Is it normal to spend the first months of a PhD only reading papers? If it is not normal, how can I set limits?

Yes,

As a policy read, rewiew and write.

The first few months should be spend on the comprehensive literature reviews. In my experience, the comprehensive literature reviews solve lots of problem during the later stages in Ph.D. Along with reading the papers, one can also learn the state of the art tools used by the researcher in the research papers.

Well! I am happy to address this question. Reading makes one perfect as everyone knows and it is clear cut in the case of research. You can collect materials and readings from all the available sources. it is a prior condition of any kind of research, of course. Why do I suggest, because it will give you

- The trend of various concerns in the area

- Innovations in methoology

- Different forms of tools and measures and trends or experiments in it, and

- Advanced and robust use of software and statistical measures

Thus, the problem will be tailored, reshaped,a nd the gap will be properly identified. It is a rigorous exercise till you finish the advanced reading of the e-version of the journal issues which would be coming up only in 2019 even.