1. Axial Force Generation and Balancing Principles

The axial forces inmultistage  vertical turbine pumps  are primarily composed of two components:

● Centrifugal force component:Liquid radial flow due to centrifugal force creates a pressure differential between the front and back covers of the impeller, resulting in an axial force (typically directed toward the suction inlet).

● Pressure differential effect:The cumulative pressure difference across each stage further increases the axial force.

Balancing Methods:

● Symmetrical impeller arrangement:Using double-suction impellers (liquid enters from both sides) reduces unidirectional pressure differential, lowering axial force to acceptable levels (10%-30%).

● Balance hole design:Radial or oblique holes in the impeller back cover redirect high-pressure liquid back to the inlet, balancing pressure differences. Hole size must be optimized via fluid dynamics calculations to avoid efficiency loss.

● Reverse blade design:Adding reverse blades (opposite to main blades) in the last stage generates counter-centrifugal force to offset axial loads. Commonly used in high-head pumps (e.g., multistage verticalturbinepumps).

2. Radial Load Generation and Balancing

Radial loads originate from inertia forces during rotation, uneven liquid dynamic pressure distribution, and residual imbalance in rotor mass. Accumulated radial loads in multi-stage pumps can cause bearing overheating, vibration, or rotor misalignment.

Balancing Strategies:

● Impeller symmetry optimization:

o Odd-even blade matching (e.g., 5 blades + 7 blades) distributes radial forces evenly.

o Dynamic balancing ensures each impeller's centroid aligns with the rotational axis, minimizing residual imbalance.

● Structural reinforcement:

o Rigid intermediate bearing housings restrict radial displacement.

o Combined bearings (e.g., double-row thrust ball bearings + cylindrical roller bearings) handle axial and radial loads separately.

● Hydraulic compensation:

o Guide vanes or return chambers in impeller clearances optimize flow paths, reducing local vortices and radial force fluctuations.

3. Load Transmission in Multi-Stage Impellers

Axial forces accumulate stage-wise and must be managed to prevent stress concentrations:

● Stage-wise balancing:Installing a balance disk (e.g., in multi-stage centrifugal pumps) uses axial gap pressure differences to automatically adjust axial forces.

● Stiffness optimization:Pump shafts are made of high-strength alloys (e.g., 42CrMo) and validated via finite element analysis (FEA) for deflection limits (typically ≤ 0.1 mm/m).

4. Engineering Case Study and Calculation Verification

Example:A chemical multistagevertical turbine pump (6 stages, total head 300 m, flow rate 200 m³/h):

● Axial force calculation:

o Initial design (single-suction impeller): F=K⋅ρ⋅g⋅Q2⋅H (K=1.2−1.5), resulting in 1.8×106N.

o After converting to double-suction impeller and adding balance holes: Axial force reduced to 5×105N, meeting API 610 standards (≤1.5× rated power torque).

● Radial load simulation:

o ANSYS Fluent CFD revealed local pressure peaks (up to 12 kN/m²) in unoptimized impellers. Introducing guide vanes reduced peaks by 40% and bearing temperature rise by 15°C.

5. Key Design Criteria and Considerations

● Axial force limits: Typically ≤ 30% of pump shaft tensile strength, with thrust bearing temperature ≤ 70°C.

● Impeller clearance control: Maintained between 0.2-0.5 mm (too small causes friction; too large leads to leakage).

● Dynamic testing: Full-speed balancing tests (G2.5 grade) ensure system stability prior to commissioning.

Conclusion

Balancing axial and radial loads inmultistage vertical turbine pumps is a complex systems engineering challenge involving fluid dynamics, mechanical design, and material science. Optimizing impeller geometry, integrating balancing devices, and precise manufacturing processes significantly enhance pump reliability and lifespan. Future advancements in AI-driven numerical simulations and additive manufacturing will further enable personalized impeller design and dynamic load optimization.

Note: Customized design for specific applications (e.g., fluid properties, speed, temperature) must comply with international standards such as API and ISO.