The present invention refers to a method for compensating measurement errors due to thermally induced structural deformations in a coordinate measurement machine.
As is known, coordinate measurement machines comprise members movable along coordinate axes for the purposes of moving a measuring sensor in a measurement volume. Typically, the movable members are constituted by a first carriage movable along a first axis, a second carriage carried by the first carriage and movable with respect thereto along a second axis orthogonal to the first one, and a spindle carried by the second carriage and movable with respect thereto along a third axis orthogonal to the first two.
In particular, the present method relates to the compensation of measurement errors due to the thermal deformation of the machine structural components that form the guideways for the movable members. These components are characterized by an elongated prismatic shape with a longitudinal dimension that is significantly larger than the others.
The components may constitute the movable part or the fixed part of the relevant slide axis.
Some non-limitative examples of these components are constituted, for example, by:
Typically, as shown in
The joint between the structural element 2 and the guide element(s) 3 is generally provided by threaded connections 4 sized in such a way that, for practical purposes, the component 1 may be considered as a single piece from the structural standpoint.
The assembled component 1 has a constant section along the longitudinal direction for substantially its entire length.
Depending on the position of the guide elements 3 on the section, the section may be asymmetric and the barycentre of the sections of the guide elements 3 might not coincide with the neutral axis of the section of the structural element 2.
Examples of asymmetric sections are shown in
In general, the structural element 2 and the guide element(s) 3 are made of different materials or, in the case where they are made of the same material (steel for example), the properties of the material may still be different due to different manufacturing technologies and the required functional characteristics.
In particular, the materials may differ with regard to the linear thermal expansion coefficient (CTE).
In use, the component is subjected to temperature changes within the range of permissible conditions for using the machine (for example, 15-35° C.). The temperature changes are intended as temporal variations; spatial temperature gradients along the component are not considered here and their effects might possibly overlap those of the temporal variations.
A temperature change causes a differential length change length between the structural element 2 and the guide elements 3, due to the different linear thermal expansion coefficients. It follows that, due to the asymmetry and non-correspondence to the neutral axis, as well to as the integral connection between the structural element 2 and the guide elements 3, component deformation is generated, in particular a curvature thereof, and therefore geometrical changes in the axis (
The object of the present invention is to provide a method for compensating the above-stated measurement errors.
The above-stated object is achieved by the present invention in so far as it relates to a compensation method according to claim 1.
For a better understanding of the invention, hereinafter a preferred embodiment is described with reference to the attached drawings, where:
The present invention relates to a method for obviating the loss of precision caused by the thermal distortion effect on the components 1 that form the slide axes in coordinate measurement machines and which are constituted by a structural element 2 and by one or more mounted guide elements 3, such as the components described above with reference to
According to the present invention, the curvature of the component may be compensated for by adding a correction factor to the geometric compensation algorithms normally implemented on the measurement machine.
The correction is based on knowledge of:
Compensation takes placed in a manner similar to other types of thermal/geometric compensation generally implemented on the machine.
As shown in the flow chart in
Assuming that the structural element 2 and the guide elements 3 are considered as beams reciprocally constrained at the two ends by interlocking joints, curvature may be calculated as described below.
The guide elements 3 may be considered as a single beam element, having the following elastic characteristics:
Similarly, the structural element 2 may be considered as a beam element having the following elastic characteristics:
In addition:
The bending of the component may be expressed with the following theoretical formula:
or, more in general, with the following expression:
R=SF*Delta_T*Delta_CTE*CF [2]
where SF is a structural calculation factor that may correspond to the analytical expression:
contained in formula [1] or derived from numerical simulations, for example, from structural analysis using the finite element method; and
CF is an experimental correction factor, the theoretical value of which is 1 (it may be noted that expressions [1] and [2] coincide in the case where SF is defined by expression [3] and CF is equal to 1).
In the case where the component under consideration is, for example, the spindle of a gantry or cantilever machine and movable along its vertical axis Z, the thus calculated bending may be used to calculate the rotation and displacement it produces on the connection flange of the probe, and consequently the measurement errors it induces.
For example,
a horizontal arm 17 cantilevered from the support structure, movable with respect to the latter along the Y-axis and defining a horizontal axis X;
a carriage 18 carried by the arm 17 and movable on the latter along the X-axis; and
a spindle 19 carried by the carriage and arranged with its own axis Z vertical.
The spindle 19 comprises a structural element 2 and guide elements 3 (see the enlarged detail in
The lower end of the spindle 19 defines a flange 20 to which a probe 21 may be fastened, and for which it is therefore necessary to calculate the rotation and displacement due to the effect of the spindle 19 bending at the current Z coordinate.
The angle of rotation Rzy at the flange 20 is defined by the expression:
Rzy=Rzy_m*(Z−Zv), [4]
where:
Rzy_m is the mean curvature on the ZY plane calculated by means of [1] or [2]; and
Zv is a dimensional characteristic of the machine, dependent on the modes of constraining the spindle 19 and representative of a height at which the rotation of the flange is null (joint point).
The displacement at the flange 20 is defined by the expression:
Ly=Rzy_m*(Z−Zv)2/2*Ly_CF, [5]
where Ly_CF is an experimental correction factor, the theoretical value of which is equal to 1.
The calculated angle and displacement are inserted in the compensation formulas, adding them to those present in the geometric compensation map of the machine. The corrections to be made to the coordinates of the measured points are then calculated.
The described calculation is cyclically updated during operation of the machine, and preferably in a substantially continuous manner, so as to correct the measured coordinates in real time.
Compensation takes place in a straightforward manner and, in the case where a temperature sensor already present on the machine is used, does not require additional components with respect to a conventional machine.
Number | Date | Country | Kind |
---|---|---|---|
14152748 | Jan 2014 | EP | regional |
Number | Name | Date | Kind |
---|---|---|---|
20050243969 | Andrews | Nov 2005 | A1 |
20100299094 | Hsu | Nov 2010 | A1 |
Number | Date | Country |
---|---|---|
1 536 205 | Jun 2005 | EP |
2013021157 | Feb 2013 | WO |
Entry |
---|
Kornel F. Ehmann, International Assessment of Research and Development in Micromanufacturing, Oct. 2005, 280 pages. |
Lin Zhang, Thermal deformation of cryogenically cooled silicon crystals under intense X-ray beams: measurement and finite-element predictions of the surface shape, Apr. 7, 2013, 14 pages. |
European Search Report dated May 14, 2014 in application No. 14 15 2748. |
Number | Date | Country | |
---|---|---|---|
20150211835 A1 | Jul 2015 | US |