The flow rate of the hydraulic pump determines the volume of liquid that can be transported in a unit of time. In the process of selecting hydraulic pumps, controlling system energy consumption, and diagnosing equipment faults, the flow data of hydraulic pumps is indispensable.
Through this article, you will learn how to calculate the flow rate of a hydraulic pump and the influencing factors, which will help you select a more suitable hydraulic pump and other components of the system.
Why is it Necessary to Calculate the Flow Rate of the Hydraulic Pump?
Determines the Operating Speed of the Actuator
The speed of the action of hydraulic actuators such as hydraulic cylinders or hydraulic motors depends on the amount of oil delivered by the hydraulic pump per minute. If the flow rate of the hydraulic pump is insufficient, it will cause the actuator to respond slowly, resulting in overpressure operation of the system.
If the flow rate of the hydraulic pump is too high, excess hydraulic oil must flow back to the oil tank through the relief valve or flow control valve under high pressure. This will cause an increase in oil temperature and energy waste.
Helps in Selecting Suitable Pumps and Components
The hydraulic pump does not operate independently. The oil it pumps out needs to pass through valve groups, pipelines, actuators and other components. The sizes of these components are determined by the flow rate passing through them.
By calculating the required flow rate in advance, you can make sure that the selected pump has sufficient oil delivery capacity. At the same time, it also avoids increasing energy consumption or wasting costs due to excessive selection.
Reduce Energy Consumption
An excessive flow rate will convert hydraulic energy into thermal energy, thereby increasing the load on the cooling system. If the flow rate is insufficient, you need to increase the rotational speed or replace a larger pump, which will also increase energy consumption.
Failure Prediction
You can analyze the problems of the system by continuously monitoring and calculating the flow rate of the hydraulic pump. By comparing the deviation between the theoretical flow rate and the actual monitored flow rate, you can quickly determine the degree of pump leakage, the condition of component wear, etc. Then you can carry out targeted maintenance.
Maintain the Stable Operation of the System
When operating under high load or high-pressure conditions, if the flow rate of the pump is not within a reasonable range, it may cause safety hazards such as overload or vibration. By pre-calculating and matching the flow, the internal pressure of the system can be balanced and its operation can be stable.
Parameters Related to the Calculation of Hydraulic Pump Flow Rate
Displacement
Displacement refers to the theoretical volume of oil discharged from the sealed working chamber for each rotation of the pump shaft. It is usually a fixed value. This value is determined by the dimensions of the internal components of the pump, such as the width and module of the gears, and the diameter and stroke of the piston.
Rotational Speed
This refers to the rotational speed of the hydraulic pump shaft. It is determined by the output speed of the motor or engine that drives the pump. The higher the rotation speed, the more oil the hydraulic pump outputs at the same displacement.
In actual working conditions, the speed is not always constant. Voltage fluctuations and load variations can cause speed deviations, thereby affecting the accuracy of flow calculation.
Volumetric Efficiency
Volumetric efficiency is the correction factor for converting theoretical flow into actual flow. It reflects the extent of the flow loss caused by internal leakage within the pump.
There is a small gap between the high-pressure chamber and the low-pressure chamber inside the pump, and hydraulic oil will experience a small amount of internal leakage under pressure.
Affected by factors such as system pressure, oil temperature, and pump body wear, the higher the pressure, the more severe the internal leakage, and the lower the volumetric efficiency.
So when calculating the actual flow rate, you need to multiply the theoretical flow rate by the volumetric efficiency. Only in this way can you know the actual output capacity of the hydraulic pump.
How to Calculate the Flow Rate of a Hydraulic Pump?
The flow rate $Q$ of the hydraulic pump is mainly determined by the pump’s displacement and rotational speed.
Theoretical Flow Rate Calculation of a Hydraulic Pump
Metric System
$Q=\frac{V\times n}{1000}$
$Q$: The flow rate of the hydraulic pump, expressed in units of $L/min$.
$V$: The displacement of the hydraulic pump, expressed in units of $cm^{3}/rev$.
$n$: The rotational speed of the hydraulic pump expressed in units of $rpm$.
$1000$: Used for unit conversion. $1 L=1000 mL=1000 cm^{3}$
Example:
Assume that the displacement of your hydraulic pump $V=50cm^{3}/rev$ and the rotational speed $n=1800 rpm$.
Then the displacement $Q=\frac{V\times n}{1000}=\frac{50\times 1800}{1000}=90L/min$.
American System
If the displacement of your hydraulic pump is measured in $in^{3}/rev$, then
$Q=\frac{D\times n}{231}$
$Q$: The flow rate of the hydraulic pump, expressed in units of $GPM$.
$D$: The displacement of the hydraulic pump, expressed in units of $in^{3}/rev$.
$n$: The rotational speed of the hydraulic pump, expressed in units of $rpm$.
$231$: Used for unit conversion. $1 \,US\;GPM=231in^{3}/min$
Example:
Assume that the displacement of your hydraulic pump $D=3 in^{3}/rev$ and the rotational speed $n=1500rpm$.
Then the displacement $Q=\frac{D\times n}{231}=\frac{3\times 1500}{231}=19.48GPM$.
Actual Flow Rate Calculation of the Hydraulic Pump
In actual operation, there are losses such as leakage and friction inside the pump, so the actual output flow rate is smaller than the theoretical value. The actual flow rate reflects the true oil transportation capacity of the pump. The formula for actual flow rate is as follows:
$Q_{act}=Q_{theo}\times\eta _{v}$
$\eta _{v}$: Volumetric Efficiency
Example:
Assume that the volumetric efficiency $\eta _{v}$ of your hydraulic pump is $ 85\% $.
The metric system:
$Q_{act}=Q_{theo}\times\eta _{v}=90\times 85\%=76.5L/min $
The American system:
$Q_{act}=Q_{theo}\times\eta _{v}=19.48\times 85\%=16.56GPM $
Flow Rate Calculation of the Variable Displacement Pump
The above calculation method is applicable to fixed displacement hydraulic pumps, such as external gear pumps. The displacement of this type of pump remains constant for each complete rotation.
However, there are also hydraulic pumps with adjustable displacement, commonly known as variable displacement pumps, such as axial piston pumps or single-acting vane pumps. They can adjust the displacement by regulating the inclination angle of the swashplate or the eccentric distance between the stator and the rotor.
So, when calculating the flow rate of a variable displacement pump, you need to use the current displacement value and calculate according to the above formulas. This can reflect the actual output of the variable displacement pump under different settings.
Factors Affecting the Flow Rate Calculation of Hydraulic Pumps
Working Pressure of the System
The working pressure of the system will affect the internal leakage of the hydraulic pump. The higher the pressure, the stronger the oil permeability at the sealing gap inside the hydraulic pump, the greater the leakage of high-pressure oil into the low-pressure chamber.
If you fail to obtain the volumetric efficiency corresponding to the operating pressure before making the calculation, it will cause the actual flow calculation result to deviate from the true output. The greater the amplitude of pressure fluctuations, the more obvious the calculation deviation will be.
Hydraulic Oil Viscosity and Temperature
The fluidity of hydraulic oil changes with temperature. Excessive oil temperature can reduce the viscosity of hydraulic oil, making it easier for it to leak through the gaps between internal parts of the pump. Then the volumetric efficiency decreases.
If you calculate the volumetric efficiency value corresponding to the conventional temperature, the calculated result will be smaller than the actual flow rate.
If the oil temperature is too low, it will increase the viscosity of the hydraulic oil and increase the suction resistance of the pump. At this point, there may be insufficient oil absorption, resulting in the actual flow rate being lower than the calculated value.
Rotational Speed of the Prime Mover
Due to voltage fluctuations and load changes, the actual speed of prime movers such as motors and engines may slightly decrease. Without speed monitoring, if you use the rated speed for calculation, it may result in an error in the final calculation of the output flow.
Internal Clearance of the Hydraulic Pump
As the operating time of the pump increases, the gears, pistons, valve plates and other components will wear out, increasing the internal sealing gap. At this point, the internal leakage of the hydraulic pump will increase and the volumetric efficiency will decrease.
If you still use the initial volumetric efficiency of the pump in the calculation without adjusting for wear duration and operating load, it will result in a big deviation between the actual flow calculation results and the actual output of the pump. And the more severe the wear is, the greater the deviation will be.
Oil Absorption Conditions
The premise for calculating the theoretical flow rate of a hydraulic pump is that the suction chamber can be filled with hydraulic oil every time the pump shaft rotates. If the oil suction pipeline is too thin, the filter element is blocked, or the fuel tank vent is not unobstructed, cavitation may occur.
In this case, the hydraulic pump flow rate calculated based on the formula cannot reflect the true oil discharge capacity of the pump.
FAQs
Can the Displacement of the Pump be Inferred Based on the Known Flow Rate?
Yes. You can work out the pump’s displacement by using the formula $ V(cm^{3}/min)=\frac{Q\times1000}{n}$ or $D(in^{3}/rev)=\frac{Q\times231}{n}$. If you need to consider leakage losses, you can calculate them by using the actual flow rate and correcting it with the volumetric efficiency.
If the Hydraulic Oil is Replaced, is it Necessary to Recalculate the Flow Rate of the Pump?
This depends on whether the viscosity of your new hydraulic oil is different from that of the previous one. If the viscosity of the new oil is close to that of the old oil, then you don’t need to recalculate.
If there is a significant difference in viscosity between the new oil and the old oil, we recommend that you recalculate the actual output flow rate of the hydraulic pump.
How can We Verify whether the Actual Flow Rate Calculated through Simple Methods is Accurate?
You can install a flow meter and a flow sensor on the outlet pipeline of the hydraulic pump. In this way, you can obtain the real-time flow rate data and compare it with the calculated values.
What is the Relationship between the Flow Rate and the Power of the Driving Motor?
The larger the flow rate, the more energy is required to pump out more liquid at the same pressure. The drive motor must provide a higher power to maintain this flow and pressure condition.
You can understand it through the calculation formula of hydraulic power in this ideal state: $P_{h}(kW)=\frac{Q(L/min)\times P(bar)}{600}$
The rated power of the actual driving motor also needs to consider the efficiency loss of the pump and transmission parts.
If the Flow Calculation Result of my Hydraulic Pump is between Two Standard Flows, how should I Choose?
We suggest that you choose a hydraulic pump with a slightly larger flow rate. In this way, during the operation of the pump, there will be no shortage of flow due to an increase in instantaneous demand.
At the same time, it can also leave a certain margin to compensate for actual losses such as efficiency decline or system leakage. It is beneficial for system stability and equipment lifespan to have a reasonable margin.
Final Thoughts
By calculating the flow rate of the hydraulic pump, you can assess the pump’s oil delivery capacity. And based on this, you can determine whether the system can meet the speed and power requirements of the actuating elements. After mastering how to calculate the flow rate of hydraulic pumps, you can better select pumps, match motors, and debug systems.
If you have any questions about calculating the flow rate of hydraulic pumps or other aspects, please feel free to contact us.
