Vibration modelling of machine tool structures

Vibration modelling of machine tool structures F. Haase, S. Lockwood & D.G. Ford The Precision Engineering Centre, University of Huddersfield (UK) Abstract Productivity in modem machine tools is acheved by using high cutting velocities, spindle speeds and feed rates. A restriction for large material removal rates is the tendency of machines to chatter (structural vibration) for large depths of cut. This work is concerned with improving machine tool performance by understanding and ultimately controlling vibration in machine structures. If vibration due to chatter under load conditions can be controlled, then component surface finish can be improved and the life of components extended. The first step in this research is to measure and interpret vibration and model the structures, which are to be controlled. Appropriate sensors need to be selected and designed to measure self-excited vibrations. The vibrations of the investigated machines need to be understood by analysing the sensor signals and surface finish. Recent advances in micro-machining technology have resulted in a new type of accelerometer that is an order of magnitude lower in cost than traditional types. Results have shown that these sensors can be successfully used to replace their more expensive counterparts. This paper describes the first step into this research. 1. Introduction to Structural vibrations in machining Machine tool vibration plays an important role in precision machining, because speeds, feeds & depth of the cut, (cutting parameters) have to be reduced in order to minimise it. Excessive vibration accelerates tool wear, causes poor surface finish and may damage the spindle bearings. Machine tool structures are multi-degree-of-freedom systems that often can not easily be described mathematically [l] and therefore, Experimental Modal

Analysis, (Structural testing) is often used to ident~fy the transfer-functions of existing systems. There are 3 main types of mechanical vibrations in machlne tools, (see figure Figure 1 : The main types of mechanical Vibrations in machine tools 1.1 Random or free vibrations Shock or impulsive loading of the machine tool causes these vibrations. An example may be when the tool strikes a hard grain during the cutting operation. When the damping is assumed to be zero the structure will oscillate at its natural frequency (Rayleigh's equation), because the involved potential energy will be converted without loss (friction-damping) into kinetic energy. In practice however real systems always have damping, which decays the oscillation amplitude with time. In machine tools, this kind of vibration is often neglected since forced or self-excited vibrations play a more important role. 1.2 Forced vibrations Forced vibrations are caused by periodic excitation, such as spindle imbalance, gear drive irregularities, electric motors, pumps, the periodic break of the chip due to the build up edge or shear angle variations, and the tooth entry impact. The machine system will oscillate at the kequency of the excitation force. These excitation forces can be amplified through the structure of the machine when a resonance frequency of the structure is excited. This kind of vibration can be reduced by removing the source, by changing the exciter frequency so that is not close to the natural frequency of the system or the excitation force can be de-coupled by passive or active dampers. 1.3 Self-exited vibrations In processes where a large amount of energy is transmitted as a steady input and mechanical damping of the system is low, a small amount of transient energy can be enough to bring the system out of balance. This can then be modulated into vibrations. Initially the system will be stable (figure 2.a) and no excitation force will be significant. At some critical depth of cut, the static cutting forces become so large, that even a small transient force (may be caused by a hard grain in the

Luser ltetroiog?~ iinri ltuchrne Pet-formunce 139 work-piece), can "trigger" a self-excitation mechanism called chatter. Forces then build up over a period of time, depending on damping and in turn. leads to the generation of variation in the chip thickness which results in further varying cutting forces. Chatter leads to the excitation of one of the structural modes of the machine tool-work-piece system (figure 2.b) and this results in a relative displacement between tool and work-piece. A wavy surface finish left during the previous revolution in turning or by a previous tooth in milling will be removed by the following revolution or tooth period. If the phase between previous cut and current cut is 180, the varying cutting forces can grow and oscillate at the Chatter frequency (close or equal to the resonance frequency of the excited mode of the structure, see figure 2.c). [2] The cutting process and the vibratory system of the machine form a closed loop, where the cutting force (F) and the relative displacement between tool and work-piece (Y) are the variables, (figure 2.d) [3]. This closed-loop characteristics of self-excited vibrations becomes unstabie when the gain, rises above a certain value. Figure 2.a Stable cutting process Figure 2.b Process starts to become unstable Figure 2.c Vibration grows until saturation Figure 2.d Closed loop behaviour of chatter

140 Laser Iletrology and Ilachrne Performance 2 Methods of preventing chatter Chatter occurs if the depth of cut is too large with respect to the dynamic stiffness of the structure and therefore improving the rigidity of the structure can help to prevent it. Decreasing the chip depth can also prevent chatter, since the cutting process becomes stable again, when the depth of cut is reduced below the critical value. In general Chatter prevention strategies include: - Changing cutting parameters (e.g. depth of cut). - Improve the stiffness at the design stage. - Passive vibration control using a tuneable passive damper. - Active vibration control by introducing anti-vibration using an actuator 3 The Sensor design The relative vibration or cutting forces between tool and work-piece, (the variables in the closed-loop model of self-excited vibration), would be the most appropriate physical quantities to measure. The cutting force can be measured using a dynamometer and the most convenient sensors for vibration measurement are accelerometers. Normally, the cost of measuring acceleration using piezo-effect accelerometers is relatively high because of the need for expensive signal conditioning units such as charge amplifiers. In this chatter investigation, several points are considered simultaneously and therefore an evaluation of lower-cost sensors was carried out. New micro-machined accelerometers from Analog Devices are integrated into a surface mount silicon chip. The sensor chosen for this work was the ADXL105, with a range of +l- 5g. Major advantages of these sensors include: - Order of magnitude less expensive that other accelerometers. - Configurable, on-chip signal conditioning circuits, - Directly produce a voltage proportional to acceleration The on-chip signal circuits were configured as a second order low-pass Bessel filter with a cut-off frequency of 3kHz. This gives a calibrated and known frequency response, (the sensor has resonance effects over SKhz). Figure 3 shows the accelerometer with its signal conditioning unit built onto a circuit board, (approximately 12mm square). l I Figure 3 The ADXL 1 OS, including signal conditioning unit

Laser \te~o/og~ uur~d \lcrclnne Perfor-nza~ce 141 In the experiments reported in this paper, the ADXL sensors produced results comparable with other types of accelerometer. 4 Investigated machine tool structure The Beaver VC35 is a vertical 3 axis-milling machine used for the chatter tests and was built in 1983. The tool moves in one direction (z-axis) and the machining table moves in two directions (X and Y-axis) on planar guide-ways. The spindle speed can be programmed from 63RPM to 5500RPM and the maximum axis feed-rate is 10 mlsec. It is important to know the sources of forced vibration before cutting tests are carried out since the output of any vibration sensor is the sum of all excitation forces, whether they are random, forced or self-excited. The frequency of forced vibrations can be established by studying all possibilities, where moving parts create periodic forces. The only way to distinguish a periodic excitation force from the vibration output spectrum is to change the amplitude of the suspected source and compare results. Most periodic energy is likely to be due to cutting tooth impact and this force will increase with the depth of cut. Figure 4 shows the vibration during a light cut using a loomm Face Mill (8 cutting edges). The vibration was measured in cutting direction on the spindle housing. The rotational speed of the spindle was 410rpm, which resulted in a tooth pass frequency of 54.5 Hz. In figure 4, the 52Hz component and its harmonics are the forced vibration due to the tooth impact. The amplitude increases, when the excitation frequency hits a resonance of the tool-work-piece structure, (compare this with the modal test later) This result also shows a significant vibration level at exactly 300Hz, which is not a harmonic of the tooth-pass frequency. It has been found that this mechanical vibration is due to the 6 pulse ripple (6x50Hz = 300Hz) generated by the thyristor drive of the spindle motor (DC-Motor). Figure 5 shows the spindle current, which caused this periodic excitation force. Several tests, (with and without load), have further shown that this excitation force, as expected, increases with load (torque). Power Spectrum of accelerometer signal for the 2mm cut at 410 RPM 0.00 500 00 1000.00 1500 00 Frequency (Hz) Figure 4, Power Spectrum for a Light Cut

142 Laser. Iletrolog~ and,shch~ne Pevjor.mcme The spindle current for the 2mm cut at 410RPM Figure 5, Spindle Armature Current for a Light Cut Other potential forced vibration sources such as spindle imbalance and bearing irregularities were not significant in the frequency spectrum and have, therefore not been considered further. 5 Dynamic and static measurements of the cutting process To see the effect of load errors, the machine must operate under cutting conditions and the varying forces applied to the machine tool structure during the cutting operation provide the main source of this error. The effect of this load on machine accuracy will depend on the machine resistance to elastic deformation or stiffness. The task was to measure and interpret self-excited vibrations using different sensors. The dynamic characteristics of the machine can be studied during cutting tests (dynamic, on-line) and Modal analysis (static, off-line). The most appropriate variables for investigating the cutting process would be the cutting force and relative displacement between tool and work-piece, (figure 2.d). However, since this is difficult and expensive to achieve, "on-line", accelerometers (X-,Y- and Z direction) have been positioned on the spindle housing and on the vice, to monitor the cutting process indirectly, (figure 6). Figure 7 shows a simplified model of one axis of the structure and the position of the accelerometers. Figure 6 Experimental set-up Cuning parametem: 01Wmm Face mdl 267mm/mm Feedrate 477RPM Spmdle specd Free culling mdd zwel

1kqTp~$7 Meas~rbromicr Spdba~crbrorda X (uorkpcc) X(rpldk houmg) M(w"rkprr") n"l'~vof-, M(cmcr, Tmi.rp,ndki,nrrurc (,p,d*twq) m% l or=c Figure 7 Simplified model of the dynamic cutting 'I), A,. ~oupbwuitix mchn: rtnrrvrs 5.1 Modal Test (Static) Since chatter always involves excitation of a dominant mode of the structure, the first step of chatter analysis on a machine tool is to measure the kequency response of the structure. The cutting forces act on both the cutting tool and the work-piece with equal but opposite amplitudes and the resulting relative displacement between the two structures can be determined. The Transferfunction between tool and work-piece can be measured experimentally to provide information about the static and dynamic stiffness. [4] There are two main ways to simulate the cutting forces for structural dynamic testing: 1.) Excite the structure with an electromagnetic or electro-hydraulic shaker 2.) Excite the structure with an instrument hammer In both cases, a piezo-electric force transducer measures the input force. Figure 8 shows the experimental set-up for measuring the transfer function using an instrument hammer. The vibration is measured using an accelerometer attached to the tool and the force is acting on the tool but not on the work-piece. The assumption made in this measurement is that the most dominant mode of the whole machine tool structure is the tool itself and that modes in this structure will be excited first under large cutting forces. Ideally the force should act between tool and work-piece with equal amplitudes in both directions and the relative vibration measured. In this case, the transfer-function between tool and spindle housing was determined (Figure 8) using both an instrument hammer and an electro-dynamic shaker. The vibration response was measured by an accelerometer attached to the spindle housing. The result in X direction (cutting direction of the dynamic test) can be seen in figure 8, where the most dominant mode appeared at 460Hz. Figure 8, Measurement of Tool-Sp~ndle housing Transfer Function

144 Laser- \[err-oiogv and \lach~rw Per-/or-nznnce There was no significant difference between the transfer-function measured by the shaker and the impact hammer. 5.2 Cutting Tests (Dynamic) The experimental set-up for the cutting tests is illustrated in figure 6 Up to 3mm depth of cut, the process was stable and the sensor signals showed forced vibration due to the tooth pass frequency and the spindle drive. The 4mm cut was stable, until the whole diameter of the cutter entered the workpiece and then the cutting force reached its stable limit and the machine started to chatter. This was clearly detectable as the vibration amplitude of all sensors increased sharply. The samples of the stable and unstable cut have been averaged and the result can be seen in figures 9.a & 9.b. Power Spectrum of "Y axis" Accelerometer Signal 1.20 1,oo 0.80 0,60 0,40 0.20 0.00 0.00 500.00 1000.00 1500,OO 2000.00 Frequency (Hz) Figure 9.a Stable conditions Power Spdrum of "Y axlr" Accelerometer Slgnal, Figure 9.b Unstable conditions 0,OO 500.00 1000.00 1500.00 200000 Frequency (Hz) The Frequency response of the first half of the cut show forced vibrations due to the tooth pass (63Hz including harmonics) and spindle drive (300Hz). The Frequency response of the unstable cut shows a large frequency component at 460Hz and it was concluded that this was the main chatter signal for this cut. The time response also shows an increase in signal amplitude during chatter and it can be seen that the frequency peaks due to forced vibration sources have almost disappeared. 6 Investigation of the surface-finish The vibrations of the investigated machine can be better understood by comparing the signals of the vibration sensors with the surface finish of the

Laser \tetroloiqr and \lcrcinne Per.for-mance 145 work-piece. The surface finish is arguably the best sensor to see the effect of vibration on machine tools, because it "stores" all the important information of the cut. Figure 10 Image of the work-piece surface after the 4mm cut

146 Lusrr \frtrdogj arzd lluchrne Performonce The vibration frequencies can be calculated from the surface scan using the following formula: tool diameter X spindle speed ' = wavelength of the vlbra~ion The wavelengths were measured using a SURFACESCAN 3D surface measurement instrument, (see figures 11 and 12) and these resulted in the following frequencies: These figures match with the vibration measurements 7 Conclusions A 3-axis milling machine was investigated to identify its dynamic characteristics. Low-cost accelerometers have been designed and calibrated and found to produce results comparable with traditional types. Forced vibration due to the tool impact and spindle motor have been identified as the main vibration sources for a stable cutting process but as a critical depth of cut was reached, chatter vibrations became dominant and this signal could clearly be identified. The vibrations were verified as chatter by crosschecking the results with the work-piece surface finish. The chatter frequency was the same as the most dominant mode of the tool-spindle transfer-function, which was measured using Modal analysis. Having identified relationships between the vibrating parts of the machine structure under chatter conditions, the next task will be to derive an appropriate model for use in a chatter control scheme. One of the biggest difficulties to overcome is the fact that whilst the results show the general form of model required, (i.e. in terms of the number of modes exhibited), the parameters will change under different conditions. For example, the dynamics will vary as the machine table moves along its slides or as the cutting parameters and tool change. On-line real-time parameter estimation techniques will therefore need to be employed. 8 References 1. Altintas, Y., "Manufacturing Automation", Cambridge University Press, 2000 2. Hardwick, B., "Identification and solution of machine tool chatter problems", LAMDAMAP 93, PP 123-140 1993. 3. Koenigsberger, F. and Tlusty, J. "Machine tool Structures", Pergamon Press, Volume 1, 1970 4. Tlusty, J., "Manufacturing Processes and Equipment", Prentice Hall, 2000