In vehicle-mounted hydraulic-system engineering, the first point at which mechanical energy is converted into hydraulic energy is the assembly where the power take-off (PTO) and hydraulic pump are connected. Full compatibility between these two components in terms of rotational speed, torque and power characteristics is an important criterion for overall system efficiency and mechanical service life. Incorrect calculation of the relationship between PTO speed and pump displacement can cause overheating, inadequate lifting speed or premature pump damage because design limits are exceeded.

Basic Logic of Flow Calculation

The amount of oil delivered by the hydraulic pump per minute—its flow rate—is a linear function of the pump’s displacement and the speed at which it is driven. The basic engineering formula is:

Q = V × ηᵥ × n × 10⁻³

Where:

• Q: System flow rate (L/min)
• V: Pump displacement (cm³/rev)
• ηᵥ: Volumetric efficiency (approximately 0.98 for gear pumps)
• n: Pump operating speed (rpm)

This mathematical relationship makes it possible to predict the pump’s flow accurately from engine speed and the PTO gear ratio. For example, a Group 30 gear pump with a displacement of 65 cm³/rev, driven at 1,500 rpm through the PTO and assuming ηᵥ ≈ 0.98, supplies approximately 95.5 L/min. This flow value is a principal input for determining the capacity of the directional control valve and the lifting speed of the telescopic cylinder.

Speed Limits: Importance of Maximum and Minimum Parameters

Every pump model has operating-speed limits defined by its internal kinematic design. These values are clearly stated in HMLIFT pump catalogues:

• Maximum Speed Limit: Depending on the pump group—Groups 25, 30, 35 and 40 or the PEX7 axial-piston series—maximum continuous speeds vary between 1,400 and 2,200 rpm. If engine speed rises and the PTO ratio causes the pump’s maximum speed to be exceeded, hydraulic oil may overheat, internal friction may increase and mechanical damage may occur. During normal operation, the pump must not be operated above the maximum speed specified in the catalogue.
• Minimum Speed Limit: This parameter is at least as critical as the maximum limit, but is sometimes overlooked. To ensure correct lubrication of internal components and formation of a stable hydraulic film, the minimum intermittent-speed limit of 300 rpm for all groups must not be undershot. Particular attention is required when the PTO is operating at engine idle.

Matching Torque and Power Demand to the Vehicle Engine

The pump not only generates flow; according to system pressure, it also demands a specific amount of torque and power from the vehicle engine.

• Torque Requirement (M): As system pressure (Δp) and pump displacement (V) increase, the torque drawn from the PTO shaft in Nm also rises. Calculation: M = Δp × V / (62.83 × ηₘ), where ηₘ is mechanical efficiency (≈ 0.90).
• Power Requirement (P): Total power required by the system in kW is a function of flow and pressure: P = Δp × V × n / (600 × 1000 × ηₜ), where ηₜ is total efficiency (≈ 0.88). The vehicle engine and selected PTO unit must be mechanically capable of meeting these torque and power demands to preserve the driveline.

Common Scenarios and System-Design Sequence

Typical field situations and their implications include:

• 1. Insufficient Flow / Slow Movement: If PTO speed or pump displacement is selected too low, the cylinder moves slowly. Trying to compensate by raising engine speed excessively brings the pump close to its speed limit and increases thermal load.
• 2. Valve Bottleneck: If pump flow exceeds the maximum passage capacity of the selected directional control valve (Tipping Valve), high flow resistance develops inside the valve. This resistance is converted directly into heat and reduces system performance.

Correct Design Sequence

First determine the mechanical characteristics of the vehicle chassis and PTO—ratio, torque and direction of rotation. Then calculate the required system flow and pressure and select the HMLIFT pump model that meets these parameters within its optimum speed range.