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Experimental study on transmission rattle noise behaviour with particular regard to lubricating oil
Journal of Sound and Vibration 341 (2015) 195–205
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Experimental study on transmission rattle noise behaviour with particular regard to lubricating oil Axel Baumann n, Bernd Bertsche Institute of Machine Components, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
a r t i c l e i n f o
abstract
Article history: Received 30 January 2014 Received in revised form 8 December 2014 Accepted 13 December 2014 Handling Editor: A.V. Metrikine Available online 13 January 2015
This article presents an experimental study on the gear rattle noise phenomenon of automotive transmissions. A single-stage gear transmission has been designed and applied to a gear rattle noise test bench. The gear transmission allows the variation of several parameters affecting the rattle noise level, e.g. tooth backlash variation. High resolution incremental encoders on the transmission input and output shaft, as well as on the idler gear, enable the acquisition of the angular relative motion of the gear pair within the range of tooth backlash. The angular relative motion evaluates the sequence of meshing gear teeth along the path of contact under rattling conditions. The analysis of the angular relative motion indicates that gear tooth impacts during rattling lead to elastic deformation of meshing gear pairs. High contact forces during impacts cause Hertzian flattening of gear tooth flanks and rising fluid viscosity with pressure in the contact zone (elastohydrodynamic lubrication regime). The elastic deformation of meshing gear pairs lead to deviations from the angular velocity ratio between two gears of a gear pair and thus from the Law of Gearing. The main source for the gear rattle noise level is the additional presence of meshing impacts at the beginning of each gear pair meshing. Gear rattle noise reduction can be achieved by avoiding meshing impacts, e.g. by using low traction gear lubricants. & 2014 Elsevier Ltd. All rights reserved.
1. Introduction Noise reduction is an important objective in passenger car development. Automotive transmissions are one of the main sources for the vehicle interior noise. Caused by downsizing and downspeeding of internal combustion engines, the torque fluctuation at the crankshaft induces torsional vibrations in the powertrain it is connected to [1]. Due to unbalanced gas and inertia forces from motion of pistons the rotational speed of internal combustion engines is not uniform it is superimposed by torsional vibrations. The rotational speed of an internal combustion engine can be approximated by a composition of a constant average speed, which is the first engine order, and thus the nominal speed of the crankshaft, superimposed on a sinusoidal oscillation with a frequency according to the main engine order. The main order of the torsional vibrations is the ignition frequency that is the result of engine firing order and number of cylinders. The 4-cylinder 4-stroke engine, which is widely used in passenger cars, has the second engine order as its main engine order [2]. The angular acceleration amplitude is crucial for the intensity of torsional vibration, and therefore for the gear rattle noise level of automotive transmissions.
n
Corresponding author. Tel.: þ49 711 68566170; fax: þ 49 711 68566319. E-mail address: [email protected] (A. Baumann).
http://dx.doi.org/10.1016/j.jsv.2014.12.018 0022-460X/& 2014 Elsevier Ltd. All rights reserved.
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Nomenclature CAD HC PAK
PAO PG TTL
computer-aided design hydrocracked oil Pruefstand-Akustik-Messsystem (Registered trademark of Mueller-BBM VibroAkustik Systeme GmbH) poly-alpha-olefin polyalkylene glycol transistor–transistor logic
List of abbreviations Leq
Δθ θ1 θ2 dw1 dw2 z1 z2
β
mn an jt t
relative angle of gear pair [1] or [rad] input shaft angle [1] or [rad] output shaft angle or idler gear angle [1] or [rad] pitch circle diameter of fixed gear [mm] pitch circle diameter of idler gear [mm] number of teeth fixed gear [dimensionless] number of teeth idler gear [dimensionless] helix angle [1] normal module [mm] normal angle of pressure [1] gear tooth backlash [mm] time [s]
continuous sound-pressure Level [dB(A)]
Manual transmissions, automated manual transmissions and dual clutch transmissions are particularly sensitive to gear rattle noise, which arises from oscillations of loose (unengaged) gear pairs with working clearance, e.g. idler gears, synchronizer rings and gearshift sleeves [3,4]. The particular sound character of gear rattle noise sounds like a marble rattling in a tin and distinguishes it from other sources of vehicle noise. This metallic type noise, which is disconcerting to the vehicle occupants as well as other road users nearby, leads to customers' complaints. For this reason, gear rattle noise behaviour of automotive transmissions has to be taken into account at an early product development stage. Gear rattle noise reduction can be achieved by using custom-made gear lubricants. The authors investigated the influence of various gear lubricants on the gear rattle noise level of a 5-speed manual transmission for front-transverse use. Different base oil and additive formulations at about the same oil viscosity were studied. The measurements taken show that gear lubricants based upon polyalkylene glycol are particularly good at reducing the rattle noise level of a manual transmission up to 6 dB(A) at commonly low kinematic viscosity characteristics to reduce drag torque [5,6]. Drag torque measurements show improvements of the transmission efficiency under loading and idle conditions with a water-soluble polyalkylene glycol, when compared to a standard mineral oil [7]. The excellent gear rattle noise damping capabilities of water-soluble polyalkylene glycol are investigated and compared to mineral oil in this article. A single-stage gear transmission has been designed and applied to a gear rattle noise test bench to compare both gear lubricants. Idler gear vibrational behaviour due to torsional excitation at the transmission input shaft is studied by acquisition of the angular relative motion of the gear pair. The basic idea to use the angular relative motion along the path of contact for evaluation of the sequence of meshing gear teeth has been suggested by other authors. Rach takes measurements of an oscillating idler gear in an experimental gear transmission. Low resolution Hall sensors are used to measure the rotary motion of the idler gear [8]. Brancati describes an experimental test set-up with high resolution incremental encoders for determination of the relative angular motion. Previously obtained simulation results are validated by these measurements [9]. Variation of the lubrication mechanism, from oil jet lubrication to dry contact, enables detection of double sided impacts of the idler gear [10]. Other researchers have also carried out the study of lubrication effects on the gear rattle noise phenomenon. Tangasawi considers the gear lubricant behaviour as a nonlinear spring damper affecting the response of idler gears during a meshing cycle. Oil viscosity matters as an important factor, which governs the vibrational behaviour of a transmission [11]. De la Cruz provides detailed analytical models of lubricated conjunctions in a multi-body dynamics simulation of a transaxle 7-speed transmission under creep rattle conditions. The results show the important role of the regime of lubrication in lightly loaded conjunctions, increasing the propensity to rattle at higher temperatures because of lower lubricating oil viscosity [12]. Theodossiades includes the effect of lubrication in his approach to understanding the interactions between the transmission gears during engine idle conditions. The influence of the lubricant on torsional vibration of lightly loaded idling gears, which promotes iso-viscous hydrodynamic conditions, is examined [13]. Crowther presents a nonlinear model for investigation of idler gears' oscillation response due to torsional excitation by an internal combustion engine. The idler gear moves back and forth within the range of tooth backlash and multiple impacts occur both on traction and thrust tooth flanks [14]. The main disadvantage of using high viscous lubricating oils to reduce the gear rattle noise level is the reduction of the transmission efficiency in the case of loaded engaged gears and thus an increase of fuel consumption of the vehicle. The present article picks up research results obtained by other authors and further contributes to the understanding of meshing gear teeth vibrational behaviour along the path of contact under rattling conditions. The following research results are found in an experimental study where lubrication effects are taken into consideration as well. 2. Test set-up for experimental study The test set-up for the experimental study and the single-stage gear transmission for rattle noise measurements are described in the following section.
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2.1. Gear rattle noise test bench The test bench used was designed to investigate the gear rattle noise phenomenon of automotive transmissions. A schematic layout of the test bench is shown in Fig. 1. The drive motor – a highly dynamic, permanent-field three-phase synchronous motor – and the testing transmission are mounted coaxially on the test bench frame. The drive motor shaft is connected to the transmission input shaft via torsionresistant shaft couplings. An identical brake motor can be coupled to the transmission output shaft for simulation of driving and overrun operating conditions. The test bench is set up in a sound-absorbing environment to simulate anechoic conditions for sound-pressure level measurements [15]. An incremental encoder is fixed to the transmission input shaft for rotational speed measurement and actual value acquisition for the closed-loop control of the drive motor. Another identical incremental encoder is fixed to the transmission output shaft. Rotary movement of the idler gear can be measured via Hall sensor by contactless scanning of a toothed impulse wheel [15]. Fig. 2 shows the test set-up of the gear rattle noise test bench with the single-stage gear transmission including positions of the incremental encoders. All measurement signals are recorded synchronously by a Mueller-BBM PAK data processor. Sound-pressure levels are measured at three defined positions in 1 m distance vertical to the transmission housing surface at a sampling rate of 51.2 kHz. The positioning of the microphones allow recording of rattle noise in the far field of the gear transmission. The continuous sound-pressure level Leq is plotted versus the angular acceleration amplitude of the transmission input shaft.
Fig. 1. Schematic layout of gear rattle noise test bench.
Fig. 2. Test set-up of gear rattle noise test bench with single-stage gear transmission.
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Fig. 3. Schematic and 3D CAD model of single-stage gear transmission. (1) Fixed gear; (2) idler gear with toothed impulse wheel; (3) input shaft; (4) output shaft; (5) synchronizer.
This diagram is called a rattle-curve. It is used for transmission rattle noise evaluation and comparison between each other. Housing acceleration is measured at a sampling rate of 25.6 kHz on the transmission housing surface for identification of impacts which are in direct time dependence on the torsional vibration excitation [16]. A sinusoidal excitation with varying amplitude and a frequency according to second rotation order (30 Hz) is superimposed on the constant input shaft rotation of 900 rev/min in all measurements to simulate conditions arising in a 4-cylinder 4-stroke engine. The main engine order of fluctuations for such an engine is the second engine order [2]. 2.2. Design of single-stage gear transmission The single-stage gear transmission consists of one gear pair with a synchronizer for the idler gear on the output shaft. A schematic and CAD model of the gear transmission are shown in Fig. 3. The input shaft includes the fixed gear, which is mounted on the shaft by a spline shaft connection. The idler gear and the single-cone synchronizer are mounted on the output shaft. The idler gear can rotate relative to the output shaft by a needle‐roller bearing. The synchronizer body with the gearshift sleeve is fixed to the output shaft and guides the synchronizer ring. Two different states of the gearshift mechanism are possible. First of all, a non-shifted condition is possible when the gearshift sleeve is not connected to the idler gear. The output shaft is standing still in this case. Secondly, a shifted condition is possible when the idler gear is positive-engaged with the output shaft. If the idler gear is connected to the synchronizer body, the output shaft rotates according to the gear transmission ratio. The following measurements cover non-shifted condition as well as shifted condition whereby the idler gear is connected to the output shaft. Both transmission shafts are guided by ball and roller bearings with a special cover construction in the transmission housing. The bearings of the output shaft are fixed in eccentric covers to vary the transmission centre distance and, therefore, tooth backlash. The housing itself is mounted on the test bench and contains oil to lubricate and cool the transmission [7]. 2.3. Acquisition of relative angular motion Photoelectric incremental encoders at a sampling rate of 25.6 kHz measure the rotational speeds of both transmission shafts. Each incremental encoder consists of two marked discs with 10,000 marks per revolution. TTL-signals are available as output signals, which are processed by the Mueller-BBM PAK data acquisition system. Angle, angular velocity and direction of rotation can be determined by the subsequent analysis of pulse number, pulse frequency and phase relation. The difference between the angle of the input shaft and the output shaft in the shifted condition yields the so-called relative angle of the gear pair. A toothed impulse wheel is fixed to the idler gear for acquisition of the idler gear relative motion.
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A magneto-resistive sensor fixed to the interior transmission housing scans the toothed impulse wheel. In the non-shifted condition, the relative angle of the gear pair can also be obtained with this measurement set-up [16]. The relative angular motion of an unloaded gear pair is the difference between the greatest and smallest deviation during gear meshing in circumferential direction, also known as transmission error. Relative angular motion corresponds to deviations of the driven idler gear in relation to its constant rotation. The smaller the relative angular motion, the more uniform the rotary motion of the idler gear. As soon as the fixed gear begins to vibrate, the torsional oscillation of the idler gear leads to relative angular motion during gear meshing. Consequently, deviations from the usual kinematic rotational relationship between the gear pair can be observed when impact dynamics is involved [7]. The evaluation of the relative angle of the gear pair Δθ on the pitch circle is expressed as Δθ ¼ θ2 −θ1
dw1 dw2
(1)
with the input shaft angle θ1 and output shaft angle θ2 in shifted condition given by the incremental encoders, respectively the idler gear angle θ2 in non-shifted condition given by the Hall sensor and the toothed impulse wheel. dw1 and dw2 are the pitch circle diameters of the fixed gear and the idler gear, respectively. By using the Law of Gearing Eq. (1) becomes
Δθ ¼ θ2 θ1
z1 z2
(2)
with the number of teeth of the fixed gear z1 and number of teeth of the idler gear z2 . Fig. 4 shows the relative angular motion of the gear pair with different vibration excitations at the transmission input shaft. Gear tooth flanks of the fixed and idler gear are in constant mesh during normal operating conditions at 0 rad s 2. Slight deviations in the relative angle are caused by eccentricities of the fixed gear on the input shaft due to manufacturing errors. Under rattling conditions at 1500 rad s 2, a movement of the idler gear within the range of tooth backlash takes place. The gear tooth flanks are in mesh on their traction flanks at positive values of the relative angle. The negative values of the relative angle correspond to the meshing of the gear tooth flanks at their thrust flanks consequently. The meshing gear tooth flanks have no contact within the range of tooth backlash. A vibration of the idler gear within the range of tooth backlash can be detected depending on the level of vibration excitation at the transmission input shaft in Fig. 4. 2.4. Parameter study on gear rattle noise level Two different gear lubricants are investigated regarding gear rattle noise level in the single-stage gear transmission. PAO/ HC1 is a fully formulated mineral base oil with a commonly used additive package for use in manual transmissions. The dynamic oil viscosity of PAO/HC1 is 9.03 mPa s at 80 1C. PG3 is a polyalkylene glycol for use in worm-gear transmissions. Dynamic oil viscosity of PG3 is 10.44 mPa s at 80 1C and, therefore, almost comparable to PAO/HC1. The oil level was adjusted at the lowest root diameter of the idler gear under static conditions in all measurements. Gear pairs with β ¼ 01 and β ¼ 201 are available for investigation of different helix angles. All gear wheels have a normal module of mn ¼ 2 mm and the normal angle of pressure is an ¼ 201. The transmission ratio of straight-cut spur gears is 0.639 using z1 ¼ 61 and z2 ¼ 39. Helical-cut spur gears provide a transmission ratio of 0.638 with z1 ¼ 58 and z2 ¼ 37. The value of tooth backlash is one of the significant influencing variables on gear rattle noise level of automotive transmissions. Tooth backlash reduction leads to minimization of gear rattle noise level [4]. In contrast, a minimum value of tooth backlash is needed to prevent the jamming of meshing gear teeth under all operating conditions. Tooth backlash jt is defined as the length of the pitch-circle arc which the idler gear can rotate relative to the fixed gear in-between traction and
Fig. 4. Relative angular motion of idler gear with excitation amplitude of (a) 0 rad s 2 and (b) 1500 rad s 2.
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thrust gear tooth flanks. The tooth backlashes jt ¼ 0:189 mm and jt ¼ 0:375 mm are investigated when using straight-cut spur gears. The values for tooth backlash for helical-cut spur gears are jt ¼ 0:198 mm and jt ¼ 0:388 mm. These values were measured under static conditions by using a lever arm and dial gauge [7]. The transmission input shaft is fastened to the test bench. The idler gear is in shifted condition and stiffly connected to the output shaft. Both driving gear flanks are in contact and the lever arm fixed to the output shaft is turned up to the contact point of opposite driven flanks. Table 1 shows the values of tooth backlash depending on the type of gear-tooth profile and conversion into radians.
3. Results The gear rattle noise behaviour of the single-stage gear transmission is studied with different values of tooth backlash, as well as with straight-cut and helical-cut spur gears. The effect of lubricating oil on the gear rattle noise level with PAO/HC1 and PG3 will also be taken into consideration.
3.1. Gear rattle noise measurements with straight-cut spur gears The following section presents the results of gear rattle noise measurements with straight-cut spur gears. Fig. 5 shows the rattle-curves in shifted condition with different values of tooth backlash and the influence of both gear lubricants on the gear rattle noise level. Sound-pressure levels are almost equal up to an excitation of 40 rad s 2 because there is no loss of contact of the meshing gear tooth flanks. The noise level in this case is independent of the value of the tooth backlash and gear lubricant. Drag torque acting on the gear wheel immersed in the oil sump and on the bearings of the output shaft prevents separation of meshing gear tooth flanks at low excitation levels. When tooth separation does not occur, there is no oil pressure perturbation in the contact zone of the gear mesh. Pressure perturbation is essential for airborne noise emission [17]. The meshing gear tooth flanks begin to lose contact with the rising angular acceleration amplitude, oscillate in the range of tooth backlash and excite impacts when reaching their boundaries. These impacts are immediately measureable in rising soundpressure levels. At 100 rad s 2, upwards sound-pressure levels depend strongly on the value of the tooth backlash. The maximum sound-pressure level is reached with jt ¼ 0:375 mm, regardless of gear lubricant. Sound-pressure levels decrease with jt ¼ 0:189 mm because of lower impact energy. In both cases, sound-pressure level characteristics are almost independent of the gear lubricant. An influence of gear lubricant on gear rattle noise level is nonexistent up to 900 rad s 2 for jt ¼ 0:375 mm and up to 700 rad s 2 for jt ¼ 0:189 mm. At higher angular acceleration amplitudes, PG3 shows higher sound-pressure levels compared to PAO/HC1 despite almost identical oil viscosity.
Table 1 Value of tooth backlash with straight-cut and helical-cut spur gears in unloaded condition. β ¼01
Helix angle Value of tooth backlash Angle of rotation of idler gear in relation to held fixed gear
jt ¼ 0.189 mm 0.2771 4.836 10 3 rad
β ¼201 jt ¼ 0.375 mm 0.5501 9.592 10 3 rad
jt ¼ 0.198 mm 0.2921 5.089 10 3 rad
jt ¼0.388 mm 0.5701 9.948 10 3 rad
Fig. 5. Gear rattle noise level with straight-cut spur gears in consideration of tooth backlash and gear lubricant.
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3.2. Gear rattle noise measurements with helical-cut spur gears In this section, gear rattle noise measurements with helical-cut spur gears are presented. Fig. 6 shows rattle-curves with helical-cut spur gears, but otherwise the same test conditions compared to Fig. 5. For both values of tooth backlash, the sound-pressure levels of PAO/HC1 are up to 3 dB(A) higher than the soundpressure levels of PG3. These noise characteristics of PAO/HC1 are existent up to an excitation of 700–900 rad s 2 compared
Fig. 6. Gear rattle noise level with helical-cut spur gears in consideration of tooth backlash and gear lubricant.
Fig. 7. Relative angular motion and corresponding housing acceleration in shifted condition with excitation amplitude of 0 rad s 2 in (a) and (c) with β ¼01, (b) and (d) with β¼ 201.
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to PG3, although the oil viscosities are almost identical. The rattle-curves of PG3 are particularly different when compared to Fig. 5, because of varying helix angle. Therefore, the minimization of the gear rattle noise level with PG3 is dependent on the lubricating film formation during gear meshing. Obviously, there is a considerable difference in lubricating film formation between straight-cut and helical-cut spur gears. Helical-cut spur gears feature an additional sliding friction speed component in the gear tooth width direction [18]. For instance, higher drag torques on the idler gear with PG3 are not responsible for gear rattle noise reduction [7].
3.3. Angular relative motion with varying helix angles An analysis of the relative angular motion of meshing gear teeth is used to describe the mechanism of gear rattle noise generation with regard to lubrication effects. Fig. 7 illustrates the relative angle (red continuous curve) of straight-cut and helical-cut spur gears under normal rolling motion with no torsional excitation at the transmission input shaft. The values of tooth backlash are adjusted to jt ¼ 0:189 mm for straight-cut spur gears and jt ¼ 0:198 mm for helical-cut spur gears. The gear lubricant PAO/HC1 is used in this case. Straight-cut as well as helical-cut spur gears indicate little relative angular motion during rolling motion due to manufacturing errors of the gear wheels. The total contact ratio of straight-cut spur gears is smaller than the total contact ratio of helical-cut spur gears. The overlap ratio of helical-cut spur gears has a positive effect on gear meshing noise under load conditions. Helical-cut spur gears cause an additional axial force in the shaft bearing which leads to little higher gearbox housing acceleration; compare Fig. 7(c) and (d). Fig. 8 shows the relative angular motion of straight-cut and helical-cut spur gears with a torsional excitation amplitude of 1500 rad s 2 at the transmission input shaft. The oscillation angle (grey dash-dotted curve), as well as the corresponding angular acceleration (blue dashed curve) of the transmission input shaft with the fixed gear, are illustrated in Fig. 8(a) and (b).
Fig. 8. Relative angular motion and corresponding housing acceleration in shifted condition with excitation amplitude of 1500 rad s 2 in (a) and (c) with β ¼ 01, (b) and (d) with β ¼20°.
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The traction flanks of the idler gear lift off from the fixed gear and move in the direction of their opposing thrust flanks at positive values in the characteristic curve of angular acceleration. The impacts of thrust flanks occur if the angular acceleration is high enough. These impacts are immediately visible in the gearbox housing acceleration, see Fig. 8(c) and (d) at positive values in the characteristic curve of angular acceleration e.g. at t ¼ 0:0233 s. The kinetic energy of the idler gear is not high enough to move the idler gear to the thrust flanks at lower angular acceleration amplitudes. The phase of free flight ends with impacts at the traction flanks in this case. If the characteristic curve of angular acceleration runs at negative values, the idler gear reacts to this oscillating movement retarded due to its inertia of mass. With response delay, the idler gear moves rearward in the direction of the traction flanks. Impacts occur as soon as the boundaries at the traction flanks are reached, which are more intense than the impacts at the thrust flanks, compare Fig. 8(c) and (d) at negative values in the characteristic curve of angular acceleration e.g. at t ¼ 0:0067 s. The maximum amplitude of the relative angle in Fig. 8(a) and (b) exceeds the angle of rotation of the idler gear in relation to held fixed gear, cf. Table 1. The maximum amplitude of the relative angle of straight-cut spur gears in Fig. 8(a) is Δθ ¼ 15 10 3 rad, and is, for that reason, approximately three times higher than the angle of rotation in the range of the tooth backlash in unloaded condition. For helical-cut spur gears, the maximum amplitude of the relative angle is about four times higher, cf. Fig. 8(b). The matter is an extension of the length of the path of contact due to gear tooth elastic deformation under impact loads. There is a difference in the position-dependent stiffness of gear teeth between straight-cut and helical-cut spur gears. A straight-cut gear tooth pair bears along the whole tooth width during gear meshing and the plane of contact is smaller. The path of contact of helical-cut spur gears runs in an inclined direction over the tooth width. The teeth of helical-cut spur gears mesh gradually from the beginning to the end of each gear pair meshing. At the beginning and the end of the gear mesh a helical gear tooth pair carries only at the tip of the tooth face. The stiffness of the gear teeth is very low in this meshing position and therefore the elastic deformation of the helical-cut spur gears is higher than the elastic deformation of the straight-cut spur gears [7].
Fig. 9. Relative angular motion and corresponding housing acceleration in non-shifted condition with excitation amplitude of 1500 rad s 2 in (a) and (c) with jt ¼0.198 mm, (b) and (d) with jt ¼ 0:388 mm.
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3.4. Angular relative motion with varying values of tooth backlash The following measurements were recorded with helical-cut spur gears and PAO/HC1 under variation of the value of tooth backlash. Fig. 9(a) illustrates the relative angle with jt ¼ 0:198 mm and torsional excitation amplitude of 1500 rad s 2 at the transmission input shaft. A value of tooth backlash of jt ¼ 0:388 mm was used in Fig. 9(b). In both cases, a periodic oscillation of the idler gear between the traction and thrust flanks is detected. Impacts are immediately identified in the gearbox housing acceleration for both values of tooth backlash when reaching the boundaries. Gear tooth elastic deformation under impact loads is identified in Fig. 9(a) and (b), in addition, the amplitude of relative angle is nearly independent of value of tooth backlash. Superimposed, high-frequency vibrations are detectable in the relative angular motion during impacts at the traction and thrust flanks for both values of tooth backlash, cf. Fig. 9(a) and (b). High peak values of housing acceleration are measureable at the same time, see Fig. 9(c) and (d) e.g. between t ¼ 0:0067 s and t ¼ 0:0183 s for impacts at traction flanks. The root cause for this vibrational behaviour is the presence of additional meshing impacts of the following meshing gear tooth flanks, because the gear meshing frequency is much higher than the excitation frequency of the torsional vibration at the transmission input shaft. Several successive meshing impacts generate high forces at the meshing gear tooth pairs, which lead to peak values of housing acceleration. The meshing impacts are the result of deviations from the ideal toothflank geometry and, therefore, from the Law of Gearing. Such meshing impacts are the leading cause for the gear rattle noise level [7].
3.5. Angular relative motion with varying gear lubricants Different gear rattle noise characteristics are detectable with PAO/HC1 and PG3 in Section 3.2, cf. Fig. 6. The different vibrational behaviour with varying gear lubricants and helical-cut spur gears at jt ¼ 0:198 mm is comprehensible in the relative angular motion and the corresponding housing acceleration, see Fig. 10.
Fig. 10. Relative angular motion and corresponding housing acceleration in shifted condition with excitation amplitude of 500 rad s 2 in (a) and (c) with PAO/HC1, (b) and (d) with PG3.
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With PAO/HC1, the typical vibrational behaviour of the idler gear in between the traction and thrust flanks with the meshing impacts is present as described in Section 3.4. Impacts with peak values of the corresponding housing acceleration are identifiable, especially at traction flanks, but also at thrust flanks, cf. Fig. 10(a) and (c). Meshing impacts are eliminated in the relative angular motion when using PG3, even though the idler gear is still vibrating in between the traction and thrust flanks, cf. Fig. 10(b). The relative angle with PG3 has a slightly higher maximum amplitude, thus, the elastic deformation of meshing gear tooth pairs is higher compared to PAO/HC1. Non-existent meshing impacts with PG3 lead to much lower peaks in the housing acceleration and, consequently, to lower gear rattle noise level of the transmission, see Fig. 10(d). 4. Conclusion The presented experimental study on the gear rattle noise phenomenon shows agreement with findings by other authors. The measurements taken indicate a periodic vibrational behaviour of the idler gear within the range of tooth backlash. However, another phenomenon is superimposed on that basic periodic vibrational behaviour. The noise damping capabilities of PG3 can only be found by using helical gear pairs, in contrast to PAO/HC1. Thus, it can be concluded that the formation of a hydrodynamic lubrication film in the gear mesh is responsible for the noise reduction compared to other factors, e.g. a higher drag torque on the idler gear. An analysis of the relative angular motion proves that gear tooth impacts during rattling lead to elastic deformation of the meshing gear tooth flanks. High contact forces during impacts cause Hertzian flattening of the tooth flanks and rising fluid viscosity with pressure in the contact zone (elastohydrodynamic lubrication regime). The elastic deformation of the meshing gear pairs leads to deviations from the Law of Gearing. The main source for the gear rattle noise level is the additional presence of meshing impacts at the beginning of each gear pair meshing. The traction coefficient in this meshing zone is very high because of the high sliding velocities of the tooth flanks [18]. A reduction of gear rattle noise level can be achieved by avoiding meshing impacts, e.g. by minimizing the traction coefficient of the gear oil or high lubrication film thickness at the gear mesh. Acknowledgements The authors gratefully acknowledge the funding of this research project by the Daimler Corporation, Stuttgart, Germany. References [1] T.G. Brosey, R.L. Seaman, C.E. Johnson, R.F. Hamilton, Effect of transmission design on gear rattle and shiftability, International Journal of Vehicle Design 7 (1986) 45–66. [2] H. Rahnejat, Multi-body Dynamics: Vehicles, Machines and Mechanisms, London, Professional Engineering Publishing, 1998. [3] G. Weidner, Klappern und Rasseln von Fahrzeuggetrieben (Ph.D. thesis), University of Stuttgart, 1991. [4] C.-H. Lang, Losteilgeraeusche von Fahrzeuggetrieben (Ph.D. thesis), University of Stuttgart, 1997. [5] A. Baumann, P. Fietkau, B. Bertsche, R. Boehnke, K. Hagemann, W. Krechberger, J. Zinsser, Reduction of the gear-rattle noise level of automotive transmissions using innovative gear lubricants, in: Proceedings of the International VDI Congress Transmissions in Vehicles, Friedrichshafen, Germany, 2010, pp. 373–393. [6] A. Baumann, P. Fietkau, B. Bertsche, R. Boehnke, K. Hagemann, W. Krechberger, J. Zinsser, Influence of the lubricant on the gear-rattle noise level of a manual transmission system, in: Proceedings of the 17th International Colloquium Tribology, Ostfildern, Germany, 2010. [7] A. Baumann, Rasselgeraeuschminimierung von Fahrzeuggetrieben durch Getriebeoele, (Ph.D. thesis), 2013, University of Stuttgart, http://elib. uni-stuttgart.de/opus/volltexte/2013/8759/ (accessed 19.11.13). [8] J. Rach, Beitrag zur Minimierung von Klapper- und Rasselgeraeuschen von Fahrzeuggetrieben (Ph.D. thesis), University of Stuttgart, 1998. [9] R. Brancati, E. Rocca, R. Russo, F. Timpone, Experimental test rig for the evaluation of oil squeeze effects between the impacting teeth of a meshing gear pair, in: Proceedings of the 5th International Conference on Tribology, Parma, Italy, 2006. [10] R. Russo, R. Brancati, E. Rocca, Experimental investigations about the influence of oil lubricant between teeth on the gear rattle phenomenon, Journal of Sound and Vibration 321 (2009) 647–661, http://dx.doi.org/10.1016/j.jsv.2008.10.008. [11] O. Tangasawi, S. Theodossiades, H. Rahnejat, Lightly loaded lubricated impacts: idle gear rattle, Journal of Sound and Vibration 308 (2007) 418–430, http://dx.doi.org/10.1016/j.jsv.2007.03.077. [12] M. De la Cruz, S. Theodossiades, H. Rahnejat, An investigation of manual transmission drive rattle, Proceedings of the Institution of Mechanical Engineers Part K: Journal of Multi-body Dynamics 224 (2010) 167–181, http://dx.doi.org/10.1243/14644193JMBD232. [13] S. Theodossiades, O. Tangasawi, H. Rahnejat, Gear teeth impacts in hydrodynamic conjunctions promoting idle gear rattle, Journal of Sound and Vibration 303 (2007) 632–658, http://dx.doi.org/10.1016/j.jsv.2007.01.034. [14] A. Crowther, C. Halse, Z. Zhang, Nonlinear Responses in Loaded Driveline Rattle. SAE Technical Paper Series 2009-01-2068, http://dx.doi.org/10.4271/ 2009-01-2068. [15] A. Baumann, P. Fietkau, B. Bertsche, Nachbildung verbrennungsmotorischer Drehschwingungen auf einem Getriebepruefstand für Rasselgeraeuschuntersuchungen, in: Proceedings of the Stuttgarter Symposium fuer Produktentwicklung, Stuttgart, Germany, 2011, pp. 96–97. [16] P. Fietkau, A. Baumann, B. Bertsche, Rasselgeraeuschpruefstand zur Untersuchung von Fahrzeuggetrieben, in: Proceedings of the Mueller-BBM VibroAkustik Systeme PAK-Tag, Herrsching, Germany, 2011, http://elib.uni-stuttgart.de/opus/volltexte/2011/6299/ (accessed 10.08.13). [17] M. De la Cruz, S. Theodossiades, P. King, H. Rahnejat, Transmission drive rattle with thermo-elastohydrodynamic impacts: numerical and experimental investigations, International Journal of Powertrains 1 (2011) 137–161, http://dx.doi.org/10.1504/IJPT.2011.042764. [18] G. Niemann, H. Winter, Maschinenelemente Band 2, 2nd ed. Springer, Berlin Heidelberg, 2003.
Contents lists available at ScienceDirect
Journal of Sound and Vibration journal homepage: www.elsevier.com/locate/jsvi
Experimental study on transmission rattle noise behaviour with particular regard to lubricating oil Axel Baumann n, Bernd Bertsche Institute of Machine Components, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
a r t i c l e i n f o
abstract
Article history: Received 30 January 2014 Received in revised form 8 December 2014 Accepted 13 December 2014 Handling Editor: A.V. Metrikine Available online 13 January 2015
This article presents an experimental study on the gear rattle noise phenomenon of automotive transmissions. A single-stage gear transmission has been designed and applied to a gear rattle noise test bench. The gear transmission allows the variation of several parameters affecting the rattle noise level, e.g. tooth backlash variation. High resolution incremental encoders on the transmission input and output shaft, as well as on the idler gear, enable the acquisition of the angular relative motion of the gear pair within the range of tooth backlash. The angular relative motion evaluates the sequence of meshing gear teeth along the path of contact under rattling conditions. The analysis of the angular relative motion indicates that gear tooth impacts during rattling lead to elastic deformation of meshing gear pairs. High contact forces during impacts cause Hertzian flattening of gear tooth flanks and rising fluid viscosity with pressure in the contact zone (elastohydrodynamic lubrication regime). The elastic deformation of meshing gear pairs lead to deviations from the angular velocity ratio between two gears of a gear pair and thus from the Law of Gearing. The main source for the gear rattle noise level is the additional presence of meshing impacts at the beginning of each gear pair meshing. Gear rattle noise reduction can be achieved by avoiding meshing impacts, e.g. by using low traction gear lubricants. & 2014 Elsevier Ltd. All rights reserved.
1. Introduction Noise reduction is an important objective in passenger car development. Automotive transmissions are one of the main sources for the vehicle interior noise. Caused by downsizing and downspeeding of internal combustion engines, the torque fluctuation at the crankshaft induces torsional vibrations in the powertrain it is connected to [1]. Due to unbalanced gas and inertia forces from motion of pistons the rotational speed of internal combustion engines is not uniform it is superimposed by torsional vibrations. The rotational speed of an internal combustion engine can be approximated by a composition of a constant average speed, which is the first engine order, and thus the nominal speed of the crankshaft, superimposed on a sinusoidal oscillation with a frequency according to the main engine order. The main order of the torsional vibrations is the ignition frequency that is the result of engine firing order and number of cylinders. The 4-cylinder 4-stroke engine, which is widely used in passenger cars, has the second engine order as its main engine order [2]. The angular acceleration amplitude is crucial for the intensity of torsional vibration, and therefore for the gear rattle noise level of automotive transmissions.
n
Corresponding author. Tel.: þ49 711 68566170; fax: þ 49 711 68566319. E-mail address: [email protected] (A. Baumann).
http://dx.doi.org/10.1016/j.jsv.2014.12.018 0022-460X/& 2014 Elsevier Ltd. All rights reserved.
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Nomenclature CAD HC PAK
PAO PG TTL
computer-aided design hydrocracked oil Pruefstand-Akustik-Messsystem (Registered trademark of Mueller-BBM VibroAkustik Systeme GmbH) poly-alpha-olefin polyalkylene glycol transistor–transistor logic
List of abbreviations Leq
Δθ θ1 θ2 dw1 dw2 z1 z2
β
mn an jt t
relative angle of gear pair [1] or [rad] input shaft angle [1] or [rad] output shaft angle or idler gear angle [1] or [rad] pitch circle diameter of fixed gear [mm] pitch circle diameter of idler gear [mm] number of teeth fixed gear [dimensionless] number of teeth idler gear [dimensionless] helix angle [1] normal module [mm] normal angle of pressure [1] gear tooth backlash [mm] time [s]
continuous sound-pressure Level [dB(A)]
Manual transmissions, automated manual transmissions and dual clutch transmissions are particularly sensitive to gear rattle noise, which arises from oscillations of loose (unengaged) gear pairs with working clearance, e.g. idler gears, synchronizer rings and gearshift sleeves [3,4]. The particular sound character of gear rattle noise sounds like a marble rattling in a tin and distinguishes it from other sources of vehicle noise. This metallic type noise, which is disconcerting to the vehicle occupants as well as other road users nearby, leads to customers' complaints. For this reason, gear rattle noise behaviour of automotive transmissions has to be taken into account at an early product development stage. Gear rattle noise reduction can be achieved by using custom-made gear lubricants. The authors investigated the influence of various gear lubricants on the gear rattle noise level of a 5-speed manual transmission for front-transverse use. Different base oil and additive formulations at about the same oil viscosity were studied. The measurements taken show that gear lubricants based upon polyalkylene glycol are particularly good at reducing the rattle noise level of a manual transmission up to 6 dB(A) at commonly low kinematic viscosity characteristics to reduce drag torque [5,6]. Drag torque measurements show improvements of the transmission efficiency under loading and idle conditions with a water-soluble polyalkylene glycol, when compared to a standard mineral oil [7]. The excellent gear rattle noise damping capabilities of water-soluble polyalkylene glycol are investigated and compared to mineral oil in this article. A single-stage gear transmission has been designed and applied to a gear rattle noise test bench to compare both gear lubricants. Idler gear vibrational behaviour due to torsional excitation at the transmission input shaft is studied by acquisition of the angular relative motion of the gear pair. The basic idea to use the angular relative motion along the path of contact for evaluation of the sequence of meshing gear teeth has been suggested by other authors. Rach takes measurements of an oscillating idler gear in an experimental gear transmission. Low resolution Hall sensors are used to measure the rotary motion of the idler gear [8]. Brancati describes an experimental test set-up with high resolution incremental encoders for determination of the relative angular motion. Previously obtained simulation results are validated by these measurements [9]. Variation of the lubrication mechanism, from oil jet lubrication to dry contact, enables detection of double sided impacts of the idler gear [10]. Other researchers have also carried out the study of lubrication effects on the gear rattle noise phenomenon. Tangasawi considers the gear lubricant behaviour as a nonlinear spring damper affecting the response of idler gears during a meshing cycle. Oil viscosity matters as an important factor, which governs the vibrational behaviour of a transmission [11]. De la Cruz provides detailed analytical models of lubricated conjunctions in a multi-body dynamics simulation of a transaxle 7-speed transmission under creep rattle conditions. The results show the important role of the regime of lubrication in lightly loaded conjunctions, increasing the propensity to rattle at higher temperatures because of lower lubricating oil viscosity [12]. Theodossiades includes the effect of lubrication in his approach to understanding the interactions between the transmission gears during engine idle conditions. The influence of the lubricant on torsional vibration of lightly loaded idling gears, which promotes iso-viscous hydrodynamic conditions, is examined [13]. Crowther presents a nonlinear model for investigation of idler gears' oscillation response due to torsional excitation by an internal combustion engine. The idler gear moves back and forth within the range of tooth backlash and multiple impacts occur both on traction and thrust tooth flanks [14]. The main disadvantage of using high viscous lubricating oils to reduce the gear rattle noise level is the reduction of the transmission efficiency in the case of loaded engaged gears and thus an increase of fuel consumption of the vehicle. The present article picks up research results obtained by other authors and further contributes to the understanding of meshing gear teeth vibrational behaviour along the path of contact under rattling conditions. The following research results are found in an experimental study where lubrication effects are taken into consideration as well. 2. Test set-up for experimental study The test set-up for the experimental study and the single-stage gear transmission for rattle noise measurements are described in the following section.
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2.1. Gear rattle noise test bench The test bench used was designed to investigate the gear rattle noise phenomenon of automotive transmissions. A schematic layout of the test bench is shown in Fig. 1. The drive motor – a highly dynamic, permanent-field three-phase synchronous motor – and the testing transmission are mounted coaxially on the test bench frame. The drive motor shaft is connected to the transmission input shaft via torsionresistant shaft couplings. An identical brake motor can be coupled to the transmission output shaft for simulation of driving and overrun operating conditions. The test bench is set up in a sound-absorbing environment to simulate anechoic conditions for sound-pressure level measurements [15]. An incremental encoder is fixed to the transmission input shaft for rotational speed measurement and actual value acquisition for the closed-loop control of the drive motor. Another identical incremental encoder is fixed to the transmission output shaft. Rotary movement of the idler gear can be measured via Hall sensor by contactless scanning of a toothed impulse wheel [15]. Fig. 2 shows the test set-up of the gear rattle noise test bench with the single-stage gear transmission including positions of the incremental encoders. All measurement signals are recorded synchronously by a Mueller-BBM PAK data processor. Sound-pressure levels are measured at three defined positions in 1 m distance vertical to the transmission housing surface at a sampling rate of 51.2 kHz. The positioning of the microphones allow recording of rattle noise in the far field of the gear transmission. The continuous sound-pressure level Leq is plotted versus the angular acceleration amplitude of the transmission input shaft.
Fig. 1. Schematic layout of gear rattle noise test bench.
Fig. 2. Test set-up of gear rattle noise test bench with single-stage gear transmission.
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Fig. 3. Schematic and 3D CAD model of single-stage gear transmission. (1) Fixed gear; (2) idler gear with toothed impulse wheel; (3) input shaft; (4) output shaft; (5) synchronizer.
This diagram is called a rattle-curve. It is used for transmission rattle noise evaluation and comparison between each other. Housing acceleration is measured at a sampling rate of 25.6 kHz on the transmission housing surface for identification of impacts which are in direct time dependence on the torsional vibration excitation [16]. A sinusoidal excitation with varying amplitude and a frequency according to second rotation order (30 Hz) is superimposed on the constant input shaft rotation of 900 rev/min in all measurements to simulate conditions arising in a 4-cylinder 4-stroke engine. The main engine order of fluctuations for such an engine is the second engine order [2]. 2.2. Design of single-stage gear transmission The single-stage gear transmission consists of one gear pair with a synchronizer for the idler gear on the output shaft. A schematic and CAD model of the gear transmission are shown in Fig. 3. The input shaft includes the fixed gear, which is mounted on the shaft by a spline shaft connection. The idler gear and the single-cone synchronizer are mounted on the output shaft. The idler gear can rotate relative to the output shaft by a needle‐roller bearing. The synchronizer body with the gearshift sleeve is fixed to the output shaft and guides the synchronizer ring. Two different states of the gearshift mechanism are possible. First of all, a non-shifted condition is possible when the gearshift sleeve is not connected to the idler gear. The output shaft is standing still in this case. Secondly, a shifted condition is possible when the idler gear is positive-engaged with the output shaft. If the idler gear is connected to the synchronizer body, the output shaft rotates according to the gear transmission ratio. The following measurements cover non-shifted condition as well as shifted condition whereby the idler gear is connected to the output shaft. Both transmission shafts are guided by ball and roller bearings with a special cover construction in the transmission housing. The bearings of the output shaft are fixed in eccentric covers to vary the transmission centre distance and, therefore, tooth backlash. The housing itself is mounted on the test bench and contains oil to lubricate and cool the transmission [7]. 2.3. Acquisition of relative angular motion Photoelectric incremental encoders at a sampling rate of 25.6 kHz measure the rotational speeds of both transmission shafts. Each incremental encoder consists of two marked discs with 10,000 marks per revolution. TTL-signals are available as output signals, which are processed by the Mueller-BBM PAK data acquisition system. Angle, angular velocity and direction of rotation can be determined by the subsequent analysis of pulse number, pulse frequency and phase relation. The difference between the angle of the input shaft and the output shaft in the shifted condition yields the so-called relative angle of the gear pair. A toothed impulse wheel is fixed to the idler gear for acquisition of the idler gear relative motion.
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A magneto-resistive sensor fixed to the interior transmission housing scans the toothed impulse wheel. In the non-shifted condition, the relative angle of the gear pair can also be obtained with this measurement set-up [16]. The relative angular motion of an unloaded gear pair is the difference between the greatest and smallest deviation during gear meshing in circumferential direction, also known as transmission error. Relative angular motion corresponds to deviations of the driven idler gear in relation to its constant rotation. The smaller the relative angular motion, the more uniform the rotary motion of the idler gear. As soon as the fixed gear begins to vibrate, the torsional oscillation of the idler gear leads to relative angular motion during gear meshing. Consequently, deviations from the usual kinematic rotational relationship between the gear pair can be observed when impact dynamics is involved [7]. The evaluation of the relative angle of the gear pair Δθ on the pitch circle is expressed as Δθ ¼ θ2 −θ1
dw1 dw2
(1)
with the input shaft angle θ1 and output shaft angle θ2 in shifted condition given by the incremental encoders, respectively the idler gear angle θ2 in non-shifted condition given by the Hall sensor and the toothed impulse wheel. dw1 and dw2 are the pitch circle diameters of the fixed gear and the idler gear, respectively. By using the Law of Gearing Eq. (1) becomes
Δθ ¼ θ2 θ1
z1 z2
(2)
with the number of teeth of the fixed gear z1 and number of teeth of the idler gear z2 . Fig. 4 shows the relative angular motion of the gear pair with different vibration excitations at the transmission input shaft. Gear tooth flanks of the fixed and idler gear are in constant mesh during normal operating conditions at 0 rad s 2. Slight deviations in the relative angle are caused by eccentricities of the fixed gear on the input shaft due to manufacturing errors. Under rattling conditions at 1500 rad s 2, a movement of the idler gear within the range of tooth backlash takes place. The gear tooth flanks are in mesh on their traction flanks at positive values of the relative angle. The negative values of the relative angle correspond to the meshing of the gear tooth flanks at their thrust flanks consequently. The meshing gear tooth flanks have no contact within the range of tooth backlash. A vibration of the idler gear within the range of tooth backlash can be detected depending on the level of vibration excitation at the transmission input shaft in Fig. 4. 2.4. Parameter study on gear rattle noise level Two different gear lubricants are investigated regarding gear rattle noise level in the single-stage gear transmission. PAO/ HC1 is a fully formulated mineral base oil with a commonly used additive package for use in manual transmissions. The dynamic oil viscosity of PAO/HC1 is 9.03 mPa s at 80 1C. PG3 is a polyalkylene glycol for use in worm-gear transmissions. Dynamic oil viscosity of PG3 is 10.44 mPa s at 80 1C and, therefore, almost comparable to PAO/HC1. The oil level was adjusted at the lowest root diameter of the idler gear under static conditions in all measurements. Gear pairs with β ¼ 01 and β ¼ 201 are available for investigation of different helix angles. All gear wheels have a normal module of mn ¼ 2 mm and the normal angle of pressure is an ¼ 201. The transmission ratio of straight-cut spur gears is 0.639 using z1 ¼ 61 and z2 ¼ 39. Helical-cut spur gears provide a transmission ratio of 0.638 with z1 ¼ 58 and z2 ¼ 37. The value of tooth backlash is one of the significant influencing variables on gear rattle noise level of automotive transmissions. Tooth backlash reduction leads to minimization of gear rattle noise level [4]. In contrast, a minimum value of tooth backlash is needed to prevent the jamming of meshing gear teeth under all operating conditions. Tooth backlash jt is defined as the length of the pitch-circle arc which the idler gear can rotate relative to the fixed gear in-between traction and
Fig. 4. Relative angular motion of idler gear with excitation amplitude of (a) 0 rad s 2 and (b) 1500 rad s 2.
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thrust gear tooth flanks. The tooth backlashes jt ¼ 0:189 mm and jt ¼ 0:375 mm are investigated when using straight-cut spur gears. The values for tooth backlash for helical-cut spur gears are jt ¼ 0:198 mm and jt ¼ 0:388 mm. These values were measured under static conditions by using a lever arm and dial gauge [7]. The transmission input shaft is fastened to the test bench. The idler gear is in shifted condition and stiffly connected to the output shaft. Both driving gear flanks are in contact and the lever arm fixed to the output shaft is turned up to the contact point of opposite driven flanks. Table 1 shows the values of tooth backlash depending on the type of gear-tooth profile and conversion into radians.
3. Results The gear rattle noise behaviour of the single-stage gear transmission is studied with different values of tooth backlash, as well as with straight-cut and helical-cut spur gears. The effect of lubricating oil on the gear rattle noise level with PAO/HC1 and PG3 will also be taken into consideration.
3.1. Gear rattle noise measurements with straight-cut spur gears The following section presents the results of gear rattle noise measurements with straight-cut spur gears. Fig. 5 shows the rattle-curves in shifted condition with different values of tooth backlash and the influence of both gear lubricants on the gear rattle noise level. Sound-pressure levels are almost equal up to an excitation of 40 rad s 2 because there is no loss of contact of the meshing gear tooth flanks. The noise level in this case is independent of the value of the tooth backlash and gear lubricant. Drag torque acting on the gear wheel immersed in the oil sump and on the bearings of the output shaft prevents separation of meshing gear tooth flanks at low excitation levels. When tooth separation does not occur, there is no oil pressure perturbation in the contact zone of the gear mesh. Pressure perturbation is essential for airborne noise emission [17]. The meshing gear tooth flanks begin to lose contact with the rising angular acceleration amplitude, oscillate in the range of tooth backlash and excite impacts when reaching their boundaries. These impacts are immediately measureable in rising soundpressure levels. At 100 rad s 2, upwards sound-pressure levels depend strongly on the value of the tooth backlash. The maximum sound-pressure level is reached with jt ¼ 0:375 mm, regardless of gear lubricant. Sound-pressure levels decrease with jt ¼ 0:189 mm because of lower impact energy. In both cases, sound-pressure level characteristics are almost independent of the gear lubricant. An influence of gear lubricant on gear rattle noise level is nonexistent up to 900 rad s 2 for jt ¼ 0:375 mm and up to 700 rad s 2 for jt ¼ 0:189 mm. At higher angular acceleration amplitudes, PG3 shows higher sound-pressure levels compared to PAO/HC1 despite almost identical oil viscosity.
Table 1 Value of tooth backlash with straight-cut and helical-cut spur gears in unloaded condition. β ¼01
Helix angle Value of tooth backlash Angle of rotation of idler gear in relation to held fixed gear
jt ¼ 0.189 mm 0.2771 4.836 10 3 rad
β ¼201 jt ¼ 0.375 mm 0.5501 9.592 10 3 rad
jt ¼ 0.198 mm 0.2921 5.089 10 3 rad
jt ¼0.388 mm 0.5701 9.948 10 3 rad
Fig. 5. Gear rattle noise level with straight-cut spur gears in consideration of tooth backlash and gear lubricant.
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3.2. Gear rattle noise measurements with helical-cut spur gears In this section, gear rattle noise measurements with helical-cut spur gears are presented. Fig. 6 shows rattle-curves with helical-cut spur gears, but otherwise the same test conditions compared to Fig. 5. For both values of tooth backlash, the sound-pressure levels of PAO/HC1 are up to 3 dB(A) higher than the soundpressure levels of PG3. These noise characteristics of PAO/HC1 are existent up to an excitation of 700–900 rad s 2 compared
Fig. 6. Gear rattle noise level with helical-cut spur gears in consideration of tooth backlash and gear lubricant.
Fig. 7. Relative angular motion and corresponding housing acceleration in shifted condition with excitation amplitude of 0 rad s 2 in (a) and (c) with β ¼01, (b) and (d) with β¼ 201.
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to PG3, although the oil viscosities are almost identical. The rattle-curves of PG3 are particularly different when compared to Fig. 5, because of varying helix angle. Therefore, the minimization of the gear rattle noise level with PG3 is dependent on the lubricating film formation during gear meshing. Obviously, there is a considerable difference in lubricating film formation between straight-cut and helical-cut spur gears. Helical-cut spur gears feature an additional sliding friction speed component in the gear tooth width direction [18]. For instance, higher drag torques on the idler gear with PG3 are not responsible for gear rattle noise reduction [7].
3.3. Angular relative motion with varying helix angles An analysis of the relative angular motion of meshing gear teeth is used to describe the mechanism of gear rattle noise generation with regard to lubrication effects. Fig. 7 illustrates the relative angle (red continuous curve) of straight-cut and helical-cut spur gears under normal rolling motion with no torsional excitation at the transmission input shaft. The values of tooth backlash are adjusted to jt ¼ 0:189 mm for straight-cut spur gears and jt ¼ 0:198 mm for helical-cut spur gears. The gear lubricant PAO/HC1 is used in this case. Straight-cut as well as helical-cut spur gears indicate little relative angular motion during rolling motion due to manufacturing errors of the gear wheels. The total contact ratio of straight-cut spur gears is smaller than the total contact ratio of helical-cut spur gears. The overlap ratio of helical-cut spur gears has a positive effect on gear meshing noise under load conditions. Helical-cut spur gears cause an additional axial force in the shaft bearing which leads to little higher gearbox housing acceleration; compare Fig. 7(c) and (d). Fig. 8 shows the relative angular motion of straight-cut and helical-cut spur gears with a torsional excitation amplitude of 1500 rad s 2 at the transmission input shaft. The oscillation angle (grey dash-dotted curve), as well as the corresponding angular acceleration (blue dashed curve) of the transmission input shaft with the fixed gear, are illustrated in Fig. 8(a) and (b).
Fig. 8. Relative angular motion and corresponding housing acceleration in shifted condition with excitation amplitude of 1500 rad s 2 in (a) and (c) with β ¼ 01, (b) and (d) with β ¼20°.
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The traction flanks of the idler gear lift off from the fixed gear and move in the direction of their opposing thrust flanks at positive values in the characteristic curve of angular acceleration. The impacts of thrust flanks occur if the angular acceleration is high enough. These impacts are immediately visible in the gearbox housing acceleration, see Fig. 8(c) and (d) at positive values in the characteristic curve of angular acceleration e.g. at t ¼ 0:0233 s. The kinetic energy of the idler gear is not high enough to move the idler gear to the thrust flanks at lower angular acceleration amplitudes. The phase of free flight ends with impacts at the traction flanks in this case. If the characteristic curve of angular acceleration runs at negative values, the idler gear reacts to this oscillating movement retarded due to its inertia of mass. With response delay, the idler gear moves rearward in the direction of the traction flanks. Impacts occur as soon as the boundaries at the traction flanks are reached, which are more intense than the impacts at the thrust flanks, compare Fig. 8(c) and (d) at negative values in the characteristic curve of angular acceleration e.g. at t ¼ 0:0067 s. The maximum amplitude of the relative angle in Fig. 8(a) and (b) exceeds the angle of rotation of the idler gear in relation to held fixed gear, cf. Table 1. The maximum amplitude of the relative angle of straight-cut spur gears in Fig. 8(a) is Δθ ¼ 15 10 3 rad, and is, for that reason, approximately three times higher than the angle of rotation in the range of the tooth backlash in unloaded condition. For helical-cut spur gears, the maximum amplitude of the relative angle is about four times higher, cf. Fig. 8(b). The matter is an extension of the length of the path of contact due to gear tooth elastic deformation under impact loads. There is a difference in the position-dependent stiffness of gear teeth between straight-cut and helical-cut spur gears. A straight-cut gear tooth pair bears along the whole tooth width during gear meshing and the plane of contact is smaller. The path of contact of helical-cut spur gears runs in an inclined direction over the tooth width. The teeth of helical-cut spur gears mesh gradually from the beginning to the end of each gear pair meshing. At the beginning and the end of the gear mesh a helical gear tooth pair carries only at the tip of the tooth face. The stiffness of the gear teeth is very low in this meshing position and therefore the elastic deformation of the helical-cut spur gears is higher than the elastic deformation of the straight-cut spur gears [7].
Fig. 9. Relative angular motion and corresponding housing acceleration in non-shifted condition with excitation amplitude of 1500 rad s 2 in (a) and (c) with jt ¼0.198 mm, (b) and (d) with jt ¼ 0:388 mm.
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3.4. Angular relative motion with varying values of tooth backlash The following measurements were recorded with helical-cut spur gears and PAO/HC1 under variation of the value of tooth backlash. Fig. 9(a) illustrates the relative angle with jt ¼ 0:198 mm and torsional excitation amplitude of 1500 rad s 2 at the transmission input shaft. A value of tooth backlash of jt ¼ 0:388 mm was used in Fig. 9(b). In both cases, a periodic oscillation of the idler gear between the traction and thrust flanks is detected. Impacts are immediately identified in the gearbox housing acceleration for both values of tooth backlash when reaching the boundaries. Gear tooth elastic deformation under impact loads is identified in Fig. 9(a) and (b), in addition, the amplitude of relative angle is nearly independent of value of tooth backlash. Superimposed, high-frequency vibrations are detectable in the relative angular motion during impacts at the traction and thrust flanks for both values of tooth backlash, cf. Fig. 9(a) and (b). High peak values of housing acceleration are measureable at the same time, see Fig. 9(c) and (d) e.g. between t ¼ 0:0067 s and t ¼ 0:0183 s for impacts at traction flanks. The root cause for this vibrational behaviour is the presence of additional meshing impacts of the following meshing gear tooth flanks, because the gear meshing frequency is much higher than the excitation frequency of the torsional vibration at the transmission input shaft. Several successive meshing impacts generate high forces at the meshing gear tooth pairs, which lead to peak values of housing acceleration. The meshing impacts are the result of deviations from the ideal toothflank geometry and, therefore, from the Law of Gearing. Such meshing impacts are the leading cause for the gear rattle noise level [7].
3.5. Angular relative motion with varying gear lubricants Different gear rattle noise characteristics are detectable with PAO/HC1 and PG3 in Section 3.2, cf. Fig. 6. The different vibrational behaviour with varying gear lubricants and helical-cut spur gears at jt ¼ 0:198 mm is comprehensible in the relative angular motion and the corresponding housing acceleration, see Fig. 10.
Fig. 10. Relative angular motion and corresponding housing acceleration in shifted condition with excitation amplitude of 500 rad s 2 in (a) and (c) with PAO/HC1, (b) and (d) with PG3.
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With PAO/HC1, the typical vibrational behaviour of the idler gear in between the traction and thrust flanks with the meshing impacts is present as described in Section 3.4. Impacts with peak values of the corresponding housing acceleration are identifiable, especially at traction flanks, but also at thrust flanks, cf. Fig. 10(a) and (c). Meshing impacts are eliminated in the relative angular motion when using PG3, even though the idler gear is still vibrating in between the traction and thrust flanks, cf. Fig. 10(b). The relative angle with PG3 has a slightly higher maximum amplitude, thus, the elastic deformation of meshing gear tooth pairs is higher compared to PAO/HC1. Non-existent meshing impacts with PG3 lead to much lower peaks in the housing acceleration and, consequently, to lower gear rattle noise level of the transmission, see Fig. 10(d). 4. Conclusion The presented experimental study on the gear rattle noise phenomenon shows agreement with findings by other authors. The measurements taken indicate a periodic vibrational behaviour of the idler gear within the range of tooth backlash. However, another phenomenon is superimposed on that basic periodic vibrational behaviour. The noise damping capabilities of PG3 can only be found by using helical gear pairs, in contrast to PAO/HC1. Thus, it can be concluded that the formation of a hydrodynamic lubrication film in the gear mesh is responsible for the noise reduction compared to other factors, e.g. a higher drag torque on the idler gear. An analysis of the relative angular motion proves that gear tooth impacts during rattling lead to elastic deformation of the meshing gear tooth flanks. High contact forces during impacts cause Hertzian flattening of the tooth flanks and rising fluid viscosity with pressure in the contact zone (elastohydrodynamic lubrication regime). The elastic deformation of the meshing gear pairs leads to deviations from the Law of Gearing. The main source for the gear rattle noise level is the additional presence of meshing impacts at the beginning of each gear pair meshing. The traction coefficient in this meshing zone is very high because of the high sliding velocities of the tooth flanks [18]. A reduction of gear rattle noise level can be achieved by avoiding meshing impacts, e.g. by minimizing the traction coefficient of the gear oil or high lubrication film thickness at the gear mesh. Acknowledgements The authors gratefully acknowledge the funding of this research project by the Daimler Corporation, Stuttgart, Germany. References [1] T.G. Brosey, R.L. Seaman, C.E. Johnson, R.F. Hamilton, Effect of transmission design on gear rattle and shiftability, International Journal of Vehicle Design 7 (1986) 45–66. [2] H. Rahnejat, Multi-body Dynamics: Vehicles, Machines and Mechanisms, London, Professional Engineering Publishing, 1998. [3] G. Weidner, Klappern und Rasseln von Fahrzeuggetrieben (Ph.D. thesis), University of Stuttgart, 1991. [4] C.-H. Lang, Losteilgeraeusche von Fahrzeuggetrieben (Ph.D. thesis), University of Stuttgart, 1997. [5] A. Baumann, P. Fietkau, B. Bertsche, R. Boehnke, K. Hagemann, W. Krechberger, J. Zinsser, Reduction of the gear-rattle noise level of automotive transmissions using innovative gear lubricants, in: Proceedings of the International VDI Congress Transmissions in Vehicles, Friedrichshafen, Germany, 2010, pp. 373–393. [6] A. Baumann, P. Fietkau, B. Bertsche, R. Boehnke, K. Hagemann, W. Krechberger, J. Zinsser, Influence of the lubricant on the gear-rattle noise level of a manual transmission system, in: Proceedings of the 17th International Colloquium Tribology, Ostfildern, Germany, 2010. [7] A. Baumann, Rasselgeraeuschminimierung von Fahrzeuggetrieben durch Getriebeoele, (Ph.D. thesis), 2013, University of Stuttgart, http://elib. uni-stuttgart.de/opus/volltexte/2013/8759/ (accessed 19.11.13). [8] J. Rach, Beitrag zur Minimierung von Klapper- und Rasselgeraeuschen von Fahrzeuggetrieben (Ph.D. thesis), University of Stuttgart, 1998. [9] R. Brancati, E. Rocca, R. Russo, F. Timpone, Experimental test rig for the evaluation of oil squeeze effects between the impacting teeth of a meshing gear pair, in: Proceedings of the 5th International Conference on Tribology, Parma, Italy, 2006. [10] R. Russo, R. Brancati, E. Rocca, Experimental investigations about the influence of oil lubricant between teeth on the gear rattle phenomenon, Journal of Sound and Vibration 321 (2009) 647–661, http://dx.doi.org/10.1016/j.jsv.2008.10.008. [11] O. Tangasawi, S. Theodossiades, H. Rahnejat, Lightly loaded lubricated impacts: idle gear rattle, Journal of Sound and Vibration 308 (2007) 418–430, http://dx.doi.org/10.1016/j.jsv.2007.03.077. [12] M. De la Cruz, S. Theodossiades, H. Rahnejat, An investigation of manual transmission drive rattle, Proceedings of the Institution of Mechanical Engineers Part K: Journal of Multi-body Dynamics 224 (2010) 167–181, http://dx.doi.org/10.1243/14644193JMBD232. [13] S. Theodossiades, O. Tangasawi, H. Rahnejat, Gear teeth impacts in hydrodynamic conjunctions promoting idle gear rattle, Journal of Sound and Vibration 303 (2007) 632–658, http://dx.doi.org/10.1016/j.jsv.2007.01.034. [14] A. Crowther, C. Halse, Z. Zhang, Nonlinear Responses in Loaded Driveline Rattle. SAE Technical Paper Series 2009-01-2068, http://dx.doi.org/10.4271/ 2009-01-2068. [15] A. Baumann, P. Fietkau, B. Bertsche, Nachbildung verbrennungsmotorischer Drehschwingungen auf einem Getriebepruefstand für Rasselgeraeuschuntersuchungen, in: Proceedings of the Stuttgarter Symposium fuer Produktentwicklung, Stuttgart, Germany, 2011, pp. 96–97. [16] P. Fietkau, A. Baumann, B. Bertsche, Rasselgeraeuschpruefstand zur Untersuchung von Fahrzeuggetrieben, in: Proceedings of the Mueller-BBM VibroAkustik Systeme PAK-Tag, Herrsching, Germany, 2011, http://elib.uni-stuttgart.de/opus/volltexte/2011/6299/ (accessed 10.08.13). [17] M. De la Cruz, S. Theodossiades, P. King, H. Rahnejat, Transmission drive rattle with thermo-elastohydrodynamic impacts: numerical and experimental investigations, International Journal of Powertrains 1 (2011) 137–161, http://dx.doi.org/10.1504/IJPT.2011.042764. [18] G. Niemann, H. Winter, Maschinenelemente Band 2, 2nd ed. Springer, Berlin Heidelberg, 2003.