"Coil stacking storage rack" (though context may slightly vary usage, this is a direct and commonly understandable translation for a structure designed to store coiled materials in stacked form) could be an appropriate way to translate "带卷垛存台架" into English. Here, “带卷” refers to coiled materials (like steel coils), “垛存” implies stacked storage, and “台架” can be understood as a rack or frame.
If a more specific or industry-specific term exists, it would depend on the exact context and industry terminology. However, in general engineering or material handling contexts, "Coil stacking storage rack" should convey the intended meaning.