In this article, we present our contribution to the ICPHM 2023 Data Challenge on Industrial Systems' Health Monitoring using Vibration Analysis. For the task of classifying sun gear faults in a gearbox, we propose a residual Convolutional Neural Network that operates on raw three-channel time-domain vibration signals. In conjunction with data augmentation and regularization techniques, the proposed model yields very good results in a multi-class classification scenario with real-world data despite its relatively small size, i.e., with less than 30,000 trainable parameters. Even when presented with data obtained from multiple operating conditions, the network is still capable to accurately predict the condition of the gearbox under inspection.