Influence of structural parameters on the load capacity of spherical gear couplings under high misalignment angle and heavy load conditions

The spherical gear coupling, as a critical component of the transmission system in heavy metallurgical equipment such as rolling mills and straighteners, is frequently subjected to high torque (>1000 N·m) and high misalignment angles (≥3°). Under these extreme operating conditions, the teeth in the rotating position will lose contact. the number of engaged teeth drastically decreases, leading to a significant increase in contact stress on the tooth surface. This can easily cause pitting or root fractures, severely compromising the reliability and service life of the equipment. Current structural designs of spherical gear couplings predominantly utilize three teeth or five teeth finite element models based on medium to low load and small misalignment angle conditions. However, these models fail to meet the requirements for parameter influence analysis on the structural design of spherical gear couplings under high misalignment states. To address this, the present study develops a three-dimensional parametric finite element model considering full tooth engagement under high misalignment conditions. It systematically analyzes the impact mechanisms of misalignment angle ( γ ) and backlash ( κ ) on the maximum contact stress on the tooth surface under different torque levels. Using Box-Behnken experimental design and response surface methodology, a multivariable regression prediction model for maximum contact stress is constructed, achieving a prediction accuracy of 97.5%. The results demonstrate that, under high misalignment angle and heavy load conditions, the effect of misalignment angle on load capacity grows non-linearly. At a misalignment angle of 7°, the maximum contact stress is approximately five times greater than at 1°. The optimal backlash range is determined to be between 0.629 and 1.221 mm. This provides a reliable theoretical basis and engineering guidance for the structural design and performance improvement of spherical gear couplings under high misalignment and heavy load conditions.