The power density of gearboxes is continuously increased through different research activities. Besides new material developments, steel cleanliness comes to the forefront in order to meet future requirements regarding load carrying capacity of gears. The experimental quantification of load carrying potentials for high quality steels is the basis for introducing cleanliness as a design parameter.

In this article, investigations on the tooth root load carrying capacity of steels with different cleanliness levels are presented. The investigations are carried out on a pulsator test rig with a standardized FZG-C gear geometry. To determine and compare the different behaviors of the tested steels, correct force application in the test rig needs to be ensured. By this, it is possible to clearly separate the endurance strength for different cleanliness levels within the same steel grade composition.

For the pulsator testing, an approach for checking and ensuring correct clamping of the gears is presented. Using this procedure, endurance tests on conventionally manufactured gears with different cleanliness levels are carried out. Resulting mean values of the tooth root strength as well as scattering of test results are evaluated, and the influence of higher cleanliness on an increasing mean value and decreasing scattering is proved. The confidence level of the mean value is discussed regarding the overall number of tests.

As a conclusion, the impact of steel cleanliness on increasing endurance strength and decreasing scattering is separated from manufacturing and testing influences. A higher level of cleanliness takes into account the influence of the occurring failure mechanisms. Especially for applications with a high manufacturing and surface quality, high quality steels show a high potential for increasing the load carrying capacity and thereby the power density.

### 1 Introduction and Motivation

For many years, demanding applications such as bearings and diesel injection systems have been driving the development of air-melt, high-volume production, clean steels. Through environmental legislation and a continuously ongoing strive to improve power density in many applications, the gear industry is now showing an increased interest for clean steels as well. This is due to steel cleanliness impact on endurance strength, relevant to many high-cycle fatigue gear applications. Also, with more frequent use of sophisticated after-processing techniques, such as superfinishing and shot peening, the importance of the material quality is increasing. This in itself is a driver for the use of cleaner steels, since previously, other factors such as surface quality has been the weakest link.

### 2 Aim and Approach

The increasing demands on gears with regard to power density require new approaches to the design of gear geometry as well as an increase in material load carrying capacity. Steels with a high cleanliness are already being used in applications with extremely high material demands. In this paper, the influence of the cleanliness of a material on the tooth root load carrying capacity and the test scatter will be investigated.

The aim is to determine the increase in load carrying capacity taking into account the test scatter and to separate it from influences from the test itself and the test geometry. For this purpose, three variants with different degrees of cleanliness for the same steel grade are investigated.

The tests are carried out on a pulsator test rig using a standardized gear geometry. In order to guarantee correct load application in the test and to reduce the influence of the test setup on the scatter, a procedure for checking the pressure distribution in the pulsator test is presented. The tests in the area of fatigue strength are analyzed with regard to mean values and scattering. Taking into account the confidence intervals, the load carrying capacities of the investigated variants are compared, and the influence of the degree of cleanliness on the load carrying capacity is highlighted.

### 3 Theoretical Influence of the Cleanliness on the Endurance Strength

Previous investigations on the influence of material defects on the load carrying capacity show that the size and distribution of defects are important parameters. The material cleanliness characterizes the number of defects and their frequency of occurrence.

Murakami investigates the influence of inclusions in the material on the load carrying capacity. Especially for hard steels with HV > 400, the size of defects or inclusions has a significant influence on the load carrying capacity [11]. Henser states in his work that a higher cleanliness leads to an increased tooth root load carrying capacity of beveloid gears [4]. Konowalczyk analyzes the influence of the defect size on the tooth flank fracture load capacity. The size of defects has a decisive influence on the load carrying capacity, independent of the core hardness and case depth. A reduction of the defect size leads to a significant increase of the load carrying capacity regarding tooth flank fracture [9].

On the basis of the existing work on the influence of material cleanliness on the load carrying capacity, it can be expected that the load carrying capacity will increase with higher cleanliness. The defect size has a primary influence on the fatigue strength. The number of defects, on the other hand, influences the scatter of the test results around the fatigue strength.

### 4 Investigated Materials and Test Gears

For the investigations, three different degrees of cleanliness of a 20MnCr5 material were considered. The investigations were carried out using the standardized FZG-C gear geometry in a pulsator test to determine the tooth root load carrying capacity. The conventional gear manufacturing chain includes the process steps turning, soft machining, heat treatment and gear grinding. All variants were heat treated in the same batch. During the grinding process, only the tooth flank was machined. In the following, the properties of the examined materials as well as the gear geometry and manufacturing quality of the examined components are presented.

#### 4.1 Material Characteristics

Three different 20MnCr5 materials were tested, with assumed different cleanliness levels, a conventional 20MnCr5 as a reference, a bearing quality 20MnCr5 (236F; steel 1), and an ultraclean isotropic quality 20MnCr5 (236Q; steel 2). Table 1 shows the chemical composition of the steels.

Steels 1 and 2 were produced in a scrap based, air-melt, and ingot cast process route, and the reference material comes from a high-volume iron ore based continuous cast process route. These differ mainly in what starting material the steel is produced from as well as the metal casting and forming processes.

Although these materials might look similar on paper, steel 2 especially, differs in its properties. Strict process control in the whole steel making process results in a type of steel that displays similar fatigue performance properties achieved normally in certain re-melting processes [10].

Clean steels reduce the probability of finding detrimental defects in the loaded volume, i.e., the inclusions are made to be as small as possible, which is achievable through inclusion control and increased area reduction through metal forming.

Cleanliness evaluation using SEM was performed, looking at approximately 7,000 mm^{2} in total for series- production material and only defects larger than 10 Āµm were detected. Defects larger than 10 Āµm as well as the longest, or largest inclusion, are recorded in this simple approach (Table 2).

Ultrasonic immersion testing is used to examine larger material volumes to establish material quality on a macro-cleanliness level, since it clearly separates clean from less clean steel. This type of testing was used to examine macro cleanliness for all three types of steel, calibrated to a 0.2 mm flat bottom hole (FBH) [16]. A volume corresponding to between 4-6 kg was evaluated for each material and no indications were found for steel 1 or steel 2 materials and only very few indications for the reference, indicating decent macro-cleanliness. Previous studies [2] have shown that little difference is normally found regarding micro-cleanliness with standard rating methods, whereas methods covering larger areas or volumes give a better understanding of the material properties.

#### 4.2 Gear Geometry and Manufacturing Quality

The investigations on the pulsator test rig were carried out on the standardized FZG-C test gear. The gear data of the pinion is shown on the left side in Figure 1. Since only one gear is needed for investigations on a pulsator test rig, only the pinion of the FZG-C gear set was used. The right part of Figure 1 shows the manufacturing quality of the tested gears for the respective variants. The evaluation of the gear quality is carried out in the form of the IT tolerance classes of ISO 1329-1:2013 [15]. For the evaluation of the gear quality, a four-teeth measurement was carried out for all tested gears on a Klingelnberg P16 gear-measuring center. Subsequently, the maximum deviations of the considered deviation variables were transferred to the IT classes of ISO 1329-1:2013.

Figure 1 shows the maximum tolerance classes of all measured gears. The correct load application in the pulsator test rig is particularly influenced by the manufacturing quality of the tooth flank. Accordingly, the deviation parameters of the flank in profile and helix direction are evaluated. The IT qualities of the three investigated variants lie in similar ranges. For the investigations, a maximum IT class of IT = 6 was defined in order to reduce the influence of manufacturing errors on the fatigue strengths determined. All examined gears comply with this tolerance limit or show a better quality. The high manufacturing quality should enable a precise determination of the tooth root endurance strength, so that the actual influence of the cleanliness of the material on the load carrying capacity can be determined.

In addition to the quality of the tooth flank, the geometry and roughness of the tooth root have a decisive influence on the tooth root load carrying capacity. The maximum tooth root stress usually occurs at the 30Ā°-tangent in the tooth root [8, 12, 14]. A small root radius at this point leads to a higher stress at the same load and thus to a reduced load carrying capacity. For this reason, the radius of the tooth root fillet in this area is considered in order to exclude any influence on the test results. Since the gears were manufactured conventionally, the tooth root was not machined after the heat treatment. All gears were blast cleaned after heat treatment to remove the surface oxidation. The root fillet was measured on a Klingelnberg P16 gear-measuring center. The radius Ļ_{F,30Ā°} in the range of the 30Ā°-tangent was then determined on the basis of the measured point cloud. The root fillet radii were determined for each investigated pinion at four gaps.

In Figure 2 the mean tooth root radii at the 30Ā°-tangent of the three considered variants are shown on the left side. Furthermore, the maximum and minimum measured radii are shown as deviation bars. The mean tooth root radii are Ļ_{F,30Ā°,Ref,mean} = 2.22 mm, Ļ_{F,30Ā°,steel 1,mean} = 2.24 mm and Ļ_{F,30Ā°,steel 2,mean} = 2.22 mm. The tooth root geometry of the three variants therefore shows no significant deviations. Since the mean values of the root radii correspond, the deviations only have an influence on the scatter determined in the pulsator tests. Due to the similar scatter of the tooth root radii of the three variants, it is to be expected that the influence on the scatter of the tooth root load carrying capacity will be similar as well.

Apart from the geometry of the tooth root fillet, the roughness in the tooth root has an influence on the achievable load carrying capacity in the test [8, 12, 14]. High roughness values act as notches and thus promote the initiation of cracks on the surface. In order to evaluate the roughness of the investigated pinions, the average roughness depth Rz was measured in the range of the 30Ā°-tangent. The measurement starts in the tooth root and runs in profile direction to the tooth tip. The curvature of the root fillet was filtered from the measurement using a fourth degree polynomial. The roughness was measured on two gears per variant at two gaps each.

On the right side of Figure 2, the Rz values of the left and right flank of the examined variants are shown. The mean roughness depths of the variants are similar. The Rz values of the variant Ref show a slightly larger scatter. However, since the influence of this measured roughness variation on the load carrying capacity according to ISO 6336 is small, no influence on the determined fatigue strength in the test is to be expected.

### 5 Test Setup and Testing Procedure

The tests on the tooth root load carrying capacity were carried out in the pulsator test as an analogy test to examine the tooth root. In contrast to the running test, the number of influencing factors on the test result is reduced in the pulsator test. Thus, it is possible to consider the influence of the material cleanliness on the tooth root load carrying capacity in an isolated way. Furthermore, the test setup in the pulsator test allows several tests to be carried out on one gear, thus reducing the number of test gears required. In the following, the test setup, the verification of the load distribution, and the testing and evaluation procedure used are explained.

#### 5.1 Test Setup and Alignment Check

The pulsator test approximates a part of the load curve in the tooth mesh. Figure 3 shows the clamping situation of a spur gear in the pulsator. The gear is clamped between two pulsator jaws. One of the two jaws is stationary and connected to a load cell. The other pulsator jaw carries out a mechanically actuated, pulsating movement and thus loads the teeth with a sinusoidal load, which is monitored by the load cell. The positioning of the pulsator jaws is based on the support of the tip of the adjacent teeth, which allows central alignment of the gear in the pulsator jaw contact.

On the right side of Figure 3, a diagram is shown with the tooth root stress over the path of contact A – E of the spur gear used. The ordinate of the diagram is normalized to the maximum tooth root stress.

Furthermore, the areas for single tooth contact ā1ā and double tooth contact ā2ā within one tooth mesh are shown. It becomes clear that the point of maximum tooth root stress lies in the outer point of single tooth contact, since only one tooth transmits the entire torque and, at the same time, the lever arm is the largest. Because the number of clamped teeth defines the contact line in the pulsator test, it is not possible to test exactly the outer point of single tooth contact. For the tests, the number of clamped teeth is selected in a way that the resulting contact line is as close as possible to the outer point of single tooth contact. For further calculations of tooth root stresses, the position of the contact line during testing is considered. A mechanical minimum preload, the upper pulsator force F_{Puls,U}, must be present for the none-positive fixation of the test gear between the pulsator jaws, so that the gear remains at its defined clamping position during the test. In contrast to the running test, the amount of preload cannot assume the minimum value zero. The associated influence on the load carrying capacity is classified as negligible, if the amount of the minimum preload lies within a range of 3-7.5 % of the amount of the maximum lower pulsator force F_{Puls,l} [17]. For the tests presented, an upper pulsator force of F_{Puls,U} = -1 kN was selected. With an expected mean lower pulsator force of F_{Puls,l} < -20 kN, the selected preload meets the Weigand criterion [17]. The number of clamped teeth was set to z_{clamped} = 3 for all tests.

The tooth root load carrying capacity determined in the test depends significantly on the correct load application in the test. The highest load carrying capacity is obtained with an even load distribution over the tooth width. Helix slope deviations of the clamped teeth, misalignment, damaged pulsator jaws or incorrect clamping lead to local stress peaks in the tooth root over the tooth width and influence the determined strengths with regard to mean value and scatter. In order to be able to analyze the influence of material cleanliness on mean value and scatter, the method shown in Figure 4 is used to check the load distribution in the pulsator test setup.

The Fujifilm Prescale pressure film can be used to determine the contact pressure in the gear-pulsator jaw contact. The pressure film turns red at loaded areas. The color density allows direct conclusions about the contact pressure. In this way, it is possible to identify and correct an uneven pressure distribution. During pulsator testing, the load distribution was checked every third test and, if necessary, corrected.

#### 5.2 Testing and Evaluation Procedure

The tests to determine the fatigue strength in the tooth root are carried out according to the staircase method. In this procedure, the load of the following test depends on the previous test result [1, 7]. In the case of damage, the load is reduced by one step and increased by one step in the case of a run out. The damage criterion is a crack in the tooth root in the area of the 30Ā°-tangent or a broken tooth. In addition to the small number of tests to determine the mean value, an additional fictitious point can be evaluated in this procedure [7]. The maximum number of cycles to be achieved for a run out is N_{G} = 6*10^{6} load cycles. The evaluation of the staircase is carried out according to HĆ¼ckās method and is shown in Figure 5. In order to make a conclusion about the scatter of the results in addition to the mean value, 15 tests were carried out for each material variant. The step distance for all tests is d = 1 kN.

In addition to the tooth root load carrying capacity, the scatter of the tests and the statistical reliability of the determined values are evaluated. For this purpose, the confidence intervals of the mean values of the variants are calculated as shown in Figure 6. The determination of a mean value from a finite number of tests corresponds to an estimated value x and usually does not correspond exactly to the true mean value Āµ. If the test points correspond to a normal distribution, the true mean value Āµ and the estimated value x can be displayed as shown in Figure 6 on the left. The highest probability of occurrence is the true mean Āµ. For different sequences of test points, different estimated values x result. The probability of occurrence of the estimated values with a normal distribution of the test points is indicated by the curve in Figure 6.

Since the true mean value Āµ is usually not known and the number of experiments to determine the estimated value x is finite, it makes sense to determine a range that contains the true mean value Āµ with a defined probability, taking into account the scatter of the test results. The confidence interval for the estimated value x indicates the range in which the true mean value Āµ with the defined coverage probability (1-Ī±) is located. The smaller the standard deviation of the experiments, the smaller the confidence interval around the estimated value. The same applies to a larger number of tests. For a larger coverage probability, the confidence interval increases. [3]

Previous investigations on case-hardened steel gears have shown that the test points are normally distributed in the staircase method [6]. Accordingly, a normal distribution is assumed for the evaluation of the tests. Furthermore, the usual coverage probability of 95 percent is selected for evaluation. Based on the comparison of the calculated confidence intervals of the respective mean values, a statement can then be made as to whether the compared mean values are identical or not from a statistical point of view.

The calculation of the tooth root stress from the pulsator forces is carried out based on the ISO 6336-3 standard calculation [14]. The used factors and equations are shown in Figure 7. The first step is the calculation of the nominal tooth root stress Ļ_{F0} for a failure probability of 50 percent.

The factors Y_{F} and Y_{S} take into account influences from the form of the tooth root fillet and variance in force application on the tooth root stress. Both factors are calculated for the clamping position in the pulsator test rig using the position of the contact line as well as the measured tooth root radius Ļ_{F}. The factor Y_{Ī²} rates the influence of the helix angle on the distribution of the tooth root stress and is one because a spur gear is tested. The K factors are all one, since the occurring loads in the pulsator test rig are measured and controlled and the load distribution in the contact of tooth and pulsator jaws is uniform.

The calculation of the allowable stress Ļ_{FE} as well as the nominal stress Ļ_{Flim} depend on several assumptions. One assumption is that the fatigue strength of the tooth root determined in the running test is 10 percent lower compared to the pulsator test because, in the pulsator test, the weakest tooth of a gear doesnāt always fail [6]. Another assumption is that it is possible to transfer the fatigue strength from a failure probability of 50 percent to 1 percent by the factor 0.86 for case-hardened steels [6]. This factor depends on the huge amount of data, which are the basis of the ISO 6336 standard. As these factors have not yet been confirmed for clean steels, a calculation of the values Ļ_{FE} and Ļ_{Flim} is subjected with uncertainties.

### 6 Test Results and Evaluation

The results of the investigations of the three material variants are presented in the following. Subsequently, a comparison of the determined load carrying capacities is made taking into account the confidence intervals and the increase in load carrying capacity of the tested steels is quantified. Finally, the resulting nominal stress numbers of the three variants are compared to the values of the ISO 6336 – 5.

#### 6.1 Reference Material

Figure 8 shows the test results of the Ref variant. The frequency of the applied load in all tests was approximately f = 30 Hz. The results were determined for a failure probability of 50 percent. All tests were carried out on the same test bench. The endurable mean double amplitude of the pulsator force is F_{ptp,mean,Ref} = 22.63 kN. The corresponding tooth root stress according to ISO 6336 is Ļ_{F0,mean,Ref} = 1302.45 N/mm^{2}. Four load steps occur in the staircase procedure. The S/N diagram of the tests carried out shows the damages lie in a range from 10^{5} to 10^{6} load cycles.

#### 6.2 Steel 1 Material

The test results for the steel 1 variant with a higher material cleanliness are shown in Figure 9. The endurable mean double amplitude of the pulsator force is F_{ptp,mean,steel 1} = 24.5 kN. The increased material cleanliness is assumed to affect the increase of the fatigue strength, but the scatter of the test points in the staircase is comparable with the scatter of the variant Ref. The S/N diagram shows that the number of load cycles of damages decreases. For steel 1, no break occurs after 6*10^{5} load cycles, which is significantly lower compared to the Ref variant.

The shift of the damages to lower load cycles is likely due to the improved material cleanliness. The reduced number and size of defects in the material result in fewer potential crack origins in the material. This reduces the local stresses in the material and increases the load carrying capacity. The defects still present in the material, however, represent potential crack starting points again under the increased load. In the case of crack initiation at a defect, the crack growth in the material progresses faster due to the increased stresses and a damage of the tooth root occurs earlier.

#### 6.3 Steel 2 Material

Figure 10 shows the test results of the steel 2 variant. The endurable mean double amplitude of the pulsator force is F_{ptp,mean,steel 2} = 24.25 kN. In contrast to the other two variants, only three load steps occur in the staircase of this variant. The scatter of the test results is therefore lower. The S/N diagram of the tests carried out shows that the average number of load cycles in the event of damage is reduced analogously to variant steel 1. Accordingly, the further increase in the cleanliness of steel 2 does not lead to a further increase in the load carrying capacity, but to a reduced test scatter and a reduced number of load cycles in case of a breakage. The reduced size of defects in the material can explain this change.

Since the size of defects for steel 2 is smaller than for steel 1, the probability that a detrimental defect is in the critical area of the tooth root with the maximum stresses is lower. The scatter of the test results decreases accordingly. At the same time, however, the probability increases that other damage mechanisms, which are not caused by material defects, will limit the load carrying capacity. Accordingly, the average endurable load does not change. Nevertheless, it is to be expected that an improved surface quality and increased residual compressive stresses will increase the differences between the different steel grades. With residual compressive stresses, for example, the occurring failure modes will probably change from surface failures to sub-surface failures because the crack initiation at the surface is prevented [5]. In this case, the higher cleanliness of the material will lead to higher strengths.

#### 6.4 Comparison of Results Considering the Confidence Intervals

The test results of the investigated variants with different material cleanliness show that the load carrying capacity is in some way affected by improved cleanliness. In addition to the load carrying capacity, the cleanliness also influences the scatter of the test results. To quantify the influences, the endurable mean pulsator forces of the three variants are compared in Figure 11. In addition to the determined mean values x, the standard deviations of the respective test series and the single-sided confidence intervals CI_{x} of the mean values are shown. The load capacity increase of variant steel 1 to the reference variant Ref amounts ā = 8.3 % or ā_{Ļ} = 107.63 N/mm^{2}. The examination of the confidence intervals shows that a significant increase in the load carrying capacity exists, taking into account the possible scattering of the mean value. The mean values of the variants steel 1 and steel 2 differ by ā = 1%. The consideration of the respective confidence intervals makes clear that the mean values of these variants are equal from a statistical point of view, since the confidence interval of steel 2 lies within the interval of variant steel 1.

The standard deviations of the experiments lie within a range of s = 2.7 – 4.1% and thus correspond well with HĆ¶hnās values [6]. A comparison of the test scatter on the basis of the calculated standard deviations is not performed, since more than the 15 tests performed per variant are necessary for a reliable determination of the standard deviation [7].

In order to classify the determined strengths of the different materials, the nominal stress numbers Ļ_{Flim} of the ISO 6336 – 5 are shown in Figure 12. The classifications ML, MQ, and ME describe the material quality. The value of the respective class indicates the expected strength of the corresponding material qualities. Furthermore, the values of the nominal stress numbers Ļ_{Flim} determined in the tests are shown. The calculation of the values is based on the formulas and factors presented in Figure 7. The class ML stands for moderate requirements on material quality and heat treatment. Experienced manufacturers can achieve the requirements of class MQ at moderate costs. The ME class represents requirements necessary for a high degree of operational safety. [13]

The strength of the Ref variant is Ļ_{Flim,Ref} = 487.10 N/mm^{2} and lies in the range of the class MQ -c so the strength of this material is already in the upper levels of the ISO 6336 – 5 classification. The variants steel 1 and steel 2 have strengths of Ļ_{Flim,steel 1} = 527.35 N/mm^{2} and Ļ_{Flim,steel 2} = 521.97 N/mm^{2}. These values correspond to class ME and represent a significant increase in the nominal stress number. Since all material variants were manufactured and heat-treated in the same way, the increase in load carrying capacity is due to the improved material cleanliness. The level of the steels with high cleanliness corresponds to the class for the highest demands on the material quality ME of the ISO 6336 – 5.

In conclusion, it can be stated that the higher cleanliness of the material steel 1 leads to an increased tooth root load carrying capacity in the tests compared to the reference material Ref. A further increase in the material cleanliness does not result in a further increase in the load carrying capacity, but does reduce the test scatter. The service life of a component can thus be predicted very precisely for the material variant steel 2, since the fatigue strength value is subject to less uncertainty. In the design, the safety factor can thus be reduced and the power density additionally increased.

### 7 Summary and Outlook

In standardized testing such as the pulsator testing for gears, it appears possible to distinguish between different steel performance levels. The investigations carried out show an increase of the fatigue strength of approximately ā = 8% for the clean steels. For the reference variant, the fatigue strength is already high with a value of Ļ_{Flim,Ref} = 487.10 N/mm^{2}. However, with clean steels, the distinction between the clean steel 1 variant and the ultra-clean steel 2 variant is more difficult to determine. Other limiting factors, including the surface quality and sometimes the test itself, can make these differences less obvious. One aspect that is apparent from the pulsator testing is that the scatter in material behavior decreases with improved cleanliness. From a statistical point of view, regarding the confidence intervals, the clean and ultra-clean variants have the same fatigue strength for the chosen test parameters. For a different residual stress state at the surface or an improved surface quality, it is assumed that the differences between the variants will increase due to changing failure modes. Regarding the classification of the ISO 6336 ā 5, the investigated variants can be classified in the top range of MQ-c and ME.

In a continuation of this investigation, further analysis on the gears is to be done to enhance the understanding of the residual stress state, hardness profiles, and deeper examination of the failed gears.ā

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*Printed with permission of the copyright holder, the American Gear Manufacturers Association, 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314. Statements presented in this paper are those of the authors and may not represent the position or opinion of the American Gear Manufacturers Association. (AGMA) This paper was presented October 2019 at the AGMA Fall Technical Meeting in Detroit, Michigan. 19FTM13*