Abstract: Abstract: A type of load pressure sensitive quantitative pump hydraulic circuit was studied, and its working principle was explained. Under the conditions, the research included two situations, which are load pressure change and main control multi-way valve spool movement. By the basic physical equations of the hydraulic units, the mathematical relationship between system outlet pressure p1, load pressure p2, fixed differential relief valve compensation spool opening xc and main control spool displacement xe was obtained; and by the analysis of above mathematical relationship, it was observed that under the situation which main control spool equivalent throttling area Ae keeps still and load pressure p2 changes, fixed differential relief valve compensation spool displacement rate Δxc/xc is inversely proportional to a pump's system outlet pressure p1, however, it is proportional to load pressure change Δp2; and as the pump outlet pressure p1 increases, the fixed differential relief valve compensation spool displacement rate Δxc/xc becomes smaller. The experimental results showed that displacement rate Δxc/xc are 0.081, 0.142 and 0.183(output pressure is 6 MPa)；0.058, 0.110 and 0.139(output pressure is 9 MPa); 0.042, 0.079 and 0.112(output pressure is 12 MPa) respectively. For constant pump outlet pressure p1, the movement range of the fixed differential relief valve compensation spool becomes larger, and that the fixed differential relief valve compensation spool displacement rate slope Δxc/xc/Δp2 has the trend to become smaller as load pressure change Δp2 increases. The theoretical analysis and experimental results (when Δp2 are 1, 2, 3 MPa, Δxc/xc/Δp2 are 0.081, 0.072 and 0.064(output pressure is 6 MPa)；0.057, 0.051 and 0.046(output pressure is 9 MPa); 0.043, 0.038 and 0.034(output pressure is 12 MPa) respectively under p1 equals 6, 9, 12 MPa) are consistent. Others, as the fixed differential relief valve compensation spool throttling ports generally is designed as U or V partial throttling groove, thus when the main control spool moves, its moving characteristics analysis is established based on U throttling groove. By its throttling structural feature, a geometric simplified throttling area calculation mathematical expression of U throttling groove was deduced, and then based on the U throttling area calculation formula, the fixed differential relief valve compensation spool characteristic movement when main control spool moves was analyzed. Then the mathematical expression between the change of the fixed differential relief valve compensation spool throttling port opening Δxc and the throttling area change ΔAe of main control valve spool was obtained. It was then observed that the fixed differential relief valve compensation spool opening change Δxc is proportional to the main control valve spool equivalent throttling area change ΔAe; and it was also found that the value of the ratio between the fixed differential relief valve compensation spool throttling port opening change Δxc and the main control valve spool equivalent throttling area change ΔAe is closely relevant to the pump system outlet pressure p1 and load pressure p2; besides p1 and p2, the ratio between the fixed differential relief valve compensation spool throttling port opening change Δxc and main control valve spool equivalent throttling area change ΔAe is relevant to the ratio between main control valve spool throttling port's flow coefficient Cqe and overflow throttling port's flow coefficient Cqc of the fixed differential relief valve chamber, and also is relevant to the throttling area gradient wc of the fixed differential relief valve throttling port. As the fixed differential relief valve compensation throttling area gradient wc becomes larger, the compensation spool opening change Δxc largely approximates to the main control valve spool U throttling groove equivalent throttling area change ΔAe. By the simplified throttling area calculation formula of U throttling groove, the mathematical relationship between the fixed differential relief valve compensation spool opening change Δxc and the main control valve spool opening Δxe is obtained, and it is helpful to the design of a machinery load sensitive quantitative pump system.