The analysis of positional tolerances is based on the evaluation of pairs of values (x-coordinate and y-coordinate). Positional tolerances are typically applied to bore holes whose position is tolerated in x-direction, y-direction and z-direction.

1    X-Y-Plot Positional tolerances

The consideration of positional tolerances is based on the evaluation of pairs of values (x and y coordinates). Positional tolerances are typically used, for example, for bores whose position is toleranced in both the x and y directions.

In the case of positional tolerances, characteristic values are described by a pair of values. Each pair of values is determined by an x-value and a y-value. This corresponds to a data structure that 3D cooridinate measuring machines already provide. In the x-y plot, the individual value pairs are represented in a Cartesian coordinate system. The specification limits are entered as a square in the graph. The tolerance itself, on the other hand, forms a circle or an ellipse.

2    Graphics settings

2.1     Representation of the regression line

In different variants, the regression line (with confidence interval) as well as its formulaic representation can be displayed.

2.2     Representation of the value pairs

There are various graphical options for displaying the value pairs; the most common ones are shown here. The data set prepared here is to be regarded as an extreme example.

Display of symbols only

Only the symbols are shown in a simple representation:

Symbols with connecting lines

Through the connecting lines it can be seen whether it is a random point cloud or whether it is a progression of measured values within the position.

Value numbers with coloured gradient

A similar view brings the display of the value numbers with a coloured gradient

Marking of the last measured value(s)

For a view of the current data, the last X value pair(s) can be specially marked

2.3     Representation of the 3D distribution

This only has an effect in the 3D view, with this the "sugar loaf" could be hidden.

2.4     Component graphics

In addition to the X-Y Plot, individual characteristic graphs of the axes can be displayed. The value chart, value plot and histogram are available for selection:

2.5     Representation of the capability ellipses

In addition to the quantile ellipses, the capability ellipses can be displayed.

2.6     "Video" mode

With the video mode, the "run" of the measured values could be played by clicking through the measurements in the lower part of the graph after activation.

2.7     Variation ellipses

For experienced users, the variation ellipses, their axes and the indication of the angles can be specified

2.8     Car Body mode

As in the value chart, the body mode is also available for positions that were determined entirely or partially in a negative range.

Requirements

Depending on where in the coordinate system the measurement was taken, either the X-axis, or the Y-axis, or both axes are in the negative range.

Just as with the body mode in the value chart, the specification must be made in K2203, but in the higher-level element, in the position deviation amount.

As an example, the original position as well as the one with both axes in the negative range:

Without body mode

With body mode

2.9     Allocation for additional data

As in the value chart, the X-Y Plot can also be graphically split on additional data. The prerequisites for this are: The additional data are written in pairs with the values of the axes, the display of the value pairs must be set to the classical symbols.

As in the value chart, the value pairs are then displayed graphically with a legend, divided according to additional data.

A breakdown by time period as in the value chart is not possible.

2.10  3D display

Via the 3D display, 2D positions as well as 3D positions can be displayed three-dimensionally.

3    Sub-types and further graphics under "Positional tolerances".

3.1     X-Y-Plot positional tolerances (detail)

The "X-Y Plot position (section)" has the number of measured values as an additional option, here as an example: The last 10 measured values

This representation is mostly used in overview graphics, as the classic X-Y plot can become confusing with a larger number of measured values, especially if the focus is to be on the new data of the current production.

3.2     Box Plot / Capabilities Positional tolerances

The other graphs are pre-filtered to show only the higher-level position deviation amounts as a BoxPlot or as a C-value graph.

4    Best Fit Move

This function is used for positional tolerances, such as those required for bores. For bores, the permissible deviation from the nominal location is defined by a tolerance circle or tolerance ellipse. A possibly required position correction of a single hole is relatively easy to realise. But what if the location of several holes has to be considered at the same time?

Often several bores are produced at once on a machine, for example engine blocks. If the location of the holes is not satisfactory, the question of correcting the location arises. Given the fact that setting up the tools is relatively time-consuming, one is looking for a "quick" way to correct the position without having to set up the tools again.

Proposal for a "simple" position correction

The "Best-Fit-Move" method may be one way to solve the problem:

The bores of an engine block are combined into a common group. Several manufactured blocks are measured. The data is entered into qs-STAT, combined into a group and evaluated with the "Best-Fit-Move" method. The programme uses a compensation algorithm to calculate the position correction of the entire engine block. The programme outputs correction values for both axis directions as well as a correction angle. The location of the workpieces to be machined is readjusted on the machine tool according to the correction values. This results in an improvement of the location of the entire hole pattern, i.e. the variations between the actual and nominal positions are now smaller.

To use this feature, you must first create a Best-Fit-Move group. To do this, select the option Best-Fit-Move under Graphics|Individual Characteristics Graphics|Positional Tolerances. The Create BestFitMove group window then opens, in which you can create Best-Fit-Move groups from existing data sets.

First you specify how many groups are to be created. All positional tolerances produced in a common step should be combined into a Best-Fit-Move group, as they are all to be checked with this method.

Then click Next to select the mode. For existing data sets with positions, it is recommended to use the default setting (radio button Use existing positional tolerances).

With another click on Next, the assignment to the groups begins in the next step. On the left you see the opened data sets and, if available, the positional tolerances. The right-hand side shows the newly created Best-Fit-Move groups. Now select a position on the left and a group on the right and click on the Assign button to assign the selected position to the selected group.

After you have closed the assignment, click OK. In the parts/characteristics list, all unassigned items and characteristics are now at the end of the data set.

Only after you have created one or more Best-Fit-Move groups can you choose between the options Best-Fit-Move Average and Best-Fit-Move Last Value under Graphics|Individual Characteristics Graphics|Positional Tolerances.

The programme can calculate the correction values for the following reference systems:

1. Reference of the correction value calculation is the centre of gravity of the borehole pattern (Best-Fit-Move - Average)
2. The reference for the correction value calculation is the point of origin (Best-Fit-Move - Last value).

The following illustration shows an example of rotation around the machine's point of origin. The small asterisk on the left of the picture is the point of origin, which is used as the reference point for the rotation angle. The correction values are thus only valid for the selected reference system.

Below the illustration you will find the numeric output of the reference values. As you can already guess from the text fields, the programme offers two calculation methods for determining the correction values:

1. Calculation method 1

Here first the correction for the displacement in the coordinate axes is calculated and then the correction value for the angle.

2. Calculation method 2:

First the correction value for the rotation angle is calculated and then the correction values for the displacement in the coordinate axes are calculated.

By default, the settings of the strategy are used, with the option Use lower setting instead of the evaluation configuration settings, own specifications can be made.

4.1     Interpretation of the Best-Fit

A very simple example is used to explain the interpretation. For each of the 3 positional tolerances, a shift of the target can be seen. Only the tolerance circle and the variation ellipse are shown:

In a Best-Fit-Move without rotation, it is now possible to calculate how the entire system would have to be moved in x and y direction in order to achieve the best fit across all 3 positions.

In addition, the symbolic representation of the displacement, starting from the centre of the tolerance circles, can be displayed.

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