New fast method for three-dimensional inspection of CNC machine accuracy Pascal Malesinski*,** Coorevits**
Jean-Marie
David**
Thierry
* RENISHAW SA 15, rue Albert Einstein 77 437 Marne La Vallée Cedex France ** ENSAM LCRMAO 8, Boulevard Louis XIV 59 046 Lille Cedex France
ABSTRACT. This article describes a new fast procedure named “3D-BB ” (Three-Dimensional Ballbar) designed to analyse CNC machine tool defects in a three-dimensional field by a single operation. This new method is a result of a research project that tried to lead to a significant reduction of the time needed to evaluate the accuracy of CNC machine tools.
The main advantage of this method is the single set up of the Ballbar in the machine associated with the data acquisition generated in 3 Dimensions. The measurement is carry out during the movement of the Ballbar on circles located on a truncated sphere (a little more than one hemisphere). The whole procedure should not exceed 15 minutes for an experimented user. New algorithms analyse overall acquisitions to define the amplitudes of many defects of the machine. We have indexed 36 analysable mesurands with one BB3D measurement and we will examine the limits imposed on this new procedure. KEY WORDS:
Ballbar, Machine tool, Three-dimensional.
Signature de l’article : nom de la revue. Volume 1 – n° 1/1998, pages 1 à x
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1. Introduction With classical methods, the exhaustive measurement of the accuracy of the Computer Numerical Commanded (CNC) machine tool requires complex methodology and many kinds of instruments. Such a method cannot be used in practice for the regular checking of machines in production. Huge progress has been made by using Ballbar. However to have global ideas of the accuracy of the 3axis machine tool, 1 measurement is required for each of the 3 plans. To reduce the time needed to evaluate the machine accuracy, we propose a new three-dimensional method.
2. Models for machine tool errors A machine tool can be regarded as a movement generator designed to position a tool around a work piece. A serial structure machine consists of serial assembly of basic circular slides and basic straight slides, which correspond to rotating and linear motions. A work piece produced on that machine structure bears the signature of machine tool errors including guideway defects and relative positioning guideway errors. In this article, we decided to limit the study to a three-axis machine, which complies with the conditions of non-deformable solid chain. The explanations are given for a milling machine whose the spindle and the worktable are show by figure 1 and the Ballbar is ready to use. Figure 1. Ballbar ready to used on a milling machine Z
Y
X
New fast method for three-dimensional inspection of CNC machine accuracy 3
A thorough assessment of a 3-axis machine-tool errors composed of a spindle and 3 translation motions and of a spindle leads us to the identification of 5 parameters and 3 times 12 functions. The parameters characterising the relative position of the 3 rectilinear motions indicated by X, Y, Z are 3 square that we can identify between the directions of the 3 translation movements (⊥ X/Y, ⊥ X/Z and ⊥ Y/Z). The locations of the spindle axis compared to the translation axes (⊥ SP/X and ⊥ SP/Y) are not taken into consideration in this procedure. The error, generated by the kinematic chain corresponding to the imperfection of the translation slide at point O, consists of 6 degrees of imperfection. For instance, for the X motion, we can describe the errors in the shape of small wrench displacements WO (XTx: accuracy defect of the translation movement X, Xty: straightness defect, XTz: straightness defect; XRx: rotation defect around X called roll, Xry: yaw defect, XRz: pitch defect) [BOU 76].
XTx W O = XTy XTz
; XRx ; XRy ; XRz O
The technologies used for the construction of machine-tool guideways give rise to backlash and plays, or hysteresis during the motion, it requires a more complete description of the guidance defects. Wo define the positions of a carriage at a standstill, it is necessary to duplicate this description with 2 wrenchs: The first concerning the forward travel WF and the second concerning the backward travel WB.
XTxF WF O = XTyF XTzF
; XRxF ; XRyF ; XRzF O
XTxB ; XRxB WB O = XTyB ; XRyB XTzB ; XRzB O
We prefer to make this description in the form of a wrench corresponding to the average of the forward travel and the backward travel WA and to introduce a second wrench WP which characterises the backlash and the plays, which means the 12 functions have to be identified to define the displacement errors of each axis.
WAO =
( WF O + 2
WB O )
WP O = WB O − WF O
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XTxM WM O = XTyM XTzM
; XRxM ; XRyM ; XRzM O
XTxM: Scale error XtyM: Straightness error XtzM: Straightness error XRxM: Roll error XRyM: Yaw error XRzM: Pitch error
XTxP WJ O = XTyP XTzP
; XRxP ; XRyP ; XRzP O
XTxP: Backlash error XtyP: Lateral play error XTzP: Lateral play error XRxP: Pivot play error XryP: Swing play error XRzP: Swing play error
3. Machine tool control strategies The exhaustive control of the machine tool performed with analytical methods and traditional equipment requires the implementation of a great number of measurement procedures. This control strategy, which has the advantage of being complete, requires many working hours, which is not always compatible with the productivity requirements. The concept of " test part ", conceived by the NASA around 1960’s when the first CNC machines appeared, makes it possible to qualify the impact of the most dreaded defects from a part that is simple to measure. This concept is the first example of total test, which implements simultaneously a great number of the CNC machine errors. The Ballbar Diagnostic measurement method of RENISHAW© also fits in this total test strategy: it has the advantage of allowing the evaluation of a machine without requiring material part and without introducing defects ascribable to the tool or the measurement method. Even if we do not know how to interpret at a time being, we can make with keeping the test result to compare it with the same test carried out later in the life of the machine under the same conditions. We can also analyse measurement and break it up into a great number of mesurands, which identify more precisely the weaknesses of the CNC machine accuracy. This technique can be used in sequence in the three perpendicular plans of a 3-axis machine, which can lead us to a three-dimensional control of a machine tool. However it requires that 3 Ballbar should be set up and it increases the measuring time. The new procedure called " 3D Ballbar " is a total strategy test, which moves the 3 translation axes of a machine with only one set up for the reference balls. The new algorithm makes it possible to characterise, in a single measurement operation, a great number of the machine tool errors.
New fast method for three-dimensional inspection of CNC machine accuracy 5
4. Description of 3D Ballbar measurement The trajectory choice described by the machine during the 3D Ballbar measurement corresponds to the reduced acquisition duration and the best evaluation of the machine errors. This trajectory consists of circular trajectories located on a sphere, which can be carried out, for example, in the following way: a complete circle located in the XY plan described in both directions, then 2 portions of 230° circles located in the XZ plan and the YZ plan described in both directions. During the constant speed circular motion, acquisitions are carried out at a sampling rate, which can reach 250 Hertz. Figure 2. 3D Ballbar trajectory for 360° × 230° sphere segment Z
Y 230°
X
This practical test gives a three-dimensional picture the deformation of the sphere segment, which would be machine. It informs its user on the confidence degree that it can grant to his production equipment. This procedure is sensitive to a great number of the 3 parameters and the 36 functions, which characterise the accuracy of the machine motion. With regard to the universal vocation software, we cannot anticipate on the machine’s solid chain framework. This ignorance and the single set up of the reference balls, does not make it possible to identify the 18 functions concerning the 3 errors inferred by the 3 rotating solids. A reduced part of rotation errors, which cannot be identified, generates variations on the values of some evaluated defects. For example, in the
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case of a cross-table with the rectilinear slide X carrying the rectilinear slide Y, the pitch movement of the X motion (XRzA) is viewed as a straightness error (XTyA). The current RENISHAW® Ballbar procedure is sensitive to 8 of the 18 functions concerning translations, whereas 3D Ballbar is sensitive to the totality of these 18 functions. Nevertheless problems of " dependence " between the defect signatures on the sphere, limit the analysis to 12 defects in the case of 2 circle portions described on 230 degrees, these aspects will be detailed in paragraph number 5. Figure 3. Comparison of traditional Ballbar software and 3DBB concerning geometrical errors Current Ballbar 3D Ballbar software (set up in XY plan) X offset ♦♦♦ ♦♦♦ Y offset ♦♦♦ ♦♦♦ Z offset ∅ ♦♦♦ XTxA (X scale mismatch error) ♦♦♦ ♦♦♦ YTyA (Y scale mismatch error) ♦♦♦ ♦♦♦ ZtzA (Z scale mismatch error) ∅ ♦♦♦ ⊥ X/Y ♦♦♦ ♦♦♦ ⊥ X/Z ∅ ♦♦♦ ⊥ Y/Z ∅ ♦♦♦ Straightness error XtyA ♦♦♦ ♦♦♦ Straightness error YtxA ♦♦♦ ♦♦♦ Straightness error XTzA ∅ ♦ Straightness error YtzA ∅ ♦ Straightness error ZTxA ∅ ♦ Straightness error ZTyA ∅ ♦ Backlash X+( XTxP) ♦♦♦ ♦♦♦ Backlash X-( XTxP) ♦♦♦ ♦♦♦ Backlash Y+( YTyP) ♦♦♦ ♦♦♦ Backlash Y-( YTyP) ♦♦♦ ♦♦♦ Backlash Z+( ZTzP) ∅ ♦♦♦ Backlash Z-( ZTzP) ∅ ♦ Lateral play X axe / XY plan (XtyP) ♦♦♦ ♦♦♦ Lateral play X axe / XZ plan (XtzP) ∅ ♦ Lateral play Y axe / XY plan (YtxP) ♦♦♦ ♦♦♦ Lateral play Y axe / YZ plan (YtzP) ∅ ♦ Lateral play Z axe / XZ plan (ZTxP) ∅ ♦♦♦ Lateral play Z axe / YZ plan (ZtyP) ∅ ♦♦♦ ♦ ♦ ♦ : The measurement method is perfectly appropriate to evaluate the defect, with an acquisition on a truncated sphere of 360° × 230°. ♦ : The measurement method is sensitive to the mesurand, but a circle portion higher than 230 degrees is necessary to evaluate the defect.
mesurands
New fast method for three-dimensional inspection of CNC machine accuracy 7 ∅ : The method is not sensitive to the defect.
An evolution of the current Ballbar apparatus, which would make it possible to obtain acquisitions on 270 degrees or more, could extend the possibilities of 3D Ballbar analysis. In addition to the geometrical errors, information on the behaviour of the controllers are indicated by the means of the spike mesurands and the differences in servo offset between the axes. Figure 4. Comparison of traditional Ballbar software and 3DBB concerning controllers errors mesurands Servo mismatch X/Y Servo mismatch X/Z Servo mismatch Y/Z (redundant) Spike X+ Spike XSpike Y+ Spike YSpike Z+ Spike Z-
Current Ballbar 3D Ballbar software (set up in XY plan) ♦♦♦ ♦♦♦ ∅ ♦♦♦ ∅ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ♦♦♦ ∅ ♦♦♦ ∅ ∅
5. Dependence issue for a ballbar measurement carried out on a circular portion The analysis technique is based on a best-fit identification of the measurement on the signature addition, which characterise each defect of the machine tool. Each defect signature corresponds to the deformation associated with the model of the defect. For example, defect XTxA is associated with a slope on the X motion scale error, which corresponds to an elliptic deformation of the circle. If 2 defects have an Y identical signature, it is not possible to share the responsibility between the 2 sources; therefore they are dependent defects. For traditional Ballbar measurement on complete circle, the signature defects do not show any X dependence problem. Diagnostic Ballbar Renishaw
α
90
+Y ?
180
-X
?
?
+X
0
?
-Y
270
SAH Echel: 3.0 µm/div SH
Figure 4. Circular Portion
3D Ballbar measurement, which aims at a finer analysis, can present signatures, which raise
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dependence problem. To qualify the dependence between the defect signatures, we introduce a dependence indicator called IND between 2 different signatures. For example, for a measurement made up of the combination of 5 defects, 10 indicators characterise all the links between the signatures. The absolute value of this indicator lies between 0 and 1, value 1 corresponds to 2 independent signatures and value 0 corresponds to 2 identical signatures. To understand the dependence study, we choose the case, related to 5 errors obtained from the analysis of a measurement performed on a circular portion of variable angular size. The 5 errors concerned are the balls positions errors, the total scale error, the scale mismatch error and the squareness error in the XY plan. Figure 6. Dependence schematic between 5 defects Offset X
Offset Y
Squareness error
Total scale error
Scale mismatch error IND (Total scale error /Scale mismatch)
3 dependence cases can arise. The first case corresponds to 2 independent, the second we call simple dependence corresponds to 2 dependent signatures and the third, which we call combined dependence, corresponds to dependences between more than 2 signatures. The calculation of the dependence indicators shows that there are 6 independent connections among the 10 existing connections between the 5 signatures. In figure 6, the thick connections are the connections, which have an indicator of dependence strictly higher than 0. Figure 7 shows the evolution for different sizes of circular portion of the 4 dependence indicators smaller than 1.
New fast method for three-dimensional inspection of CNC machine accuracy 9 Figure 7. Evolution of 4 dependence indicators
1
Ind.(Total scale error / X Offset) Ind.(Scale mismatch / X Offset)
0,5
Ind.(Y Offset/ Squareness) Ind.(Total scale error /Scale mismatch) 0 360 320 280 240 200 160 120 80
40
alpha : circle portion angle (deg)
The curves of figure 8 and figure 9 represent the Ballbar length variation in a Cartesian reference mark and they visually show the similarity between the signatures. In our example, two groups of distinct characteristics shows similarities, which are represented in figure 8 and figure 9. Figure 8. Simple dependence case 1,5
Y offset Squareness
1
Figure 9. Combined dependence case X offset
1,5
Scale error 1
0.6* S.mis.-0.7*S.total
0,5
0,5
0 0
90
180
270
360
-0,5
0
-1
-0,5
0
-1,5
α
90
180
270
360
-1
α
Some series of measurements carried -1,5 out on different machines have shown that the measurements carried out with some portions of 2 circles having from 230 to 240 degrees of acquisition are sufficient to qualify 12 out 18 parameters proposed. It is possible to obtain some correct results for an analysis from one hemisphere, provided the machine does not show fast space variation on the scale errors and the straightness errors.
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6. Conclusion The 3D Ballbar is a new procedure, which allows the fast control of the characteristics of the machine tool, made up of 3 axes of translation. This technique is not a selective procedure, which makes it possible to give a precise picture of a particular machine tool’s defect; it constitutes a practical test, which qualifies the total behaviour of a machine in its three-dimensional workspace. In practice, the results have a suitable exactness for a measurement sphere segment of 230 degrees × 360 degrees (a little more than one hemisphere) what is in keeping with the study about the dependence of the defect signatures. This procedure characterised by its short measuring time and its three-dimensional analysis field is a relevant tool for the periodic control of a CNC machine, the preliminary diagnosis of the machine’s behaviour and the study of the stability of the defects.
7. References [BOU 76] BOURDET, P., CLEMENT A., “Controlling a complexe surface with a 3 axis measuring machine”. Annals of the CIRP, vol 25/1, p359-361, January 1976. [DAM 96] DAMAK, M., Théorie et instrumentation pour l’étalonnage statique des robots : vers une programmation hors-ligne industriellement plus efficace. Thèse de doctorat, ENSAM de Lille, juillet 1996. [FLO 98] FLORUSSEN, G.H.J.; DELBRESSINE, F.L.M.; SCHELLEKENS, P.H.J.. Accuracy Analysis of multi-axis machines using double Ballbar. Proceeding on improving machine tool performance, v2, p533-543, July 1998. [KAK 87] KAKINO, Y, IHARA, Y., NAKATSU, Y., Measurement of motion errors of NC machine tools and diagnosis of their origins by using telescoping magnetic Ballbar method. CIRP Annals, v 36, n 1, p 377-380, Berne, January 1987. [PAH 97] PAHK, H.J, KIM, Y.S., MOON, J.H., New technique for volumetric error assessment of CNC machine tools incorporating Ballbar measurement and 3D Volumetric error model. International Journal of Machine Tools & Manufacture. v. 37, p 1583-1596, 11 November 1997.
