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In this paper, we present a robust spherical harmonics approach for the classification of point cloud-based objects. Spherical harmonics have been used for classification over the years, with several frameworks existing in the literature. These approaches use variety of spherical harmonics based descriptors to classify objects. We first investigated these frameworks robustness against data augmentation, such as outliers and noise, as it has not been studied before. Then we propose a spherical convolution neural network framework for robust object classification. The proposed framework uses the voxel grid of concentric spheres to learn features over the unit ball. Our proposed model learn features that are less sensitive to data augmentation due to the selected sampling strategy and the designed convolution operation. We tested our proposed model against several types of data augmentation, such as noise and outliers. Our results show that the proposed model outperforms the state of art networks in terms of robustness to data augmentation.