Gears are important components of rotating machinery, and accurate fault identification can help prevent the deterioration of rotating machinery system failures, thereby ensuring their safe operation. In response to the issues of severe performance degradation of existing intelligent gear identification models under noisy conditions, as well as poor stability and generalization across different datasets, a 1DQCNN model that incorporates quadratic convolution operations into a 1D convolutional neural network is proposed to achieve intelligent identification of gear faults. During training, strategies such as the ReLinear algorithm and L2 regularization were employed to address problems related to overfitting and convergence difficulties associated with the quadratic convolution operation. The model was validated using two public datasets and laboratory-collected dataset, demonstrating good noise resistance, stability, and generalization, with practical engineering application capabilities.