im busy working分析下working

I'm busy working=I'm busy in working. 也就是说,working是动名词,充当宾语.
类似：
I spent two days (in) finishing the work.
I had no trouble (in) finding his house.
本句结构就是这样：忙于做某事的意思
这个busy与后面的词是没有修饰关系的.
I am busy我很忙
I am busy working.我忙于工作.
He is busy writing something.他在忙于写东西.
He is busy with some important things,

其实busy doing 算是固定用法吧，完整的用法应该是be busy in doing .
简单一点讲，busy working 是表语，再细一点的话，working 是表语（busy)的补足语。

请参考！

这里 working 是现在分词，做状语，修饰 be busy
再比如：
② 现在分词（短语）在（be）busy doing中作状语。如：
The workers were busy unloading carts.
工人们忙着卸车。
He was busy packing.
他正忙着收拾行装。