Tire Inflation Systems
Power Tank High Performance Air System:
The air compressor on your HDT is designed to keep a system pressure of between 100 psi and 120 psi. And your truck air system is not a high volume system. The truck compressor will build to 120 psi and shut off and will not turn back on until the system pressure drops to 100 psi.
You will have problems getting your tires up to pressure with your onboard compressor as you can never seem to add those last few pounds of pressure to get your tires up to 110/120 psi.
You can try to bleed air out of the air tanks so the compressor cuts in and try to add a pound or two of pressure as the compressor tops out. That can take a lot of time topping off the truck and trailer tires.
You might consider a Power Tank High Performance Air System. The Power Tank is filled with CO2 gas and delivers at least 170 psi of pressure for tire filling and is silent.