In the design of transmissions, the high demands on running and noise behavior are fulfilled by specific topography designs, therefore a compromise must be found between low gear excitation, sufficient load carrying capacity, and high efficiency.

The noise behavior of transmission is mainly caused by the excitation in the gear mesh. The standardized design and calculation methods for gears concentrate on the reduction of the excitation level. However, often the physical noise characteristics do not conform with the human noise perception. Thus, gear design rules and guidelines are required that are able to rate the excitation according to the perception.

The effect of the targeted topography scatter generally described is the reduction of the gear mesh amplitudes with an increase of the background noise. In this report, the noise behavior of bevel gears is investigated with a targeted topography scattering. The excitation and noise behavior are analyzed from the excitation in tooth contact by transmission error measurements up to noise emission in the form of airborne noise. Finally, it is the objective to evaluate the impact of individual topography scattering on the dynamic noise behavior. The analysis of the noise behavior of two variants are compared regarding the difference in psychoacoustic parameters such as loudness and tonality. The potentials of the topography deviation for the optimization of ground bevel gears in terms of tonality reduction will be shown by test results. A test fixture for the evaluation of the operational behavior under loaded and dynamic conditions will be used. Finally, the method is applied to a vehicle transmission and the noise behavior on the test bench and inside of the vehicle is investigated and evaluated.

Increasing sensitization for the topic noise, reduced masking noises and increased customer demands lead to an increasing importance of transmission noise. Especially due to the tonal characteristic of gear whining, gear noises move quickly and negatively into the customer’s focus [1]. One of the most important criteria in the qualitative evaluation of gear transmissions in automotive engineering is the noise behavior [2]. The control of vibrations and the optimization of noise behavior inside of the vehicle is therefore an important development aim of automobile and transmission manufacturers [3]. A large part of the vibrations and noises inside of a vehicle is generated in the drive train. Especially in motor vehicles, the reduction of masking noise sources through downsizing as well as electrification and hybridization of the drive train increases the importance of a low-noise transmission [4].

However, increasing the quality of the gears and decreasing the gear excitation does not prevent the gear noise from being perceived as annoying. For an improvement of the perceived noise quality, a reduction of the noise level alone is not always the best solution. The characteristics of the noise and thus the human perception are decisive [5].

In the design of transmissions, the high demands on running and noise behavior are fulfilled by specific topography designs. A compromise must be found between low gear excitation, sufficient load carrying capacity, and high efficiency. The selection of the target topography for an optimized operational behavior over a wide torque range is the challenge in gear design [6]. Up to now, the quasi-static transmission error of a gear set is used as an evaluation variable for the resulting noise behavior. The transmission error of a transmission is the excitation source of the dynamic system, which leads to a dynamic load fluctuation in the gear mesh due to interaction with the operating point-dependent dynamics of the drive train [5].

1 State of the Art

1.1 Source-Path-Receiver Concept of the Bevel Gear Transmissions

The dominant noise characteristic of gears is howling and whining at high frequencies. This is caused by rolling the gear pair under load. Figure 1 shows the source-path-receiver concept of a gear. The source- path-receiver concept systematically describes the origin and transfer of the gear whining up to the hearing-related evaluation of the noise. Here, the noise behavior of a transmission can be represented by the machine acoustic transfer chain consisting of noise excitation (source, tooth mesh), noise transfer (path, structure-borne noise), and noise radiation (receiver, airborne noise).

Figure 1: Source-Path-Receiver concept of bevel gear transmission [5].

The starting point of the noise generation chain is the quasi-static gear excitation. The gear excitation is quantifiable as the transmission error of a gear set and leads in interaction with the operating point- dependent dynamics of the drive train to a dynamic load fluctuation in the gear mesh. The resulting vibrations in the tooth contact are transmitted as structure-borne noise to the shaft bearing system and subsequently to the housing surface. Depending on the structural dynamic properties of the transmission, the structure-borne noise is converted into airborne noise in the form of noise-pressure fluctuations on the surfaces. Psychoacoustic evaluation methods are used to evaluate the effect of physical noise on the human hearing. The principle illustrates the connection between the gear excitation and the perception- specific noise characteristics of a transmission [5]. 

1.2 Psychoacoustic Metrics for the Evaluation of Human Noise Perception

The loudness describes the frequency-dependent sensitivity of human noise perception and has the unit sone. DIN 45631/A1 describes a standardized procedure for determining loudness based on a loudness comparison between sinusoidal tones and noises, compare Figure 2. Thus, as shown in the audible frequency range, according to Zwicker it is divided into 24 frequency groups (0 bark to 24 bark), and the respective sound level is weighted according to human hearing sensitivity. The method is suitable for comparing the loudness of noises with different spectral resolution [7, 8].

Figure 2: Psychoacoustic metrics for the evaluation of human noise perception [7, 8, 9, 10].

An essential feature for the characterization of gear noise is the tonality. Noise is perceived as annoying if it is composed of individual, strongly pronounced tones or narrow-band frequencies. The Sottek hearing model is used to determine tonality. Previous algorithms for calculating tonality did not take into account or did not take sufficient account of short-term changes in tonality due to the low-time resolution. In addition, tonalities below the hearing threshold are considered, although they are irrelevant for the human hearing. The new method according to Sottek includes the human hearing limit and the dependence of noise perception on psychoacoustic loudness. The method determines the loudness of tonal and non-tonal noise components using a permanently performed autocorrelation function. By means of a high temporal resolution, short-term and strongly fluctuating tonalities can be examined. The algorithm also allows the strength and frequency of the tonality to be determined relative to the time and rotational speed. The tonal value according to the Sottek hearing model is described in the unit tuHMS [9, 10]. Both psychoacoustic metrics loudness and tonality have a linear scale of intensity. In addition, the metrics were developed and validated in extensive listening tests [7, 8, 9, 10].

1.3 Approaches to the Optimization of the Psychoacoustic Behavior of Gear Noise

In the following section, various approaches in the field of gear and transmission technology are presented in order to optimize the psychoacoustics of gear noise. The approaches represent industrial practice and the state of research.

1.3.1 Noise Optimization of a Continuously Variable Transmission by Random Pitch Sequence

A continuously variable transmission (CVT) enables smooth speed change by adjusting, for example, the wrap diameter of a transmission chain. The advantages of a continuously variable transmission include high driving comfort due to the smooth speed change, low fuel consumption, and good driving dynamics. Power is transmitted via the CVT-chain with wrap elements, which consists of chain plates, rocker pressure pieces, and safety elements. The acoustic behavior of the drive train is optimized by the targeted use of different chain linkage lengths in a defined sequence. The CVT-chain can be designed and acoustically optimized on the basis of simulations by specifically adjusting the mixing ratio and the pitch sequence. The result is an improvement of the unpleasant tonality of the chain mesh. Figure 3 compares the acoustic measurements of a CVT inside of the vehicle with tabs of the same size in the initial state (equal pitch chain) and the sequence of parts after optimization. The sound level peaks of the equal pitch chain result from the meshing of the tab into the disk sets and can be reduced by tab lengths in random order [11].

Figure 3: Noise Optimization of a CVT-chain by random pitch sequence [11].

1.3.2 Optimization of Gear Noise by Stochastic Surface Structures

An approach to improve the excitation behavior of ground bevel gears is the MicroPulse process developed by Stadtfeld et al. The MicroPulse process produces quasi-random surface modifications. The quasi-random structure of the flank surface produces a diffuse structure like a lapped surface and reduces the amplitudes of the higher harmonic excitation of the gear mesh [12, 13].

1.3.3 Optimization of Gear Noise by Sinusoidal Transmission Error Characteristics

Stadtfeld shows the possibility of designing a sinusoidal transmission error curve through a targeted EaseOff design. This approach reduces the amplitudes of the higher harmonic gear mesh orders in the transmission error spectrum. A gear set with a sinusoidal transmission error curve produces a calm and quiet noise. [14]

1.3.4 Optimization of Gear Noise through Targeted Topography Scattering

A targeted topography or micro geometry scattering on the pinion and gear achieves an individual transmission error design of the individual tooth meshes to generate a higher background noise level. In addition to increasing the background noise level, the amplitudes of the gear mesh orders in the transmission error spectrum can be significantly reduced [15].

The analysis of the noise behavior with psychoacoustic parameters shows a low topography scattering on pinion and gear can influence the noise behavior characteristics of bevel gears [16]. The tonality is significantly reduced by up to 50 percent by increasing the background noise component and reducing the transmission error amplitudes of the gear-mesh orders. Furthermore, the test results of Geradts et al. show the other psychoacoustic parameters are not adversely affected by low topography scattering [17].

In the research work of Kasten et al., restrictions for the design of topography scattering on ground bevel gears were developed. In addition, it could be shown that an optimization of the excitation behavior can already be achieved by applying a topography scattering with two to four different topographies, which are randomly distributed over all teeth of the component. The complexity of manufacturing and quality control of gears with mixed topographies is reduced by this insight. By comparing different types of scattering, the random application of topography parameters and the random distribution of the different topographies from tooth to tooth were identified as the successful approach. The identification of the main influencing variables of the topography parameters showed the scattering of the angle modifications (profile and flank angle modifications) have a significant influence on the psychoacoustically optimized excitation behavior. By separately applying topography scattering to the pinion and the gear, it could be demonstrated that the complete optimization potential of topography scattering on gears can be achieved by generating mixed topographies on pinion and gear [18].

1.4 Conclusion from the State of the Art

The generation of noise in a transmission is essentially determined by the vibration excitation in the gear mesh [6]. In the case of the improvement of the excitation behavior over a wide torque range, the topography of the gears is optimized, e.g. by the targeted application of flank modifications. Nevertheless, the gear noise can be perceived as unpleasant for the human ear, although the product quality is increased, and the excitation level is reduced [5]. Therefore, it is not the reduction of the noise level that is relevant, but rather the investigation of the noise composition and characteristics for an optimization of the gear noise perceived by humans [5].

There are already approaches in industry for reducing the tonal components in the noise spectrum of a transmission, for example by a stochastic surface structure of the tooth flanks [12, 13] or a random pitch sequence of chain tabs of a CVT [11]. Similarly, the tonality of the gear noise can be reduced by a targeted scattering of the topography [18].

Topography scattering has not yet been applied to a vehicle transmission. Moreover, measurements on the transmission test bench and vehicle measurements do not exist to verify the psychoacoustic optimization objectives in the design of topography scattering.

2 Objective and Approach

The investigations described in the present paper were conducted as a part of a project sponsored by German Research Foundation (DFG) [Project Number BR 2905/82-1], which is carried out with the cooperation partners Daimler AG and Klingelnberg GmbH. The objective of the research project is the development of a method for the perception-oriented design of ground bevel gears by the application of a targeted topography (micro geometry) scattering. The subjective noise behavior of ground bevel gears is to be improved without resulting in a loss of load capacity or productivity.

With the minor disturbance of the meshing conditions by topography scattering, the regularity of the transmission error signals in the time domain is disturbed and the background noise is increased. This is a new approach for the design of the target geometry of gears.

The objective of this research report is: Reduction of the tonality of gear noise for ground bevel gears.

The approach to achieve the research objective is shown in Figure 4. At the beginning, a micro geometry scattering is designed and manufactured for a ground bevel gear set from the automotive industry. The gear sets are then tested for their excitation behavior in a bevel gear tester and a measuring cell. A single flank test is performed in the bevel gear tester to measure the transmission error at low load. In addition, the dynamic excitation behavior under load and higher rotational speed in a bevel gear measuring cell is investigated. For a better understanding of the influence of topography scattering on excitation and noise behavior, the acoustic behavior along the source-path-receiver concept is investigated. The noise behavior of bevel gears with targeted topography scattering is then analyzed using psychoacoustic metrics to verify the design objectives.

Figure 4: Approach to reduce of the tonality of the gear noise.

The design method is then transferred to a vehicle transmission (light commercial vehicle rear axle). The gear sets are again designed and manufactured (change of the micro geometry). The new gear sets are mounted in the rear axle and acoustically measured and analyzed on the transmission test bench. Finally, the rear axles are installed in the vehicle, and the noise inside of the vehicle is analyzed with psychoacoustic metrics.

3 Test Gears and the Bevel Gear Measuring Cell

3.1 Test Gears

The gear set was developed for an automotive application. All the bevel gears investigated in this report have the same macro geometry. The reference gear set is ground with high pitch quality and low topography deviation. Two further variants are based on a lapped gearing with regard to their manufacturing deviation. These have a small individual deviation from tooth to tooth, also with small pitch deviation. By means of mixing the topographies of the individual tooth flanks, the noise behavior of ground gear sets is adjusted to the noise behavior of a lapped gear set [16, 19]. The values of the crowning (PC = profile crowning, LC = lead crowning) and angular modification (α = pressure angle, β = spiral angle, cv = twist) are shown in Figure 5, bottom left. The variant R02 has a random distribution of the maximum values of 2 μm or 0.02°. For variant N10, however, the values for the individual flank modifications were selected according a normal distribution around the nominal design. The maximum allowed values are 10 μm or 0.10°.

Figure 5: Test gear set.

The averaged topography of the mixed topography variants equals the nominal topography of the reference variant. Both variants with micro geometry scattering have a small pitch error of Q2 on pinion and gear. For the basic design of the micro geometry of the drive flank, high lead and profile crowning have been selected, which can be seen from the Ease-Off. Due to the high crowning values, the contact pattern displacement under load is reduced, and the gear set is less sensitive to mounting deviations with regard to the excitation behavior.

All modifications should be realized in the grinding machine by manipulation of the machine axes and not by redressing the grinding wheel. Therefore, the degree of freedom in the topography scatter was limited. The pinion is ground in the generating process, which means all deviations (i.e. angle and crowning deviation in lead and profile direction and flank twist deviation) can be varied. The flanks of the gear are ground with a plunging process. The plunging is restricted in the micro geometry variation. Therefore, only pressure angle and spiral angle deviations are allowed. This restriction reduces the complexity of grinding micro geometry scattering.

3.2 Bevel Gear Measuring Cell

The bevel gear measurement cell used for the excitation — and noise behavior investigations at operational conditions for bevel gears — is shown in Figure 6. The fixture consists of a modular frame structure on which the bearing plates are assembled. An adjustment of the hypoid offset is realized by additional bearing plates for the pinion side (3). The base is built by the stiff frame structure, which is milled out of solid material. The characteristic mounting dimensions of the gear sets to be tested can be set with high precision and repeated accuracy. The pinion and gear mounting dimensions are positioned using two-piece shim plates (1,2) ground in pairs. The axle offset V is determined by the pinion cartridge plate (3) and the axle cross angle by the housing plates of the pinion and gear. The angular encoders (4) for the quasi-static transmission error measurement of the type Heidenhain 4202 C are based on a photoelectric scanning principle, and each consists of a rotor and a stator. The scale drum provides 20,000 increments per revolution and, hence, generates very small signal periods for the output signal. The high resolution of the rotational angle signal ensures the detectability of higher harmonic excitation of the transmission error. The non-contacting, optical measurement principle requires an atmosphere free of oil and dirt.

Figure 6: Bevel gear measuring cell for the investigation of excitation and noise behavior.

Furthermore, a high accuracy is necessary as the nominal radial distance between scale drum and reader head is 0.1 mm. The reader head is attached to the ground plate of the bevel gear fixture. The encoder-specific error due to assembly or geometric tolerances occurs only once per revolution. Therefore, it influences only the rotational order of the transmission error signal. The measurement of the differential torsional acceleration is realized by an acceleration measurement system (5) with a telemetric system on the pinion and the gear shaft. The acceleration measurement system (5) consists of two structure-borne noise sensors tangentially arranged on a reference diameter with a 180° offset against each other and housed in an aluminum rotor disk. The energy supply is realized by an induction coil wound around the outer diameter of the rotor housing. The acceleration signals are summed up to compensate radial vibrations. The data transfer to the stator is done via a high frequency modulation. The stator is attached to the housing and is positioned with a radial distance of 1 mm above the rotor, which allows a measurement at dynamic conditions [17].

The rotary acceleration measurement system is insensitive to running in oil, which allows a close position to the bearing package without an additional sealing. The encoder system needs to run in a dry, oil-free environment. The oil supply is realized by injection lubrication using a temperature controlled external oil supply unit. The central oil inflow is divided with a separately regulated two-way valve. One pipe feeds the oil in the gear mesh, and the other supplies oil to the bearing positions. Finally, structure-borne noise sensors close to the bearing points and an airborne noise microphone are applied [17].

4 Investigation of the Quasi-static Excitation Behavior

Figure 7 shows the order spectra of the transmission error of the single flank test and the curves of the loaded transmission error for the first and second gear mesh orders. The quasi load-free single flank test was performed on an Oerlikon bevel gear tester T60. All data on the transmission error are normalized. The measured signals from the single flank test are transferred into the frequency domain. The relative reduction of the gear mesh amplitudes in comparison to the reference variant is displayed. The transmission error spectra of the individual gear set variants clearly show the effect of micro geometry scattering on the excitation behavior. The variants R02 and N10 with micro geometry scattering are characterized by reduced amplitudes of the transmission error of the gear mesh orders (1st fz, 2nd fz, 3rd fz and 4th fz). In addition, the topography scattering leads to a significant increase in the rotational orders below the first gear mesh order and to a background noise in the spectrum. The amplitudes of the low order range of the R02 variant are at a comparable level to the first gear mesh amplitude. In contrast, for variant N10, the amplitudes below the first gear mesh orders 1st fz are higher than the first gear mesh amplitude. In general, the variant N10 has the highest background noise as well as the lowest amplitudes of the gear mesh orders in the transmission error spectrum.

Figure 7: Single flank testing of the gear sets in a bevel gear tester and the bevel gear measuring cell.

The measurement of the loaded transmission error (LTE) using the bevel gear measurement cell shows the effect of the topography scattering under operating conditions, compared in lower diagrams in Figure 7. By using the bevel gear measuring cell, it is possible to specifically examine a bevel gear set up to an output torque M2 = 1,200 Nm. In order to test the quasi-static excitation of the gear set variants, the single flank test was carried out at a low rotational speed of n1 = 60 rpm. Due to the low-test rotational speed, dynamic interaction with the drive train can be avoided. The amplitudes of the first and second gear mesh order (1st fz and 2nd fz) are significantly reduced compared to the reference variant.

Summarizing the effect of the novel optimization method using a targeted topography scattering, the tonal character of the transmission error caused by the regularity of the gear meshes was broken up. Non-gear mesh amplitudes rise in the low frequency range below the first gear mesh order for the variants R02 and N10. The higher harmonic excitation was reduced significantly, which was masked by the background noise.

5 Investigation of the Dynamic Excitation Behavior and Noise Behavior

This section analyzes the measurement along the Source-Path-Receiver concept. The effects of micro geometry scattering on the noise behavior will be investigated. The sensor technology for the investigations is shown in Figure 6. The noise behavior of gears depends on the interaction between the dynamics of the drive train and the excitation from the tooth mesh. If the excitation frequency of the gears hits a natural frequency of the drive train, increased vibration amplitudes result.

5.1 Evaluation of the Excitation and Noise Behavior based on the Source-Path-Receiver Concept

The measurement of the differential rotational acceleration (dynamic gear excitation), the structure-borne noise (vibration transfer), and the airborne noise (physical noise) was carried out at a constant output torque of M2 = 400 Nm and a speed ramp of n1 = 600 rpm to 3,400 rpm. The results of the different sensors are displayed in Figure 8. As an example of the effect of micro geometry scattering on the noise behavior of bevel gears, variant R02 was analyzed in more detail and compared with the reference gear set. The order spectra of the gear sets show a gear mesh excitation up to the third order.

Figure 8: Evaluation of the excitation and noise behavior based on the Source-Path-Receiver concept.

The analysis along the Source-Path-Receiver chain shows the effect of micro geometry scattering on bevel gears. The reduction of the transmission error amplitudes of the gear mesh orders, as well as an increase of the background noise in the transmission error spectrum in the quasi-static, can be found in the dynamic gear excitation. As in the quasi-statics, dynamic gear excitation also shows the amplitudes below the first gear mesh order are increased. However, the vibrations in the dynamics do not appear as strongly as in the quasi-statics. In the structure-borne noise spectrum, the increased vibration amplitudes below the first gear mesh order cannot be detected. The reduction of the gear mesh order and its higher harmonics through the application of a micro-geometry scatter is visible in structure-borne noise. In airborne noise, the characteristic tonal excitation of the reference variant is perceptible. In the variant R02 with topography scattering, the gear mesh orders, apart from the first one, are lost in the background noise.

5.2 Psychoacoustic Evaluation of the Noise Behavior

Comprehensive investigations with regard to the transferability of psychoacoustic parameters as airborne noise events on the measured structure-borne noise at transmissions show a high quality [5, 20]. For this reason, the structure-borne noise at the ring gear bearing location is used as the evaluation parameter for psychoacoustic analysis.

Tonality is an essential attribute for the characterization of gear noise. Noises are perceived as annoying if they are composed of individual, strongly defined tones or narrow-band frequencies. To determine the tonality, the hearing model according to Sottek is used [9, 10]. The tonality with the unit tuHMS has a linearity to human perception. A quantitative comparison of the tonality of the gear set variants is shown in the upper part of Figure 9. In the upper left diagram, the tonality is plotted at an output torque of M2 = 400 Nm versus the speed. The reference gear set with the single tooth topography has a clearly higher tonal excitation in the speed range from n1 = 1,500 rpm to 3,500 rpm. In order to investigate the tonality at different load levels, the tonality is plotted as a single value over the output torque M2 in the upper right diagram. The single-number value is the mean value over a speed ramp-up at a constant load. The torque is investigated from M2 = 100 Nm to 1,000 Nm at the drive flank. Here, the advantages of the individual topographies from tooth to tooth can be clearly seen. By reducing the amplitudes of the gear-mesh orders and increasing the background noise in the spectrum at the same time, the tonality of the gears with mixed topographies has decreased significantly.

Although the tonality of the reference variant increases with the load, the variants R02 and N10 show load-independent behavior in the investigated torque range. The micro-geometry scattering from tooth to tooth is greatest in the N10 variant in terms of magnitude, which is also characterized by the lowest tonality of all variants.

The psychoacoustic parameter of loudness according to DIN 45631/A1 in the unit sone represents the frequency-dependent sensitivity linear to perception [7]. In analogy to tonality, the loudness of the gear set variants is compared in Figure 9. The loudness curve over the rotational speed at a constant torque of M2 = 400 Nm is shown in the lower left diagram. This shows that, in all variants, the loudness increases with rising speed. There are no significant differences between the variants. Only in the variant R02 with micro geometry scattering, the loudness curve does not correlate with the speed from n1 = 2,500 rpm. The single-number values of the loudness over the torque are shown in the lower right diagram. The loudness curve over the load of the reference variant correlates with the curve of the loaded transmission error (LTE), see Figure 7. The variants with mixed topographies show a more load-independent behavior and do not correlate with the loaded transmission error curve over the torque.

Figure 9: Psychoacoustic evaluation of the noise behavior.

Overall, the evaluation of the excitation and noise behavior along the source-path receiver concept shows the method for a perception-oriented design of micro-geometry scattering on ground bevel gears can usefully optimize the acoustic behavior.

6 Transfer of the Method to a Vehicle Application

Due to the promising results of the method for perception-oriented design of micro-geometry scattering on bevel gears, the method is transferred to a vehicle transmission. The vehicle transmission is a beam style rear axle in a light commercial vehicle. During the transfer of the method, the macro geometry from section 4.1 was retained. The micro geometry was adapted for the vehicle transmission with lower crowning.

6.1 Investigation of the Noise Behavior of a Light Commercial Vehicle Rear Axle

First, the noise behavior of the rear axle is investigated on a transmission test bench. New gear sets were designed and manufactured without topography scattering (reference) and with topography scattering (MixTop). After the manufacturing of the gear sets, they were mounted in the rear axle. Figure 10 shows the structure-borne noise (SBN) signal at the transmission input (pinion bearing) as a frequency spectrum for the two variants Reference and MixTop. For this purpose, a speed ramp-up from n1 = 500 rpm to 4,500 rpm was carried out with a torque M1 = 300 Nm in drive mode.

Figure 10: Frequency spectra of the structure borne noise of a light commercial vehicle rear axle with and without mixed topographies.

The comparison of the frequency spectra clearly shows the advantage of topography scattering. The MixTop variant has significantly lower amplitudes of structure-borne noise, especially for the higher harmonics of the gear mesh order (2nd to 8th fz). This means that single frequencies in the spectrum do not appear so dominant.

Especially the natural frequency of the drive train at approximate fnatural = 3,900 Hz is excited very tonally by the reference variant. Whenever a gear-mesh frequency hits the natural frequency, there are strong vibration amplitudes. Due to the irregular course of the transmission error during a topography scattering, however, a broadband excitation does not lead to such a strong excitation of single frequencies in the spectrum. The significant natural frequency of the drive train at approximate fnatural = 3,900 Hz is excited by the variant MixTop in a broadband way and not so tonal.

The effect of the different excitation and noise behavior of the variants in the vehicle axle can be described by psychoacoustic metrics. Figure 11 shows the two psychoacoustic metrics tonality and loudness over rpm. The average value for rpm ramp-up is also evaluated and shown.

Figure 11: Psychoacoustic evaluation of the structure-borne noise of the rear axle.

The evaluation of the tonality of the structure-borne noise signal at the transmission input clearly shows the variant with topography scattering (MixTop) shows low tonality over the rpm range. This is due to the broadband excitation of the gear set. On average, the tonality could be reduced by 30.1 percent over the complete rpm range, which is considered as a significant improvement. A consideration of the average value is very well verifiable with psychoacoustic metrics, because the values of the metrics are linearly scaled.

The evaluation of the loudness shows the broadband excitation of the MixTop variant does not lead to a more audible loudness of the vehicle axle compared to the reference variant. On the contrary, the optimized noise behavior of the MixTop variant even leads to a reduction in average loudness. In the speed range from n1 = 4,000 rpm to 4,500 rpm, the fifth gear mesh order (5th fz) hits the natural frequency fnatural = 3,900 Hz, see Figure 10. In this range the tonality as well as the loudness of the reference is clearly increased in comparison to the MixTop variant, due to the small band excitation of the gear mesh orders.

6.2 Psychoacoustic Evaluation of the Vehicle Inside Noise

After investigating the noise behavior of the vehicle axles on the transmission test bench, the vehicle axles are mounted in the vehicle and acoustically measured in a defined driving cycle. Figure 12 shows the evaluation of airborne noise inside of the vehicle using psychoacoustic metrics. The noise inside of the vehicle is recorded via a headphone system with microphones. The driver wears the headphone system so the airborne noise is recorded from the driver’s perspective. With the recording of airborne noise, all noise-emitting components inside of the vehicle will be recorded. In the low-frequency range, this is mainly the combustion engine. At higher speeds, the proportion of tires and wind noise increases. The measurement is carried out in 4th gear (i4thGear = 1) of the manual transmission. The driver adjusts a constant torque M1 = 250 Nm by adjusting the gas pedal position.

Figure 12: Psychoacoustic evaluation of the airborne noise inside of the vehicle.

The psychoacoustic evaluation of the noise inside of the vehicle also shows very positive effects due to topography scattering. In the same way as in the investigation of the noise behavior of the vehicle axle, the behavior of tonality and loudness over a speed range (n1 = 1,500 rpm to 3,500 rpm) is plotted during the psychoacoustic evaluation, and the average values are displayed. The tonality of the noise inside of the vehicle with the reference vehicle axle shows strong peaks in the speed ramp. In particular, the strong increase at n1 = 1,600 rpm can be rated as very negative. During vehicle testing, the rotational speed of the propeller shaft can easily be converted into the driving speed. The propeller shaft speed of n1 = 1,600 rpm corresponds to a driving speed of v = 31 mph (assumption: i4thGear = 1, iRearAxle = 4.18, rdyn = 346 mm/13.6 inches). At these low speeds, there is only low masking noise from wind and tire noise so that noise from a transmission can be recognized easier. Therefore, the peak of tonality in this range is very critical. The MixTop variant does not show any prominent peaks in the vehicle, especially not in the critical low-speed range. Over the entire vehicle speed range, the tonality was reduced by an average of 22.4 percent. The loudness of the noise inside of the vehicle was not influenced by the vehicle axle with topography scattering.

7 Summary and Outlook

In order to improve vehicle acoustics, the engineer is continuously faced with new challenges. A major part of the vibrations and noises inside of a vehicle are caused by the drive train. Especially in motor vehicles, the reduction of masking noise sources through downsizing, as well as electrification and hybridization of the drive train, increases the importance of a low-noise transmission. The optimization of transmission acoustics should not be based on the reduction of physical noise alone. Rather, aspects of noise composition and quality come to the foreground. Hence, the objective of improving transmission acoustics is to make noise more pleasant and less annoying to the human ear.

A novel NVH optimization approach is introduced. A targeted topography scatter is applied on the gear teeth in order to manipulate the regularity of the conventional gear-mesh excitation. The effect of the targeted topography scatter generally described is the reduction of the gear-mesh amplitudes with an increase of non-gear-mesh amplitudes in the low order range and an increase of the background noise. Thereby, the prominence of the gear mesh amplitudes is reduced. The higher harmonics were already canceled out at moderate scatter values. The great advantages, especially the reduction of tonality of topography scattering, could be demonstrated in noise investigations from the gear mesh in the transmission to the noise behavior inside of a vehicle.

The optimization approach with a targeted topography scatter represents a novelty in the gear design and shows a high potential for improving the NVH behavior of transmissions. However, more in-depth analyses of the influence of micro-geometry scatter on the load carrying capacity and efficiency must be carried out. With these findings, a complete design of micro-geometry scatter can be carried out, taking into account the excitation behavior as well as the efficiency and the surface stress. A transfer of the design method to cylindrical gears is also a goal. The design method is to be applied to other vehicle transmissions. The design objectives are to be verified by further measurements on the transmission test bench and by vehicle measurements.


The investigations described in the present paper were conducted as a part of a project sponsored by German Research Foundation (DFG) [Project Number BR 2905/82-1]. This project is carried out in cooperation with the industrial partners Daimler AG and Klingelnberg GmbH. 


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