Yes you should write JavaDoc for private methods, and even when it is only for yourself. In 3 years when you have to change the code, you will be happy that you documented it.
If you leave the company, or have to work on another project, your co-workers will be happy to have a documented code. Undocumented code has much lower value.
And look how the real professionals do it. Here is an excerpt from the source code of ArrayList class by Sun Microsystems:
/**
* The array buffer into which the elements of the ArrayList are stored.
* The capacity of the ArrayList is the length of this array buffer.
*/
private transient Object[] elementData;