The working pressure and displacement of hydraulic motors are two core parameters with completely different calculation logic:

Work pressure "is a dynamic parameter determined by actual working conditions (determined by load torque and motor efficiency), essentially" the pressure required to overcome the load ";

Displacement "is a fixed parameter determined by the motor structure (independent of operating conditions), essentially" the theoretical volume of hydraulic oil sucked in/discharged by the motor per revolution ".

The following is the specific calculation method, including formula derivation, unit explanation, and example verification, taking into account both theory and practice:

1、 Calculation of working pressure of hydraulic motor

The working pressure of a hydraulic motor (usually referred to as the inlet and outlet pressure difference Δ p, which is the difference between the high-pressure chamber pressure p ₁ and the low-pressure chamber pressure p ₂. The low-pressure chamber pressure p ₂ is generally very small and can be approximately ignored as 0, simplified as Δ p ≈ p ₁), and the core logic is that the torque generated by pressure needs to balance the load torque.

1. Core Formula (Universal Version)

First, clarify the key relationship: the theoretical output torque T ₜ of the hydraulic motor is proportional to the working pressure difference Δ p and the theoretical displacement V ₜ, and then combined with the mechanical efficiency ηₘ (the ratio of actual torque to theoretical torque), derive the working pressure: \ (\ Delta p=\ frac {2 \ pi Tl} {\ eta_m V_t} \) or simplify (ignoring the return oil pressure p ₂): \ (p1 \ approximate \ frac {2 \ pi Tl} {\ eta_m V_t} \)

2. Explanation of Formula Parameters (Units must be Unified)

How to obtain the meaning of parameter symbol units

The calculation result of the pressure difference between the motor inlet and return ports (core calculated value) with a working pressure difference of Δ p MPa (megapascal), or measured through a pressure gauge

The total load torque (including working load, friction load, etc.) that the motor needs to drive is calculated based on the equipment operating conditions (such as lifting heavy objects and driving rotating components)

Mechanical efficiency ηₘ - (dimensionless) The ratio of actual output torque to theoretical torque (considering friction loss) can be found in the motor product manual (commonly 0.75~0.95, higher for high-pressure/precision motors)

Theoretical displacement V ₜ mL/r (milliliters/revolution) The theoretical volume of hydraulic oil sucked in by the motor per revolution (structural parameters) can be found in the motor product manual (e.g. 100 mL/r means sucking in 100 milliliters of oil per revolution)

3. Key premise: Calculation of load torque Tl (to avoid user jamming)

The core of work pressure is "load torque", which needs to be calculated first before being substituted into the formula. Common load torque calculation scenarios include:

Scenario 1: Driving rotating components (such as gears, rollers)

\(T_L = F \times r\)

(F=circumferential force borne by the component, N; r=radius of action of the force, m）

Scenario 2: Lifting heavy objects (such as crane hoists)

\(T_L = m \times g \times R \times \frac{1}{i}\)

(m=mass of heavy object, kg; g=acceleration due to gravity 9.8 m/s ²; R=radius of the winch drum, m; i=transmission ratio, if there is no transmission, i=1)

4. Example calculation (close to practical application)

Given that the theoretical displacement of the rotary motor of a certain excavator is V ₜ=250 mL/r, the mechanical efficiency is η ₘ=0.9, and the required load torque to be driven is TL=1500 N · m. Ignoring the return oil pressure, calculate the working pressure p ₁? Solution: ① Unified unit: V ₜ=250 mL/r=250 × 10 ⁻⁶ m ³/r (no manual conversion is required, mL/r is directly used in the formula, and the result is automatically MPa, as 1 MPa=1 N/mm ²=10 ⁶ N/m ², the unit will be self consistent); ② Substituting into the formula: \ (p1=\ frac {2 \ times3.14 \ times1500} {0.9 \ times250} \ approximate 41.89 \, \ text {MPa} \) Conclusion: The actual working pressure of the motor is about 42 MPa (it is necessary to ensure that the rated pressure of the motor is ≥ 42 MPa to avoid overload).

2、 Calculation of displacement of hydraulic motor

The displacement of hydraulic motors is divided into "theoretical displacement V ₜ" and "actual displacement V ₐ":

Theoretical displacement V ₜ ": determined by the structure, fixed value (core parameters during selection, directly marked in the product manual), no on-site calculation required, only understanding the derivation logic;

Actual displacement V ₐ: the actual volume of oil suction and discharge after considering internal leakage (can be calculated on site through flow rate and speed).

（1） Theoretical displacement V ₜ (structural parameters, core focus)

Theoretical displacement refers to the total volume change of the sealed working chamber for each revolution of the motor. The calculation formula for different types of motors varies (due to structural differences), with a focus on three common types:

Explanation of theoretical displacement calculation formula for core structural parameters of motor type

Gear type hydraulic motor (closest to gear pump) module m (mm), number of teeth z, tooth width B (mm) \ (V_t=2 \ pi m ^ 2 z B \ times 10 ^ {-3} \) (result unit: mL/r) The total volume of the tooth slot between two gears, m=gear module (standard value, such as 2, 3 mm), z=number of teeth per gear, B=gear width

Blade type hydraulic motor stator inner diameter D (mm), rotor radius r (mm), number of blades z, blade width B (mm) \ (V_t=\ pi (D ^ 2-r ^ 2) B \ times 10 ^ {-3} \) (result unit: mL/r) The total volume change of the sealed cavity formed by the stator and rotor, D-r=eccentricity related (stator inner curve is elliptical/cycloid)

The total stroke volume of all plungers in a piston hydraulic motor (axial) is determined by tan θ, which includes the number of plungers z, plunger diameter d (mm), plunger distribution circle diameter D (mm), and inclined plate angle θ (°) \ (V_t=\ frac {\ pi d ^ 2 z D \ tan \ theta} {4} \ times 10 ^ {-3} \) (result unit: mL/r). tan θ determines the plunger stroke (the larger θ, the larger the displacement)

Example of gear motor (echoing the previous gear pump, easy to understand)

Given that the gear module m of a certain gear type hydraulic motor is 3 mm, the number of teeth z is 12, and the tooth width B is 20 mm, calculate the theoretical displacement V ₜ? Solution: \ (V_t=2 \ times3.14 \ times3 ^ 2 \ times12 \ times20 \ times10 ^ {-3}=2 \ times3.14 \ times9 \ times12 \ times20 \ times10 ^ {-3} \ estimate 13.57 \, \ text {mL/r} \) Conclusion: The gear motor theoretically inhales 13.57 milliliters of hydraulic oil per revolution (the product manual will indicate ≈ 14 mL/r, rounded up).

（2） Actual displacement V ₐ (can be calculated on site, considering leakage)

The theoretical displacement is the "ideal value without leakage". In practical work, due to internal leakage (high-pressure oil leaking back into the low-pressure chamber), the actual suction and discharge volume of oil will be larger than the theoretical value. The calculation formula is: \ (V_a=\ frac {Q'a} {n} \)

How to obtain the meaning of parameter symbol units

Actual displacement V ₐ mL/r Calculation result of the actual volume of hydraulic oil sucked in by the motor per revolution

Actual input flow rate Q ₐ L/min (liters/minute) actual flow rate from pump to motor (including leakage compensation) measured by flow meter

Actual motor speed n r/min (revolutions per minute) Actual speed of motor output shaft measured by tachometer

Example calculation

Known: The actual flow rate Q ₐ=30 L/min of the input motor is measured by a flow meter, and the motor speed n=1500 r/min is measured by a tachometer. Calculate the actual displacement V ₐ? Solution: ① Unit conversion: Q ₐ=30 L/min=30 × 1000 mL/min=30000 mL/min; ② Substituting the formula: \ (V_a=\ frac {30000} {1500}=20 \, \ text {mL/r} \) If the theoretical displacement of the motor V ₜ=18 mL/r, it indicates the presence of internal leakage (actual displacement>theoretical displacement), and the internal leakage amount=Q ₐ - V ₜ × n=30000-18 × 1500=3000 mL/min=3 L/min.

3、 Key Explanation (Avoiding Calculation Misconceptions)

Work pressure ≠ rated pressure:

The working pressure is the actual working condition value (varying with load), and the rated pressure is the maximum pressure that the motor can withstand for a long time (indicated in the product manual, such as 25 MPa, 31.5 MPa). The calculated working pressure must be ≤ the rated pressure, otherwise the motor will be damaged.

The displacement is a 'structurally fixed value':

The theoretical displacement V ₜ is determined by the motor design and cannot be changed once production is completed (such as a 100 mL/r motor with a fixed theoretical oil absorption per revolution). The actual displacement V ₐ only changes due to leakage, and V ₐ ≥ V ₜ.

Unit unity is key:

If V ₜ in the formula is expressed in mL/r, Tl in N · m, and η ₘ in 0.7~0.95, the calculated Δ p will automatically be MPa (without additional conversion); If the units are chaotic (such as using m ³/r for V ₜ), they need to be unified first (1 m ³=10 ⁶ mL).

The impact of efficiency:

The mechanical efficiency ηₘ only affects the calculation of working pressure (the actual pressure needs to overcome friction and is greater than the ideal pressure); Volumetric efficiency ηᵥ=V ₜ/V ₐ (measures the degree of leakage), if leakage is ignored (ηᵥ=1), then V ₐ=V ₜ.

summary

The calculation core of "work pressure" is determined by the load torque, using the formula Δ p=2 π Tl/(ηₘ V ₜ), first calculate the load torque, and then substitute it into the motor parameters (V ₜ, η ₘ);

Theoretical displacement calculation core: determined by structural parameters, different types of motors have different formulas (corresponding to gear type, blade type, and plunger type), and there is no need to calculate on site, just refer to the manual;

The calculation core of "actual displacement" is determined by the measured flow rate and speed, and can be used to determine whether the motor leakage exceeds the standard using the formula V ₐ=Q ₐ/n.

The calculation of these two parameters is the basis for selecting hydraulic systems and matching working conditions (such as calculating working pressure based on load and selecting motors that match rated pressure; calculating displacement based on speed and flow rate to ensure sufficient power).