Analogy test rig for the generation of tooth flank fractures at large gears (WZL-double pulsator)—commissioning and first test results

A challenge in the investigation of gear damages is the difference in damage types typical for gears and the associated multitude of causes, which need to be considered. The probability of occurrence of the individual damage types changes depending on influencing factors such as gear geometry, surface condition, lubricant selection and load condition. Thus, not all damage types can be analyzed with a single gear geometry in the running test, since a gear will fail with a critical damage type depending on its design.

For the reasons mentioned above, analogy tests enable the investigation of influencing factors on the development of specific gear damages. In contrast to the running test, which comes close to the real application, the damage types can be analyzed separately in the analogy test. In addition, the analogy test is characterized by a more economical operation compared to the running test. The preferred analogy test depends on the investigated damage type, cf. Figure 1.

The tooth flank damages pitting, micropitting and scuffing can be investigated with the aid of the disc-on-disc test rig, Fig. 1 top [5]. The advantages of using the analogy test are the isolated investigation of the tooth flank load-carrying capacity without influences from the tooth root and tooth flank fracture load-carrying capacity, as well as the local reproduction of different contact conditions. The variable slippage from tooth flank contact on the test discs can be realized by using non-circular gears in the transmission gearbox [1].

The investigation of the tooth root load-carrying capacity can take place on pulsators in a time- and cost-efficient manner and detached from other damage types. In addition to the investigation of spur gears, the experimental determination of the tooth root load-carrying capacity of helical gears as well as a qualitative and quantitative transfer to the running test is the focus of research work. For this purpose, a special construction allows clamping of helical gears in the pulsator test rig. [2, 3].

An analogy test for the investigation of tooth flank fractures, analogous to the disc-on-disc test and the pulsator test, does not exist. Since tooth flank fractures occur in particular on large gears, which cannot be investigated economically when using the back-to-back test rig, there is great potential for investigating this type of damage by means of an analogy test. For this reason, an analogy test rig for the generation of tooth flank fractures is being developed and tested as part of the DFG research project BR 2905/90 1 “Analogy test rig for tooth flank fractures”.

An analogy test rig is necessary for the economical investigation of tooth flank fracture load-carrying capacity in isolation from other damage types. Chapter 1 shows that analogy test rigs are a proven concept for the isolated investigation of individual damage types and that they already exist for the common gear damage types such as pitting, scuffing, micropitting and tooth root breakage. Tooth flank fracture is influenced by both the stress due to Hertzian contact and the downstream stress due to tooth bending. For this reason, an analogy test rig is required that represents both loading scenarios. In preliminary work, a test rig concept (WZL-Double pulsator) was developed which reproduces the local stress at the point of crack initiation (POI: point of interest) appropriate in FE-simulations [17, 18, 20]. Based on the preliminary work, the following objective is derived for the successful use of a tooth flank fracture analogy test rig:

In order to validate the simulated stresses, a strain measurement in the tooth root using strain gauges is conducted and compared to the FE-simulation. In a second step, the commissioning of the test rig is done by analyzing the measured pulsator force profiles under dynamic loading with different nominal pulsator force profiles. The analysis includes the quality of imaging the nominal pulsator force profile. The quality of imaging the nominal profile is an indicator of the dynamic stability of the test rig, since the measured pulsator force profile gets worse if the controllability of the test rig is struggling with the required nominal pulsator force profile. In the last step, endurance tests are carried out in order to generate tooth flank fractures with the analogy test concept.

The FE model is validated with the aid of strain gauge measurements. Since a strain measurement was not possible due to the risk of collision between the pulsator jaw and the strain gauge directly at or below the force application point, strain measurements were carried out in the tooth root. For this purpose, a strain gauge was applied to the tensile stress side of a cut tooth segment. The strain was measured separately for the primary and secondary actuators as a function of the applied pulsator force, cf. Figure 6. Afterwards, the measured strain was compared to the calculated primary strains at the surface of the hexahedron-meshed tooth. The comparison between measurement and simulation is shown in Fig. 6 on the right. The comparison shows that the measured strain for both actuators is higher than the calculated strain. The maximum deviation between measurement and calculation is ∆ε_{Tension,primary} = 1.25⋅10⁻⁴ (≙ 26.3 MPa) for the primary actuator and ∆ε_{Tension,secondary} = 2.15⋅10⁻⁴ (≙ 45.2 MPa) for the secondary actuator. The relative deviation for both actuators is in the range 7% ≤ (ε_measurement − ε_calculation)/ε_calculation ≤ 12%, cf. Figure 6, bottom right. It can be assumed that the deviations are attributed to neglected components in the simulation which, due to their deformation under load, lead to an angular deviation between the pulsator jaw and tooth segment and consequently cause a higher circumferential force (e.g. load cells, hydrostatic piston bearings).

The implementation of an automatic test procedure as part of the research project allows the operation of the test rig. During a test, manually preset force and displacement parameters serve as limit values for a test stop. Furthermore, a peak-valley detector monitors the change of the displacement signal for both actuators and stops the test run when the displacement delta exceeds a limit value. After completion of the test by premature termination or reaching the limiting load cycle number, the actuators automatically return to their starting position. To determine the test rig limits with the elaborated concept and the optimized control parameters, tests were carried out with the individual loading profile and the phase-shifted double sinusoidal profile, cf. Figure 7. The individual loading profile is the optimized pulsator force sequence from the FE optimization. In the phase-shifted double sinusoidal profile, the load of the primary and secondary actuator is applied as a sinus function containing a phase-shift with the maximum force of one actuator acting when the clamping force is applied to the other actuator. Figure 7 shows the comparison of the nominal and actual profiles of both actuators during a load cycle with the individual loading profile and the phase-shifted double sinusoidal profile. The imaging quality of the nominal signal by the actual signal is evaluated with the coefficient of determination R². In addition, the phase-shift deviation ∆t is plotted for different test frequencies. The phase-shift deviation ∆t describes the percentage offset between the time of the measured, maximum actual force on the secondary actuator and the time of the maximum nominal force on the secondary actuator.

The analysis of the imaging quality of the individual loading profile was carried out for the test frequencies f = 0.1 Hz, f = 1 Hz and f = 10 Hz, see Fig. 7 top. The pulsator force profile corresponds to a torque equivalent at the pinion of M_pinion ≈ 600 Nm in the running test and thus relatively low loads. Tests were also carried out with varying loads and the same test frequency. Due to the similar control behavior for varying loads, the results are not shown separately. For the pulsator force profile investigated, the nominal signal can be reproduced well for the test frequencies f = 0.1 Hz as well as f = 1 Hz. For the test frequency f = 10 Hz, a worse quality of imaging can be observed. On the one hand, there is an undershooting of the clamping force at the secondary actuator. Falling below the clamping force can lead to hammering, since the pulsator jaw lifts off the tooth flank as soon as the force exceeds the zero crossing. Furthermore, the required maximum force on the secondary actuator is not reached and there is an increase in the phase-shift deviation ∆t = 5.5%. If the phase-shift deviation ∆t is too high, the secondary actuator reaches its maximum force while the primary actuator is already actively applying load. There is a correlation between the coefficient of determination R² and the phase-shift deviation ∆t. The general phase-shift between nominal and actual signal is filtered in advance for the primary and secondary actuator and only the phase-shift leading to an interference between primary and secondary load is analyzed. This is equivalent to a poor quality of imaging for the secondary actuator with respect to the temporal offset between nominal and actual signal. For the individual loading profile, the test rig limit was accordingly reached at a test frequency of f < 10 Hz and a load equivalent of M_pinion = 600 Nm, so that the individual loading profile is not suitable for long-term tests. Assuming that the type of loading is negligible compared to the maximum loads applied, the pulsator forces of primary and secondary actuator can be applied by a phase-shifted double sinusoidal profile [21]. With respect to the calculation of the tooth flank fracture load-carrying capacity, the approximation does not result in any load-carrying capacity differences. Here, the load on primary and secondary actuator is imposed by a sinusoidal profile with the force limits clamping force and maximum force, and the nominal phase-shift between primary and secondary pulsator force corresponds to φ = 0.5 π. Hydraulic controllability of a phase-shifted double sinusoidal profile is better compared to the individual loading profile. Accordingly, the analysis could be performed at higher loads and test frequencies, see Fig. 7 bottom. The maximum forces analyzed were F_prim,max = −80 kN for the primary actuator and F_sec,max = +40 kN for the secondary actuator. The test frequencies analyzed were f = 1/10/20/30 Hz. For the test frequencies f = 1 Hz and f = 10 Hz, a good reproduction of the nominal signal was demonstrated. With increased test frequencies f, the coefficient of determination R² decreases and the phase-shift deviation ∆t increases. For a test frequency f = 30 Hz, a similarly poor control behavior could be observed as for the individual loading profile at f = 10 Hz. For the phase-shifted double sinusoidal profile, the test rig limit was accordingly reached at a test frequency of f = 20 Hz and a running test load equivalent of M_pinion = 4800 Nm.

The geometry investigated for the research project was tested experimentally with respect to the tooth flank fracture load-carrying capacity both on the analogy test rig as well as on the back-to-back test rig according to DIN ISO 14635 with center distance a = 200 mm [22]. The comparison of the results is shown in Fig. 8.

The blue crosses and circles represent tooth flank fractures and run-outs on the back-to-back test rig, where the limiting load cycle number was defined as N_L = 50 ∙ 10⁶ load cycles. As an example, two damage patterns at a pinion torque M_pinion = 2600 Nm and M_pinion = 3000 Nm are shown in Fig. 8. With the geometry, tooth flank fractures could be reproducibly generated in the running test. The tooth segments selected for the analogy test came from gears of the identical batch. The yellow (or unfilled, light) circles show test points where a previously unloaded tooth flank was examined in the analogy test. The first tests were performed at moderate forces (primary actuator: −34 kN ≤ F_prim ≤ 43 kN, secondary actuator: 11 ≤ F_sec ≤ 13 kN), which after recalculation corresponds to an equivalent torque in the running test of 2000 Nm ≤ M₁ ≤ 2540 Nm. A majority of the tests were subsequently carried out at pulsator forces F_prim = −70 kN and F_sec = 30 kN, which corresponds to an equivalent torque M_pinion = 4130 Nm and is thus within the time yield strength of the gear stage with respect to tooth flank fracture. One test was performed at the test rig limit with pulsator forces F_prim = −80 kN and F_sec = 40 kN, which corresponds to an equivalent torque M_pinion = 4720 Nm. With the unloaded tooth segments, no tooth flank fracture could be generated in the analogy test. Furthermore, tests were carried out with tooth segments that had previously been subjected to a load in the back-to-back test rig. The gears selected for this purpose have previously experienced a pinion torque in the range 2600 Nm ≤ M_pinion ≤ 3000 Nm at a load cycle number 3.8∙10⁶ ≤ N_L ≤ 20.3∙10⁶. Also, no damage occurred in the analogy test for the tooth segments with preload.

Since the test results did not meet expectations, the calculations and tests were reflected with a view to differences between the two test methods. Since tooth flank fracture is usually initiated at a non-metallic inclusion, the first step was to compare the total number of teeth tested. It became clear that the number of teeth tested in the analogy test and thus the volume tested in the analogy test corresponded to only 3.7% of the running test, cf. Figure 8 “tested teeth”. For future investigations, consideration must be given to analyzing gears in advance of the tests by means of ultrasonic measurement for large, non-metallic inclusions in individual teeth and using those teeth for the analogy test.

In the second step, the highly stressed volumes were compared by FE calculations in Abaqus CAE. The highly stressed volume HSV₉₀ is the volume, which experiences 90% or more of the maximum material exposure in the component. The comparison in Fig. 9 on the left between the running and analogy tests shows that the highly stressed volume is 10% lower in the analogy test than in the running test (HSV₉₀ = 7.0%). This is due to the stationary load application in the analogy test, which causes a lower volume stressed by Hertzian contact.

In the last step, the stress tensors at the POI were evaluated in detail. The evaluation is shown in Fig. 9 on the right. It can be seen that the maximum magnitudes of the different stress components in the running test are phase-shifted and in the analogy test they are simultaneous. This circumstance cannot be considered by the currently applied equivalent stress hypotheses [4, 9, 23‐26]. For this reason, focus in future work should lie on the extension of existing equivalent stress hypotheses for the representation of the equivalent stress in rolling-sliding contacts.

Tooth flank fractures occur more frequently due to the continuous optimization with regard to pitting and tooth root load-carrying capacity. The characteristic of tooth flank fracture is a crack initiation in the material volume, usually at a non-metallic inclusion. Since the probability of large, non-metallic inclusions increases with component size, large-modulus gears in particular are at risk of tooth flank fracture. An economical and statistically proven load capacity test of such gears is currently not possible. For this reason, an analogy test rig was developed in the DFG research project BR 2905/90‑1 “Analogy test rig for tooth flank fractures” where a tooth segment of a gear is loaded with two hydraulic actuators in such a way that the stress sequence corresponds as closely as possible to the real tooth flank contact. Previous work was carried out on the implementation of a method for the determination of the pulsator forces as well as on the design and manufacturing of the analogy test rig [17, 18, 20].

In order to verify the FE-simulations, measurement of the principal strain in the tooth root by means of strain gauges was carried out and provided appropriate agreement with the calculated principal strains in the FE simulation. In the next step, the dynamic commissioning was carried out and the tests were performed. To this end, tooth segments were cut out of gears by EDM and clamped in the analogy test rig. Since the load-optimized pulsator force profile could only be controlled with limited dynamic stability, a simplified phase-shifted double-sinusoidal profile was successfully implemented and tested. This pulsator force profile leads computationally to an identical stress state and can be controlled in a dynamically stable manner so that pulsator forces up to the test rig limit can be applied with a test frequency of f = 20 Hz. In the test series, no tooth flank fracture could be generated with the new test concept, whereby both previously unloaded tooth flanks as well as tooth flanks previously loaded in the running test were tested in the area of time yield strength with regard to tooth flank fracture. For this reason, a critical reflection of the test rig concept was carried out. Possible causes could be the reduced number of tested teeth and the reduced highly stressed volume HSV₉₀ compared to the running test. In addition, due to the fixed positioning, the analogy concept is not able to reproduce the phase-shift between the maxima of the individual stress tensor components, which is characteristic for the rolling-sliding contact.

For future work, consideration must be given to ultrasonic measurement techniques to examine gears for large, non-metallic inclusions in order to identify teeth at risk of tooth flank fracture for the analogy test. Furthermore, the current equivalent stress hypotheses for evaluating rolling-sliding strength problems need to be questioned and extended with focus on phase-shifted stress maxima.