magento2 – Magento 2 – Change order shipping method

In Magento 2, I try to change the shipping method for orders programmatically.

I did this

$order->setShippingMethod('my_new_method');
$order->save();

The shipping_method attribute is changing as expected, but I also need to recalculate order shipping prices according to the new method.

Do you know how to do it?