Nội dung

442 Chapter 9 . Figure 219. Machine tool spindle error plots, illustrating spindle condition. [Courtesy of Lion Precision] Machining and Monitoring Strategies . Figure 220. A typical UHSM spindle cardridge listing some of factors affecting such a spindle’s design and its operation 443 444 Chapter 9 . Figure 221. Attainable cutting parameters – with differing milling spindles, plus HSM is affected by the feedrate and distance to be traversed, prior to the desired velocity being achieved – for conventional slideway motions Machining and Monitoring Strategies NB Pneumatic spindles can be rotated at exceptional speeds, by virtue of the ‘ideal condition’ of minimal metal-to-metal contact, although one serious disadvantage being they suffer from a low power output, or to be more specific – torque. • Hybrid spindles (Fig. 214-top) – have been de­ veloped to answer the major drawback to utilising pneumatic spindles. The hybrid spindle as its name suggests, is a combination of conventional ballbearing and pneumatic spindles. Here, the spindle design incorporates an aerodynamic thrust bearing with transversal spiral grooves (Fig. 214-top right) thereby creating an intense pressure wave profile, which can withstand up to 300% greater static loads to that of a conventional aerostatic bearing. A typical hybrid aerodynamic spindle bearing allows the assembly to achieve rotational speeds ranging from: 20,000 to 40,000 rev min–1, with >15.5 kW power at peak speed. NB Hybrid spindle cartridges are significantly less expensive than the magnetic ‘active’ spindles, but more expensive than pneumatic spindle cartridges. In both of these latter versions, they have a relatively long in-service life, as wear-rates are minimised, but do not have the stock-removal capability of the former cartridge. In Figs. 220 and 221a, are shown some of the principal factors that affect UHSM spindle performance. In Fig. 220, these factors are represented in an Ishikawa (i.e. ‘Cause-and-effect’) diagram. Here, the many of the inter-related effects can be seen, although other factors can also be added, depending upon the local conditions of usage: cutting data; workpiece material; wet, dry, or near-dry cutting; together with the machine tool’s overall condition. 9.2 HSM Dynamics – Acceleration and Deceleration If the HSM spindle cartridges – mentioned above – are fitted to conventional CNC machine tools, or the more likely low-cost scenario would be to simply fit a 445 ­mechanically-driven speed-increaser. Then the result of this HSM spindle fitment, will enable high rotational speeds to be produced, but it leaves the CNC-processors somewhat compromised in its ability to produce the desired acceleration and deceleration capabilities. As a practical example of the problems likely to be encountered, the graphs produced in Fig. 221b and c, were drawn from an industrial HSM machining experience at a precision metrology company’s premises, using several of the latest vertical machining centres with the spindle of each machine, being fitted with a mechanically-driven speed-increaser (i.e. see Fig. 243a). By utilising the inboard CNC clock – having a resolution of 0.0001 seconds, the elapsed times for slideway motion over varying distances was established. In Fig. 221b, an exponential relationship is depicted for the X-axis, this being a typical situation for the other axes on the machine tool. By a determination of the required motional distance to attain specific velocities, it was possible to illustrate the restrictive nature of both acceleration and deceleration for small slideway motions. In Fig. 221c, this illustrates the effect of the required distances to be executed at various velocities. From Fig. 221c – by way of an example, if a feedrate of 8,000 mm min–1 was utilised, then it would be necessary for a minimum movement of the slideway to be 16 mm to momentarily achieve the desired feedrate, which is typical for a machining centre having an acceleration of 1.08 m sec2. This physical problem in actual positioning to the required component’s dimensional feature is not too great a problem for long linear feeding distances – as the slideway velocity could be reached, but acceleration and deceleration becomes exacerbated by the smaller more intricate prismatic features normally found on the more minute, or smaller parts often produced by HSM milling operations, leading to potential scrappage problems. From the results of inspection procedures conducted on the HSM over a range of standardised testpieces, it was concluded that virtually all of the detrimental dimensional effects introduced by the HSM milling operations, could be attributed to severe ‘servo-droop’ – more will be mentioned on this subject shortly. Prior to manufacturing the HSM testpieces, they were designed on a CAD system and their respective tool paths were post-processed by the integrated CAM software. Hence, with regard to machining cycle times, they were either calculated by the CAD/CAM, or were the actual in-cut times – see Table 15. With re- 446 Chapter 9 . Table 15. A comparison of the theoretical and actual machining times for the manufacture of testpieces, by various production routes Machining Method: Theoretical Cad/ Cam Time: Actual In-cut time: Conventional 3.86 3.71 High-speed 1.26 1.50 High-speed (G61)* 1.16 1.55 NB All times in minutes * G61 is the ‘Exact-stop’ mode of machine command and, when activated, the machine tool will not initialise another movement until the previous axis command has been completed (i.e the targetpoint), thus ensuring an accurate and final slideway positioning. [Source: Smith and Maxted, 1995] gard to these cycle-times for testpiece manufacture, a significant improvement accrues when utilising HSM milling techniques. Although the increase of actual cycle-time from that of the theoretical high-speed CAD/ CAM estimation, can be due to a number of factors as previously noted by Smith and Hanson (1993). Not least of which was found in this case, where the CAM system tended to under-estimate the actual time to machine a component feature. This time-difference is marginally compounded by the ‘servo-droop’ effects. If the machine tool’s G61 (‘Exact-stop’) mode was employed, the actual cutting time in general showed only a marginal increase, over the normal HSM cutting time, although the dynamics of motion tended to be somewhat jerky in action as the command ensured it reached its targeted positions. At normal HSM milling performance, another exacerbating reason for the increase in cutting time over theoretical, was attributable to the axis acceleration/deceleration parameters (i.e see Figs. 221b and c). Thus, these machine tools basically failed to reach the required slideway acceleration/deceleration then maintain these velocities for about 20% of the total in-cut times, this was for a component of somewhat moderate dimensional size and pocketing intricacy (i.e. the overall testpiece dimensions were approximately: 150 mm in squareness, by 50mm deep). From the testpiece results, various remarks can be made concerning the advantages of employing an HSM strategy over conventional milling practices, these are: • Despite a reduced cut depth, the HSM cycle times are a 66% improvement over conventional milling production techniques, • Using HSM it will significantly reduce burr formation – although not entirely eliminating it, when compared to that of conventional practice, • Distortion of the thin wall features was minimised by HSM, • When employing a speed-increaser (Fig. 243a), its bearing’s stiffness is critically important in order to obtain an acceptable milled surface texture. Finally, by utilising even the most elementary form of HSM approach – using a speed-increaser, highlights the production advantages to be gained from adopting this strategy, albeit for limited periods of continuous cutting time, which normally dictates such ‘increaser’s’ practical usage. 9.2.1 HSM Dynamics – Servo-Lag Most of today’s CNC machine tools use ‘proportional servo-systems’ , where the axis velocity is proportional to the difference between the actual position and the command position (Fig. 222a). This ‘error signal’ is utilised by the system to determine any acceleration/ deceleration necessary as well as the steady-state velocities. As one can visualise from Fig. 222a, the distance between the actual and commanded positions is commonly termed ‘servo-lag’. This explanation can be taken a stage further in Fig. 222b, where the illustration depicts how a ‘proportional servo-system’ is used to mill a sloping line. In this example, DX and DY are the total programmed changes in position on both the X- and Y-axes, respectively, to go from point ‘A’ to point ‘B’. Conversely, DXL and DYL are the amount of lag on each axis at point ‘C’ along the tool’s path from ‘A’ to ‘B’. Furthermore, in such a system the lag on the X-axis must be proportional to a similar lag in the Yaxis, in order to accurately follow the slope of the line. This affect can be mathematically-represented by the following relationship: DX L DX = = Slope of the line. DYL DY In Fig. 222c, we can gain an appreciation of just what happens when the servo-lag on both axes is not proportional. As the machine tool’s axes travels from point ‘A’ to point ‘B’ , the lag on the X-axis is proportionally Machining and Monitoring Strategies . Figure 222. The CNC control problem of servo-lag and its affect on the associated HSM motional kinematics 447 448 Chapter 9 less than the lag on the Y-axis. This error might be the result of the ‘servo-gains’12 between the X- and Y-axes not being properly synchronised. Normally, ‘servogain’ can be expressed in units of: mm min–1 [i.e. velo­ city / mm (i.e. distance in 0.001)] of lag. Thus, lag can be determined using the following relationship: Lag L (mm) = Feedrate F ,  = = . mm. Gain G �. For example: If a machine tool’s moving axis is travelling along its slideway at 2,500 mm min–1 and the servo has a gain of 2, the lag will be 1.25 mm, as indicated in the following calculation: L (mm) = F ,  = = .mm. G �. 9.2.2 Effect of Servo-lag and Gain on Corner Milling If two axes with correctly matched servo-lags can move in a straight line from point ‘A’ to point ‘B’ , then to comprehend the effect of gain, let us consider what occurs when milling a right-angled corner at a constant feedrate without stopping (Fig. 222d). Whilst milling the corner from ‘A’ to ‘B’ and the onward to ‘D’ , the servo develops a steady lag (DXL), until sufficient command signals have been generated to reach point ‘B’. It is at this position that the control begins to generate commands toward point ‘D’ , although the actual slideway has not yet reached point ‘B’ , owing to the servo-lag (DXL). At this point the Xaxis will begin to decelerate and, simultaneously, the Y-axis begins to accelerate, that is the velocity is proportional to the distance between the command signal and the actual position. Acceleration factors affect the slideway motions producing the result that the distance from ‘B’ to ‘C’ is always greater than DXL. Furthermore, this curved path is not a circular arc, but an exponential curve, with the amount of variance from the sharp right-angled corner being dependent on the 12 ‘Gain’ or to be more specific: ‘servo-gain’ , in this instance, is a measure of the servo’s responsiveness. Thus, the higher the gain, the lower the lag. magnitude of servo-lag13, which itself depends upon the affect of feedrate and gain – according to the previous formula. 9.2.3 Effect of Servo-Lag and Gain Whilst Generating Circular Paths For one to fully understand just what happens when milling complex contours, it will be helpful to consider the simple case of a milled path where two straight lines are joined by a semi-circle (Fig. 222e). In this situation, the milling operation occurs at a constant feedrate moving from point ‘A’ in a straight line until the command dimension reaches point ‘B’ . However, at this point, because of the effect of servo-lag, the axis motion will have only reached point ‘BL’. Therefore, as the control command is moving forward at a constant rate, it begins to generate commands toward point ‘C’. This action results in the axis motion beginning to move away from the desired path at point ‘BL’. The dotted line depicted in Fig. 222e, shows the actual path taken by the cutter and as one can visually observe, from points ‘BL’ to ‘CL’ , the deviation from the desired path is shown as ‘e’. In this example, the magnitude of ‘e’ is determined as a function of the: feedrate; gain; plus the desired radius. When the radius error approaches the programmed radius, the resulting machined profile appears distorted and is hence, impracticable. Specifically, if one needed to mill a 25 mm radius at a feedrate of 2,500 mm min–1 with a machine tool gain being: 25 mm/min/0.001, then the error generated would be approximately 0.125 mm, equally, if the gain was increased to 100 mm/min/0.001, the maximum error ‘e’ will be considerably reduced to approximately 0.008 mm. A machined curve is an approximation on CNC machine tools, in that the profile is constructed from a series of short connected segments, or chords. The controlling factor on the length of such segments is the deviation between the centrepoint of any chord 13 ‘Servo-lag’ , is sometimes referred to in the literature as: ‘Servo-droop’ – due to its ‘rounding-effect’ at the corners, this being particularly prevalent when fast feedrates are selected, creating fast tool path velocities, particularly when normally undertaking high-speed milling operations. Machining and Monitoring Strategies and a point at right angles on the programmed curve. The linear distance between these two points is usually termed the ‘maximum allowable chordal deviation’ and is a function of the CNC controller’s executive software. So, the resultant machined curve is a combination of the chordal deviation and the servo-lag for a particular machine tool. To illustrate this condition, Fig. 220f shows the culmination of servo-lag when following a contour, with the curve ‘C1’ being the desired contour, ‘C2’ a linear approximation (i.e. the programmed path), ‘C3’ is the actual generated path resulting from servo-lag utilising a high gain servo and finally, ‘C4’ being the path generated by a low gain servo. Through servo-lag, a smoothing of any contour occurs owing to the lagged cutter path, this causes severe contour problems with respect to part accuracy and precision for the simple arc geometry depicted in Fig. 222e. Clearly then, servo-lag and gain promote a variety of effects on complex shapes, depending upon their geometry and tolerance, with these errors becoming still more complicated when one considers three-dimensional milling contouring. In many circumstances the cutting of three-dimensional profiles may necessitate utilising four, or more axes with either one, or two of them being rotary axes being necessary to create the required tool paths to produce the component. The servo-lag and gain on all axes must be considered when manufacturing complex part geometries. Regardless of the workpiece’s geometry, or the number of axes utilised, there is one factor that should be emphasised concerning potential errors created by servo-lag. If servo-lag is extremely large, then this ‘lag’ can easily exceed the positioning errors in the machine tool’s basic specifications. 449 be read, interpreted, the activated to obtain dynamic slideway motions. This CNC exercise is usually referred to as the ‘block processing time’. The maximum allocated time for block processing of information is dependent on the length of slideway stroke (i.e. chord length) and its associated feedrate. It is possible to calculate the maximum block processing time (Tb), as follows: Tb = Maximum stroke length Feedrate Tb = . . = = . s, or  ms , �  For example: if we require a profile’s chord length (i.e. stroke length) of 0.50 mm, in order to maintain contouring accuracy whist milling at 3,000 mm min–1, or 50 mm s–1, with a maximum block processing time, then this ‘time’ should be less than: Possibly the main factor limiting contouring speed is the CNC’s inherent processing speed, with each programmed-block14 generated for every axis having to Many CNC’s have block processing times typically within the range of 30 to 60 ms, as can be seen from the above example, the CNC program would suffer from ‘data starvation’ , whilst the controller attempts to catch up on its data processing. Such ‘starvation’ would cause hesitation in the slide motions, slowing down the cutting time and leaving ‘dwell marks’15 on the machined workpiece’s surface. Since this ‘data starvation’ effect is unacceptable, a lower feedrate must now be programmed to overcome the problem and as a result, the cycle-time increases. In the above example, if an older CNC was fitted to the machine tool with the controller’s block processing time being 60 ms, the cut would have taken six times longer to generate the profile, than a more modern CNC controller having a processor capable of 10 ms. So that we can fully-comprehend the CNC processing speed problem, let us now consider two widely differing machining applications: 1. Complex three-dimensional milling of a hob – to manufacture a die utilised in the production of intricate and expensive military metal buttons. Such 14 ‘Programmed blocks’ , these are basically the ‘G-’ and ‘M-’ and ‘Auxiliary-codes’ which make up each individual block’s line, with successive blocks in a logical sequence containing the whole CNC program. Generally speaking, the smaller the number of blocks – for the successful production machining of the part, the more efficient and refined has been the programming. (Smith et al., 1993) 15 ‘Dwell marks’ , here are the result of an ‘untimed delay’ in the program’s execution, created in this instance, by data starvation (i.e. block processing speed was simply not fast enough). These untimely delays in the activation of programming blocks cause the rotating cutting tool to rest and press against machined surface and thus, generate minute ‘gouging-effects’ in the surface. (Source: Seames, 1990; Smith, 1993) 9.2.4 CNC Processing Speed 450 Chapter 9 a hob will more than likely have very fine detailed work on its surface, perhaps with radii as small as 0.25 mm, requiring a tool tip radius of 0.025 mm. In order to machine the button’s elaborate features with such a small milling cutter, the spindle speeds might need to reach 40,000 rev min–1, utilising a feed per revolution of 0.008 mm, giving a feedrate of 320 mm min–1. Many production engineers would not consider this as an example of high-speed milling, but let us look more closely at this particular machining problem. If the controller has a servogain of 4, with a feedrate of 320 mm min–1, this means that the servo-lag would be 0.75 mm min–1, which is consistent with milling radii of 0.25 mm. However, if the servo-gain was 1, this would cause a servo-lag of 0.320 mm min–1 and in this case, it obviously could not machine that button’s intricate detailing. In such circumstances, it would be necessary to appreciably reduce the feedrate to say, 75 mm min–1 to generate the button’s contours, leading to the cycle-time increasing by 400%. Let us also now consider the impact of block processing time under these conditions. To mill a radius as small as 0.25 mm, we would need to produce linear stroke lengths of just 0.075 mm – to reproduce acceptable button detailing. This intricate contouring work requires a block processing time of 15 ms. If the CNC controller has a block processing time of just 60 ms, then the feedrate must be limited to 75 mm run–1 which again, increases milling time by a factor of four. 2. ECM pattern electrode for a Turbine fan (i.e large aluminium casting) – here, the electrode’s geometry has very gentle three-dimensional curves. In this situation the chosen CNC machine tool’s milling spindle has a 250,000 mm min–1 capability, coupled to adequate power to cut at a feed of 0.25 mm rev–1. This production requirement produces a feed­ rate of 62,500 mm min–1 (i.e. being the product of: 250,000 x 0.25) would be possible. For accuracy and precision, a chordal deviation (Cd) of 0.005 mm would indicate a stroke length of 0.75 mm – if the minimum radius of curvature for the Turbine fan’s geometry was 25 mm. Assuming that the servogain of 1 was available, then we would obtain errors as large as 0.125 mm and with such errors, the machine tool would not produce an acceptable part. Further, at 62,500 mm min–1, if the block processing time (Tb) was 60 ms, this ‘timing’ would require stroke lengths of 2.5 mm instead of the 0.75 mm we needed for the required accuracy and precision. Therefore, in order to eliminate the effects of low gain, or slow processing time, it is necessary to depress the feedrate, resulting in the cutting time being increased up to 400%. When considering these two practical examples from a metaphorical sense, the former method can be compared to that of racing a go-kart on a small tight track, while the latter method is similar to a highly tuned sports car racing on a longer and smoother track. The go-kart may only reach speed a of 30 km h–1, whereas the sports car may hit speeds of >200 km h–1. The corner forces and reaction times are similar for both methods, even though the speeds are vastly different. Looked at from yet another viewpoint, we can say that the frequency of response of both the drive and car, that is their servo-gain and processing time, are very similar in both examples even though the speeds (feed­ rates) are radically different. In the day-to-day production environment, the duplication of specific and precise contours is the end result of a combination of many inter-related factors. As the number of machine tool axes required to produce sculptured part surfaces increases, the difficulty of obtaining the desired profile also becomes proportionally problematic. So, machine tools that would normally produce excellent general-purpose machining work, may not be either accurate, nor efficient enough to manufacture complex part contouring geometries. That is, unless their CNC processors can achieve block processing speeds of <10 ms, with servo-system gains of up to 4, having sufficient ‘look-ahead’16 capabilities (i.e. see Fig. 222g) that are required, for any realistic and practical HSM applications. 16 ‘Look-ahead’ facilities, are when the controller has the ability to look-ahead through the following sequenced programming blocks* to determine successive motions and actions – an important feature for any HSM applications. Many of today’s sophisticated CNC controllers can look-ahead through a considerable number of these blocks, thereby prompting the controller’s response, prior to undertaking any command exe­ cutions. *A ‘Block’ can be defined as: A set of words, characters, digits or other elements handled as a unit – hence, the term ‘block’ – which creates a sequence of lines of a computer programming language, that can then be activated upon by the machine tool‘s CNC controller, producing the necessary programmed-actions. (Source: Smith et al., 1993) Machining and Monitoring Strategies 9.3 HSM – with NonOrthogonal Machine Tools and Robots Variax/Hexapod – Design Concept Non-orthogonal machine tools such as the one simulated, designed and developed for HSM applications is typically illustrated in various ways in Figs. 223 to 225: utilising ‘virtual’ six axes kinematics (i.e. namely: X-, Y-, Z-, A-, B- and C-axes), therefore these axes operate without having any ‘true’ slideways. This particular kinematic concept has actuators that cross each other forming X’s instead of meeting at apexes to form triangles, as they occur in aircraft flight simulators, which uses conceptually similar mechanisms – known as Stewart platforms, these configurations being a form of ‘parallel kinematic link mechanism’ (Fig. 223). To develop this new concept for a machine tool, the manufacturer utilised computer-aided technology which played a pivotal role in creating the structural design (Fig. 223). In particular, the application of a totally three-dimensional design environment was employed, utilising both finite element analysis (FEA) in conjunction with kinematic analyses. However, the ‘Variax’ design uses a range of uncomplicated, or standard mechanical components in its design. While new forms of motion actuators were discarded in favour of conventional and well-proven ballscrew technology, with its accompanying motor and drive machinery. Even the gimbals that secure the legs at the base and the spindle carrier, are relatively simple devices. With the design of such a high thrust machine, a significant problem to overcome was the connection of the spindle to the six legs (Fig. 223a). The answer to the connection problem was a simple space frame design, allowing all the forces to be either in tension, or compression along the structural elements – similar to a bridge design. If one compared this ‘Variax design’ with that of a ‘plate-type design’ to secure the spindle to the legs, then the former space frame concept improves the mass-to-stiffness ratio by 275%. While another key development problem to be overcome was that of how a spindle supported and driven by six axes kinematically moves in space, moreover, was it even mathematically possible to control the motional members? For example and by way of illustration of this complex mathematical/control problem: a simple ‘X-axis’ linear kinematic translation requires all six 451 legs to simultaneously move, but each leg will move at different speeds, either accelerating, or decelerating at different rates through the whole ‘linear movement’ – requiring very complex multi-axes mathematical solutions to achieve this action. By employing a system of novel mathematical transformation runs in real-time by the CNC’s multi-processor this mathematical translation action was achieved, but from a programmer’s viewpoint, conventional ‘word-address format’17 of programming knowledge was all that was needed to successful operate the machine tool. Non-Orthogonal Versus Orthogonal Machine Tool Designs The ‘Variax’s’ machine capabilities and benefits differ significantly from those found on conventional slideway-based orthogonal machine tools. So, on an orthogonal machine the slideways must be perfectly straight, parallel and at 90° to each other. On these machines, an axis must have accuracy and precision control along the slideway having linear and rotary degrees of freedom carefully managed by the ground way being scraped to minimise any impending errors/ uncertainties. As mentioned earlier, these orthogonal axes have kinematically 21 degrees of freedom, with: linear motion; rotational – i.e. yaw, pitch and roll; plus 17 ‘Word-address format’ of CNC programming, can be considered as: A system of coding instructions whereby each word in a block is addressed by using one, or more alphabetic characters identifying the meaning of the word. [Source: Valentino and Goldenberg, et al. 2000] For example, some typical ‘G- and M-codes’ are: G00 – rapid movement/ traverse of the tool (modal); G01 – linear interpolation (ie. tool moved at a prescribed feedrate) (modal); G02 – circular interpolation clockwise – CW (modal); G03 – circular interpolation counter clockwise – CCW (modal); G04 – programmed dwell (*non-modal); G40 – Cancel cutter diameter compensation (modal); G41 – tool diameter cutter compensation (i.e. radial-offset) on left-hand side of workpiece (modal); G42 – tool diameter cutter compensation (i.e. radial-offset) on right-hand side of workpiece (modal); M00 – Program stop; M02 – End of program; M03 – spindle on (CW); M04 – spindle on (CCW). NB Many more codes/auxiliary functions exist, utilised in ‘word-address format’ programs.*Non–modal commands are only active in that actual block. [Source, Smith et al., 1993]