Presenting the increasing requirements for efficient gearing production for e-motive applications from a machine tool manufacturer’s point of view as well as the influencing factors of the NVH behavior regarding the gear-generating process.

The topic of this article is the changing focus in gear design and the resulting challenges in gear production, in particular for continuous generating gear grinding with the rising influence of the E-mobility in the automotive industry. Especially the subdomain Noise-Vibration-Harshness, also known as NVH, has become one of the most important topics in the development of automotive drive trains.

Besides the current challenges of E-mobility drivetrains and the working mechanisms behind gear noise excitation, the authors will show a quick technological overview of the most important characteristics of the continuous generating grinding process.

Knowing the characteristics of the generating grinding process, as well as the root causes of gear noise excitation in the gearbox, methods for optimizing the NVH-behavior of a gear will be presented. A comprehensive approach has to consider the whole process containing the gear design and all the involved manufacturing processes.

Even though all influence factors of the grinding process have been optimized according to best practice, it is still possible that ground gears fail on the end-of-line test bench due to increased noise level. In this case, it is important to know which tools are available to reliably identify the sources of NVH issues and therefore be able to fix them. In particular, the external excitation of components in the grinding machine, which typically results in NVH issues, will be discussed. In this context, the article will show the fundamental effects of external excitation frequencies in the grinding machine and an approach to solve the problem.

1 Introduction

1.1 Noise Excitation in the Electric Drivetrain

Electric mobility poses new challenges to the development of transmissions. As a rule, the gear stages feature high gear ratios due to high input revolutions. This leads to specific characteristics in the gear tooth meshing. The high input revolutions directly influence the dynamic excitation of the drive train and the transmission’s housing structure, and therefore, gear noise. The problem is reinforced by the lack of noise masking from the internal combustion engine and the electric motor’s low noise emissions.

In fast-running transmissions, the occurring short-wave excitations only have an impact regarding the first tooth meshing order, whereas with increasing revolutions, the higher harmonics fall outside the audible range, see Figure 1. In contrast, the order of rotational symmetry and the higher harmonics are within the audible and sensitive range of human perception across a wide frequency band.

Figure 1: Excitation Behavior of an Electric Drive Train [1].

1.2 Mechanics of Gear Noise Excitation

Two main components are responsible for noise excitation within a gearbox [2]:

Gearings:

  • Changing lever ratios in the meshing process and thus changing meshing stiffness and paired gear tooth stiffness, changing the stiffness of the overall system.
  • Changing curvature radii in Hertzian contact.
  • Deviation from the ideal gearing contour.

– Modification of the gear teeth (changing deformation under load).

– Process-related deviations such as process-induced twist.

  • Surface structure (waviness) and roughness of gear flanks.

– Periodic deviations (waviness) on the gear flanks
due to excitation in the hard finishing process. Shaft-Bearing-System:

  • Rotational irregularities such as out-of-roundness of gear shafts.
  • Self-excited vibrations of the roller bearings.

To make gear noise “visible,” specific methods are widely used in industrial praxis, e.g., torsional and bending acceleration at the gear bodies, structure-borne sound at the bearing shields or housing, and rotational angle of the gears. Therefore, a so-called “End-of-Line” (EoL) test rig equipped with appropriate measuring equipment is used to evaluate NVH issues.

The analysis of the discrete-time signals is usually done in the frequency domain (Fast Fourier Transformation FFT) – as a Campbell diagram in frequency order representation. The order representation is a proven method for the spectral analysis of rotating machine elements. The excitation order is, therefore, a multiple of the rotational speed of the shaft or gear. The resulting excitations within the tooth meshing frequency and higher harmonics correspond to the excitation orders number of teeth and their multiples. [3]

For drawing a fast correlation between the EoL-results and a gear measurement, the so-called “Waviness Analysis” is often used in industrial applications [4]. It allows the direct determination of the profile and lead waviness on the individual test gear. As this method establishes the periodic deviations directly on the individual test gear, it is a useful addition to the measurement via the machine or test rigs. However, a waviness analysis cannot predict a gear pair’s noise excitation behavior.

2 Principles of Continuous Generating Grinding

Continuous generating grinding is a generating process according to the principle of a screw gear pair with contact on the left and right flank simultaneously. It is a highly productive process due to tools with a multiple number of starts and, therefore, very short process times. Corundum or CBN grinding tools can remove the material with a geometrically undefined cutting edge, yielding positive characteristics such as small pitch and runout deviations and the possibility to grind the root area. Nevertheless, process-induced feed marks or profile shape deviations and micro-geometric waviness can occur.

Figure 2: Characteristics and kinematics of generating grinding [3].

In principle, the kinematics of the continuous generating gear grinding process, as shown in Figure 2, can be understood as a worm drive, with an additional abrasive machining process consisting of an infeed X, a vertical feed-rate Z, and a lateral shifting motion Y, all working together simultaneously.

In the case of involute-shaped workpiece flanks, the flanks of the generating worm have an involute shape. Due to the screw gear pair kinematics, the spatial line of contact between the workpiece and grinding worm is the common intersection line between the two tangent planes of the base cylinders, including the pitch point. The common reference profile has contact lines on its flanks that are inclined at the base helix angle.

3 Influences of the Manufacturing Process on the Gear Noise Excitation and NVH-optimized Measures

3.1 Force Fluctuation and Optimization of the Meshing Behavior

Due to periodic fluctuations of the cutting force during one generation, profile waviness on the workpiece profile can occur, especially on gears with a low number of teeth. A variable number of flanks causes this during one generation period, and the chip forming force progression across the generation of one flank, see Figure 3. The wavelength of the resulting profile waviness corresponds to the normal base pitch and therefore appears mainly as waviness with tooth meshing order.

Figure 3: Non-optimized contact conditions during generating grinding [6].

Optimizing the grinding worm’s meshing behavior, the imbalance of the contact forces can be eliminated, and periodic deviations can be reduced. The computer aided optimization alters the pressure angle and the normal module on the threaded wheel simultaneously to fulfill the constraint of equal base pitches on the workpiece and threaded wheel [5], see Figure 4.

Figure 5 shows the practical application of optimizing the meshing condition regarding grinding forces of a workpiece with a normal module of 6mm and a profile angle of 20 degrees. The right side of the figure shows the corresponding spectra resulting from an all-tooth measurement with a subsequent Waviness- Analysis. On the upper part, profile measurement of a part with an unbalanced meshing condition having comparably large amplitudes in the first tooth meshing order can be seen. The results of an optimized or balanced process and the adjusted normal module and profile of the grinding worm are depicted on the lower part of the figure. All other parameters of the grinding process were held constant. Comparing both results, the profiles of the optimized gear show a much smaller form error in the profile line and therefore also a reduced first tooth meshing order and their higher harmonics.

Figure 4: Optimized contact conditions during generating grinding [5].

3.2 Waviness due to Surface Roughness Structure

The roughness structure depends on the type of hard-finishing process and particularly on the direction of the cut. In the case of grinding processes, the roughness peaks and valleys are oriented in the direction of the face width. Therefore, a surface roughness corresponds structurally to a surface with short-wave deviations yielding tonal excitations. For tooling pressure angles αnss = 15 to 20° wavelength of about 0.5 to 0.7mm or 1.1 to 1.5 mm are to be expected [3]. This leads to an immediate excitation frequency in the module range of 0.15 to 4.0 mm. This excitation results in vibrations and, thus, in waviness with frequencies that may correspond to the resonance frequencies in the system machine — tooling — clamping fixtures — workpiece. Subsequently, this may show up as profile waviness on the workpiece.

To avoid tonal excitation, Reishauer AG developed Low-Noise-Shifting (LNS). A special shift strategy ensures the long grinding marks are interrupted in the lead direction and reduced to comma-like characteristics. This surface with a more diffuse structure results in a less tonal excitation characteristic. Figure 6 shows the general appearance of the roughness structure with and without LNS compared to a surface produced by honing.

Figure 5: Practical application of optimized meshing conditions.

3.3 Waviness due to Surface Roughness

Fine and polish grinding improves the bearing ratio and reduces the loss of transfer power of gears. The additional aim is to reduce the total excitation level caused by the surface roughness structure. For fine grinding, the wheel consists of a vitrified roughing section and a vitrified bonded fine grinding section. Polish grinding wheels consist of a vitrified bonded roughing section and a resin bonded polishing section. The direct comparison of roughness charts for three grinding variants shows the difference in surface waviness due to the roughness of the coarse sinusoidal shape of standard continuous generating grinding, compared to the fine sinusoidal shape of continuous generating fine grinding and to the non-sinusoidal shape of continuous generating polish grinding. However, avoiding noise excitation may reinforce the excitation of noise in the case of non-optimal gear flank modifications.

Figure 7 shows representative surface characteristics of gears produced by standard continuous grinding, fine grinding, and polish grinding. The amplitudes of dominant wavelengths on the surface, which can lead to noise critical excitation, is significantly reduced by fine grinding and polish grinding compared to the standard continuous generating grinding.

Figure 6: Different types of roughness structures produced by honing and generating grinding.

4 Solving specific NVH issues

Solving specific NVH issues is often an iterative process, especially with finding the root cause. The first step is the grinding process, which can be monitored by the Reishauer ARGUS System. During production, a geometrical measurement is performed in order to determine geometrical deviations and assure the constant quality of the manufactured gears. Typically, a small sample of the whole production is measured, since the measuring process is time and cost-intensive.

The gathered data can be used to perform a waviness analysis in order to see small changes in the process that can be detrimental for the NVH behavior. It is best practice to assess the NVH-behavior of the produced gear on an “End-of-Line” test rig.

The data is commonly evaluated as frequency domain data. The “End-of-Line” test rig provides the most appropriate data evaluating the excitation behavior of the gear in the drive train, because it is a direct measurement of the noise level produced under realistic conditions including all interactions within the drive train. The drawback of this testing method is the cost-intensive and time-consuming realization on the test rig.

Figure 7: Surface roughness characteristics of different grinding process.

Therefore, the usage of a simulation of the grinding process, considering the whole process parameters and the geometric specification of workpiece and grinding worm, is often very helpful to correlate NVH- issues to the manufacturing process. This simulation helps to reproduce the process virtually and understand the effect of oscillations in the grinding machine.

If an abnormality occurs that influences the noise excitation level of a gear in a negative way, all these tools and data help to solve the problem. The Reishauer ARGUS monitoring system plays a central role in the problem-solving process [8]. The intention of ARGUS in the context of NVH-issues is to detect problems in the grinding process before they are detected in the geometrical measurement or the “End- of-Line” test. This preventive strategy saves time and money without producing plenty of NOK-parts.

If there is an NVH-issue, ARGUS is an important tool that can provide detailed data of the grinding process and help to identify machine-related root causes with the component monitoring module.

All these tools and methods are important to identify and solve irregularities regarding the excitation behavior of a gear.

4.1 Machine and Ghost Orders

With regard to the generating gear grinding process, arbitrary vibrations can occur anytime. Therefore, interference orders, commonly known as “ghost orders,” cannot be excluded before grinding a workpiece. Thus, a root cause analysis is difficult for noise excitations outside of tooth meshing orders and their higher harmonics, as the cause of excitation often can be assigned to the finishing process on the machine.

Figure 8: Evaluating and solving NVH issues.

Besides the number of interference waves over one workpiece circumference, some process parameters such as rotational frequencies or feed rate, as well as geometric parameters such as numbers of teeth, etc., have to be known in order to identify interference orders. Possible causes therefore can include [6]:

  • Balance quality of the grinding worm.
  • Bearing damage on the grinding spindle.
  • Malfunction of the X-axis.
  • Bearing damage on the tailstock or workpiece axis.
  • Inaccurate tailstock alignment.
  • Sideband modulation with zWS/zSS around harmonic orders.
  • Disturbance due to peripheral devices (e.g., pump, filter).
  • Encoder bearings malfunction at the tool axis.
  • Poor quality of synchronous belt drive.
  • Torsional natural oscillation of the workpiece axis (within
      combinations of inappropriate clamping devices).
  • Disturbance due to motor pole pairs of workpiece axis.

4.2 Investigation of External Excitations

To get a better understanding of how external excitation orders affect the surface of a flank, a geometrical model is introduced. The model is a simplification of  real and much more complex geometric relationships but is suitable to show the basic effects of external excitation on the workpiece flank.

Figure 9 shows the plane of action, assuming the area of the depicted rectangles being representative for all the right or the left flank surfaces over one revolution of the gear. If all these flank surfaces are concatenated in their order according to the transverse overlap ratio of the gear, they form the shown surface, and each surface is correctly related to the rotational angle of the gear. Applying an external excitation with the integer order of 6, the phase of the external oscillation after one revolution of the gear is the same as at the beginning of the rotation. This is very intuitive, because it is an integer order with respect to one rotation of the gear.

During the next rotation of the workpiece, the waviness has the same phase compared to the rotation before. Due to the axial feed motion, the distance between two paths of contact is the axial federate sz of the grinding worm. Finishing the whole stroke results in a two-dimensional waviness on the gear flanks. Hence, the phase on all single paths of contacts is equal; the waviness is parallel to the lead line.

Assuming an external oscillation with the order of 6.25, the non-integer order consists of the integer part of the order 6 and the non-integer part of the order 0.25.

Continuing the oscillation for the following revolutions of the gear, the non-integer part yields a constant phase shift for every revolution with respect to the previous revolution. The result is a two-dimensional waviness, which is not parallel to the lead line.

The wavelength of the two-dimensional waviness in the profile direction is calculated by the generating length over one revolution and the excitation frequency order OP.

The wavelength in lead λP direction is dependent on the axial federate and the non-integer part of the excitation frequency order.

The wavelength in the lead direction can be derived by looking at the axial section of the plane. Picking the amplitude of the oscillation at each path of contact and mapping it to the axial section results in the wavelength of the two-dimensional waviness in the axial direction (see Figure 10, right).

As the non-integer part in this example is 0.25, respectively one quarter, the same phase at the starting point of the revolution is reached after four revolutions. Therefore, the wavelength in the axial direction is four times the axial feed per revolution of the gear. The angle of the waviness βw can simply be calculated by the wavelengths in the profile and lead direction:

Before analyzing the main influence factors, the definition of an example process in order to make the interpretation more intuitive seems appropriate. The following calculations are conducted with a spur gear with 29 teeth and a normal module of 3 mm meshed with a grinding worm with four starts. The rotational speed of the grinding worm is set to 5,000 rpm, resulting in a rotational speed of the workpiece of approximately 690 rpm according to the transmission ratio. This process yields a rotational frequency of the workpiece of approximately 11.5 Hz. The axial federate is set as sZ = 0.1 mm/mm-stroke. Assuming an external excitation frequency of 50 Hz, the order in profile direction of OP = 4.35 with respect to one revolution of the workpiece can be calculated.

Figure 9: Simplified geometrical model of waviness formation on the workpiece flank.

Considering the defined example process, the wavelength in profile direction λP can be calculated depending on the order of the external excitation frequency OP according to Equation 2. The far left diagram in Figure 11 shows a decreasing wavelength in profile directions with an increasing order of the external excitation frequency .

Due to the periodic characteristic of the non-integer part of the profile order with increasing order of the external excitation frequency, the wavelength in the lead direction shows a periodic characteristic as well. In contrast to the wavelength in the profile direction, the wavelength in the lead direction reacts very sensitively with respect to the profile order. This means that a small variation of the profile order yields a large change of the wavelength in the lead direction. The same sensitivity can be observed for the angle of the waviness close to the integer profile orders (See Figure 11, right).

Figure 10: Mechanism of waviness formation (simplification).

According to the definition, the profile order depends on the external excitation frequency fext and the rotational frequency of the workpiece fWP:

The external frequency cannot be modified since it is not directly controllable; consequently, the workpiece frequency offers the possibility to influence the profile order OP by means of the grinding worm rotational speed nGW. Since the frequency of the workpiece seems to be a variable to influence the waviness on the gear flank, a rescaling of the abscissa with respect to the grinding worm speed nGW is performed, see Figure 12.

The direction of the increasing profile order has changed due to the axis transformation. The diagram in the center of Figure 12 shows a comparable sensitivity of the wavelength in the lead direction with respect to the grinding worm rotational speed nGW compared to the order representation in Figure 11.

Figure 11: Sensitivity of order in profile direction.

Changing the wavelength in the lead direction can help to reduce the amplitude of a two-dimensional waviness on the workpiece flank. To understand this approach better, it is helpful to have a closer look at the axial section of the gear flank during the continuous generating grinding process.

Figure 12: Wavelength and waviness angle as a function of grinding worm speed.

In a first step, two kinematic waveforms in lead direction, which are different in their wavelength but have the same magnitude, can be assumed. The axial section of the gear flank is created with a discrete removal of material each time the path of contact between the workpiece and grinding worm passes the axial section, which occurs once per revolution of the workpiece. The distance along the lead direction between those single material removements corresponds to the axial feed per revolution. The resulting geometry of the axial section is the envelope of all the single material removements, represented by the red curve in Figure 13.

Figure 13: Influence of the wavelength in lead direction on the waviness amplitude.

The irregularities in the resulting curve are called feed marks. The same procedure is repeated for the kinematic oscillation with the same magnitude but a shorter wavelength in the lead direction (see Figure 14). This is the shortest wavelength possible that can be reached with a non-integer part of the profile order of 0.5. In this case, the wavelength corresponds to the double axial feed per revolution. Due to intersection effects, every second revolution does not contribute to the final surface, see Figure 14.

The magnitude of the resulting surface waviness strongly depends on the wavelength of the kinematic oscillation with the same magnitude. Therefore, it might be beneficial to influence the wavelengths in the lead direction by a modification of the grinding process in order to influence the gear flank surface.

Figure 14: Influence of the wavelength in lead direction on the waviness amplitude.

This approach could be demonstrated in a practical application in which a waviness based on an external excitation of the grinding machine could be observed. The measured topography shows a two- dimensional waviness on the workpiece flank, which is the reference state (Figure 15). A variation of the rotational speed of the grinding worm, keeping all other process parameters constant, yields a significant change in magnitude and waviness pattern. The best result was achieved by decreasing the grinding tool speed by -3.36% with regard to the reference process. Therefore, it was not necessary to perform the ”trail-and-error” methodology, as the simplified model was able to predict the suitable process parameter changes.

Even with a small modification of the process, the waviness pattern and the magnitude are changing drastically, which confirms the theoretical considerations.

5 Summary

Regarding e-mobility trends, NVH issues of gearboxes are currently in the focus of developments at transmission and gearing suppliers. Due to primarily high input revolutions, the gear stages feature, in general, high gear ratios. These ratios lead to specific characteristics in the gear-tooth meshing. The problem is reinforced by the lack of noise masking from the internal combustion engine and the electric “motors” low noise emissions. These issues pose new challenges to the surface quality of hard-finished gears and reflect new technology features of the generating gear grinding machines.

Figure 15: Practical example for external excitation problem.

This article presents the increasing requirements for efficient gearing production for e-motive applications from a machine tool manufacturer’s point of view. It also presents the influencing factors of the NVH behavior regarding the gear-generating process. On this basis, measuring methods for the evaluation of the NVH behavior of gearing are discussed by practical applications. Moreover, the article discusses technologies with a positive impact concerning NVH issues during the generating grinding process of gears, for example:

  • Design of dressing tools with optimized geometry.
  • Low-Noise-Shifting.
  • Fine and polish grinding.
  • These and further measures focus on lowering the amplitudes of tooth meshing orders and their harmonics. Besides, ghost frequencies can occur aside from tooth meshing frequencies due to dynamic excitations during the generating gear-grinding process. The root cause analysis for these cases is often challenging and is facilitated by a process and component monitoring system.

Therefore, the presented simplified model of evaluating external excitations helps significantly to avoid cost-intensive trial-and-error tests or replacing machine components if not necessary, as only small process changes are able to lower magnitude and appearance of flank waviness and can be calculated in advance. 

Bibliography

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