H4000 positioner is obsolete but it is calibrated much as any force-balance positioner. Zero-adjustment is a thumbwheel at the bottom of the spring. Span adjustment is at the top of the spring and changes the stiffness by changing the number of active coils,but that does interact with the zero setting. Once the span adjustment is set it does not drift, and the only adjustment you should ever have to touch again should be the zero if you disturb the cam or move the positioner to a different valve. Current replacement for the H4000 is the APEX type 5100 positioner, which has noninteractive zero and span.
To set the zero, apply 4 ma to the contacts and watch the output gage. Apply very small movements to the zero screw until the valve begins to move. Back off on the screw until the valve closes and the Output Pressure needle just falls to zero. Best to make very small movements and wait to see what happens for 15-20 seconds. Once the unit is zeroed, apply 18 ma, then 19, then 20, and the valve should stroke to full travel at 20 ma. Since the span and zero are interactive, if you find it necessary to set the span, you will need to reset the zero. You can chase yourself for hours unless you set the span first and then dial in the zero.
To set the span, first loosen the lock screw at the top of the spring so the spring can be rotated. At zero signal, adjust the span spring a tiny amount. apply signal gently and record the signal at which the valve starts to move. Do not touch the zero adjustment. Keep increasing signal and record the signal at which the valve becomes fully open. When you have the span correctly set the difference should be 16 ma. If you don't have a 16ma span, Tweak the adjustment and repeat the span measurement until you get 16ma. THEN set the signal at 4 ma and adjust the zero adjustment until the output gage goes to zero. Make small adjustments. You can overshoot and miss the correct zero setting easily especially with such a large actuator. It takes a while to respond to tiny incremental changes.
Automax refer to the R312 as a "Heavy-Duty" actuator. If you go to the flowserve.com site,and select literature, automation, automax, and instructions, it will lead you here:
Download the instruction bulletin for the actuator.
312SR80 does have 2 air chambers as you mention but since it is spring-opposed the inner one is not used. The pneumatic connection to the inner chamber ( the one nearest the scotch-yoke housing) should be vented with a screened vent. If you leave the hole open you may get dirt-daubers. If the vent hole is plugged the valve will not open fully.
Not picking on you but this is widely mis-specified. The positioner does NOT have a 3-15 psi output. The output of any positioner you'd care to measure is from zero to full supply pressure. The 80 in the model code 312SR80 means that the actuator is supplied with a spring-pack optimized for 80 psi supply. Feed it 3-15 and it will never even lift off the stop.