An XFEM-Based Approach to Fatigue Crack Growth in Press-Fit Spur Gears

Gears mounted on a shaft via interference fit are the subject of an internal pressure which is essential for power transmission between gear and shaft. The pressure between shaft and gear is responsible for additional stresses occurring both in shaft and gear. This study examines the effect of stresses arising due to the interference on the crack growth that exists at the root of the gear tooth. The numerical analyses were conducted on models having different rim thicknesses by using the extended finite element method that allows mesh-independent crack modeling and does not need re-meshing. The results showed that internal pressure yields additional stresses in the tangential direction. The increment in tangential stress changed the location and intensity of the maximal 1st principal stress and accelerated crack growth. As the tightness of the fit increased, the crack turned towards the rim rather than towards the tooth. As the crack growth through the rim may cause a catastrophic failure of gear, the increment in tangential stress due to internal pressure is crucial for the fatigue life of the gear.

Influence of Metal Gear Tooth Geometry on Load and Wear within Metal-Polymer Gear Pairs

Gear pairs made of the material pairing metal-polymer provide advantages, such as a reduced weight, beneficial damping properties and the possibility to be operated in dry running conditions. However, the service life of the pairing is limited due to wear. The properties of the metallic gearing have a significant influence on the wear behavior of the material pairing. From previous investigations, the influence of the surface topography and the flank hardness of the metal pinion is known. With regard to resource saving and efficient manufacturing of the metal pinion, cold forging offers benefits. Through cold forging, metallic gears for the material pairing can be produced ready-to-use in a process suitable for serial production. In order to enable manufacturing by extrusion, the application of gear radii is necessary. The gear radii significantly affect the extrusion process and the achievable gear properties. However, the influence of gear radii on wear within the metal-polymer material pairing has not yet been investigated. Within this contribution, the influence of the gear radii on the contact behavior as well as the resulting local load and wear of the tooth flank is determined. For this purpose, wear tests with aluminum (AlMgSi1) and steel (16MnCr5) gears with different gear radii within the pairing with polyamide (PA66) gears were performed. It has been shown that the local wear of the tooth flank can be attributed to the local load and that adjusted gear radii lead to a varying load and wear of the metal and polymer gears. Based on the findings, functional relationships regarding the choice of gear radii and the wear behavior are derived which can be applied in the design of cold forged gears.

Cutter Head Approximation Machining Method of Line Contact Spiral Bevel Gear Pairs Based On Controlling Topological Deviations

To improve the meshing performance and increase the bearing capacity and service life of spiral gear pairs, the cutter head approximation machining method based on controlling topological deviations was proposed to solve the problem where line contact spiral bevel gears with tapered teeth depth cannot be directly machined by cutter heads. First, the mathematical model of line contact conjugate flanks was established, and meshing equations and conjugate flank equations of bevel gear pairs were derived. Second, the gear tooth flank was set as the datum tooth flank for priority machining, and the pinion theoretical tooth flank which is fully conjugate with the gear tooth flank and the pinion machining tooth flank matching with the gear were solved. Then, the geometric topological deviations model of the comparison between the pinion machining tooth flank and its theoretical tooth flank can be established. Finally, with the pinion machining tooth flank approaching its theoretical tooth flank as the modification, the additional cutting motions and machining compensation parameters of cutter heads were obtained to control the pinion machining tooth flank deviations and reduce them to the allowable deviations of its theoretical tooth flank. The contact simulation analysis and rolling test verified the correctness of the line contact conjugate flank model and feasibility of the cutter head approximation machining method.

Sensor-integrating gears: wear detection by in-situ MEMS acceleration sensors

Gear tooth wear is a common phenomenon leading to malfunctions in machines. To detect wear and faults, gear condition monitoring by vibration is established. The problem is that the measurement data quality for detection of wear by vibration is not good enough with currently established measurement methods, caused by long signal paths of the commonly used housing mounted sensors. In-situ sensors directly at the gear achieve better data quality, but are not yet proved in wear detection. Further it is unknown what analysis methods are suited for in-situ sensor data. Existing gear condition metrics are mainly focused on localized gear tooth faults, and do not estimate wear related values. This contribution aims to improve wear detection by investigating in-situ sensors and advance gear condition metrics. Using a gear test rig to conduct an end of life test, the wear detection ability of an in-situ sensor system and reference sensors on the bearing block are compared through standard gear condition metrics. Furthermore, a machine-learned regression model is developed that maps multiple features related to gear dynamics to the gear mass loss. The standard gear metrics used on the in-situ sensor data are able to detect wear, but not significantly better compared to the other sensors. The regression model is able to estimate the actual wear with a high accuracy. Providing a wear related output improves the wear detection by better interpretability.

Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Toothed gears are the most common mechanical gears in machine building, which are characterized by high reliability and durability, a constant transfer number, and which can transmit high torque. During toothed gear operation, the surfaces of the teeth slide, which gives rise to friction forces and wears their working surfaces. To prevent this, the surfaces of the teeth need constant lubrication. This paper considers the design of a gear tooth engagement, which does not have friction between the surfaces of the teeth since they roll over each other without slipping. The profile of the tooth of such a gear is outlined by congruent arcs, symmetrical relative to the line that connects the center of rotation of the toothed wheel with the top of the tooth. These symmetrical curves at the top of the tooth intersect at the predefined angle. In the depressions of the wheel, adjacent teeth also intersect at the same angle. Such a condition can be ensured by a curve that at all its points crosses the radius-vector emanating from the coordinate origin, also at a stable angle equal to half of the given one. This curve is a logarithmic spiral. If the number of teeth of the drive and driven wheels is the same, then their teeth are congruent. Otherwise, the profiles of the teeth would differ but they could be outlined by congruent arcs of the same logarithmic spiral of the same length taken from different areas of the curve. The minimum possible angle at the top of the teeth is straight. At acute angle, the toothed gear operation is impossible. To build gear wheels with a right angle at the top of the tooth, it would suffice to set the number of teeth of the drive and driven wheels. The center-to-center distance is calculated using the derived formula. The transfer number of such a gear is variable but, with an increase in the number of teeth, the range of its change decreases. The algorithm of wheel construction is given.