An orthographic camera (luckily) does not ignore z. Simply said, it is basically a different projection, namely it has a box frustum instead of a pyramid. Check this article for a more in depth explanation: http://www.badlogicgames.com/wordpress/?p=1550
Note that by default the camera near value = 1f and the far value = 100f. In your case, you're exactly moving 100f units away from your model. In other words: the model is on the far plane. Depending on various factors you'll see the model partially, if at all.
Now, when you do this:
new OrthographicCamera(Gdx.graphics.getWidth(), Gdx.graphics.getHeight());
You're basically saying that one unit in your world should map to one pixel. Thus your model (a 50x50x50 box) will be about 50 pixels wide/height. If you want to map one world unit to e.g. two pixels, you could do:
new OrthographicCamera(Gdx.graphics.getWidth() /2f, Gdx.graphics.getHeight() / 2f);
And so forth. If you want better control on this, you could consider using a Viewport, see: https://github.com/libgdx/libgdx/wiki/Viewports
Also be careful to not place your camera inside your model and, as daniel said, dont lookAt
your position
, it will cause your direction
to be zero.