A deeper investigation into the thermal drift of a linear axis

Transcription

1 A deeper investigation into the thermal drift of a linear axis O Beltrami STANIMUC Ente Federate UNI via A. Vespucci 7725 Torino, Italia Abstract This presentation shows the results of actual tests performed on the shop floor of the user company with a view to understanding the real behaviour of the machine structure. The machine involved was a milling machine with table of fixed height, used for machining dies, whose 3 m long X axis, i.e. the table travel on the bed, was submitted to the test, because significant deviations occurred during normal use. The test lasted 1 minutes, and it was performed moving continuously the table at the rapid traverse rate between the two ends of the travel for 65 minutes, with measurements still being made for 35 minutes during the cool down period, with the table resting in the middle of the travel. Every 5 minutes the following quantities were measured, stopping the table at both ends of the travel: 2 linear positioning deviations EXX of the table, by laser 2 angular pitch deviations EBX of the table, by electronic level 2 angular roll deviations EAX of the table, by electronic level 2 angular yaw deviations ECX of the table, by a second laser 2 angular pitch deviations of the column, by electronic level 2 angular roll deviations of the column, by electronic level 3 temperatures, measured in different points of the bed. The three major sources of the total elongation of the travel, responsible for more than 8% of the final positioning deviation, have been identified and quantified. 1 Introduction A machine component could maintain its shape while warming up only if the thermal growth could be exactly the same in all the points of its structure, i.e. if there were only temperature gradients in the time but not in the space.

2 358 Laser Metrology and Machine Performance Unfortunately this does never happen in the practice, because the heat generation takes place in well defined parts of the machine, creating temperature gradients inside the structure, with different expansions among different points of the same component, and therefore angular distortions, with loss of the original shape. It is therefore extremely important to measure angular deviations in addition to linear deviations in order to properly assess the thermal behaviour of a part of the machine structure. 2 Object The present report refers to a set of measurements of linear and angular deviations carried out on the work-holding table travel (X axis) of a milling machine with table of fixed height and universal head, with the purpose of assessing the distortions caused by a variety of heat inputs during a sequence of programmed movements of the axis. The results of these measurements prove that angular distortions are much more responsible for the final deviations than the simple linear elongation of the components involved. 3 Installation and operation of the machine 3.1 Installation conditions The machine was regularly installed at the user's premises and anchored to the ground by means of levelling fixtures. The machine was equipped with a numerical control unit and the measurement system of the X axis was consisting of a linear encoder made by an adjustable steel strip. 3.2 Operating conditions The test was programmed to last 1 minutes. During thefirst65 minutes the X axis was traversed continuously in both directions on a 29 mm travel at the rapid traverse, i.e. 8 mm/min. During the last 35 minutes the work-holding table was kept still in the middle of the travel and moved to the travel ends (X and X 29) only at the times agreed for recording the readings. 4 Methods of measurement 4.1 General Since the measurements were aimed at investigating on the performance of the X axis (work-holding table motion), the other moving elements of the machine, as Y and Z axes and the spindle, were kept still for the whole duration of the test. Both during thefirst65 minute movement, and during the last 35 minute rest, every 5 minutes the work-holding table was stopped at the two travel ends for the time strictly necessary for recording the readings of the two laser

3 Laser Metrology and Machine Performance 359 interferometers and the levels. During both periods, for all 1 minutes, the following measurements were made at the agreed 5 minute intervals: - N 3 temperatures on machine components by three temperature sensors - N 2 linear positioning deviations by one laser interferometer - N 8 angular pitch and roll deviations by two dual axis electronic levels - N 2 angular yaw deviations by the other laser interferometer. 4.2 Temperature measurements During the test three magnetic temperature sensors were placed on the X axis bed in the following positions: - Ti-in proximity of the linear encoder with a coefficient of thermal expansion conventionally considered equal to 11,7 im/m C - T2 - under the bottom of the bed, in order to assess the temperature gradients between top and bottom of the bed - Ta - in proximity of one of the ball screw bearings. Graph N 1 shows the temperature variations measured by the three sensors. 4.3 Linear positioning measurements Linear positioning measurements were carried out by a laser interferometer, in order to assess the variation of the relative position of both ends of the table travel referred to the spindle, and the consequent variation of length of the test travel. The distance interferometer was fixed to the head, close to the spindle, and the retro-reflector was fixed to the work-holding table, by means of a steel bar in order to traverse the whole travel length without any risk of crushing the optics. Graph N 2 shows three plots, respectively related to the linear drifts of the two ends of the test travel, and to the consequent variation of travel length. 4.4 Angular pitch and roll measurements on the machine One dual axis electronic level was placed on the work-holding table in order to measure angular variations in the two vertical planes, longitudinally and transversely. A second identical level was placed on the spindle head, in order to provide information on the movements of the whole structure on the floor, and to assess then the stiffness of the clamping and/or the foundation stability. Two sets of measurements were carried out by the levels as well, at the agreed 5 minute intervals, with the work-holding table at the two ends of the travel. Both graphs N 3 and N 4 show four plots, respectively related to the longitudinal and transverse angular deviations of the work-holding table and of the structure when the work-holding table was standing still at the two ends of the travel. 4.5 Angular yaw measurements Angular yaw measurements were carried out by a laser interferometer, in order to assess the variation versus time of the angular deviation of the work-holding table in the horizontal plane at the two ends of the test travel (X and X 29).

4 36 Laser Metrology and Machine Performance Angular optics were mounted on the samefixturesof the distance optics (see 4.3); the angular interferometer was fixed to the spindle head, close to the spindle, and the angular retro-reflector was fixed to the work-holding table, by means of a steel bar in order to traverse the whole travel length without any risk of crushing the optics. Graph N 5 shows two plots, respectively related to the angular drifts of the two ends of the test travel and to the consequent variation of bending of the travel. 5 Presentation of results Measurement results are shown graphically in graphs N 1 to N 5 versus time. In graph N 2, showing the linear positioning deviations, an increase in the values means a drift towards the positive values of the travel, and the third plot (DL) shows the algebraic difference of the deviations at the two ends of the test travel; an increase in its values means then an increase in the travel length. In graph N 3, showing the longitudinal angular (pitch) deviations, an increase in the values means a raising of the positive side of the work-holding table (or a lowering of the negative side) in the vertical longitudinal ZX plane. Similarly, an increase in the values of the longitudinal angular deviations of the structure (column and head) means atiltingof the column towards the operator, and viceversa a decrease in the values. In graph N 4, showing the transverse angular (roll) deviations, an increase in the values means a raising of the external side of the work-holding table, i.e. atiltingof the work-holding table towards the column. Similarly, an increase in the values of the transverse angular deviations of the level placed on the spindle head means a raising of the spindle nose, or atiltingof the column backwards. 6 Observations 6.1 Temperature variations The test was carried out between 16, and 17,4, with all initial temperatures between 18,5 and 19,1 C. Temperature Ti of the linear encoder grew from 18,82 a 2,67 C during the 65 minute warm-up period, and later still grew slowly up to 2,99. Temperature T2 of the bottom of the bed slowly but continuously grew from 18,58 to 19,41 C for the whole 1 minutes test, due to the progressive spreading of heat from the top downwards, starting from the sources where heat is generated by friction (ball screw, screw bearings and guideways). Temperature Ts in proximity of the screw bearing grew faster than the others during the 65 minute warm-up period, from 19,7 to 22,81 C, growing still up to 23,4 C in the first 1 minute rest, and then decreasing in the last 25 minutes.

5 Laser Metrology and Machine Performance Linear deviations The maximum deviations reached in the 65 minute warm-up are hereunder shown. Deviations in microns XO X29 DL Elongation Test start 5,5 5,5 199,4 65 minutes - 13,6 74,3 24,9 In the above table the positioning deviations at the beginning of the test and after the 65 minute warm-up period are shown, at both ends of the table travel (X and X 29), as well as the initial andfinaldl deviation of the actual 29 mm travel length, and finally the elongation undergone by the travel during the 65 minute rapid traverse of the X axis. In these measurements the variables mainly affecting both the absolute drifts of the two ends of the travel, and consequently the travel elongation, are the absolute temperature of the linear encoder, whose coefficient of thermal expansion is conventionally considered to be equal to 11,7 jim/m C, and the bed bending in the two longitudinal planes, readable in the vertical ZX plane through the pitch measurements, and in the horizontal XY plane through the yaw measurements. Owing to the Abbe's error, both bending components in the two planes cause an elongation of the travel of the retro-reflector, which was placed on the workholding table, located at approximately 7 mm vertical distance and approximately 2 mm horizontal distance from the linear encoder (see 6.6.2). 6.3 Angular pitch deviations in the vertical longitudinal ZX plane The maximum deviations reached in the 65 minute warm-up are hereunder shown. Deviations in mm/m Test start 65 minutes Work-holding table XO,7 X29,19 -,38 AP,19 -,18 XO -,1 Spindle head X29 -,9 -,1 AP -,9 -,9 EBX = AP table - AP head,28 -,99 Bed bending -,127 Figures in this table give the following results: - at the beginning of the test: - the level placed on the work-holding table showed an apparent concavity of the travel Ap =,19/1, considered as the angular pitch variation between X and X 29;

6 362 Laser Metrology and Machine Performance - at the same time, the level placed on the spindle head, not participating in the test movements, showed atiltingmovement of the structure Ap = -,9/1, when the work-holding table was moving from X to X 29; - the readings on the work-holding table, taking into account the readings on the spindle head, give an initial pitch deviation of the travel EBX =,28/1, resulting in a bed concavity higher than the apparent one; - after the 65 minute warm-up period: - the level placed on the work-holding table showed an apparent convexity of the travel Ap = -,18/1; - at the same time, the level placed on the spindle head showed a tilting movement of the structure A(3 = -,9/1, equal to the initial one; - the readings on the work-holding table, deducted the readings on the spindle head, give a pitch deviation of the work-holding table EBX = -,99/1, resulting in an actual convexity of the warmed up bed slightly lower than the apparent one. The shape of the bed changed then in the 65 minute warm-up period from an initial,28/1 concavity to a final -,99/1 convexity, with an absolute,127/1 bending. Measurements showed that the warming up of the components affected by friction, mainly the ball screw, the ball screw bearings and the slideways, cause first an expansion of the bed top, with consequent bending of the bed itself. 6.4 Angular roll deviations in the vertical transverse YZ plane The maximum deviations reached in the 65 minute warm-up are hereunder shown. Deviations in mm/m Test start 65 minutes Work-holding table XO -,8 X29,1 -,1 Act,1 -,2 X,1 Spindle head X29 -,5,5 Act -,5 -,5 EAX = Act table - Act head,15,3 Bed twist -,12 Figures in this table give the following results: - at the beginning of the test: - the level placed on the work-holding table showed an apparent twist of the travel Act =,1/1, considered as the angular roll variation between X and X 29; the positive sign means that at X 29 the work-holding table was tilting towards the column; - at the same time, the level placed on the spindle head, not participating in the test movements, showed atiltingmovement of the structure Act = -,5/1, when the work-holding table was moving from X to X 29;

7 Laser Metrology and Machine Performance the readings on the work-holding table, taking into account the readings on the spindle head, give an initial roll deviation of the travel EAX =,15/1, resulting in a bed twist towards the column, slightly higher than the apparent one; - after the 65 minute warm-up period: - the level placed on the work-holding table showed an apparent roll of the travel Aa = -,2/1; - at the same time, the level placed on the spindle head, although starting from a different value than the initial zero, still showed a tilting movement of the structure Aa = -,5/1, equal to the initial one; - the readings on the work-holding table, taking into account the readings on the spindle head, give a roll deviation of the work-holding table EAX =,3/1, still showing a slight twist of the warmed up bed towards the column. The shape of the bed changed then in the 65 minute warm-up period from an initial,15/1 twist to a final,3/1 twist, with a consequent,12/1 distortion. It is however important to point out a distortion which, although not contributing to the X axis deviations, would significantly contribute to other deviations, which were not the object of the test. This distortion can be detected through the comparison between the angular roll readings of the work-holding table and those of the spindle head in the same position of the X axis at, respectively at the beginning of the test and after the 65 minute warm-up. The readings on the work-holding table shifted from to -,8/1, while the readings on the spindle head shifted from to,1/1. The bed tilted outward, whereas the column tilted backwards, with,18/1 relative angular drift between each other. Also in this direction measurements showed that the warming up of the components affected by friction cause first an expansion of the bed top, with consequent bending of the structure as well. 6.5 Angular yaw deviations in the horizontal XY plane The maximum deviations reached in the 65 minute warm-up are hereunder shown. Deviations in mm/m Test start 65 minutes XO -,23 X29,57,84 ECX = AY,57,17 Bed bending,5 Figures in this table give the following results: - at the beginning of the test the angular interferometer showed a concavity of the table travel outward Ay =,57/1, considered as the angular yaw variation between X and X 29; - after the 65 minute warm-up period the angular interferometer showed a concavity of the travel Ay =,17/1;

8 364 Laser Metrology and Machine Performance The shape of the bed changed then in the 65 minute warm-up period from an initial,57/1 concavity to a final,17/1 concavity, with an absolute,5/1 bending. However, it should be noted that the bed concavity in the horizontal XY plane still increased in thefirstten minute rest up to,113/ Contributions to the deviations Initial travel length At the beginning of the test the 29 mm travel was 5,5 im longer. The linear encoder temperature was 18,82 C = (2-1,18) C. Considering a coefficient of thermal expansion of the linear encoder conventionally equal to 11,7 jim/m C, the following relation is valid: -1,18 C 11,7 ^im/m C 29 mm = - 4, pirn. Furthermore the bed shape, as from tables N 3 and N 5, is characterized at the beginning of the test by a,28/1 concavity upward in the vertical ZX plane, and by a,57/1 concavity outward in the horizontal XY plane. Taking into account that the distance between the laser beam path (over the work-holding table) and the path of the scanning unit on the linear encoder (between the bed slideways) was about 7 mm in the vertical direction and about 2 mm in the horizontal direction, the contribution due to the Abbe's error in the vertical plane is given by the following relation:,28/1 7 mm = 19,6 jam (negative) and in the horizontal plane by the following relation:,57/1-2 mm = 11,4 p.m (positive). The sum of the three calculated contributions gives the following result: - 4, jam - 19,6 jam + 11,4 jim = - 48,2 jun, which would cause the 29 mm travel to be 48,2 jim shorter, whereas it resulted 5,5 ^m longer. Neglecting the uncertainties of the different measurements, the steel strip linear encoder should then be adjusted to be about 53,7 jam shorter on the 29 mm travel, compared to the actual situation Travel elongation As already mentioned in 6.2, the two main causes of the travel elongation (199,4 p.m) are the linear encoder elongation and the bed bending in the two planes. The linear encoder was warmed up by 1,85 C, from 18,82 C to 2,67 C. Its elongation is then given by the following relation: 1,85 C 11,7 nm/m C 29 mm = 62,8 urn. The shape of the bed, as mentioned in 6.3, changed in the 65 minute warm-up period from an initial,28/1 concavity to a final -,99/1 convexity, with an absolute bending of,127/1. Following the same principles of the previous clause, the contribution due to the Abbe's error in the vertical plane is given by the following relation:,127/1 7 mm = 88,9 jam and in the horizontal plane by the following relation:,5/1-2 mm = 1, pirn (positive). The sum of the three calculated contributions gives the following result:

9 Laser Metrology and Machine Performance ,8 ^im + 88,9 jim + 1, pun = 161,7, which gives reasons for 81% of the deviation read by the laser interferometer (199,4 pirn); this confirms what mentioned earlier in 6.2, taking into account that several sources of uncertainty are involved; the travel elongation detected by the laser interferometer is much more due to the angular deflections of the bed than to the linear expansion of the linear encoder, although it contributes by more than one third of the whole. Graph N 1- Temperature variations Time in minutes

10 366 Laser Metrology and Machine Performance Graph N 2- Linear deviations of X axis 25 <A 2 I O 1 C c o is I Time in minutes Graph N» 3- Longitudinal angular (pitch) deviations,8 -,4 o o Time in minutes

11 Laser Metrology and Machine Performance 367 Graph N 4 - Transverse angular (roll) deviations -,15 Time in minutes Graph I\T 5 - Horizontal angular (yaw) deviations,1 -,4 Time in minutes