A method and arrangement for determining the linear (heat) expansion of elongated bodies

Abstract: A method for determining and, when appropriate, compensating for the linear (heat) expansion of elongated bodies (1), such as physical length scales (1) or of elongated bodies which are intended to support physical length scales on, e.g., instruments or measuring machines equipped with physical length scales, in which measurement errors occur because of length deviations of the scale (1) as a result of deviations from a reference temperature at which the scale was calibrated. The method is mainly characterized by measuring the linear expansion of the body (1) is relation to at least one reference (6) made of a material whose coefficient of linear (heat) expansion (α) deviates from the coefficient of linear (heat) expansion of the body material, and thereafter determining, when appropriate, a compensation factor for correcting the body length. The invention also relates to an arrangement for carrying out the method.

Description: The present invention relates to a method for determining and, when appropriate, comprising for thermal linear expansion of elongated bodies, such as physical length scales or elongated bodies intended to carry physical length scales on, e.g., instruments or measuring machines equipped with physical length scales in which measuring errors may occur as a result of length deviations of the scale due to deviations from a reference temperature at which the scale was calibrated. The invention also relates to arrangement for carrying out the method. When measuring lengths with the aid of instruments or measuring machines that are equipped with physical length scales, temperature deviations from a reference temperature will constitute a source of error. The temperature that prevails during a measuring occasion will normally deviate from the reference temperature. The reference temperature can normally only be included in particularly well-equipped measuring laboratories. Three types of measurement errors occur when measuring in temperature conditions that are not ideal: 1) Errors which are caused by dimensional changes in the measured object due to linear (heat) expansion. 2) Errors due to changes in the geometry of the machine or corresponding arrangement due to thermal linear expansion. 3) Errors caused by changes in the measurement of the length reference, i.e. the graduated measuring scale, due to linear (heat) expansion. The present invention relates to a method and to an arrangement for determining and correcting errors of this last mentioned kind. In some instances, the inventive method and arrangement may also be used to determine and correct errors according to (2) above. It has earlier been proposed to manufacture scales from material whose coefficient of linear expansion is equal to zero, or close to zero. This proposal, however, is encumbered with several drawbacks. For example, such material is very expensive and creates difficult construction problems when the material is to be incorporated in arrangement and machines of the kind intended here, which are often constructed from material whose coefficient of linear expansion deviates from zero and which has a coefficient of linear expansion which greatly deviates from zero. It has also been proposed that because the change in length of these scales is often repeatable in these contexts, the temperature of the scale can be measured and the linear expansion then calculated on the basis of the coefficient of linear expansion of the scale material, in accordance with the formula: δ = α · dT · L where δ = the total linear expansion α = the coefficient of linear expansion of the scale dT = the deviation from the reference temperature L = scale length. One serious drawback with this method, however, is that it is necessary to measure temperature extremely accurately and also to measure temperature at several places along the scale, since the temperature is liable to vary along said scale, and also that the coefficient of linear expansion must be known to extreme degrees of accuracy. In DE-A-2 008 813 the actual position of and end part of an arm is determined. The compensation corrects the possible displacement of the measuring head as a whole. The present invention relates to a method and to an arrangement which are not encumbered with the drawbacks of the known technique and which will enable the linear (heat) expansion of elongated bodies, such as scales, to be determined very accurately, and also to enable compensation to be made for such expansion. Thus, the invention relates to a method having the features stated in claim 1. The invention also relates to an arrangement according to Claim 9. The invention will now be described in more detail with reference to exemplifying embodiments thereof and also with reference to the accompanying drawings, in which Figure 1 illustrates principly a first embodiment of an inventive arrangement, seen transversely to the long axis of the physical length scale; Figure 2 illustrates schematically a second embodiment of an inventive arrangement as seen transversely to the long axis of the scale; Figure 3 shows the arrangement of Figure 2 as seen from the right in Figure 2; Figures 4 and 5 illustrate schematically two different embodiments of inventive arrangements, in which several references are used; Figure 6 illustrates schematically the use of a reference which has a coefficient of linear expansion distinct from zero; Figure 7 illustrates schematically a beam which supports a scale, a scale reference, and references for different parts of the beam, said beam being seen in the direction of its longitudinal axis; Figure 8 illustrates schematically an embodiment which is essentially similar to the embodiment of Figure 7 but which lacks a separate scale reference; Figure 9 is a schematic, axial section view of one embodiment of a reference which has the form of a relatively thin filament or wire placed under tension; and Figure 10 illustrates schematically a portal type three-axis coordinate measuring machine constructed in accordance with the invention and seen generally perpendicular to the plane of the main extension of the portal. The embodiment illustrated in Figure 1 includes an elongated body in the form of a physical length scale which is firmly fixed to a scale-supporting part 2 at its one end 3, and which is preferably placed on supports 4, 5 such as to enable linear changes to take place freely where linear (heat) expansion of the body is to be determined and where compensation is intended to be made for such linear expansion, in appropriate instances. The reference 6 identifies a rod-like reference which is made from a material whose coefficient of linear (heat) expansion is known and which is firmly mounted on said supporting part 2 at its one end 6′ and which extends parallel with the scale 1. The embodiment also includes a length indicator 7 which is located at the free end 6″ of the reference 6 and which functions to measure the linear expansion of the scale in relation to the reference. According to one embodiment, the reference 6 is made from a material whose coefficient of linear expansion, α, is essentially equal to zero. With this illustrated arrangement, the indicator shows the linear expansion of the scale directly, since the length of the reference is constant. The reference 6 is made, for instance, from a ceramic material retailed commercially under the trade name Zerodur. In the case of the embodiment illustrated in Figure 2 and Figure 3, the scale 1 is fixed, for instance glued, to a supporting bar 8, forming a scale-supporting body, said bar 8 preferably having the same α-value as the scale. In accordance with one preferred embodiment of measuring machines, the supporting bar 8 is comprised of a machine shaft or axle. The reference 9 identifies a rod-like reference which extends in a bore 10 passing along the hole length of the bar, and is firmly mounted in the bar at one end 11. The reference 12 identifies a sensor, preferably an electronic sensor, which is intended to determine the position of the free end 13 of the supporting bar 8 in relation to the position of the free end 14 of the reference 9. Figures 4 and 5 illustrate respective different modifications of the arrangement illustrated in Figure 2, in which references 9 are disposed at different locations as seen in the cross-section of the supporting bar (the supporting body), thereby enabling local linear expsions to be determined and, when appropriate, to be corrected, for instance expansions which tend to bend the bar/body. It is assumed in the aforedescribed and illustrated embodiments that the reference 9 is made from a material whose coefficient of linear (heat) expansion α is essentially equal to zero, although it will be shown below that the reference 9 can also be made from material whose α-value differs from zero. In this case, however, in order to obtain an absolutely precise measurement of the linear expansion of the control bar, it is also necessary to know the coefficient of linear (heat) expansion α of the bar material. In distinction to the accurate temperature-measuring process based on the known method mentioned above, very small demands are made in this case on the accuracy of the α-value of the bar material. The precision afforded by standard textbooks is quite sufficient, while when applying the temperature-measuring method, the value of α must be known to a precision greater than 2*10-8 in the last decimal. Figure 6 illustrates schematically an embodiment in which a reference 9' has a coefficient of linear (heat) expansion α' which may differ from zero, and a bar 9'' which has the known coefficient of linear (heat) exansion α''. For the sake of simplicity, it is assumed in the following description that the length values L of the two bars are equal, although this is not a requirement. Indicators, sensors or the like are used to measure δI, which constitutes the difference in linear expansion between the two bars. The linear expansion of the reference 9' and the bar 9'' can be calculated in accordance with the following. If the reference and the bar are subjected to the same change in temperature dT, the following changes in length will occur: Reference 9': δ9' = dT · α' · L Bar 9'': δ9'' = dT · α'' · L The relative change in length detected by the indicator/sensor is: δI = δ9' - δ9'' From the relationship (1) - (3), it is possible to calculate δ9' to δ9' = δI/(1 - α''/α') Since α' and α'' are constants, the relationship (4) can be written as δ9' = K' · δI Correspondingly, δ9'' can be calculated as δ9'' = K'' · δI It will be evident from the relationships (5) and (6) that the temperature need not be known or measured. The indicator/sensor reading is graduated with a factor which is dependent on the α-value of respective materials, namely on the α'-value and the α''-value. No high demands are placed on the accuracy with which the α'-value and α''-value are determined, since it is the quotient formed by the α'-value and α''-value that is effective. When the length L of the reference and the bar differ, the lengths L′ and L'' will also be included in the graduating factor. No great accuracy is demanded of these terms. In the embodiments illustrated in Figures 7 and 8, the bar 8 is a box-beam of generally square cross-section, preferably rectangular cross-section, in which a reference is mounted preferably internally and preferably at each corner 15 of the beam, for the purpose of measuring linear expansion of the beam, thereby enabling deformations corresponding to curvature of the beam locally to be determined. Figure 7 illustrates an embodiment in which a separate reference 9 is provided for the scale 1, said scale being arranged adjacent a contact body 8′ provided on the beam, wherein an arrangement essentially according to Figure 2 is provided on the beam. Figure 8 illustrates a simpler arrangement, in which the scale 1 is placed, glued, on one side 16 of the beam adjacent a reference 9 which functions to measure local linear expansion of the beam, such as a reference located in a corner 15, as illustrated in Figure 8. Embodiments which lack a glued scale can also conceivably be used solely for the purpose of detecting variations in the straightness of a reference straight-edge, for instance. Figure 9 illustates a preferred embodiment of the arrangement. In Figure 9, the reference 8 identifies the elongated body whose linear expansion is to be monitored, the reference 9 identifies the reference element, and the reference 12 identifies an electronic sensor comprised of an iron core 16 and coils 17, the sensor in this case being a differential transformer type sensor. The reference element is firmly mounted at one end on the elongated body 8 by means of a device 11. The arrangement also includes a spring 18 whose one end acts on the elongated body 8 and the other end of which acts on a seating 19 firmly connected to the reference 9. The characteristic feature of this arrangement is that the reference 9 is placed under strain. This prevents the reference 9 from bending laterally as a result of the bukling phenomenon which can occur when the reference is subjected to a compression force, particularly when the cross-section of the reference 9 is small in relation to its length. This enables the reference 9 to have the form of a thin wire or filament made of Invar material, or some other appropriate material. It will be understood that various modifications can be made to this embodiment. For example, the electronic sensor and the spring 18 can be combined to form a "pulling" sensor unit which is connected to the free end of the reference 9. The channel 20 to which the reference 9 extends may conveniently be filled with some kind of suitable grease, for instance silicone grease, so as to improve the heat transfer between the elongated body 8 and the reference 9 and to dampen any resonant oscillations that may occur in the reference 9. Figure 10 illustrates an example of use in which the inventive arrangements are used to monitor the geometry of a machine. Figure 10 illustrates schematically a three-axis coordinate machine of the so-called portal kind. The reference 21 identifies the measuring table/base plate of the machine. A portal, which is comprised of legs 22, 24 and a beam 23 extending in the X-coordinate, can be moved in the Y-direction on air bearings 25, i.e. in a direction perpendicular to the plane of the paper. A "Z-unit" 26 is journalled on the X-beam 23. The Z-unit can be moved along the X-beam, i.e. in the direction of the arrows 27. A measuring spindle 28 is journalled in the Z-box 26 and can be moved in the direction of one of the arrows 29. The measuring scales in the X-axis 23, the Y-axis 25 and the Z-axis 28 of the machine shown in Figure 10 may be provided with the aforedescribed arrangements for determining and compensating the length errors in the measuring scales caused by thermal expansion. Curvature of the beams 23, 25 and/or 28 can be determined and compensated for by means of the arrangements described in Figure 7 and Figure 8. None of the legs 22 and 24 carry a measuring scale, but nevertheless affect the measuring result in the Z-direction, since they form a reference in the Z-direction together with the bearings 25 and the measuring table 21. If the two legs have mutually the same difference with regard to the reference temperature, a resultant parallel displacament of the X-beam in the Z-direction occurs. If the differences are unequal, the result is a displacement in the Z-direction and also a change in the parallelity between the X-beam and the bottom plate 21. The geometry of the machine is affected in both instances. When each of the legs is provided with an inventive arrangement 30, the variations in lengths of the legs can be determined and compensated for. The inventive method and the manner of operation of the inventive arrangement will be understood in all essentials from the aforegoing. The linear expansion of an elongated body, such as a physical length scale or a body to which such a scale is affixed, is measured in relation to a reference which has a known coefficient of linear (heat) expansion, which may he equal to zero or approximately equal to zero. The reference and the elongated body may be compared directly with regard to linear expansion, although the reference can also be compared with another body which has the same coefficient of linear (heat) expansion as the first body, said reference and said second body need not necessarily have the same length as the first body. In the case of the Figure 10 embodiment , both the spindle 28 and the legs 22, 24 are provided with inventive reference-measuring devices. In this case, the measurement values opined with the spindle 28 may be corrected with three correction factors, namely: 1. From the reference system in the spindle 28. 2. From the reference system in the one leg 22. 3. From the reference system in the other leg 24. In this case, 2 and 3 are weighted with factors which are dependent on the position of the Z-units along the X-axis. It will be evident from the aforegoing that the invention affords important advantages. For example, the linear (heat) expansion which is to be determined in order to enable the correction of measuring values determined at a temperature which deviates from the temperature at which the length of an elongated body was calibrated is determined without needing to determine temperature and the coefficient of linear (heat) expansion to any great degree of accuracy. Furthermore, according to one embodiment, such determination is effected without the use of references in which the α-value is substantially equal to zero. Although the invention has been described and illustrated with reference to exemplifying embodiment thereof, it will be understood that other embodiment and minor modifications are conceivable without departing from the invention as claimed.

Claims: A method for determining and, in appropriate cases, compensating for the linear expansion of elongated bodies in, e.g., instruments or measuring machines, in which measurement errors occur because of length deviations as a result of deviations from a reference temperature, by measuring the linear expansion of the body (1,8,28) in relation to at least one reference body (6, 9) made of a material whose coefficient of linear expansion (α) deviates from the coefficient of linear expansion of the body material, measuring the linear expansion of the body being a physical length scale (1) or of an elongated body (8, 28) supporting a physical length scale (1) in relation to the reference body (6;9,9') and thereafter determining factor ( ) for correcting the scale length. A method according to Claim 1, characterized by the reference body (6, 9) made of a material whose coefficient of linear expansion is essentially equal to zero. A method according to Claim 1, characterized by the body (8, 28) supporting a physical length scale which body is made of a material whose coefficient of linear expansion (α) deviates from zero, and by the reference body (9, 9'') made of a material whose coefficient of linear expansion (α) deviates from the coefficient of linear expansion of the supporting body material, and by measuring the difference (δI), of linear expansion between the supporting body and the reference body, and calculating the linear expansion (δ9', δ9'') of the supporting body and the reference body proportionally to the measured linear expansion difference. A method according to Claim 1, 2, or 3, characterized by arranging reference bodies along an elongated supporting body (8) supporting a physical length scale at different locations, thereby enabling local linear expansion in relation to respective references to be measured and the geometric changes in the supporting body to be determined. A method according to Claim 4, characterized in that the elongated supporting body (8) is a beam element and in that reference bodies are mounted in said beam, preferably extending internally thereof. A method according to Claim 1, 2, 3, 4, or 5, characterized in that said reference or references (6, 9) is/are in the form of a rod-like body which is firmly held at one end (6) thereof and which at a reference temperature has the same length as the supporting body or scale whose linear expansion is to be determined. A method according to any one of the preceding Claims 1-6, characterized by subjecting the reference body (9) to a tension force. A method according to Claim 7, characterized in that the reference body is comprised of a relatively thin wire. An arrangement for performing the method of claim 1, including devices (7, 12) for measuring the linear expansion of the supporting body (1, 8, 22, 24, 28) in relation to at least one reference body (6, 9) made of a material whose thermal coefficient of linear expansion (α) is known and which deviates from the coefficient of linear expansion of the supporting body material, whereby that said body (1, 8, 28) is a physical length scale (1) and/or an elongated element (8, 28) supporting a physical length scale. An arrangement according to Claim 9, characterized in that the reference body (6) is made of a material whose coefficient of linear expansion is essentially equal to zero. An arrangement according to Claim 9 or 10, characterized by the body (8, 28) supporting a physical length scale and the reference body (9, 9'') which are made of materials having mutually different coefficients of linear expansion (α', α'') which both deviate from zero; and in that means are provided for measuring the difference in linear expansion (δI) between the supporting body and the reference body, thereby enabling the linear expansion of the supporting body and of the reference body to be calculated proportionally to the measured linear expansion difference (δ9', δ9''). An arrangement according to Claim 9, 10 or 11, characterized in that reference bodies are disposed along an elongated body supporting a physical length scale at different locations thereon, wherein the local linear expansion of the supporting body in relation to respective reference bodies is measured for determining geometric changes in the supporting body. An arrangement according to Claim 12, characterized in that the supporting body is a beam element, which-carries a scale (1); and in that the reference bodies are mounted on the beam, preferably extending internally thereof. An arrangement according to Claim 12 or 13, characterized in that the reference body (9) for the scale (1) is mounted adjacent the scale. An arrangement according to Claim 12, 13 or 14, characterized by the reference body common to both the scale and to a beam part located adjacent said scale. An arrangement according to Claim 12, 13, 14 or 15, characterized in that the beam is a box beam of square, preferably rectangular, cross-section; and in that the reference bodies are disposed internally of the beam at locations adjacent the corners (15) of said beam. An arrangement according to Claim 9, 10, 11, 12, 13, 14, 15 or 16, characterized in that said reference or references is/are rod-shaped. An arrangement according to Claim 9, 10, 11, 12, 13, 14, 15, 16 or 17, characterized in that said reference or references is/are firmly mounted at one end (6', 11) and at the reference temperature have the same length (6) as the supporting body whose linear expansion is to be determined. An arrangement according to any one of the preceding Claims 9-18, characterized in that the reference or references (9) is/are subjected to a pulling force. An arrangement according to Claim 19, characterized in that the reference or references is/are a relatively thin wire.

Inventors: GUSTAFSSON CARL-ERIK, GUSTAFSSON, CARL-ERIK
Applicants: JOHANSSON AB C E, C.E. JOHANSSON AB
Application year: 1992
Main classification: G01D3
IPC codes: G01B21, G01N25, G01D3, G01B5