GEAR TEST RIG FOR NOISE AND VIBRATION TESTING OF CYLINDRICAL GEARS

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1 GEAR TEST RIG FOR NOISE AND VIBRATION TESTING OF CYLINDRICAL GEARS Mats Åkerblom Volvo Construction Equipment Components AB SE Eskilstuna, Sweden Abstract Gear noise is sometimes the dominating noise in commercial vehicles. Noise testing of complete gearboxes is very time-consuming and expensive. A test rig has been designed for testing gears under controlled conditions. The test rig is of the recirculating power type. Finite element analysis has been used to predict the dynamical properties of the gear test rig. Experimental modal analysis has been carried out on the gearbox housing to verify the theoretical predictions of natural frequencies. The test rig can be used for noise and vibration testing of gears with different manufacturing errors and different design parameters. In addition to noise testing, the rig can be used for gear life testing and measurement of efficiency. Keywords: gear, noise, vibration, test rig, modal analysis 1. Introduction In commercial vehicles and construction machines, for example wheel-loaders, gear noise from the transmission is sometimes the dominating noise. Even if the gear noise from the transmission is not the loudest, the pure high frequency noise can easily be distinguished from other noise sources, and noise of this kind creates an impression of bad quality. In order not to be heard, gear noise must be db below other noise sources, for example engine noise. One approach to reduce noise from gears is to produce more accurate gears, usually this means that the manufacturing method must be changed and the cost increases. Besides the gear accuracy, also the dynamic properties of the gears, shafts, bearings and the gearbox housing are important for the noise level from a gearbox, [2] and [3]. Since noise testing of complete gearboxes is very time-consuming and expensive, a test rig has been designed and built to allow noise testing of gears in a controlled environment. The test rig can be used for noise and vibration testing of gears with different manufacturing errors and different design parameters. In addition to noise testing, the rig can be used for gear life 1

2 testing and measurement of efficiency. The experimental noise and vibration measurements will be used to verify different theoretical prediction methods, for example calculations of transmission error, finite element models and multi-body system dynamic models. 2. Design of the test rig The design process started with evaluation of different test rig principles. Due to that the test rig will also be used for gear life testing, which requires high torque and high speed during long time, some kind of power recirculation was desirable. The principle for recirculation of power usually used in test rigs of this kind is electrical, hydraulic or mechanical recirculation. The mechanical principle was chosen because of the relatively low cost and high performance. It is possible to have a high power circulating between the gearboxes and use a relatively small electric motor for driving the rig, replacing power due to power dissipation in the gearboxes. The test rig consists of two identical gearboxes, connected to each other with two universal joint shafts. A torque is applied by tilting one of the gearboxes around one of its axles. This tilting is made possible by bearings between the gearbox and the supporting brackets. A hydraulic cylinder creates the tilting force. The torque is measured with a load sensor placed between the cylinder and the gearbox. Hydraulic Cylinder Slave or Master Gearbox Electric Motor Load Sensor Test Gearbox Microphone Articulated Attachment Figure 1. Sketch of test rig. Accelerometer The noise will be measured with one or more microphones and vibrations will be measured with accelerometers on the gearbox housing. Free shaft ends on the test gearbox makes it possible to measure transmission error with optical encoders or measure rotational vibrations with accelerometers. There might be a risk that the slave gears interfere with the test gears when noise is measured [1]. To reduce this risk, the slave gearbox will be equipped with extra wide precision ground gears and the test gearbox can be shielded off from the rest of the test rig. The gearboxes are mounted on a concrete bed, which is placed on rubber blocks to insulate from vibrations. Each gearbox has its own oil-system with the possibility to filter and control the temperature of the oil. The vibrations that cause noise are induced in the gear-mesh and then transmitted through the gears, shafts and through the bearings to the housing, which vibrates and emits noise. To reduce the influence of the housing, test rig gearboxes are often made of thick welded steel plates and very rigid. In this test rig the intention is to include the influence of the housing in the investigations. Therefore the shafts, bearings and housing have been designed to be as 2

3 similar in character as possible to a wheel-loader transmission. This is achieved by using gears, shafts and bearings from an existing gearbox and making the housings of the same material (nodular iron) and thickness similar to the housing of a wheel-loader transmission. Figure 2. Test gearbox (CAD model). 3-D CAD was used for the design of the housing and rapid prototyping was used to create a model in plastic, which was used as a casting model. With this method it is possible to make small series of cast parts at a relatively low cost. The test gears can be seen as some kind of average gears in a wheel loader transmission. The test gears have technical data according to table 1. pinion gear Number of teeth Normal module (mm) Pressure angle 20º 20º Helix angle 20º 20º Centre distance (mm) Face width (mm) Profile shift coefficient Tip diameter (mm) Table 1. Technical data for test gears. The centre distance can be changed from to mm by turning the eccentric covers (see figure 2 and 4) 180 º. The centre distance 160 mm is chosen to allow testing of another existing gear-pair. An arbitrary centre distance between 160 and 192 mm can be obtained by making new covers. In addition to noise and vibration testing the gear test rig can be used for gear life testing and measurement of efficiency. The measurement of efficiency is possible by measuring the torque and rotational speed of the shaft from the electric motor. This power corresponds to the 3

4 power dissipated in the gearboxes. Possible investigations can be how different oils, surface finish, surface treatment or gear geometry influence the efficiency. Figure 3. Gear test rig. Figure 3 shows the complete test rig and its technical data are listed in table Theoretical modal analysis Torque Nm Rotation speed rpm Power of electric motor 110 kw Maximum power through gearboxes 1400 kw Oil temperature ºC Table 2. Technical data for the test rig. Finite element analysis has been used to predict the natural frequencies and mode shapes for gears with shafts, the empty housing, the complete gearbox and finally for the complete test rig. Figure 4. FE model of the gearbox with gears, shafts and bearings. 4

5 In the figures 5 and 6 some examples of mode shapes and corresponding frequencies are shown. Boundary conditions for the housing are free free, and for the gear and shaft the bearing outside diameter is fixed. Mode 1, 1895 Hz Mode 2, 2169 Hz Mode 3, 2676 Hz Figure 5. The first three natural frequencies and corresponding mode shapes for one of the gears mounted on the shaft and with bearings included (displacements not to scale). Mode 1, 900 Hz Mode 2, 1098 Hz Mode 3, 1215 Hz Figure 6. The first three natural frequencies and corresponding mode shapes for the housing (displacements not to scale). The modal analysis of the complete gearbox resulted in about 30 natural frequencies in the frequency range Hz. It is of course difficult to draw conclusions from these results but they will be valuable for the evaluation of the measurement results. The FE-model of the complete gearbox was also used in a harmonic response analysis. A sinusoidal varying force was applied in the gear mesh and the corresponding vibration amplitude at a point on the gearbox housing was predicted. The frequency was swept from 1000 Hz to 2500 Hz. In this frequency range the amplitude has a number of peaks, see fig. 7. The peak at 1895 Hz corresponds to the first mode of gear on shaft, see fig. 5. 5

6 2190 Hz Amplitude at this point Z-dir 1540 Hz 1895 Hz X-dir. Y-dir Figure 7. Example from the response analysis results. 4. Experimental modal analysis Experimental modal analysis has been carried out on the empty gearbox housing without shafts and gears. When comparing the results from the experimental modal analysis with the results from the FE predictions, the five first modes from the FE predictions could be identified. Mode # Measured frequency (Hz) FE predicted frequency (Hz) Error in predicted frequency % % % % % Table 3. Comparison between experimental and FE modal analysis. The experimental modal analysis shows, see table 3, that it is possible to predict natural frequencies for the housing, with FE analysis, at least in the frequency range Hz, with an error less than 10 %. 5. Summary 1000 frequiency (Hz) 2500 A gear test rig has been designed and built. The test rig will be used for gear noise and vibration testing. Finite element analysis has been used to predict the natural frequencies and mode shapes for individual parts and for complete gearboxes. Experimental modal analysis has been carried out on the gearbox housing and the results show that the FE predictions are in good agreement with measured frequencies. 6

7 6. Acknowledgements The author would like to thank The Program Board for the Swedish Automotive Research Program for financial support, Alfgam Optimering AB for performing FE analysis and Ingemanson Technology AB for performing experimental modal analysis. 7. References [1] Houser D. R., Blankenship G. W., Methods for Measuring Gear Transmission Error Under Load and at Operating Speeds, SAE Technical Paper , [2] Hellinger W., Raffel H. Ch., Rainer G. Ph., Numerical Methods to Calculate Gear Tranmission Noise, SAE Technical Paper , [3] Campell B., et al., Gear Noise Reduction of Automatic Transmission Trough Finite Element Dynamic Simulation, SAE Technical Paper ,