An investigation into the relative accuracy of ball-screws and linear encoders over a broad range of application configurations and usage conditions

Transcription

1 An investigation into the relative accuracy of ball-screws and linear encoders over a broad range of application configurations and usage conditions A.J. White, S.R. Postlethwaite, D.G. Ford Precision Engineering Unit, School of Engineering, University of Huddersfield, Queensgate, Huddersfield, HD1 3DH, United Kingdom aj. white@hud. ac. uk Abstract It has been found that ball-screw expansion is the single largest thermal error source within a broad range of CNC machine tool configurations and over a wide range of running conditions when rotary encoder position measurement is used. This paper describes thermally related axis positioning errors exhibited by ballscrew with rotary encoder and linear encoder feedback systems when used within CNC machine tools. Indicative data resulting from many thermal tests has been used to support the analyses. The paper details the thermal error components that make up the total thermal error in both types of positioning system. It is known that the position of the measuring system on an axis can affect the accuracy achieved at the component through the Abbe error. It is accepted that machining often occurs in uncontrolled environments and that thermal errors from external sources can combine to cause additional thermal errors on the work-piece. The study proposes that an axis using a ball-screw and rotary encoder for position measurement exhibits offset, scale and reversal errors that change quickly according to the thermal state of the ball-screw. Linear encoder measurement systems exhibit the same error categories, but generally with smaller maximum values, and slower rates of change. The thermal errors exhibited by ball-screws are primarily due to an inability to decouple the measuring system from the heat in the ball-screw and mounting system that sets the position of the tool relative to the work-piece.

2 346 Laser Metrology and Machine Performance Introduction Most CNC machine tools use a ball-screw and ball-nut driven by an electric drive to provide both motion, and reaction to cutting forces. Axis position is estimated using the pitch of the ball-screw and a rotary encoder that records the number of complete and fractional turns of the ball-screw. Such a system is robust, as the encoder and ball-screw can be well isolated from the aggressive environment of the cutting enclosure. However, changes in the frictional heat generated by the ball-nut running along the ball-screw cause the ball-screw to expand and contract, producing incorrect positioning of the axis. Pre-loading of the thrust bearing(s) which maintain the axial position of the ball-screw relative to the bed of the machine causes additional heat to be generated during running. White* has found that the error in axis position caused by ball-screw expansion can far exceed that caused by any other single error source (geometric, load or thermal) unless a major mechanical problem is present. Consequently it is common tofita separate linear position measurement device to remove the ball-screw from the control loop. This device measures the actual axis position relative to a datum on the machine. This paper deals with a comparison between the accuracy of ballscrew/rotary encoder combinations and linear encoders after thermal excitation of the axis. 1 Scope of this paper This paper only identifies one-dimensional thermal errors associated with a single axis, and makes no attempt to estimate volumetric error resulting from the interaction of the errors on several axes. The thermal error exhibited by a particular machine axis in isolation from the cutting tool and the work-piece does not give a complete indication of the level of thermal error that will exist in a machined work-piece. Machine design is generally based upon cost, ease of construction, ease of maintenance, and the reduction of the risk of contamination of axis bearings. Thermal errors may be made worse by the machine design used to meet these objectives. In older machine tools, thermal effects may not have been considered during the machine design. Linear positioning errors due to thermal effects are isolated from other errors on an axis by selecting a measurement line that reduces or eliminates other errors from the measurement. Testing with the axis cold, and then re-testing under heating or cooling conditions eliminates non-thermal errors when the errors in the cold condition are subtracted. Other axis errors may change during the course of the test, but the strategy described will ensure these are small in comparison to the linear positioning thermal errors. This paper has resulted from thermal tests on a wide variety of machine configurations under simulated machining conditions. Test results have been used as indicators of the underlying thermal errors in ball-screw and linear encoder measurement systems. It must be noted that it is rarely possible to fully test an axis on a built-up machine due to the limitations of guarding and time.

3 Laser Metrology and Machine Performance 347 Further work is to be undertaken on a dedicated axis to confirm the analyses given here. 1.1 Thermal Datura The thermal datum is an important concept when defining thermal errors on a machine tool. The thermal datum is regarded as a position on the machine from which thermal growth can be considered to emanate. It may be attached to a particular machine feature such as a thrust bearing, or it may have no obvious physical position on a machine structural element such as the centre of a ballscrew. It can be stationary or moving with time. Thermal growth between machine structural elements can be measured between thermal datum points, and summation of this thermal growth used to estimate the total thermal error at the work-piece. There are always many thermal datum points on a machine tool. 2 Errors resulting from the thermal excitation of a ball-screw with rotary encoder positioning system A ball-screw with rotary encoder measures the axis position along the line of the application of force. The position of the ball-screw in the machine structure is fixed by the need to ensure the ball-screw has a stiff mounting and is protected from chips and coolant. Thus the measurement line is fixed at a certain distance from the cutting line, causing Abbe error. According to the machine design, and the effects of thermal distortion, this may contribute significantly to the axis positioning error. Thermal errors in a ball-screw itself are caused by heat entering the ball-screw, and the fast temperature changes result in fast changes in thermal error. When a pre-tensioned ball-screw is heated, the tension is reduced. Very little heating is required for all pre-tensioning to be lost. A pre-tension of 50^m per metre only requires a 4.3 C global temperature increase on a 1 metre ball-screw for pre-tensioning to be completely lost. Such small temperature increases occur quickly with only medium speed axis movements. 2.1 Axis offset error in non pre-tensioned ball-screws A non pre-tensioned ball-screw will expand from the thermal datum set by the position of the thrust bearing at one end. This will cause the axis minimum position to move relative to the thrust bearing, producing an offset error that is independent of axis position. The offset error is caused by heat generated in the electric drive, transmission, thrust bearing, and the ball nut, conducting along the ball-screw. This error will vary with time as a result of axis movement. The offset error can be calculated if the thrust bearing to axis minimum position distance and the temperature profile of the ball-screw between these points is known. Shortening the length of unused ball-screw between the thrust bearing and the minimum axis position will reduce this error. In most machines heat from the electric drive and transmission will have less effect on the temperature of the ball-screw than the thrust bearing and ball-nut.

4 348 Laser Metrology and Machine Performance Figure 1 shows a schematic of the effect of thermal excitation on a non pretensioned ball-screw. The thermal error components A, B and C in this figure are the links between the cutting tool and the work-piece. They may be composed of many thermal components, which are not discussed in this paper.. ; V ftl A= Tablethermal growth. 5 B ji ' B= Structural thermal growth. *, % - 'rjggl;^/: C=Work piece thermal growth. of constraint.!: ' \ ^-Pomi Rotary { f ^ ^ Encoder ^ ' ^ J ^^ rxj~mxl \^i, i*p*j i! P p. j rj 77/ /7/77/7777/7) 77/7 1 ^ I Ol K\'v>^^ ^SM i Thermal^ Tl^ 'offset;" ^'^ Scale ^ i Datum Error I Error i Minimum Pvlaximum axis position a> :is position Figure 1. Thermal errors in a non pre-tensioned ball-screw arrangement 2.2 Axis offset errors in pre-tensioned ball-screws For the purposes of convenience it is normal to define the offset error in a pretensioned ball-screw as a movement of the axis minimum position relative to the machine bed. The ball-screw mounting bracket and thrust bearing datum are not used as they may deflect as a result of the large forces acting on them. The BS3800 part 3^ (and ISO230-3, soon to be ratified) tests produce an approximately even temperature distribution along the length of the ball-screw between the minimum and maximum axis positions. This results in thermal movement of the axis minimum and maximum positions of the form shown in figure 2. It should be noted that the offset moves in the opposite direction to that of the non pre-tensioned ball-screw. This is because the thermal datum on this arrangement is near the middle of the ball-screw, and thermal growth flows outwards from this point. If the ball-screw loses all its tension and is axially constrained at only one end, then the offset is measured from the constrained end. A B S3 800 part 3 test has been observed to cause a pre-tensioned ball-screw to enter compression and lock-up after only a few minutes of oscillation at lom/min (rapid traverse for this machine). During machining the temperature distribution along the entire ball-screw will only be even when the ball-screw is cold. Actual machining results in a continuous variation in the size and rate of change of the offset error.

5 Laser Metrology and Machine Performance 349 E k ȯ k_ LLJ O) C "c o +3 (% O Q r- ~~~ ' ^ ^ ^ X Axis Linear Positioning JEjuJJL- ' -" Therm al Datum JEnd 2 ^ " ~^ ~~ ' _ ^ ^ ~" Number of Runs Figure 2. Thermal growth of a pre-tensioned ball-screw undergoing a BS3800 part 3 test. 2.3 Scale errors in non pre-tensioned and pre-tensioned ball-screws Scale error is a result of errors in the pitch of the ball-screw and is position dependent. This may be caused by manufacturing inaccuracies, over or under pre-tensioning of the ball-screw and thermal expansion. It is known that pretensioning of the ball-screw sometimes drops as the machine ages. It is not uncommon for a loss in pre-tension of up to 25% to occur within the 6 months of machine commissioning^. On an axis with an initial pre-tension of 50um/m this equates to a 12um error over a metre length. The compensation value within the machine controller must be updated to minimise this error. Manufacturing pitch deviation is likely to be dominated by the thermal expansion in even the slowest axis movements. This causes any axis movement to be measured incorrectly. The scale error at any point on a non pre-tensioned axis may be calculated if the temperature profile of the ball-screw between the axis minimum position and current axis position is known. To understand scale errors on a pre-tensioned ball-screw, it should be viewed as a spring. In the unheated state the spring is tensioned. Heat entry into any part of the ball-screw will cause the heated part to expand and for the tension of the ball-screw to be reduced. A simplified description of what happens when a portion of a ball-screw is heated is shown in figure 3. It is assumed that before heating is applied, the position error throughout the axis travel is zero. It is also assumed that the ball-screw mountings are infinitely stiff, and that there is no spread of heat from heated portion of the ball-screw to the unheated portions. Starting from the minimum axis position and moving towards the right it can be seen that the unheated portion 'A' has a position error going in the negative direction. This is because the heated portion has expanded and reduced the tension, causing the unheated portion 'A' to contract. The heated portion 'B' has expanded, causing a position error changing in the positive direction. The unheated portion 'C' has contracted due to the loss in tension, and so has a position error that changes in the negative direction. It should be noted that the

6 350 Laser Metrology and Machine Performance net change in position error is zero. It should also be noted that the slopes of the unheated portions of the ball-screw *A' and 'C' are identical because their temperatures and tensions are equal. The temperature distribution on a ball-screw during actual machining will be significantly different. Conduction of the heat along the ball-screw will merge the heated and unheated portions causing the slope in position error to be complex with axis position. The slopes shown in figure 3 are averages. Peak slopes resulting from actual machining will be higher. 4-\/p» *»_ O W.2 *c/3 0 O< i Unheated; - * ~ + Heated^" * * 7 I -ve i r '.. Minimum Axis F osition Unheated y^^^^ #%/^^ \ ^^s. ^\^ / V ^ Axis Position *. ^ * <. Maximum Axis Position Figure 3. Position error change as a result of a heated portion in a pre-tensioned ball-screw. The frictional heat generated between the ball-nut and the ball-screw produces significant amounts of heat. Figure 4 shows the results of a B S3 800 part 3 test at a speed of 5m/min (half rapid traverse) on a pre-tensioned ball-screw with rotary encoder. A combined scale and reversal error of 3 Hum over 0.8m was recorded. This equates to an average ball-screw temperature of 50 C over this length. 2 UJ Figure 4. Ball-screw scale and reversal errors.

7 Laser Metrology and Machine Performance 351 A non pre-tensioned hydro-screw axis positioning system has been tested. The hydro-screw has a lead-screw type profile, and cooled hydrostatic oil is fed at pressure into the ball-nut. High speed oscillation tests (lom/min) of this system produced a ball-nut temperature increase of less than 1 C during the course of the test. The thrust bearing increased in temperature by over 7 C. Figure 5 shows the scale error on the axis fitted with a hydro-screw. The distance between the position error lines on figure 5 remains the same throughout the test, indicating no change in scale error. Almost all error on this arrangement comes from an offset error arising from heat generated in the conventional thrust bearing conducting along the ball-screw o 0. "^ *^msa^ X axis Hydroscrew Expansion ^" "Y^_^ c = % -10 -^ a "~^ * «_, -20. ' -^ Run Number Position -POO (fw d ) Po s ition 0 (f w d ) pn< jtjnn -200 (r«v) -^r* &/\\ ^ -V^A^ Vv " =" & Figure 5 - Offset error but no scale error on a hydro-screw Most machine controllers have the facility to enter a single scale error correction per axis. This correction is quickly overwhelmed by thermal expansion of the ball-screw under even light machining conditions. 2.4 Reversal errors in non pre-tensioned and pre-tensioned ball-screws Reversal error can be caused by inaccuracies in the transmission between the rotary encoder and the ball-screw, and axial movement of the ball-screw and ballnut. Transmission errors are usually not strongly temperature dependent. Reversal error may be exacerbated by a particular mechanical arrangement and by the forces that have to be applied to cause axis movement along the guideway. Carriage axes on sliding guide-ways may require a force of up to 12% of the static weight of the carriage to overcome the dynamic friction*. Such forces may cause significant loading of the axis even with no cutting forces. Figure 4 shows an increase in reversal error from 4um to 90 um on a pre-tensioned ballscrew undergoing a BS3800 part 3 test Low pre-load of the thrust bearings and low pre-tension of the bail-screw may allow axial movement of the ball-screw, particularly under heating conditions.

8 3 52 Laser Metrology and Machine Performance Low pre-load of the thrust bearing may be due to wear or heating. Pre-tension of the ball-screw may be lost as a result of ageing and heating. Deflection of the ball-screw bearing supports may occur as a result of heavy cutting forces. The data recorded from the hydro-screw system with a conventional thrust bearing (figure 5) shows that some thrust bearing arrangements control axial movement of the ball-screw well. Axial movement of the ball-nut is caused by low pre-load of the ball-nut. Loss of pre-load on the ball-nut is as a result of ageing^ wear, or heating. It is normal to enter a single reversal error compensation value into the machine controller. Changes in reversal error due to thermal effects can quickly invalidate a value measured with the machine cold. 2.5 Summary of thermal errors in ball-screws with rotary encoders The distance between the ball-screw line and the cutting line amplifies geometric, load, and thermal errors. The high rate offrictionalheat generation, and consequent quick temperature change causes fast changes in thermal errors. A pre-tensioned ball-screw with rotary encoder feedback system can generate linear thermal errors of 314pm over 0.8 metre when oscillating at Sm/minute. The ball-nut is the main cause of heat generation in a ball-screw system. Scale and reversal errors can change rapidly, invalidating the compensation values entered into the machine controller. Pre-tensioned ball-screws with two-way axial constraint can enter compression under high-speed operation. 3 Errors resulting from the thermal excitation of a linear encoder positioning system A linear encoder can be positioned anywhere within a machine structure that provides good protection against chips and coolant. However, in order to reduce the effect of Abbe error on linear positioning error, the linear encoder measurement line should be positioned as close as possible to the cutting line. Linear encoders are generally attached to parts of the machine that change temperature slowly, and thus the thermal errors change slowly. Linear encoders are very accurate measuring devices when their temperature is maintained at 20 C, with errors of ±5}im per metre on a standard grade encoder and ±3jim per metre on a high grade encoder. Most linear encoders have a coefficient of linear expansion about 85% of steel, but versions are available to match steel. Certain axes with a low stiffness or high reversal error in the driving system may not be well controlled under dynamic conditions even when fitted with a linear encoder. 3.1 Offset errors in a linear encoder measurement system Linear encoders are generally pinned to the machine tool structure in the centre of encoder travel. Offset errors independent of axis position arise from changes

9 Laser Metrology and Machine Performance 353 in the distance between this point and the cut point caused by expansion of the machine. Figure 6 shows measurements recorded from a linear encoder mounted close to a hydrostatic guide-way. The cut point is positioned 0.7m away from pinned point of the linear encoder, measured along its length. Heating of the machine by the hydrostatic oil between the linear encoder pinned point and the work-piece centreline causes an offset of nearly 45um. On this machine the work-piece is rotated, thus doubling the offset error and requiring expensive and time-consuming probing to re-establish the position of the work-piece relative to the cut point. Infeed axis position error during hydrostatic heating Time (x1 0 seconds) Figure 6. Offset and Scale error on an axis fitted with a linear encoder. 3.2 Scale errors in a linear encoder measurement system Scale errors in a linear encoder are caused by expansion of the encoder relative to parts of the machine, and the work-piece. A linear encoder at a different temperature from the machine bed or work-piece will cause a scale error to be present. Figure 6 shows a scale error of 15um over 200mm caused by heating of the linear encoder by hydrostatic oil in a guide-way. The guide-way temperature change over a portion of the test is shown in figure 7. This is an estimator of the actual linear encoder temperature. It is thus important that the linear encoder, the structure to which it is mounted, and the work-piece are all maintained at the same temperature.

10 354 Laser Metrology and Machine Performance Guide-way Temperature overtime p 2 0Q. 1? T3 0) '5 O _. ' r^^. ** ^T^^^ X" / / / f / Time (seconds) Figure 7 - Guide-way temperature over time 3.3 Reversal errors in a linear encoder measurement system The force required to move the read head of a linear encoder along its length is very small compared with the forces caused by friction in the guide-ways. Thus the reversal error in a system fitted with a linear encoder is dependent upon any thermal or loading generated distortion of the structure between the read head and the cut point. Geometric errors will also contribute to the reversal error through the Abbe error. 4 Summary of linear encoder thermal errors The distance between the linear encoder measurement line and the cutting line amplifies geometric, load, and thermal errors. A linear encoder is generally attached to a part of the machine whose temperature changes slowly. Thus the temperature and thermal errors within the linear encoder change slowly. Linear encoders should be mounted such that they are at the same temperature as the work-piece, and the part of the machine that links the axis position to tool position. Axes utilising pre-tensioned ball-screws featuring two-way axial constraint can enter compression as a result of high-speed operation, regardless of the feedback system. Lack of axis stiffness can reduce the ability of the axis to position in dynamic conditions, even when fitted with a linear scale.

11 Laser Metrology and Machine Performance 355 References 1. White A J., An identification and study of mechanisms causing thermal errors in CNC machine tools, Proceedings of Fourth International Conference on Laser Metrology and Machine Performance - Lamdamap '99, University ofnorthumbria atnewcastle, July British Standard BS3800, Part 3: General tests for machine tools. Part 3: Method of testing performance of machines operating under loaded conditions in respect of thermal distortion., British Standards Institution, Patterson G., Micro Metalsmiths Ltd, Personal communication, 3/3/ Braasch J., Eberherr A., Position Measurement on Machine Tools: By Linear Encoder or Ballscrew and Rotary Encoder?, Proceedings of the ASPE 1998 Annual Meeting, P , 1998.