2016 Volume 63 Issue 7 Pages 568-572
Bending durability tests were carried out using P/M spur gears made from 1.5Cr-0.2Mo pre-alloy sintered steel powder (FL520X) with a density of 7.40 Mg/m3 (GH1) and 7.55 Mg/m3 (GH2). The P/M gear specimens were machined from the sintered packs made by the single-press single-sinter route, and some were surface-rolled using a CNC form-rolling machine of two roller-dies type. All of the test gears were case-carburized. The bending durability was investigated by single tooth bending fatigue tests using a pulsator. A two-dimensional finite element simulation model were constructed and examined the effects of the void distributions and the surface densification depths on the bending stress distributions at the critical section on the root fillet of gear tooth flank. Both the experimental and the analytical results show that the bending durability and the stress level of surface-rolled GH1 completely matches that of GH2, whose bending fatigue strength is higher than the target level of 1 GPa.
Recently, some high-density and high-strength sintered steels for auto-motive power train gears were developed on the mixing completely pre-alloy steel power. In addition, surface rolling technology gives the very cost effective high precision processing of P/M gears with full surface density to improve the load bearing capacity. It has already been demonstrated that case-carburized P/M gears with a density above 7.5 Mg/m3 made of 1.5Cr-0.2Mo pre-alloy sintered steel can achieve bending strength of 1.0 GPa1,2), which match with those of case-carburized gears made of the typical Cr-Mo wrought steel most commonly used for transmission gears. However, some serious problems occur as the density of the preform gear increases: the short die life and the damage of gear preforms in the compaction process, the heterogeneous void distribution in the gear teeth, the crack initiation at the tooth tip of surface-rolled gears, and so on. Thus, in the actual manufacturing process, we expect that the density of P/M gears after sintering may be restricted up to 7.40 Mg/m3 due to the complexity of the transmission gear shape having a large helix angle and a high tooth depth.
In the present study, single tooth bending fatigue (STBF) tests were first performed using the case-carburized Cr-Mo pre-alloy sintered steel gears with different densities, and each S-N curves was obtained. Examining these data, we investigated the effects of the initial density of P/M material, the surface densification of gear tooth flank by finish gear rolling and the case-carburized conditions on the bending fatigue strength of P/M gears. We then constructed a finite element (FE)-simulation model including voids to analyze the stress distributions around the critical section on the root fillet of gear tooth flank. The purpose of this study is to resolve the effects of void distributions and surface densification level on the bending fatigue strength by comparing the experimental and the analytical results.
Table 1 compares the P/M preform characteristics, dimensions and process routes of spur gear specimens with different densities using in single tooth bending fatigue (STBF) tests, which were made from the same Fe-1.5Cr-0.2Mo-0.23C (called FL520X hereafter) completely pre-alloy powder using a 1P1S route. Those chemical compositions are close to the wrought alloy steel of JIS SCM415, which corresponds to DIN15CrMo5. The wrought alloy steel of SCM415 was currently used as a gear material, which selected to the comparison material in this study. The compaction pressure of the target material GH1 and GH1R with a lower density was reduced by 20 % and sintering temperature of which was 30K lower, compared with the case of GH2 and GH2R used in the previous study1,2). Gear surface rolling was conducted using a CNC form-rolling machine of two roller-dies transverse-type, as shown in Fig. 1. These rolling dies were spur gears with an involute tooth profile meeting the accuracy of DIN4, and were designed to roll both the tooth flank and root fillet near the critical stressed point simultaneously. A tool rotation speed was 60 min−1. The die radial displacement speed was 0.167 mm/rev, and the amount of radial displacement for the die was set to 1.0 mm to secure the amount of stock rolled normal to the tooth flank surface at 0.1 mm. Fig. 2 shows the case-carburizing conditions for P/M gears of the pattern 1 (GH1, GH1R) and the pattern 2 (GH2, GH2R), respectively. Fig. 3 shows a diagram of single tooth bending fatigue (STBF) test machine and the typical dimensions of a STBF test gear tooth. The load Pn was applied at the tooth tip of the gear in pulsating bending and the operating speed was set to 710 cycles per minute. The test was stopped at 5 × 106 cycles and considered a non-failure if the tooth had not broken. The tooth root bending stress σt was calculated using the equation proposed by Aida and Terauchi3).
| Gear designation | GH1 | GH1R | GH2 | GH2R | GS |
|---|---|---|---|---|---|
| Material | Fe-1.5Cr-0.2Mo-0.23C (completely FL520X pre-alloy sintered powder) | JIS SCM415 (comparison) | |||
| Manufacturing process | 1P1S | — | |||
| Compaction pressure | 800 MPa | 1000 MPa | — | ||
| Sintering condition | 1523 K × 3.6 ks | 1553 K × 3.6 ks | — | ||
| Density [Mg/m3] | 7.40 | 7.55 | — | ||
| Module | 3 | 3 | |||
| Pressure angle [°] | 20 | 20 | |||
| Number of tooth | 24 | 26 | |||
| Face width [mm] | 10 | 10 | |||
| Surface rolling | As-sintered (GH1, GH2) Surface rolled (GH1R, GH2R) |
— | |||
| Heart treatment | Case-carburized Pattern 1 | Case-carburized Pattern 2 | Case-carburized | ||
Photograph of P/M gear specimen after surface rolling.
Temperature pattern drawings of case-carburizing conditions for P/M gear specimens. (a) Pattern 1 (GH1, GH1R), (b) Pattern 2 (GH2, GH2R).
Schematic diagrams of single-tooth bending fatigue (STBF) test machine and typical dimensions of a STBF test gear tooth.
We performed a finite element (FE)-simulation to analyze the bending stress on the root fillet surface of P/M gears in STBF tests. Fig. 4 shows the initial state of the FEM segment model in two-dimensional plane-strain condition constructed in this study, in which the 4 nodes iso-parametric elements are used. The configuration of the gear tooth segment and the loading flat rigid-tool are identical to those used in the experiments. The FE-gear is elastic body. All boundary nodes with the black dash-line triangle marks are fixed. Then, the rigid-tool is gradually moved downward to push the gear tooth tip until a total bending load reaches a default value of 1 kN. FE-simulation area considering void distribution was located only near the critical stress section on the root-fillet surface layer to save the calculating time. Fig. 5 (a) and (b) compare the actual metallographic structure and the corresponding FE-mesh, in which the dark areas are filled with void-elements. This domain of 0.7 mm width and 0.8 mm depth was divided by a fine square mesh 8 μm on each side. The instructions of making this FE-model are as follow; if the half area of each element was assumed to be a cavity when the FE-mesh was superimposed on the metallographic digital-image, the element was replaced by the void-element. In this characteristic domain, Young’s modulus of the normal matrix-element and the void-element were set each in 205.8 GPa and 49.0 GPa. The former value of 205.8 GPa (E0) was quoted that of the Cr-Mo wrought steel from reference4). The latter value of 49.0 GPa (E′) was obtained in the following procedures. First, the average Young’s modulus (Ē) of the sintered steel with the same density as the test gear was calculated from the following equations based on the Machenzie’s theory5).
Initial state diagram of FEM segment model.
Comparative diagrams of actual metallographic structure and corresponding FE-mesh. (a) actual metallographic structure of GH1 gear, (b) corresponding FE-mesh.
| (1) |
Here, ɛ is the porosity and ν0 is Poisson’s ratio of wrought steel. Ē was also used for all elements not belonging to the characteristic domain. Next, a simple tensile FE-simulation was carried out using a plane-strain rectangle workpiece of 1 mm width and 3 mm height in which the void-elements were arranged as shown in Fig. 5 (b) to obtain a stress-strain relation in the elastic deformation area. Ē of void-element was finally determined to make the inclination of the stress-strain curve coincide with Ē. The Poisson’s ratio of void-elements ν′ was set in 0.3 which is the same as that of normal matrix-element ν0, because the void areas in this FE-model were assumed to be a deformable solid given a lower Young’s modulus E′, and a little difference of ν′ hardly influenced the stress analysis results. Then, the surface densification state was expressed by replacing all void-elements existing in a certain depth from the surface to the normal matrix element.
Fig. 6 compares the porosity distributions around the critical section of P/M gears with and without rolling. The porosity in the flank layer around the root fillet of the surface rolled gears decreased to less than 2 % from the surface down to a depth of approximately 0.5 mm. Observing in detail, the densification level of GH1R with a lower density of 7.40 Mg/m3 is slightly higher than that of GH2R with a higher density of 7.55 Mg/m3. Fig. 7 (a) and (b) compare the S-N curves of STBF test and the bending fatigue limit after 5 × 106 cycles as calculated from (a), respectively. The ordinate shows the tooth root bending stress (σt) at the critical section. The bending fatigue strength levels of both GH1 and GH2, as-sintered and case-carburized, were almost equivalent to that of GS, and surface rolling increased those of GH1R and GH2R by approximately 20 %, making them remarkably higher than that of GS. These experimental results indicated that the surface rolled P/M gears with the initial density from 7.40 Mg/m3 to 7.55 Mg/m3 made from FL520X powder could obtain the sufficient bending fatigue durability to replace gears made of typical Cr-Mo case-carburized wrought alloy steel.
Porosity distributions for P/M gear specimens.
Results of S-N curves measured by STBF test and bending fatigue limit after 5 × 106 cycles. (a) S-N curves, (b) bending fatigue limit.
Fig. 8 (a) and (b) compare the maximum principal stress (σ1) distributions around the critical section on the root fillet surface of gear flank, as determined by FE-simulation. The abscissa indicates the distance from the critical stress point, and the right positive side is the tooth tip direction. The stress distribution profile of every model follows the same pattern of a reverse parabola having the peak value near by the zero point; those clearly agree well with the case provided from the theory of elasticity. Fig. 9 shows the relationship between the peak maximum principal stress (σ1_max) and the surface densification depth (δ). σ1_max tends to decrease as δ increases for both gears. Specifically, σ1_max of GH1R-model with a density of 7.40 Mg/m3 decreases almost linearly in the δ range from 0.06 mm to 0.2 mm, and the same tendency can be observed in the case of GH2R-model with a density of 7.55 Mg/m3 in the δ range from 0.06 mm to 0.15 mm. Hence, the surface densification could substantially enhance the bending fatigue strength by reducing σ1_max, and this effect was more remarkable for a lower density case. Here, we notice that the FE-simulation results are clearly different from the experimental ones as for the as-sintered gears, since the STBF strength of GH1 is a little higher than that of GH2. This is because STBF strengths of gears without surface densification tend to be affected by many kinds of factors (for example the size, shape, and distribution of voids on the tooth flank surface, the stress concentration state around each void and so on), whose influences are currently being examined through experimental and analytical approaches. On the other hand, when δ reaches 0.2 mm or more, σ1_max of GH1R-model become very close to that of GH2R-model. Since the full densified depth of gears employed in this study is higher enough than this level of 0.2 mm, it is assumed the difference of the bending fatigue strength was hardly observed between GH1R and GH2R. Therefore, FE-simulation results using the surface densified model seem to explain the experimental phenomenon of the surface rolled P/M gears well.
Maximum principal stress distributions around critical section on gear root fillet surface calculated by FE-simulation. (a) GH1R-model (with a density of 7.40 Mg/m3), (b) GH2R-model (with a density of 7.55 Mg/m3).
Relationship between peak maximum principal stress and surface densification depth in FE-simulation.
