May. 13, 2024
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Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that system.[2] The force applied on a surface in a direction perpendicular or normal to the surface is also called thrust. Force, and thus thrust, is measured using the International System of Units (SI) in newtons (symbol: N), and represents the amount needed to accelerate 1 kilogram of mass at the rate of 1 meter per second per second.[3] In mechanical engineering, force orthogonal to the main load (such as in parallel helical gears) is referred to as static thrust.
Examples
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A fixed-wing aircraft propulsion system generates forward thrust when air is pushed in the direction opposite to flight. This can be done by different means such as the spinning blades of a propeller, the propelling jet of a jet engine, or by ejecting hot gases from a rocket engine.[4] Reverse thrust can be generated to aid braking after landing by reversing the pitch of variable-pitch propeller blades, or using a thrust reverser on a jet engine. Rotary wing aircraft use rotors and thrust vectoring V/STOL aircraft use propellers or engine thrust to support the weight of the aircraft and to provide forward propulsion.
A motorboat propeller generates thrust when it rotates and forces water backwards.
A rocket is propelled forward by a thrust equal in magnitude, but opposite in direction, to the time-rate of momentum change of the exhaust gas accelerated from the combustion chamber through the rocket engine nozzle. This is the exhaust velocity with respect to the rocket, times the time-rate at which the mass is expelled, or in mathematical terms:
T = v d m d t {\displaystyle \mathbf {T} =\mathbf {v} {\frac {\mathrm {d} m}{\mathrm {d} t}}}
Where T is the thrust generated (force), d m d t {\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}} is the rate of change of mass with respect to time (mass flow rate of exhaust), and v is the velocity of the exhaust gases measured relative to the rocket.
For vertical launch of a rocket the initial thrust at liftoff must be more than the weight.
Each of the three Space Shuttle Main Engines could produce a thrust of 1.8 meganewton, and each of the Space Shuttle's two Solid Rocket Boosters 14.7 MN (3,300,000 lbf), together 29.4 MN.[5]
By contrast, the simplified Aid For EVA Rescue (SAFER) has 24 thrusters of 3.56 N (0.80 lbf) each.[6]
In the air-breathing category, the AMT-USA AT-180 jet engine developed for radio-controlled aircraft produce 90 N (20 lbf) of thrust.[7] The GE90-115B engine fitted on the Boeing 777-300ER, recognized by the Guinness Book of World Records as the "World's Most Powerful Commercial Jet Engine," has a thrust of 569 kN (127,900 lbf) until it was surpassed by the GE9X, fitted on the upcoming Boeing 777X, at 609 kN (134,300 lbf).
Concepts
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Thrust to power
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The power needed to generate thrust and the force of the thrust can be related in a non-linear way. In general, P 2 ∝ T 3 {\displaystyle \mathbf {P} ^{2}\propto \mathbf {T} ^{3}} . The proportionality constant varies, and can be solved for a uniform flow, where v ∞ {\displaystyle v_{\infty }} is the incoming air velocity, v d {\displaystyle v_{d}} is the velocity at the actuator disc, and v f {\displaystyle v_{f}} is the final exit velocity:
d m d t = ρ A v {\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}=\rho A{v}}
T = d m d t ( v f − v ∞ ) , d m d t = ρ A v d {\displaystyle \mathbf {T} ={\frac {\mathrm {d} m}{\mathrm {d} t}}\left(v_{f}-v_{\infty }\right),{\frac {\mathrm {d} m}{\mathrm {d} t}}=\rho Av_{d}}
P = 1 2 d m d t ( v f 2 − v ∞ 2 ) , P = T v d {\displaystyle \mathbf {P} ={\frac {1}{2}}{\frac {\mathrm {d} m}{\mathrm {d} t}}(v_{f}^{2}-v_{\infty }^{2}),\mathbf {P} =\mathbf {T} v_{d}}
Solving for the velocity at the disc, v d {\displaystyle v_{d}} , we then have:
v d = 1 2 ( v f − v ∞ ) {\displaystyle v_{d}={\frac {1}{2}}(v_{f}-v_{\infty })}
When incoming air is accelerated from a standstill – for example when hovering – then v ∞ = 0 {\displaystyle v_{\infty }=0} , and we can find:
T = 1 2 ρ A v f 2 , P = 1 4 ρ A v f 3 {\displaystyle \mathbf {T} ={\frac {1}{2}}\rho A{v_{f}}^{2},\mathbf {P} ={\frac {1}{4}}\rho A{v_{f}}^{3}}
From here we can see the P 2 ∝ T 3 {\displaystyle \mathbf {P} ^{2}\propto \mathbf {T} ^{3}} relationship, finding:
P 2 = T 3 2 ρ A {\displaystyle \mathbf {P} ^{2}={\frac {\mathbf {T} ^{3}}{2\rho A}}}
The inverse of the proportionality constant, the "efficiency" of an otherwise-perfect thruster, is proportional to the area of the cross section of the propelled volume of fluid ( A {\displaystyle A} ) and the density of the fluid ( ρ {\displaystyle \rho } ). This helps to explain why moving through water is easier and why aircraft have much larger propellers than watercraft.
Thrust to propulsive power
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A very common question is how to compare the thrust rating of a jet engine with the power rating of a piston engine. Such comparison is difficult, as these quantities are not equivalent. A piston engine does not move the aircraft by itself (the propeller does that), so piston engines are usually rated by how much power they deliver to the propeller. Except for changes in temperature and air pressure, this quantity depends basically on the throttle setting.
A jet engine has no propeller, so the propulsive power of a jet engine is determined from its thrust as follows. Power is the force (F) it takes to move something over some distance (d) divided by the time (t) it takes to move that distance:[8]
P = F d t {\displaystyle \mathbf {P} =\mathbf {F} {\frac {d}{t}}}
In case of a rocket or a jet aircraft, the force is exactly the thrust (T) produced by the engine. If the rocket or aircraft is moving at about a constant speed, then distance divided by time is just speed, so power is thrust times speed:[9]
P = T v {\displaystyle \mathbf {P} =\mathbf {T} {v}}
This formula looks very surprising, but it is correct: the propulsive power (or power available [10]) of a jet engine increases with its speed. If the speed is zero, then the propulsive power is zero. If a jet aircraft is at full throttle but attached to a static test stand, then the jet engine produces no propulsive power, however thrust is still produced. The combination piston engine–propeller also has a propulsive power with exactly the same formula, and it will also be zero at zero speed – but that is for the engine–propeller set. The engine alone will continue to produce its rated power at a constant rate, whether the aircraft is moving or not.
Now, imagine the strong chain is broken, and the jet and the piston aircraft start to move. At low speeds:
The piston engine will have constant 100% power, and the propeller's thrust will vary with speed
The jet engine will have constant 100% thrust, and the engine's power will vary with speed
Excess thrust
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If a powered aircraft is generating thrust T and experiencing drag D, the difference between the two, T − D, is termed the excess thrust. The instantaneous performance of the aircraft is mostly dependent on the excess thrust.
Excess thrust is a vector and is determined as the vector difference between the thrust vector and the drag vector.
Thrust axis
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The thrust axis for an airplane is the line of action of the total thrust at any instant. It depends on the location, number, and characteristics of the jet engines or propellers. It usually differs from the drag axis. If so, the distance between the thrust axis and the drag axis will cause a moment that must be resisted by a change in the aerodynamic force on the horizontal stabiliser.[11] Notably, the Boeing 737 MAX, with larger, lower-slung engines than previous 737 models, had a greater distance between the thrust axis and the drag axis, causing the nose to rise up in some flight regimes, necessitating a pitch-control system, MCAS. Early versions of MCAS malfunctioned in flight with catastrophic consequences, leading to the deaths of over 300 people in 2018 and 2019.[12][13]
See also
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For more information, please visit drone can carry weight.
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References
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Measuring an axial thrust load with a load cell requires a clear understanding of both axial thrust and load cell designs. This depth of understanding clearly influences the choice of measuring technique and the load cell type to use. Therefore this article aims to provide a foundation for this knowledge. It explains axial thrust in rotating equipment, using the specific example of a centrifugal pump.
By examining the meaning of each word “axial” and “thrust” individually, its compound meaning becomes apparent.
“Axial” is an adjective that describes something relating to the axis of an object. In this case, the axis of an object is an imaginary line usually parallel to the vector of force (such as gravity) applied on the object when it is resting in a stable position. If the object is irregular in shape, it is generally symmetrical at any cross section that is perpendicular to the axis.
Thrust is a noun that describes the action of pushing/propelling an object against a platform in a specified direction. It is the vector of force in the above definition.
Figure 1. Axial ThrustPutting the two meanings together, axial thrust refers to a propelling force applied along the axis (also called axial direction) of an object in order to push the object against a platform in a particular direction. The direction can be negative (tensile) away from the platform, or positive (compressive) toward the platform depending on the point of reference.
Axial thrust can also refer to the driving force generated in propulsion of an airplane, a pogo stick, steam turbines, stage pumps, or double suction impellers.
For a closer look at axial thrust, the next sections will examine the specific example of a centrifugal pump. We choose this example since it requires a load cell to balance axial thrust.
A centrifugal pump is a machine that converts rotational kinetic energy (of a rotor) to hydrodynamic energy for the purpose of transporting fluids from one place to another. It generates centrifugal forces to push out the fluids entering it.
The term suction side refers to the inlet side of the machine through which fluid particles enter. The term discharge side refers to the outlet side through which the fluid particles escape. The pressure at the discharge side is greater than the pressure at the suction side.
Centrifugal pumps have two major components other than the driving unit (e.g. an electric motor).
These are:
The casing protects the pump and houses balancing holes. The balancing holes are points where balancing weights are affixed; these weights ensure that the pump’s internal components’ collective center of mass aligns with the center of mass of the driving unit’s rotor (motor’s rotor shaft).
The other parts of the centrifugal pumps are:
In single stage pumps, as the device powers on and the shaft begins to rotate, two sets of forces act on the shaft (refer to Figure 1). The first are radial forces created by unbalanced pressure due to the casing design (recall it widens along the fluid path). The second are the axial forces, caused in part by the pressure difference between the shaft where it directly attaches to the back side of the impeller and the front side of the impeller.
As the fluid moves to the discharge side of the pump, parts of the liquid tend to push against the casing thereby pushing the shaft outwards along its axis through the driving unit. This force acting along the shaft’s axis also contributes to the axial thrust.
Figure 2. Axial Force in Centrifugal PumpOther axial forces on the shaft occur with use. Over time, fluids carry dirt particles that deposit on the blades, causing an unbalance in the system. This generates axial thrust components on the shaft and the motor.
In multistage pumps axial thrust on the shaft is more common. The difference in pressure between multiple impellers further contributes to a misalignment in the total axial balance.
The process of balancing axial thrust is very important to the pump’s proper functioning. A force offsetting the axial thrust accomplishes this.
Some offset techniques include:
This balancing reduces stress and damage to the pump structure. Specifically it reduces stress exerted on shaft bearings (wearing rings, loose rings, and thrust bearings) and prevents damage to the pump’s protective seal.
As highlighted in the example, balancing axial loads is important for the proper maintenance of the equipment bearing these forces. But how does one know the extent of the axial load, particularly since it builds over time and use? This is where load cells, such as those in the Tacuna Systems product line, are important.
Load cells are sensor devices. Sensors are used to detect a physical stimulus and then produce an output (electrical or mechanical) that is proportional to that stimulus. Load cells detect loads and forces, such as axial thrust.
Several types of load cells (described in An Overview of Load Cells) exist. However for many applications, including for measuring thrust, a strain gauge load cell is the most convenient and cost-effective. It is a passive transducer, meaning it requires an excitation voltage. Figure 3 below shows a simple strain gauge load cell.
Figure 3. Single-Ended Beam Load CellWhen a force is applied to the loading point of this type of load cell, the strain gauges within it deflect. This increases the overall electrical resistance across the gauges. This measured difference in resistance creates an electrical signal directly proportional to the force applied by the load. This signal is generally very small, on the order of millivolts, and must be amplified for proper readings. (See The Versatile Strain Gauge Load Cell for a more detailed explanation of this device’s operation.)
This load cell output is processed and signaled to displays that notify operators if the axial thrust balancing mechanisms are working. They can also be the input signal of control systems that stop the rotating machinery before damage can occur, should the balancing fail.
The sections above establish how axial loads are produced and that they must be mitigated. This section brings these two ideas together by explaining how to quantify axial thrust.
The steps to create an axial force measurement system follow.
It is essential to determine the limits of the force that the propeller or the engine will generate. This is done mathematically using the constants and variables of the engine. This step is necessary in selecting a load cell with a rated output capacity equal to or greater than the expected maximum force.
Thrust is a reaction force that acts in the opposite direction of the original force generated in an engine. Therefore both compression and tensile forces act on the spinning shaft. The selected load cell must support both directions of forces.
Each load cell manufacturer produces a datasheet giving maximum rated loads and other figures pertinent to its operating environment. (See How to Read a Load Cell Datasheet.) Select the load cell that suits the basic requirements determined in steps 1 and 2, meets the requirements of the operating environment, and has the required certifications. Certifications ensure the load cell device has been tested and approved for safe use.
The load cell will always require a mounting kit to ensure an accurate result. This mounting kit is then built into a thrust frame (see Figures 4 and 5), which must adhere to the following:
A strain gauge’s output, unconditioned, is usually very small (of the order of mV) and can be affected by noise. Conditioning filters this background noise, amplifies the filtered signal and converts it from an analog to digital signal. A microcontroller can further process the digital signal to display the thrust force and desired units of measurement. (See Why do I need a Load Cell Amplifier (and Other Signal Conditioners)?)
Calibration ensures the force measurement system gives accurate results, both at installation and periodically over continued use. A simple calibration system for this purpose might use a screw jack driven by an electric motor to apply both compressive and tensile forces to the load cell through a series of levers and pull rods. Further calibration procedures give the tare of the load cell and also set up automatic calibration over use. Our Tacuna Systems cell calibration system is an example.
The final step is to mount the engine in the measuring system. Perform all the necessary checks before powering on the system. Ensure this done in a controlled environment under proper supervision and approval.
Figure 4. Simple Test Thrust Stand Figure 5. Vertical and Horizontal Thrust Test StandThis article has explained the idea of axial forces and their impact on the longevity of a rotary system such as a centrifugal pump. It has also explained the use of load cells to quantify these forces so that they can be mitigated. Tacuna Systems provides a variety of load cells for this application.
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