For Spannsystm, I agree with clamping system. For Teiledurchlauf, other possibilities I know are in use by a very large manufcturer of OEM parts for the auto industry are: parts throughput, parts flow, even material flow. HTH, Beth

The logic of the three cited sentences suggests that this Spannsystem may be more than just a chuck or a couple of jaws. (As so often, more context would help.) Depending on context, you may want to consider using the most general and technical English term for such a system, _workholding system_ (sometimes: _work holding system__. Another term used, and not just for preventing access or entry, is _locking system_. --
Workholding Tool Manufacturers --
http://www.rmtcorp.com/workhold/index.htm -- --
A comprehensive line of workholding systems--
http://hardingeworkholding.com/w3workholding.html -- --
DIMAC designs and manufactures a wide range of work holding products. --
http://www.dimac.com.au/catalogue.htm -- --
Company Profile -- Production Dynamics designs and manufactures collet workholding systems for CNC machine tool applications. ---
Mission Statement -- Our goal as a workholding system supplier is to work with our customers to determine their needs and respond with cost effective timely solutions.
http://www.prodyn.com/profile.htm