Spend time doing something

It is not an idiomatic expression, but it is a typical structure to express such an idea. Here are a few others in this pattern:

Have fun studying English.
Make friends exercising in the park.

The present participles aren't gerunds because they are not functioning as nouns. They are verbals.

AnonymousIs that an idiom or a typical phrase?

I would put it in the category of "typical phrase". There are a number of such phrases that are completed with an expression in -ing.

spend [ time] ---ing ...
have [trouble] ---ing ...
have fun --- ing ...
be busy --- ing ...

I'll have to spend two hours writing this report

Anonymous"Spend time doing something"

I would say that "doing something" is a participle clause which is a complement of the direct object "time" (i.e., direct object of the verb "spend").

AnonymousI would say that "doing something" is a participle clause which is a complement of the direct object "time" (i.e., direct object of the verb "spend").

You might argue that, but then you'll have to show how the structure is the same as found in sentences like the following.

The committee elected Mr. Preston chairman.
is structurally

CalifJimI'm not saying you're wrong, but you will need some strong evidence (in the form of a lot of examples) to support your theory.

What conviced me about it is the regularity in your examples:

I'll have to spend two hours writing this report.
Elizabeth has trouble pronouncing Chinese words.
The workmen ran into some diffic

AnonymousI think that the participle clause works, here, as a noun clause.

In that case it's not a participle clause but a gerund clause, of course.

Anonymousas in the pattern "I consider this offer a big improvement" (verb + object + noun).

But if you're only tallying up phrases as sequences of lexical categories, then you