In the calculation of gear strength and tooth profile design, the concept of gear meshing misalignment is mentioned. Then how to define the gear meshing misalignment, what factors does it mainly relate to, and how to reduce the gear meshing misalignment in the design?

Definition of gear meshing misalignment

The gear meshing misalignment refers to the deviation between the actual contact points of the two meshing tooth surfaces along the meshing line, caused by factors such as system deformation, manufacturing errors, and assembly clearance. This misalignment can manifest as uneven loading or displacement in the contact area. The magnitude of the meshing misalignment directly affects the smoothness of gear transmission, the distribution of contact stress, and NVH performance. Excessive meshing misalignment can lead to uneven loading on the tooth surfaces, causing localized stress concentration, which can result in gear vibration noise and reduced fatigue life.

According to ISO6336 standard, the calculation of gear meshing misalignment involves manufacturing deviation, deformation and displacement of gear shaft and bearing, and only considers the relevant components in the meshing plane. The calculation of gear meshing misalignment can be expressed by the following formula:

Among these, Fβx— the gear meshing misalignment, um; fsh1— the meshing misalignment caused by the deformation and inclination of the pinion shaft; fsh2— the meshing misalignment caused by the deformation and inclination of the large gear shaft; fma— the meshing misalignment due to manufacturing and installation errors of the gears; fca— the meshing misalignment caused by the deformation of the housing; fbe— the meshing misalignment due to the deformation and clearance of the bearings. Based on the understanding of the formula for calculating gear meshing misalignment, we can categorize it into two types: one is the meshing misalignment caused by design factors, including elastic deformation and inclination of the gears and shafts, deformation and clearance of the bearings, and elastic deformation of the housing; the other is the meshing misalignment caused by manufacturing and installation errors, including manufacturing errors of the gears, errors in the bearing seat hole of the housing, and parallelism errors of the shafts. Additionally, when designing and calculating, it is important to note that the meshing misalignment of a pair of gears refers to the meshing misalignment of a gear pair. In the formula, the various factors causing the meshing misalignment of the large and small gears are directional (positive or negative), and the components can either compensate for each other or add up.

2) Factors affecting the misalignment of gear meshing

Elastic deformation of gear and shaft: mainly includes torsional deformation and bending deformation of gear shaft. For large gears, the influence of elastic deformation of gear spokes and rim structure should be considered; for high-speed gears, thermal deformation and deformation caused by centrifugal force should be considered.

The influence of bearing clearance and deformation: the bearing supporting the gear shaft is deformed under load or due to the existence of clearance, which will lead to the tilt of the gear shaft during operation, resulting in gear meshing misalignment. For tapered bearings, the size of the preload will affect the amount of gear meshing misalignment, which should be paid special attention to.

Deformation of the shell and structural components: When the shell components deform under load, it can cause the gear shaft to tilt. For planetary transmission structures, the torsional deformation of the carrier must be considered. When external forces act on the shell or input/output ends of the gearbox, the impact on gear meshing misalignment should be taken into account. The influence of manufacturing and installation errors of gears: Manufacturing errors primarily involve the helical deviation fHβ1 and fHβ2 of the small and large gears. Installation errors mainly include the coaxiality error of the bearing seat holes in the shell, as well as the parallelism errors fΣa and fΣβ of the gear shafts

3) Measures to Improve and Compensate for Gear Meshing Misalignment Based on the above analysis, we can summarize the following design methods to reduce and compensate for gear meshing misalignment: Enhance the stiffness of the gear shaft to minimize deformation, change the support method to use symmetrical supports, and reduce the bearing span; For large gear structures, increase the thickness of the rim or spokes to reduce bending deformation; Optimize the shell stiffness by increasing the support stiffness at the bearing seat to reduce deformation under load; For planetary gear sets, optimize the structure of the planetary carrier to reduce torsional deformation; Control the helix manufacturing error of gears by correcting the tooth profile or the tooth end slope to compensate for meshing misalignment caused by manufacturing errors; Control the coaxiality error and parallelism error of the bearing seat hole in the housing; During the design phase, if the gear meshing misalignment is significant, compensate for it by using helix angle correction + tooth profile correction, thereby improving the contact condition of the tooth surface.