righteousness) disqualifies the feature for use in alignment - Set in a point of the piece (RIM, Center of a circle),
(etc.)
*datum terciarium*[C]. Thereby hangs the last degree of freedom, (Tx) of the piece in inspection. Figure 5 plate serves to illustrate the use of this method. The six degrees of freedom are marked by Tx, Ty, Tz (translations) and Rx, Ry, Rz (turns).

Fig. 5. The six lock
degrees of freedom |

**3.2 Method BESTFIT**

- Identify representative points on the piece in the frame of reference the MMC. These points are usually centres of drills, 3D intersection between axes of cylinders or result of the geometric relationship between measured elements. Requires a minimum of 4 points, but with the most points the final result improves.
- Edit the array of theoretical coordinates of measured points, while respecting the order of exploration
- Call the program computer, capable of calculating (linking the) (actual coordinates with the theoretical) translations and the necessary turns to generate more accurate reference system. The program performs calculation iterations until that the standard deviation of the errors is minimal.

Should make a comment on the matter: the coordinates of the points measured in the resulting system approaching the theoretical values with very unlikely to agree. Any translations for one the coordinates of the other points are made worse by coincidence.

**3.3 Method of alignment by
comparison with the computer model**

*General precautions to
take into account*

- In the identification of characteristics which are used for alignment, try to take points in movement of perpendicular approach to the surface
- In the lineup by a plane, set on 3 levels, make sure that the piece is fixed in a position that this theoretical level is parallel to one planes of projection measuring machine
- Verify the validity of the alignment after each graphic transformation measuring elements reference
- At the end the phase of alignment with success, we should save under name Surely the correct system.

**4. WHAT IS POSSIBLE TO ALIGN BY ONLY THREE POINTS?**

Find the answer to this question has been one of the challenges of the Group of work of the laboratory of metrology of Asacmm technology centre. This concern arose from practical needs such as:

- Tube inspection doubled, lined by the coordinates of the points of intersection between the cylindrical segments components;
- Inspection of subsets of automotive, lined by the coordinates of the points of fixing them.

It was intended to simulate the behavior during mounting by the alignment, in a way that the first mounted point meets the 3 coordinates, the second point is obliged to carry out only 2 coordinates (elongated hole mounting) and the third point is obliged to carry out only one of the coordinates (greater hole mounting). Figure 6 reproduces this situation.

In this representation the point A must comply with the predicted values of X, Y, Z, point (b) has freedom in the performance of the coordinate and whereas point C only It has to comply with the coordinate X.

Fig. 6 Fastening by three points with varying degrees of
freedom |

The use of the BESTFIT method or the method of alignment by comparison with the computer model It may not meet requirements of differential treatment for the points of interest. Was this need that gave impetus to the development of a dedicated programme baptized A3P, able to solve problems of alignment by only 3 points. The mathematical abstraction of the problem leads to two solutions. It turned out complicated the task of choosing the right solution. This is similar to the study of static system of bars, in three areas, as shown in the schematic representation of Figure 7.

To end the system of barcode is a spherical joint, which has three twists and the three blocked transfers. The area of the end (b) download your weight in a Prism "V"-oriented along the X axis. Thus the B side is obliged to comply with the coordinates and Z and freedom of travel to along the x-axis. The end with the C area rests on the plate base and undertakes to fulfill only the coordinate z. You can imagine that you rotating the system about the axis that are centres of the areas A and B are two positions of balance (a marked with lines) to the end C. While the two met the Z height, one will only be with values in X and And close to schedule.

Fig. 7. Static with two solutions balance |

A similar logical process is implemented in the A3P program, written in "agent for Windows". This program allows the Interactive introduction of theoretical coordinates of the points, then the measurement of the actual points and then performs the calculation process offered by:

- Information on the diversion of the distances between the three points Royal on the theoretical distance;
- Information on the position of the second and third points error (the first always matches);
- Appropriate reference system, in which the first point meets the three coordinates, the second meets two coordinates and the third just one of the proposed coordinates.

Application in inspection from pipes

Application in inspection of piece set

dy ("TRZ =" ", TRZ,"rozx ="ROZX") dy ("") dy("SE) ("they find these deformations:") dy("DAB_=_",DAB,"_DAC_=) ", DAC," DBC = "(CCD)" dy("SE) ("they manage these position errors:") dy ("EPA") = ", EPA,"EPB =", EPB," CLD = "(EPC)" If ((EPB_lt_U)) AND (EPC lt or)) then dy ("piece") ("and almost perfect alignment!") elsif ((EPB_gt_250*U) OR (CLD gt 250 * U)) then dy ("No") ("is an appropriate alignment!") end_if FORA: endstat end_program |

End of instructions in the program
source A3P |

**5 COMMENTS**

- If the three distances between the participants in the process are stretched, we have a piece with error in the calculation of the coefficient of contraction;
- If two of the real distances are less than the theoretical and the third is more, we have a piece of distorted, twisted;
- The error in position of the third point, understood as the radius of the sphere that includes the actual point and have as Center the theoretical point, it is also a synthetic indicator to express the degree of conformity between the Royal piece and its theoretical model.

**6 PERSPECTIVES**

- Intends to continue the development of the program to be able to analyze between the coordinates of various points (no more than 9) are the three points that offer the most accurate alignment on the basis of the minimum error position.
- Proposed intercomparison of results and exchange of information with other metrological bodies