Binder jetting in gears

Due to near netshape production, powder metallurgically manufactured (PM) gears have a high potential to increase cost and resource efficiency. Compared to conventionally machined gears, the advantages of PM gears are the different local density distribution in the component and the potential integration of secondary design elements. These advantages are accompanied by the reduction of weight and the possibility of optimizing the NVH-behavior of a gear. PM gears may be manufactured by both, die pressing and additive manufacturing (AM). The powder bed-based additive manufacturing processes for metals can be classified into binder-based (e.g. Binder Jetting, BJT) and beam-based thermal processes (e.g. Laser Powder Bed Fusion, LPBF). Due to the specific process technology, the manufacturing of PM gears by die pressing is only economical for large batch sizes in series production. For small batches, AM offers an approach to manufacture gears that meet the requirements in terms of quality, strength, acoustics and economic efficiency of the manufacturing process. This report describes the potential of BJT gears made of stainless steel 17-4PH (X5CrN-CuNb16-4) with a relative density of ρ0,rel ≈ 99% regarding the tooth bending strength. The reliability of the process and thus the tooth bending strength can be increased further by a specific adjustment of process parameters. Subsequently, the gears are tested with regard to the tooth bending strength on the pulsator test rig. The results are summarized in a SN-curve.


Introduction and motivation
Due to near netshape production, powder metallurgically manufactured (PM) gears have a high potential to decrease costs and increase resource efficiency.Compared to conventionally machined gears, the advantages of powder metallurgically manufactured (PM) gears are the different local density distribution in the component and the potential integration of secondary design elements.These advantages are accompanied by the reduction of weight and the possibility of optimizing the NVH-behavior of a gear [24].Due to the expected future shift of the automotive industry from combustion engines to electrified powertrains, the optimization of the noise behavior of transmission components is becoming increasingly important [28].Powder metallurgical gears may be manufactured by both, die pressing and additive manufacturing (AM).The powder bed-based additive manufacturing processes for metals can be classified into binder-based (e.g.Binder Jetting, BJT) and beam-based thermal processes (e.g.Laser Powder Bed Fusion, LPBF).Due to the specific process technology, the manufacturing of PM gears with die pressing is only economical for large batch sizes in series production.For small batches, additive manufacturing offers an approach to manufacture gears that meet the requirements in terms of quality, strength, acoustics and economic efficiency of the manufacturing process.
Additively manufactured products contribute to increasing individualization and variety, as undercuts and functional elements can be integrated directly into the component.These can only be integrated into the design using additive manufacturing processes due to the additional degrees of freedom.The achievable geometric complexity in the design offers new possibilities for use and optimization and requires increasing flexibility in manufacturing [5].
This report describes the potential of BJT gears made of stainless steel 17-4PH (X5CrN-CuNb16-4) with a relative density of ρ0,rel 99% in terms of tooth bending strength.The reliability of the process and thus the bending strength of the teeth can be further increased by specific adjustment of the Binder Jetting process parameters.Both endurance and fatigue strength of 17-4PH BJT gears are investigated and the results are summarized in a SN-curve.In addition, the endurance strength of cold rolled gears made of 17-4PH (ρ0,rel 93.98%) is determined in screening tests and evaluated by comparison with load capacity results of densified gears made of 316L (stainless steel X2CrNiMo17-12-2).In this case, the development of the process parameter is not part of this report.

Manufacturing of binder jetting gears considering the tooth bending strength
Binder Jetting (BJT) of gears is a multi-stage additive manufacturing process.The components are produced in two or more operations [9].The BJT process produces green compacts of gears which are sintered by secondary heat treatment processes.During the sintering process, the powder particles form a diffusion bond [3], the porosity decreases and the component volume shrinks [21].Both the pow-K der mixture and the binder are prepared according to the defined recipe.Subsequently, the "printing", the layer-bylayer generation of the green gear, takes place by applying the liquid organic binder locally to the powder bed (buildbox) and bonding both the powder particles and the existing layers together.Since no additional heat is generated during the production process, it does not have to be dissipated via specific constructions.After the printing process, the binder is cured.For this purpose, the entire buildbox is moved into the curing oven with the printed gears and the unused, recyclable powder.Afterwards the gears are removed from the powder bed.Afterwards, the binder is removed from the produced green gears by a thermal treatment.The following sintering and heat treatment process produces the final strength and densifies the green gears by shrinkage.
After the heat treatment steps, the gear is transformed into a purely metallic state [2].The material powder used for additive manufacturing must have good flowability as well as a high filling density [3].To date, commercial systems mainly process stainless steels (316L, knife steel 420, 17-4 PH) as well as titanium alloys such as Ti6A14V and copper [2,4,12,15].In the following, previous investigations on the Binder Jetting of gears made from stainless steels 316L and 17-4PH are described.

Gears made of stainless steel 316L
Initial investigations on the manufacturing of gears using BJT as well as the analysis of the tooth bending strength were conducted with the material 316L (stainless steel X2CrNiMoN17-12-2).This metallic material is certified and established for the binder jetting process [2].The gears were sintered after printing with regard to a relative core density of ρ0,rel 92%.In analogy to the process chain of die pressing in series production, the near surface zone of the BJT gears is compacted by densification rolling using the machine PROFIROLL PR 15HP.The material 316L shows ductile properties and therefore can be coldformed without problems [26].After manufacturing, both the fatigue strength and the endurance strength of the gears were analyzed.The results were summarized in a SNcurve.The experimental investigations of the ground gears were performed on a pulsator test rig.With regard to the fatigue strength, the endurable double amplitude as well as the tooth root stress were determined.The mean value of the endurable double amplitude (NG = 3 10 6 LC) was 2 FA,mean = 6.26 kN, corresponding to an endurable tooth root stress of σF0 = 351.14N/mm 2 calculated according to ISO 6336-3 [17].This value of the double amplitude corresponds to the fatigue strength characteristic value for a failure probability of Pa = 50%.The intersection of the endurance and fatigue lines was located at the double amplitude force of 2 FA,mean = 6.26 kN and the number of load cycles of N = 1,940,000.Both within the test points of a gear and within the BJT batch, there was hardly any variation in the results and load cycles achieved.The reproducibility of the results verifies the suitability of BJT in gear production for the first time [20].A pressed and sintered gear made of the material Fe + 0.85% Mo + 0.25% C was tested as a reference on the pulsator test rig.The mean value of the endurable double amplitude (NG = 3 10 6 LC) was 2 FA,mean = 8 kN [20].Comparable studies regarding the tooth bending strength of Binder Jetting gears should be conducted with a certified metallic material, which has significantly higher strength values and therefore implies a higher tooth bending strength.

Gears made of stainless steel 17-4PH
The material 17-4PH (stainless steel X5CrNiCuNb16-4) has a significantly higher mechanical strength compared to 316L and thus implies an increase in the tooth bending strength of the manufactured gears [1,6,8].Compared to the BJT gear production from the material 316L, a new design of the BJT process parameters is essential due to different material characteristics.The impact of different process variations along the process chain of BJT gears made of the material 17-4PH was investigated [19].During the printing process of the green gear, the powder and binder application have been identified as the main influencing factors on the final print result.The most relevant variables for powder application are the layer thickness Ds as well as the application direction and speed vp as a function of the processed material powder [19].When applying powder in two directions, a larger amount is introduced into the powder bed at a constant layer thickness Ds and thus the density of the green gear increases.A higher green density implies a lower shrinkage during sintering.This results in a reduction of the induced stresses and a decrease in crack formation [19].Subsequently, support structures for gear manufacturing by means of BJT were discussed, which are particularly relevant for the subsequent post-treatment processes curing and sintering to minimize the risk of fracturing.Structural support structures correspond to small components that are additionally produced with the gear in a printing process.While curing, the stresses are induced by the static and dynamic interactions of the powder.The process stability of debinding and sintering was significantly increased by the use of a mesh disk between the gear and the ceramic sintering base [19].Effects of the sintering furnace on the printing result, especially if a retort furnace is used, also have to be considered.The identified process parameters are summarized in Fig. 1.
When powder was applied in two directions (outward and backward path above the buildbox) at a constant powder application speed vp = 50 mm/s, the amount of applied binder (Dark-Level) was reduced.In addition to the optimizations in powder application, the part quality can be further increased by adjusting the control variables for binder application.Basically, the binder is applied to the BJT system DM P2500 via two cartridges.The amount of binder applied can be adjusted by varying the number of nozzles (number of pixels) of the respective cartridge.The green gear geometry is described in the layer by pixels.Thus, pixels can be eliminated from the binder application based on defined patterns, similar to that of a chessboard.At least 50% of all pixels (Dark 0) of a component geometry must be printed.Dark Level 1 corresponds to 55.56% of the maximum amount of binder that can be applied, Dark Level 3 to 66.67% and Dark Level 8 to the maximum amount of binder (100%).During curing, the buildbox with the printed gears and the unused, recyclable powder is heated from ambient temperature to the curing temperature TC = 200 °C over a defined period of time tR (ramp time) immediately after printing.Afterwards the gears remain in the oven at the temperature TC for a calculated holding time tH.The process times in the oven can be calculated by the amount of binder used during printing and the number of layers.Thus, the times are varying for each print.When simultaneously printing four gears made of material 17-4PH, the ramp time is approximately tR = 10 h and the holding time at TC is approximately tH = 8 h.Debinding was realized in a muffle furnace and sintering in a retort furnace.The relative density of the gears made of the material 17-4PH after sintering was ρ0.rel 97.4% [19].
Despite the process modifications explained previously, some of the gears cracked depending on their position in the furnace after sintering (cf.Fig. 1, bottom right).Thus only a screening could be conducted to investigate the tooth bending strength.In addition, an uneven grinding allowance respectively undersize on the flanks was detected.The mean value of the endurable double amplitude (NG = 3 10 6 LC) of the BJT gears was 2 FA,mean = 10.60 kN, corresponding to an endurable tooth root stress of σF0 = 688.26N/mm 2 .The comparison with load capacity results of densified gears made of 316L (stainless steel X2CrNiMo17-12-2) showed an increase of almost 95% [20].

Objective and approach
The additive manufacturing process of Binder Jetting is intended to enable the production of individualized gears in small batch sizes, through which all requirements with regard to quality, strength, acoustics and cost-effectiveness can be implemented.The objective of this report is to optimize the process for gear manufacturing using 17-4PH (stainless steel, X5CrNiCuNb16-4), see Fig. 2. The evaluation is based on the one hand on the process-reliable reproducibility of the gears and on the other hand on the resulting tooth bending strength.Proceeding from the knowledge already developed for gear production from the material 17-4PH at a relative component density ρ0,rel 97.4%-production and use of support structures, knowledge of the main factors influencing the final print result, as well as initial process parameters along the process chain-the reliability of the process and thus the tooth bending strength is increased through a specific adjustment of the process parameters.Both the endurance strength and the fatigue strength of the BJT gears made of material 17-4PH are analyzed and the results are summarized in a SNcurve, see Fig. 2.
Due to already established results on the tooth bending strength of cold rolled gears made of the material 316L [20], gears are manufactured of 17-4PH with an allowance for densification (ρ0,rel 93.98%) for screening tests.The densification of the surface zone by the rolling results in a graduation of the density from the surface to the core.Subsequently, the gears are examined in screening tests with regard to the tooth bending strength on the pulsator test rig.Thus, in this report describes the influences of relevant process parameters on the component properties and the tooth bending strength of the gears.

Gear manufacturing with optimized process parameters
Based on the process parameters developed in Chap.

Powder application
The previous occurrence of crack formations at some gears could result from variations in the relative green densities depending on the positioning in the powder bed.Generally, a cube (measuring 10 × 10 × 7 mm) was produced in each of the four corners of the build box for the previous print jobs.As the volume of the cubes and the density of the material 17-4PH were known, the relative green density could be calculated.The relative green density of the previously manufactured gears var-ied in a range of ρrel = 2.2% based on the four cubes.In addition, only low values of the relative green density were obtained in the lower limit of the desired range of ρrel = 50-60%.For the analysis of the relative green density distribution over the entire powder bed and thus in the printing area of the gears, 16 further test cubes, distributed in the buildbox, were manufactured subsequently, cf.Fig. 3. Printing was done with the process parameters deduced in Chap.2: powder application in two directions of motion, 56.26% of all pixels were wetted with binder (Dark Level 1), layer thickness of Ds = 42 µm, powder application speed vp = 50 mm/s and binder application speed of vd = 200 mm/s.The average value of the relative green density of the cubes was ρrel,min = 49.8% and the maximum density was ρrel,max = 52.4%.The decrease of the green density in the powder bed from the print head side to the powder magazine side was notable.The decrease was approximately ρrel = 1%.In addition to powder application in two directions of motion, the reduction of the powder application speed vp is another possibility to increase and stabilise the green density.A higher green density implies a lower shrinkage during sintering.This results in a reduction of the induced stresses and a decrease in crack formation.The application speed was therefore reduced to vp = 40 mm/s while the layer thickness Ds was kept constant.Hence, a larger quantity of powder is inserted into the powder bed, the green density increases further.However, the productivity decreases.After reducing the application speed vp, an average green density of ρrel,m = 53.4% was reliably achieved during the process.The determined average density of green gears was assumed to be sufficient for the following prints.It could be kept constant in the range of ρrel = 1.7% over all gear prints conducted.

Scaling of the gear and thermal processes
After sintering the gears, the geometric analysis revealed a partial undersize on the flanks and thus an insufficient grinding allowance.Therefore, the scaling factors of the printed gear were increased in X-, Y-and Z-direction ( = 3.43%) to prevent sintering shrinkage, see Fig. 4.
The adjustment of the scaling factors leads to an increasing amount of binder during printing and thus an extension of the curing process.When simultaneously printing four gears made of material 17-4PH, the increased amount of binder resulted in a ramp time of approximately tR = 11 h 30 min.The holding time at TC kept constant at tH = 8 h.Based on the previous experience of debinding in a muffle furnace and sintering in a retort furnace, the gears were debinded and sintered at identical process conditions in a continuous furnace using a protective gas atmosphere (hydrogen H2).After sintering, no visible damage or cracks at the gears was detected.16 gears has been printed.All of them had sufficient oversize and a relative density of ρrel = 99%.The resulting relative density was higher than the relative

Critical Area
Target After Hard Finishing After Sintering Δ = + 3.43 % Fig. 4 Tooth Space before and after adjusting the scaling factors density of the variant tested in the screening trials [19].Thus, the type of sintering furnace has a significant influence on the final component quality.The previously developed mesh disc was used as a support structure during sintering.

Hard machining
The BJT gears were profile ground using a KAPP KX 500 FLEX gear grinding machine.Due to the partially high allowance in the area of the tooth root and tooth tip, cf.Fig. 4, the final geometry was produced in two roughing and one finishing cut to avoid grinding burn.
The gear quality was measured on a KLINGELNBERG P65 gear measuring machine.The measurement was conducted on all gears in order to achieve the best possible statistical validation of the evaluation.In addition to the profile and helix deviation, the single and accumulated pitch errors fp as well as the radial runout error FR were measured.
All measured values of the BJT gears averaged minimum within IT5 according to DIN EN ISO 1328 [7].
The surface roughness of the respective tooth profiles of the BJT gears was measured after grinding using the tactile roughness measuring device HOMMEL ETAMIC NANOSCAN 855.The evaluation of the roughness values and measurement reports was performed in accordance with DIN EN ISO 21920-3 in the direction of the profile [10].In total, six roughness measurements were performed for each gear.Of four teeth evenly distributed over the circumference, a roughness measurement was taken on both the right and the left flank of the respective tooth.The mean value of all Rz measurements (maximum height of the roughness profile) after hard finishing was Rz = 2.3 µm, the arithmetic average roughness value Ra = 0.3 µm.The roughness of the ground tooth roots of all the gears examined was within this range as well.

Validation of the binder jetting process chain regarding the tooth bending strength
The following chapter describes the results of the tooth bending strength tests of the additively manufactured BJT gears (ρ0,rel 99%).The results are summarized in a SNcurve.Furthermore, in analogy to the results already obtained on the tooth bending strength of cold rolled gears made of 316L [20], gears were manufactured from 17 4PH with an allowance for cold rolling (relative core density ρ0,rel 93.98%).The gears were classified in the state of the art by comparison with cold rolled gears made of 316L.

Experimental design and description
Gear-critical load types are stresses on the tooth flank due to rolling and bending fatigue in the tooth root [13,27].
The experimental investigations of the ground gears with regard to the tooth bending strength were performed on a pulsator test rig.The pulsator is an analogy test rig which approximates a part of the stress curve occurring in tooth meshing with an alternative concept of load application, see Fig. 5.According to the definition of the ISO 6336-3 standard, the tensile and compressive stresses σZ and σD resulting from the mechanical load reach the maximum at the tooth root in the area of the 30°tangent [17].
The main advantage of the pulsator test compared to the running test is the possibility of multiple use of a gear.In addition, no counter gear is required.The number of possible test points depends on the contact line to be examined and the number of teeth z2 of the gear.The BJT gear contains four test points.The gear is clamped over several teeth between two plane-parallel pulsator clamps-four teeth are clamped at the BJT gear.The tooth normal force from the running test is applied to the gear.One clamp performs an oscillating movement and, in this way, introduces a sine-shaped force curve into the tooth.The other stationary clamp absorbs the applied force.The force applied is monitored and controlled by using a load cell.

Investigation of the tooth bending strength
In order to describe the component characteristics, 10 tests were performed in the endurance strength load range using the stair-step method [29] on two load levels.Another 14 tests were conducted at the transition to the fatigue strength load range using the stair step method [11].The stair step method was evaluated according to HÜCK [16].The load step of the endurance limit of the BJT gears is shown in Fig. 6.
The fictitious point formed the 15th test point.The load step increase per double amplitude was 2 FA = 1 kN.The ratio of a load step to the standard deviation was approximated according to HÜCK [16].The limiting number of oscillations for the tooth bending strength is set to NG = 3 10 6 load cycles (LC) according to ISO 6336 part 3 [17].Termination criteria during the pulsator test are reaching the limit number of load cycles and tooth root fracture [22].According to the HÜCK staircase method, the following test depends on the previous test result.In the case of a tooth root fracture before reaching the limit number of load cycles NG, the load or the stress is reduced by one step (2 FA = 1 kN).Otherwise, in the case of a run-out, the load or the stress is increased by one step [11].The Y-axis (Fig. 6) shows on the one hand the force 2 FA of the double amplitude, which indicates the stress range, and on the other hand the tooth root stress σF0 calculated accord-Fig.6 Endurance Limit for BJT gears made of 17-4PH (ρrel = 99.0%)according to HÜCK [16] Fig. 7 Fatigue Strength of the BJT gears (17-4PH, ρrel = 99.0%)according to the Horizon Method ing to ISO 6336 part 3 [17].The tooth root stress describes the local load in the tooth root.The test frequency of the pulsator test rig was fP1 = 143 Hz and thus below the critical test frequency of fcrit = 200 Hz, below which no influences of the test frequency on the results are to be expected [18].The mean value of the endurable double amplitude (NG = 3 10 6 LC) was 2 FA,mean = 12.07 kN, corresponding to an endurable tooth root stress of σF0 708.96N/mm 2 .The mean value of the double amplitude corresponds to the endurance strength characteristic value for a failure probability of Pa = 50%.The standard deviation was s = 2%.
To determine the fatigue strength (NG < 3 10 6 LC), a defined number of tests were performed according to the hori-zon method at two different load levels [25].The difference between the two load levels should be as large as possible in order to be able to make the best possible estimation of the fatigue strength line with regard to its slope and position.The minimum number of tests should be five [29].Five test runs were performed at both tested load levels of 2 FA,1 = 18kN as well as 2 FA,2 = 15 kN, see Fig. 7.
The corresponding load cycles N of each test were ranked in increasing order on the respective load level.For each test point, the probability of failure Pa was calculated based on the logarithmic normal distribution according to ROSSOW's method [14,25].After transferring the paired values of probability of failure Pa (Y axis) and number of K Fig. 8 SN-Curve of the 17-4PH gears (ρrel = 99.0%)load cycles N (X axis) into a suitable probability diagram, the best fit line for fatigue strength was created [22].For the load level of the double amplitude of 2 FA,1 = 18 kN, the probability of failure distribution Pa = 50% [29] was used determining the number of load cycles of N50%,1 = 69,444 LC.Similarly, the number of load cycles for a load level of 2 FA,2 = 15 kN was calculated to be N50%,2 = 145,925 LC.The statistical evaluation of the test points in accordance with ROSSOW provided the supporting points for the fatigue strength line in the SN-curve, as shown in Fig. 8.
The SN-curve, which provides a connection between the load level of the double amplitude (Y axis) and the endurable number of load cycles N until fatigue damage Fig. 9 Comparison of the tooth root stress of all gear variants occurs (X axis), is only valid for the defined probability of failure Pa = 50%.The intersection of the creep and fatigue lines was located at the double amplitude force of 2 FA,mean = 12.07 kN and the number of load cycles of N50%,SP = 353,631 LC.Furthermore, no pores were visible on the microscopic images of the fracture surfaces.Generally, it should be considered that the crack initiation, causing failure, was originated in the tooth root area on the surface of the 30°tangent.
To compare the tooth bending strength in the fatigue load range, the tooth root stresses of further tests on additional additively manufactured gear variants are shown in Fig. 9.The Y-axis shows the tooth root stress σF0 calculated ac-cording to ISO 6336 part 3 [17].The tooth root stress is calculated as a function of the tooth root geometry.Ideally, the tooth root geometry of all variants is congruent, but slight deviations were still possible due to the process parameter settings.Therefore, a practical classification of all variants is not possible by the force of the double amplitude 2 FA.The tooth root stresses were calculated on the basis of the real tooth root radii.In addition to the investigations described in Chap. 2 for the tooth bending strength of the material 316L and the gears made of 17-4PH with a relative density of ρrel = 97.4%, the calculated tooth bending strength of the optimized process variant with a relative density of ρrel = 99.0%and the tooth bending strength of a further variant (ρrel = 93.98%)are shown as well.
The gears made of 17-4PH were manufactured with the process parameters derived in Chap.2.2 and sintered by reducing the sintering temperature (TSinter = 1280 °C) to achieve a relative target density, i.e. the core density after the cold rolling process, of ρrel = 93.98%.Although cold forming of the material 17-4PH is only possible in the annealed condition [26], the gears have been provided with a rolling stock allowance.As a result, the blanks do not feature an involute profile.Due to the densification of the surface zone by the rolling process, there is a density gradient from the surface to the core.The process parameters for cold rolling using the PROFIROLL PR 15HP rolling machine were adapted from KLEE [20].During the rolling process, cracks occurred on the gears starting from the tip of the tooth.The cracks also spread on the tooth flank to a small extent.Due to the cracks, the gears were no longer usable.The cracks were caused by the material properties [26].The mean value of the endurable double amplitude of the rolled gears with a relative density of The tests on the tooth bending strength of the variant with a relative density of ρrel = 99.0%showed a slight increase of = 3.01% in the fatigue strength of the gears compared to the gears tested in the screening tests (ρrel = 97.4%).The increased bending strength is related to the process parameters set.In particular, the adjustment of the process parameters ensured that only flawless gears made of 17-4PH with a relative density of ρrel = 99.0%could be reproducibly and reliably produced.Compared to the screening tests of the rolled gears with a relative core density of ρrel = 93.98%,an increase in bending strength of = 30.36%was achieved.In comparison with the results of the gears made of the material 316L, significant increases in bending strength were achieved for all 17-4PH variants.This is due to both the specific material properties and to the optimization of various process parameters, which are summarized in the following chapter.

Influences of relevant process parameters on component characteristics
The following chapter summarizes the optimized process parameters for the production of Binder Jetting gears made of 17-4PH stainless steel as well as the influences of the most relevant process parameters on the resulting component properties.The validation and evaluation of the process chain was conducted in terms of process reliability and reproducibility on the one hand and the achievable tooth bending strength on the other hand.An overview of the process parameters developed in Chap. 4 and the calculated tooth root stress σF0 (described in Chap.5) are shown in Fig. 10.Based on the process parameters described in Chap.2.2 with a constant powder application speed of vp = 50 mm/s and two-sided powder application and a binder quantity of dark level 1 (66.67% of the maximum binder quantity that can be applied), further process adjustments were necessary due to crack formation after the sintering process, see lower part of Fig. 10.Due to the larger scaling of the gears and the resulting higher amount of binder applied, the ramp time for curing was extended accordingly to tR = 11 h30.Both debinding and sintering took place in a continuous furnace.
Sintering was realized at a sintering temperature of at least TSinter = 1305 °C over a total process time of t = 13 h.The effects of the main process parameters on the resulting gear properties are summarized in Fig. 11.Reducing the powder application speed vp resulted in a more constant green density ρ throughout the powder bed of the buildbox.Reducing the powder application speed by vp = 10 mm/s led to a decrease of the green density variation during the print from ρgr,rel = 2.2% to ρgr,rel = 1.7%.This led to a decreasing risk of cracking on the one hand and an increasing component density on the other hand.
The position of the gear in the buildbox during the printing process only marginally influenced bending strength of the tooth (Fig. 11, top centre).After considering all the test points for each gear variant, an average tooth stress curve was determined.For position 1 in the buildbox, there were not enough data points for the relative densities of ρrel = 93.98% and ρrel = 97.4% to calculate a useful average.For positions 2, 3 and 4, there was no effect of the gear position on the tooth bending strength was detected.Extending the ramp time tR during curing reduced the risk of cracking in the process.A ramp time of tR = 10 h was determined to be process reliable, depending on the green part scaling.A lower (dark level 1) compared to a higher amount (dark level 3) of binder led to a reduced risk of cracking during debinding as well.A similar effect was registered during curing.However, reducing the amount of binder too much will result in an insufficient green strength of the gears.This has to be considered depending on the size of the component.A higher sintering temperature TSinter implies an increase in the relative density of the components ρrel after sintering.For the material 17-4PH, a minimum required sintering temperature of TSinter = 1305 °C was determined to achieve a relative density of ρrel = 99%.Higher tooth root capacities have also been achieved as a result of the increased gear density.Therefore, the objective of the process design of the Binder Jetting process chain for the production of 17-4PH gears with the highest possible tooth root load-bearing capacity is always aims to achieve a high relative component density.

Summary and outlook
In this report, the potential of gears manufactured by Binder Jetting (BJT), using the material 17-4PH (stainless steel X5CrNiCuNb16-4), has been analyzed with regard to the tooth bending strength.The relative density of the gears was increased up to ρ0,rel 99% by specific adjustment of the BJT process parameters.In addition, the reliability of the process and therefore the bending strength of the gears was increased as well.Both endurance and fatigue strength of 17-4PH BJT gears were investigated and the results were summarized in a SN-curve.
Different process variations along the process chain as well as their benefits were discussed [19].The relative den-sity of the gears made of the material 17-4PH after sintering was ρ0.rel 97.4% [19].Despite the process modifications explained previously, some of the gears cracked depending on the furnace position after sintering.Based on the parameters determined by KLEE [19], further modifications to the process were required.Modifications were made to the powder application, the component scaling and thus the curing process as well as the debinding and sintering process.The previous occurrence of crack formations at some gears could result from variations in the relative green densities depending on the positioning in the buildbox.In general, a higher green density implies a lower shrinkage during sintering.This results in a reduction of the induced stresses and a reduced risk of crack formation.In addition to powder application in two directions of motion, the reduction of the powder application speed to vp = 40 mm/s while keeping the layer thickness Ds constant lead to an increasing average green density by ρrel,m = 2.4%.The average density of green compacts could be kept constant in the range of ρrel = 1.7% over all gear prints conducted.After sintering the gears, the geometric analysis revealed a partial undersize on the flanks and thus an insufficient grinding allowance.Therefore, the scaling factors of the printed gear were increased in X-, Y-and Z-direction ( = 3.43%) to prevent sintering shrinkage.The adjustment of the scaling factors leads to an increasing amount of binder and thus an extension of the curing time.The gears were debinded and sintered at identical process conditions [19] in a continuous furnace using a protective gas atmosphere (hydrogen H2).After sintering, no visible damage or cracks at the gears were detected.16 gears have been printed.All were completely undamaged, had sufficient oversize and a relative density of ρrel = 99%.This value is higher than the value of the relative density of the variant tested in the screening trials [19].The quality of the gears was measured after grinding using a gear measuring machine.All measured values averaged within quality class IT5 according to DIN EN ISO 1328 [7].Subsequently, the tooth bending strength was tested on a pulsator test rig.The mean value of the endurable double amplitude (NG = 3 10 6 LC) was 2 FA,mean = 12.07 kN, corresponding to an endurable tooth root stress of σF0 = 708.96N/mm 2 .The fatigue strength (NG < 3 10 6 LC) was determined according to the horizon method.The probability of failure was Pa = 50%.The intersection of the creep and fatigue lines was located at the double amplitude force of 2 FA,mean = 12.07 kN and the number of load cycles of N50%,SP = 353,631 LC.The tests on the tooth bending strength of the variant with a relative density of ρrel = 99.0%showed a slight increase of = 3.01% in the fatigue strength of the gears compared to the gears tested in the screening tests (ρrel = 97.4%).The increased bending strength is related to the process parameters set.In particular, the adjustment of the process parameters ensured that only flawless gears made of 17-4PH with a relative density of ρrel = 99.0%could be reproducibly and reliably produced.Moreover, the endurance strength of cold rolled gears made of 17-4PH (ρ0.rel 93.98%) was determined in screening tests.The mean value of the endurable double amplitude of the rolled gears with a relative density of ρrel = 93.98% was 2 FA,mean = 7.93 kN, corresponding to an endurable tooth root stress of σF0 = 543.83N/mm 2 .
In short term, the influence of variable binder moistening and different relative densities on the mechanical properties will be investigated on bending and compressive specimens as an analogue sample to the gears.The validation will be realized by comparing the results to the bending strength results of the gears presented in this report.In long term, the development and certification of further materials, especially common gear steels such as 16MnCr5, is planned for the BJT.
Funding Open Access funding enabled and organized by Projekt DEAL.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material.If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Fig. 1
Fig. 1 Initial process parameters for the production of BJT gears from 17-4PH

Fig. 3
Fig. 3 Relative Green Density in the Buildbox

Fig. 5
Fig. 5 Analogy test for determining the tooth toot load capacity

Fig. 10
Fig. 10 Process Parameters of BJT Gear Manufacturing and the resulting Tooth Root Stress

Fig. 11
Fig. 11 Influences of relevant Process Parameters