Accurate prediction of calendering width is critical to ensuring product quality and production efficiency in the rubber calendering process for tire manufacturing. However, traditional deep learning models have high computational costs and slow inference speeds, making it difficult to meet the real-time prediction requirements in actual production. To address this issue, this paper proposes a lightweight modeling method based on knowledge distillation to reduce computational costs and improve inference efficiency. First, a teacher model with a Transformer-MLP architecture is constructed, fully utilizing the self-attention mechanism to extract complex dynamic features in the calendering process. Then, knowledge distillation technology is used to transfer the knowledge of the teacher model to a lightweight MLP student model, maintaining high prediction accuracy while reducing computational complexity. Experimental results demonstrate that, the proposed method achieves a substantial increase in inference speed, while significantly reducing model size, thereby enhancing its practicality for industrial applications with constrained computational resources.