Condition Monitoring by Position Encoders

Transcription

1 Condition Monitoring by Position Encoders Max FROMBERGER ; Uwe WEINBERGER 2 ; Bernhard KOHN 3 ; Thanak UTAKAPAN 4 ; Michael OTTO 5 ; Karsten STAHL 6 Gear Research Centre Technical University of Munich, Germany ABSTRACT Detecting damages in machinery before they lead to a complete system failure is an important aim in modern machine maintenance and diagnostics. Early and automated detection of damages in gearboxes allows for longer maintenance intervals, less downtime and lower total costs. One mechanism of gear failure is the occurrence of pitting on the flanks of gear teeth. Pitting progress leads to a change in the noise excitation behaviour of the gear mesh. Common condition monitoring devices rely on acceleration measurements on the gearbox housing. Angular position encoders are capable of providing precise data on transmission error, but work preferably at low rotational speeds. Transmission error is widely used to characterize the tooth flank form. It is a challenge for measurement instrumentation to record and process precise encoder signals sufficient for detecting beginning flank damage at high rotational speeds. An FZG spur gear test rig used for gear pitting tests was equipped with angular position encoders and data acquisition units. This sensorial equipment is capable of performing synchronous, high-frequency combined measurements of angular positions of the shafts and acceleration signals on the gear housing. A detailed evaluation shows that an early damage detection with position encoder signals is possible. Keywords: Gears, Machine Diagnostics, Measurement Instrumentation I-INCE Classification of Subject Numbers:..3, 72.9, INTRODUCTION This paper covers the acquisition of acceleration and full-speed absolute angular position data from gear test rigs as well as a possible use for these measured variables: gear damage detection. In the following chapters an overview on the basics of common test rig data acquisition (acceleration signals and angular position signals) is given. Additionally a feasibility test to employ the presented measuring method in failure detection is presented. 2. EVALUATING THE NOISE EXCITATION BEHAVIOR OF GEARS: TRANSMIS- SION ERROR A widely spread way of evaluating the noise excitation behavior of a gear mesh is measurement or calculation of the loaded transmission error (LTE) of the mesh. Gregory et al. () and Baethge (2) proposed using the LTE to evaluate the excitation behavior, Baethge (2) showing a relation between airborne sound and the transmission error. The LTE indicates the non-uniform part of the rotary motion transfer from one meshing gear to the other. The LTE as the name implies is defined for non-zero torque. The LTE is typically defined quasi-static (n 0). fromberger@fzg.mw.tum.de 2 weinberger@fzg.mw.tum.de 3 kohn@fzg.mw.tum.de 4 utakapan@fzg.mw.tum.de 5 otto@fzg.mw.tum.de 6 fzg@fzg.mw.tum.de 6565

2 The simulated and measured LTEs in this paper have the unit millimeter, and are defined as the sum of angular gear positions (ϕ) relating to the involute base diameter (d b ) of the corresponding gear (see eq. ). x = ϕ db 2 + ϕ 2 db2 2 () 2. Calculating the Transmission Error Several software programs are capable of calculating the LTE for a spur gear pair. For example, Inalpolat, Handschuh et al. (3) developed a torsional dynamic model for simulating quasi-static and dynamic transmission error signals based on measured LTEs from a test rig. As the LTE is defined quasi-static, the acceleration and velocity terms of the equation of motion are becoming zero. The LTE is then depending on mesh stiffness and external load. In general loaded gear pairs show a non-uniform transfer of rotary motion from one gear to the other. This is caused by variable mesh stiffness, which is mesh position dependent. In figure the relationship between mesh position and mesh stiffness is shown: single tooth stiffness depends on the position of the point of contact, which defines the length of the bending lever arm. Additionally the number of meshing teeth depends on the mesh position. Transitions between single and double engagement show as discontinuity points in the graph of c s in figure. Wheel Wheel Pinion Wheel Pinion 2 Wheel Pinion 2 Wheel 3 Pinion Pinion Tooth stiffness 2 Angular position c = Stiffness of single tooth c s = Stiffness of mesh c = mean stiffness of mesh Figure : Relationship between tooth contact position and mesh stiffness In figure 2a multiple software-generated LTEs for multiple loads of a gear mesh are shown. They have been calculated by the software program DZP (4). DZP has been developed and enhanced during several research projects that were funded by the German Federal Ministry for Economic Affairs and Energy (BMWi) and the German Power Transmission Research Association (FVA). In this example the range of variation has a minimum for one specific value of torque. In figure 2b a spectral view of the LTE is shown, amplitudes being correlated to gear mesh orders. Transmission error / mm 0 2 Time t/t 0 Transm. error ampl. / mm 0 3 Gear mesh order (a) Transmission error for different loads (b) spectral view Figure 2: Loaded transmission error and the corresponding spectrum 6566

3 2.2 Measuring the Transmission Error In addition to simulating, the LTE can be measured by means of angular position sensors while revolving the gears at slow rotational speed. This is often done with the help of incremental angular encoders at pinion an wheel shafts, although other techniques exist: for example Zhao-yao, Xiao-ning et al. (5) recently developed an LTE measuring device following the single-flank rolling principle utilizing a high precision spindle. With one angular encoder on each shaft of two meshing gears and knowledge of the base diameters of the gears, the measured LTE can then be derived from the measured angular position signals acc. to eq.. In figure 3 an extract of a measured LTE covering five mesh periods is shown. This signal has been filtered to remove low-frequency signal components coming from e.g. shaft imbalance. It has been measured at a revolution speed of around 60 min. Transmission error / mm Time t /s Figure 3: Measured loaded transmission error 3. ENHANCING THE ANGULAR MEASUREMENT CAPABILITIES OF GEAR TEST RIGS As mentioned in the previous section, transmission error measurements are often conducted with incremental encoders. The available encoders often require a trade-off between number of increments and maximum rotational speed, as the increment detecting sensor hardware is limited to a certain count of increments per second. Beyond the maximum specified rotational velocity a sensor can e.g. miscount increments. This can limit LTE measurements by incremental encoders to low angular velocity. Recently, robust angular encoders capable of measuring absolute angle values became available. Those angular values are often transmitted to the host as digital TTL signals, complying with encoder protocols like SSI or BiSS. Instead of counting increments, they offer a fixed measurement frequency and are often compatible with high speeds up to several thousand revolutions per minute, whilst offering high accuracy up to a few angular seconds of error. Table : Technical properties of used angular encoder (6) Property Value type optical, absolute max. operating temperature 80 C system accuracy (angular seconds) ±3.82 max. measurement frequency ca. 25 khz electric signal 5V TTL data protocol BiSS 6567

4 To be equipped at FZG gear test rigs, an angular encoder consisting of a sensor head and a bar code ring has been chosen. The sensor head optically captures and evaluates a seamless bar code on the ring, which is designed to be unique for every possible section the sensor head can have in its field of view. The technical properties of this encoder system are summarized in table. The rings were mounted as close to the test gears as possible in order to minimize transfer path influences from the point of excitation (the gear mesh) to the point of measurement. Figure 4 shows the test gear case of a standard FZG test rig with attached absolute angular encoders (on the left in the photo). Figure 4: Gear test rig: test gear case and angular encoders 4. FULL-SPEED TRANSMISSION ERROR EVALUATION With the installed angular position encoders LTE measurement at full revolution speed is possible. Figure 5 shows a LTE signal measured at full revolution speed of 2250 min at the pinion shaft. Transmission error / mm Time t /s Figure 5: Measured loaded transmission error at full speed Because of the higher angular velocity of this measurement (compared with the LTE measurement in Figure 3 that has been measured at around 60 min ), less angle measurements per shaft revolution can be captured when measurement frequency is assumed constant. This results in a more coarse resolution of single 6568

5 meshing periods in the LTE signal sequence. Specific orders, e.g. gear meshing order, eventually exceed the frequency limit of the corresponding spectrum if rotational speed is increased. In general low-speed and high-speed LTEs of the same gear mesh are not identical, as dynamic effects come into play with increasing speeds: for example resonance elevation or phase shifting can occur. 5. PITTING DAMAGE DETECTION 5. Pitting Failure Mode of Gears General Aspects of Gear Failure Like many other machine elements, gears have to be designed to withstand the designated strain. If a gear is not capable of sustaining a certain strain (i.e. power being transferred from one gear to another meshing gear), several mechanisms of failure can occur. Some gear failure mechanisms proceed slowly over time, others lead to a near-immediate failure of the gear. Whether a damage occurs and from which failure mechanism it results depends on numerous influence factors, some of them being: gear macro geometry: defined by e.g. teeth count, gear module, face width, profile angle and profile shift, the macro geometrical shape of a gear determines values like radii of curvature and bending lever arms which are relevant to damage mechanisms. gear micro geometry: with local modifications of the tooth flank topology more evenly spread flank pressure distributions can be achieved. material properties like alloy composition, gradient of hardness and grain sizes have influence on e.g. the highest permanently endurable Hertzian pressure in the tooth contact. composition and temperature of the used lubricant along with film thickness of the lubricant has influence on several gear failure mechanisms. the applied load spectrum (time dependent rotational speed and torque) results in varying Hertzian pressure values and stresses at the tooth fillet. Characteristics of Pitting Failure Mode A gear flank photography of a pitting defect is shown in Figure 6. Pitting defects are caused by local material Figure 6: gear flank photography showing pitting damage fatigue on gear flanks, when the material strength gets surpassed by the local rolling contact strain. Pitting defects are characterized by shell-shaped material losses. They mainly occur in gear contact regions where the relative sliding velocity of two meshing gears reaches negative values, hence in the flank area below the pitch circle. Standardized Pitting Test For the standardized pitting test pitting test gears designed to specifically generate pitting defects are used. These gears are mounted in an FZG back-to-back gear test rig (see figure 7) which can load the test gears with 6569

6 test wheel torque indicator electric motor retransmission stage loading clutch test pinion Figure 7: FZG standard gear test rig (left: perspective sketch, right: schematic diagram) defined torque and apply defined rotational speeds. The test rig is also capable of controlling the temperature of the applied transmission oil. The FZG test rig consists of a two-shaft setup with two gear stages: one test gear pair, and another gear pair (the retransmission stage) with the same transmission ratio, closing the power loop. Static torque can be inserted into the two-shaft loop with a loading clutch during standstill. To do this, one half of this clutch is fixed to the test rig platform and the other half is twisted, e.g. by using a lever with defined weights (see figure 7). As power is transferred from one shaft to the other in the testing stage and then back to the first shaft in the retransmission stage, the electric motor has to provide just the dissipating power, not the total power transferred through the gear stages. The standardized pitting test procedure can be performed on the aforementioned back-to-back test rig. Testing and evaluation conditions are defined in (7): before the actual pitting test a running-in phase takes place after the running-in procedure pitting test runs are performed en bloc. The gears are inspected for damage after each block of load cycles. 5.2 Damage Detection: Feasibility Test Utilizing the now available full speed angle signals, a feasibility test for detection of pitting damage was conducted. Therefore, in addition to the angular encoders piezoelectric acceleration sensors were mounted on the test gearbox case of an FZG test rig. Using a common time axis, synchronous acceleration and angle measurements with a duration of five seconds and an interval of ten minutes were gathered. The acceleration signals were then based on the angular sensor s data split, assigned to single teeth of the test pinion, and recomposed to now discontinuous per-tooth sub signals. This is schematically shown in figure 8 for a hypothetical gear with a tooth number of three. Subsequently a relative signal power value L s according to Ohm (8) for each of the sub signals was calculated and observed over the course of measurements. Signal power L s is defined in equation 2, with s(t) 6570

7 case acceleration tooth x tooth y tooth z tooth x tooth y shaft angle tooth z Figure 8: schematic representation of initial acceleration signal for all pinion teeth (left), split into discontinuous per-tooth signals (right) being the signal value at the time t. L s = lim T 2T T T s(t) 2 dt (2) Figure 9 shows the the development of per-tooth signal power values over time for one actual exemplary pitting test run. The four colored lines show the four signals with the highest arithmetic mean value of power, representing the four teeth with the presumably highest level of noise excitation. The other teeth s signals are uniformly drawn as black dotted lines. signal power between lines: about 5 hrs tooth 4 tooth tooth 6 tooth 3 Day - 6:48 Day - 9:2 Day - 2:36 Day 2-00:00 Day 2-02:24 Day 2-04:48 Day 2-07:2 time Figure 9: tooth-specific signal power values At the end of the shown time span the test rig was shut down automatically by an external vibration monitor (pre-loaded leaf spring system) connected to the test rig s PLC. This vibration was induced by heavy pitting of the test pinion. Several conclusions can be drawn from the shown signal power graphs: 657

8 during non-damaged operation the per-tooth power signals show a repeatable and low level, i.e. an acceptable signal-to-noise ratio significant signal power gain occurs several hours before vibration monitor shutdown (e.g. ca five times higher signal level compared to non-damaged level at teeth 4 five hours before shutdown). non-damaged teeth are staying at low signal levels for the whole time of measurement, thus proving the per-tooth signal splitting an adequate instrument of tooth-specific diagnosis. Note: the signal power values are shown without unit. Because the values only allow for a relative evaluation, no calibration data has been taken into account. Figure 0 shows photographies of the examined test pinion. The real flank damage location generally fits the signal values, although some deviation exists: e.g. tooth 5 though physically mostly intact shows relatively high levels of signal power towards the end of the experiment. Possible explanations for this include: no exact alignment of angular tooth positions under static load was performed: the actual tooth number of a damaged tooth was of minor importance in the conducted research. the test gear mesh s transverse contact ratio is >. This means, on average there is more than one tooth pair in contact and vibration generated by one specific tooth is not clearly separable from vibration induced by its neighbor teeth. #3 #5 #4 #6 Figure 0: photographies of damaged test pinion and some of its tooth flanks 6. SUMMARY This paper presents a way of measuring absolute angular positions of gear test rig shafts at high rotational speeds. As a possible use for this kind of measurement, a feasibility study regarding the detection of pitting damage has been conducted, showing that detecting pitting with means of full-speed acceleration and angle measurement is generally possible. 6572

9 REFERENCES. R. Gregory, S. Harris, and R. Munro. Dynamic behaviour of spur gears. In Proc. Inst. Mech. Eng., Vol. 78 Pt I No 8, S Inst. Mech. Eng, J. Baethge. Drehwegfehler, Zahnfederhärte und Geräusch bei Stirnrädern. PhD thesis, TH München, M. Inalpolat, M. Handschuh, and A. Karaman. Impact of indexing errors on spur gear dynamics. GEARTECHNOLOGY, pages 64 70, Forschungsvereinigung Antriebstechnik e.v. (FVA), Frankfurt/Main. FVA-Heft Nr. 937: DZP, Version 5.0 und DZPopt, Version 2.0, S. Zhao-yao, L. Xiao-ning, C. Chang-he, and L. Jia-chun. Development of transmission error tester for face gears. In Proceedings of the Sixth International Symposium on Precision Mechanical Measurements, RENISHAW plc. RESA absolute angle encoder, data sheet, T. Radev. Entwicklung eines praxisnahen Pittingtests. FVA Informationsblatt Nr. 37, Frankfurt am Main, J.-R. Ohm and H. D. Lueke. Signalübertragung. Springer, Berlin, Heidelberg,