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89-416: A dynamometer or "dyno" is a device for simultaneously measuring the torque and rotational speed ( RPM ) of an engine , motor or other rotating prime mover so that its instantaneous power may be calculated, and usually displayed by the dynamometer itself as kW or bhp . In addition to being used to determine the torque or power characteristics of a machine under test, dynamometers are employed in

178-423: A data acquisition system rather than being recorded manually. Speed and torque signals can also be recorded by a chart recorder or plotter . In addition to classification as absorption, motoring, or universal, as described above, dynamometers can also be classified in other ways. A dyno that is coupled directly to an engine is known as an engine dyno . A dyno that can measure torque and power delivered by

267-534: A force is allowed to act through a distance, it is doing mechanical work . Similarly, if torque is allowed to act through an angular displacement, it is doing work. Mathematically, for rotation about a fixed axis through the center of mass , the work W can be expressed as W = ∫ θ 1 θ 2 τ   d θ , {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \ \mathrm {d} \theta ,} where τ

356-478: A torque sensing coupling or torque transducer. A torque transducer provides an electrical signal that is proportional to the torque. With electrical absorption units, it is possible to determine torque by measuring the current drawn (or generated) by the absorber/driver. This is generally a less accurate method and not much practiced in modern times, but it may be adequate for some purposes. When torque and speed signals are available, test data can be transmitted to

445-461: A computer. Most systems employ eddy current, oil hydraulic, or DC motor produced loads because of their linear and quick load change abilities. The power is calculated as the product of angular velocity and torque . A motoring dynamometer acts as a motor that drives the equipment under test. It must be able to drive the equipment at any speed and develop any level of torque that the test requires. In common usage, AC or DC motors are used to drive

534-438: A fixed inertial mass load, calculates the power required to accelerate that fixed and known mass, and uses a computer to record RPM and acceleration rate to calculate torque. The engine is generally tested from somewhat above idle to its maximum RPM and the output is measured and plotted on a graph . A 'motoring' dynamometer provides the features of a brake dyno system, but in addition, can "power" (usually with an AC or DC motor)

623-399: A force F A acting on a point that moves with velocity v A and the output power be a force F B acts on a point that moves with velocity v B . If there are no losses in the system, then P = F B v B = F A v A , {\displaystyle P=F_{\text{B}}v_{\text{B}}=F_{\text{A}}v_{\text{A}},} and

712-411: A hydraulic pump (usually a gear-type pump), a fluid reservoir, and piping between the two parts. Inserted in the piping is an adjustable valve, and between the pump and the valve is a gauge or other means of measuring hydraulic pressure. In simplest terms, the engine is brought up to the desired RPM and the valve is incrementally closed. As the pumps outlet is restricted, the load increases and the throttle

801-449: A known mass drive roller and provide no variable load to the prime mover. An absorption dynamometer is usually equipped with some means of measuring the operating torque and speed. The power absorption unit (PAU) of a dynamometer absorbs the power developed by the prime mover. This power absorbed by the dynamometer is then converted into heat, which generally dissipates into the ambient air or transfers to cooling water that dissipates into

890-485: A logarithmic measure relative to a reference of 1 milliwatt, calories per hour, BTU per hour (BTU/h), and tons of refrigeration . As a simple example, burning one kilogram of coal releases more energy than detonating a kilogram of TNT , but because the TNT reaction releases energy more quickly, it delivers more power than the coal. If Δ W is the amount of work performed during a period of time of duration Δ t ,

979-452: A means for measuring torque and rotational speed. An absorption unit consists of some type of rotor in a housing. The rotor is coupled to the engine or other equipment under test and is free to rotate at whatever speed is required for the test. Some means is provided to develop a braking torque between the rotor and housing of the dynamometer. The means for developing torque can be frictional, hydraulic, electromagnetic, or otherwise, according to

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1068-400: A more cost-effective solution is to attach a larger absorption dynamometer with a smaller motoring dynamometer. Alternatively, a larger absorption dynamometer and a simple AC or DC motor may be used in a similar manner, with the electric motor only providing motoring power when required (and no absorption). The (cheaper) absorption dynamometer is sized for the maximum required absorption, whereas

1157-547: A number of other roles. In standard emissions testing cycles such as those defined by the United States Environmental Protection Agency , dynamometers are used to provide simulated road loading of either the engine (using an engine dynamometer) or full powertrain (using a chassis dynamometer). Beyond simple power and torque measurements, dynamometers can be used as part of a testbed for a variety of engine development activities, such as

1246-510: A particular purpose. A 'brake' dynamometer applies variable load on the prime mover (PM) and measures the PM's ability to move or hold the RPM as related to the "braking force" applied. It is usually connected to a computer that records applied braking torque and calculates engine power output based on information from a "load cell" or "strain gauge" and a speed sensor. An 'inertia' dynamometer provides

1335-420: A periodic function of period T {\displaystyle T} . The peak power is simply defined by: P 0 = max [ p ( t ) ] . {\displaystyle P_{0}=\max[p(t)].} The peak power is not always readily measurable, however, and the measurement of the average power P a v g {\displaystyle P_{\mathrm {avg} }}

1424-762: A single point particle is: L = r × p {\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} } where p is the particle's linear momentum and r is the position vector from the origin. The time-derivative of this is: d L d t = r × d p d t + d r d t × p . {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times {\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {r} }{\mathrm {d} t}}\times \mathbf {p} .} This result can easily be proven by splitting

1513-498: A twist applied to turn a shaft is better than the more complex notion of applying a linear force (or a pair of forces) with a certain leverage. Today, torque is referred to using different vocabulary depending on geographical location and field of study. This article follows the definition used in US physics in its usage of the word torque . In the UK and in US mechanical engineering , torque

1602-446: A variable frequency drive and AC induction motor, is a commonly used configuration of this type. Disadvantages include requiring a second set of test cell services (electrical power and cooling), and a slightly more complicated control system. Attention must be paid to the transition between motoring and braking in terms of control stability. Dynamometers are useful in the development and refinement of modern engine technology. The concept

1691-648: Is a general proof for point particles, but it can be generalized to a system of point particles by applying the above proof to each of the point particles and then summing over all the point particles. Similarly, the proof can be generalized to a continuous mass by applying the above proof to each point within the mass, and then integrating over the entire mass. In physics , rotatum is the derivative of torque with respect to time P = d τ d t , {\displaystyle \mathbf {P} ={\frac {\mathrm {d} {\boldsymbol {\tau }}}{\mathrm {d} t}},} where τ

1780-470: Is calculated based on rotational speed x torque x constant. The constant varies depending on the units used. If the dynamometer has a speed regulator (human or computer), the PAU provides a variable amount of braking force (torque) that is necessary to cause the prime mover to operate at the desired single test speed or RPM. The PAU braking load applied to the prime mover can be manually controlled or determined by

1869-412: Is constant, the amount of work performed in time period t can be calculated as W = P t . {\displaystyle W=Pt.} In the context of energy conversion, it is more customary to use the symbol E rather than W . Power in mechanical systems is the combination of forces and movement. In particular, power is the product of a force on an object and the object's velocity, or

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1958-407: Is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined. In three dimensions, the torque is a pseudovector ; for point particles , it is given by the cross product of the displacement vector and the force vector. The direction of the torque can be determined by using

2047-452: Is given by P ( t ) = p Q , {\displaystyle P(t)=pQ,} where p is pressure in pascals or N/m , and Q is volumetric flow rate in m /s in SI units. If a mechanical system has no losses, then the input power must equal the output power. This provides a simple formula for the mechanical advantage of the system. Let the input power to a device be

2136-675: Is more commonly performed by an instrument. If one defines the energy per pulse as ε p u l s e = ∫ 0 T p ( t ) d t {\displaystyle \varepsilon _{\mathrm {pulse} }=\int _{0}^{T}p(t)\,dt} then the average power is P a v g = 1 T ∫ 0 T p ( t ) d t = ε p u l s e T . {\displaystyle P_{\mathrm {avg} }={\frac {1}{T}}\int _{0}^{T}p(t)\,dt={\frac {\varepsilon _{\mathrm {pulse} }}{T}}.} One may define

2225-437: Is needed to carry away the heat created by absorbing the horsepower). The housing attempts to rotate in response to the torque produced, but is restrained by the scale or torque metering cell that measures the torque. In most cases, motoring dynamometers are symmetrical; a 300 kW AC dynamometer can absorb 300 kW as well as motor at 300 kW. This is an uncommon requirement in engine testing and development. Sometimes,

2314-471: Is referred to as moment of force , usually shortened to moment . This terminology can be traced back to at least 1811 in Siméon Denis Poisson 's Traité de mécanique . An English translation of Poisson's work appears in 1842. A force applied perpendicularly to a lever multiplied by its distance from the lever's fulcrum (the length of the lever arm ) is its torque. Therefore, torque

2403-399: Is simply opened until at the desired throttle opening. Unlike most other systems, power is calculated by factoring flow volume (calculated from pump design specifications), hydraulic pressure, and RPM. Brake HP, whether figured with pressure, volume, and RPM, or with a different load cell-type brake dyno, should produce essentially identical power figures. Hydraulic dynos are renowned for having

2492-418: Is suspected. In the rehabilitation , kinesiology , and ergonomics realms, force dynamometers are used for measuring the back, grip, arm, and/or leg strength of athletes, patients, and workers to evaluate physical status, performance, and task demands. Typically the force applied to a lever or through a cable is measured and then converted to a moment of force by multiplying by the perpendicular distance from

2581-401: Is the electrical resistance , measured in ohms . In the case of a periodic signal s ( t ) {\displaystyle s(t)} of period T {\displaystyle T} , like a train of identical pulses, the instantaneous power p ( t ) = | s ( t ) | 2 {\textstyle p(t)=|s(t)|^{2}} is also

2670-425: Is the moment of inertia of the body and ω is its angular speed . Power is the work per unit time , given by P = τ ⋅ ω , {\displaystyle P={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }},} where P is power, τ is torque, ω is the angular velocity , and ⋅ {\displaystyle \cdot } represents

2759-405: Is the newton-metre (N⋅m). For more on the units of torque, see § Units . The net torque on a body determines the rate of change of the body's angular momentum , τ = d L d t {\displaystyle {\boldsymbol {\tau }}={\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}} where L is the angular momentum vector and t

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2848-499: Is the limiting value of the average power as the time interval Δ t approaches zero. P = lim Δ t → 0 P a v g = lim Δ t → 0 Δ W Δ t = d W d t . {\displaystyle P=\lim _{\Delta t\to 0}P_{\mathrm {avg} }=\lim _{\Delta t\to 0}{\frac {\Delta W}{\Delta t}}={\frac {dW}{dt}}.} When power P

2937-465: Is the product of the torque τ and angular velocity ω , P ( t ) = τ ⋅ ω , {\displaystyle P(t)={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }},} where ω is angular frequency , measured in radians per second . The ⋅ {\displaystyle \cdot } represents scalar product . In fluid power systems such as hydraulic actuators, power

3026-1748: Is time. For the motion of a point particle, L = I ω , {\displaystyle \mathbf {L} =I{\boldsymbol {\omega }},} where I = m r 2 {\textstyle I=mr^{2}} is the moment of inertia and ω is the orbital angular velocity pseudovector. It follows that τ n e t = I 1 ω 1 ˙ e 1 ^ + I 2 ω 2 ˙ e 2 ^ + I 3 ω 3 ˙ e 3 ^ + I 1 ω 1 d e 1 ^ d t + I 2 ω 2 d e 2 ^ d t + I 3 ω 3 d e 3 ^ d t = I ω ˙ + ω × ( I ω ) {\displaystyle {\boldsymbol {\tau }}_{\mathrm {net} }=I_{1}{\dot {\omega _{1}}}{\hat {\boldsymbol {e_{1}}}}+I_{2}{\dot {\omega _{2}}}{\hat {\boldsymbol {e_{2}}}}+I_{3}{\dot {\omega _{3}}}{\hat {\boldsymbol {e_{3}}}}+I_{1}\omega _{1}{\frac {d{\hat {\boldsymbol {e_{1}}}}}{dt}}+I_{2}\omega _{2}{\frac {d{\hat {\boldsymbol {e_{2}}}}}{dt}}+I_{3}\omega _{3}{\frac {d{\hat {\boldsymbol {e_{3}}}}}{dt}}=I{\boldsymbol {\dot {\omega }}}+{\boldsymbol {\omega }}\times (I{\boldsymbol {\omega }})} using

3115-545: Is to use a dyno to measure and compare power transfer at different points on a vehicle, thus allowing the engine or drivetrain to be modified to get more efficient power transfer. For example, if an engine dyno shows that a particular engine achieves 400 N⋅m (295 lbf⋅ft) of torque, and a chassis dynamo shows only 350 N⋅m (258 lbf⋅ft), one would know that the drivetrain losses are nominal. Dynamometers are typically very expensive pieces of equipment, and so are normally used only in certain fields that rely on them for

3204-451: Is torque, and θ 1 and θ 2 represent (respectively) the initial and final angular positions of the body. It follows from the work–energy principle that W also represents the change in the rotational kinetic energy E r of the body, given by E r = 1 2 I ω 2 , {\displaystyle E_{\mathrm {r} }={\tfrac {1}{2}}I\omega ^{2},} where I

3293-818: Is torque. This word is derived from the Latin word rotātus meaning 'to rotate', but the term rotatum is not universally recognized but is commonly used. There is not a universally accepted lexicon to indicate the successive derivatives of rotatum, even if sometimes various proposals have been made. Using the cross product definition of torque, an alternative expression for rotatum is: P = r × d F d t + d r d t × F . {\displaystyle \mathbf {P} =\mathbf {r} \times {\frac {\mathrm {d} \mathbf {F} }{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {r} }{\mathrm {d} t}}\times \mathbf {F} .} Because

3382-466: Is used to blow air to provide engine load. The torque absorbed by a fan brake may be adjusted by changing the gearing or the fan itself, or by restricting the airflow through the fan. Due to the low viscosity of air, this variety of dynamometer is inherently limited in the amount of torque that it can absorb. An oil shear brake has a series of friction discs and steel plates similar to the clutches in an automobile automatic transmission. The shaft carrying

3471-506: Is valid for any type of trajectory. In some simple cases like a rotating disc, where only the moment of inertia on rotating axis is, the rotational Newton's second law can be τ = I α {\displaystyle {\boldsymbol {\tau }}=I{\boldsymbol {\alpha }}} where α = ω ˙ {\displaystyle {\boldsymbol {\alpha }}={\dot {\boldsymbol {\omega }}}} . The definition of angular momentum for

3560-624: Is zero because velocity and momentum are parallel, so the second term vanishes. Therefore, torque on a particle is equal to the first derivative of its angular momentum with respect to time. If multiple forces are applied, according Newton's second law it follows that d L d t = r × F n e t = τ n e t . {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} _{\mathrm {net} }={\boldsymbol {\tau }}_{\mathrm {net} }.} This

3649-414: The fundamental theorem of calculus , we know that P = d W d t = d d t ∫ Δ t F ⋅ v d t = F ⋅ v . {\displaystyle P={\frac {dW}{dt}}={\frac {d}{dt}}\int _{\Delta t}\mathbf {F} \cdot \mathbf {v} \,dt=\mathbf {F} \cdot \mathbf {v} .} Hence

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3738-581: The geometrical theorem of the same name) states that the resultant torques due to several forces applied to about a point is equal to the sum of the contributing torques: Power (physics) Power is the amount of energy transferred or converted per unit time. In the International System of Units , the unit of power is the watt , equal to one joule per second. Power is a scalar quantity. Specifying power in particular systems may require attention to other quantities; for example,

3827-424: The mechanical advantage of the system (output force per input force) is given by M A = F B F A = v A v B . {\displaystyle \mathrm {MA} ={\frac {F_{\text{B}}}{F_{\text{A}}}}={\frac {v_{\text{A}}}{v_{\text{B}}}}.} The similar relationship is obtained for rotating systems, where T A and ω A are

3916-460: The right hand grip rule : if the fingers of the right hand are curled from the direction of the lever arm to the direction of the force, then the thumb points in the direction of the torque. It follows that the torque vector is perpendicular to both the position and force vectors and defines the plane in which the two vectors lie. The resulting torque vector direction is determined by the right-hand rule. Therefore any force directed parallel to

4005-414: The scalar product . Algebraically, the equation may be rearranged to compute torque for a given angular speed and power output. The power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied (this is equivalent to the linear case where the power injected by a force depends only on

4094-469: The "water brake housing" for cooling. Environmental regulations may prohibit "flow through" water, in which case large water tanks are installed to prevent contaminated water from entering the environment. The schematic shows the most common type of water brake, known as the "variable level" type. Water is added until the engine is held at a steady RPM against the load, with the water then kept at that level and replaced by constant draining and refilling (which

4183-482: The PM and allow testing of very small power outputs (for example, duplicating speeds and loads that are experienced when operating a vehicle traveling downhill or during on/off throttle operations). Torque The term torque (from Latin torquēre , 'to twist') is said to have been suggested by James Thomson and appeared in print in April, 1884. Usage is attested the same year by Silvanus P. Thompson in

4272-721: The above expression for work, , gives W = ∫ s 1 s 2 F ⋅ d θ × r {\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} } The expression inside the integral is a scalar triple product F ⋅ d θ × r = r × F ⋅ d θ {\displaystyle \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} =\mathbf {r} \times \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}} , but as per

4361-446: The air gap between the rotor and the coil. The resulting flux lines create "chains" of metal particulate that are constantly built and broken apart during rotation, creating great torque. Powder dynamometers are typically limited to lower RPM due to heat dissipation problems. Hysteresis dynamometers use a magnetic rotor, sometimes of AlNiCo alloy, that is moved through flux lines generated between magnetic pole pieces. The magnetisation of

4450-406: The air. Regenerative dynamometers, in which the prime mover drives a DC motor as a generator to create load, make excess DC power and potentially - using a DC/AC inverter - can feed AC power back into the commercial electrical power grid. Absorption dynamometers can be equipped with two types of control systems to provide different main test types. The dynamometer has a "braking" torque regulator -

4539-421: The average power P avg over that period is given by the formula P a v g = Δ W Δ t . {\displaystyle P_{\mathrm {avg} }={\frac {\Delta W}{\Delta t}}.} It is the average amount of work done or energy converted per unit of time. Average power is often called "power" when the context makes it clear. Instantaneous power

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4628-583: The beginning and end of the path along which the work was done. The power at any point along the curve C is the time derivative: P ( t ) = d W d t = F ⋅ v = − d U d t . {\displaystyle P(t)={\frac {dW}{dt}}=\mathbf {F} \cdot \mathbf {v} =-{\frac {dU}{dt}}.} In one dimension, this can be simplified to: P ( t ) = F ⋅ v . {\displaystyle P(t)=F\cdot v.} In rotational systems, power

4717-435: The calibration of engine management controllers, detailed investigations into combustion behavior, and tribology . In the medical terminology, hand-held dynamometers are used for routine screening of grip and hand strength , and the initial and ongoing evaluation of patients with hand trauma or dysfunction. They are also used to measure grip strength in patients where compromise of the cervical nerve roots or peripheral nerves

4806-439: The definition of torque, and since the parameter of integration has been changed from linear displacement to angular displacement, the equation becomes W = ∫ θ 1 θ 2 τ ⋅ d θ {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}{\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}} If

4895-411: The derivative of a vector is d e i ^ d t = ω × e i ^ {\displaystyle {d{\boldsymbol {\hat {e_{i}}}} \over dt}={\boldsymbol {\omega }}\times {\boldsymbol {\hat {e_{i}}}}} This equation is the rotational analogue of Newton's second law for point particles, and

4984-405: The dynamometer can receive payment (or credit) from the utility for the returned power via net metering . In engine testing, universal dynamometers can not only absorb the power of the engine, but can also drive the engine for measuring friction, pumping losses, and other factors. Electric motor/generator dynamometers are generally more costly and complex than other types of dynamometers. A fan

5073-406: The element and of the voltage across the element. Power is the rate with respect to time at which work is done; it is the time derivative of work : P = d W d t , {\displaystyle P={\frac {dW}{dt}},} where P is power, W is work, and t is time. We will now show that the mechanical power generated by a force F on a body moving at

5162-454: The equipment or "load" device. In most dynamometers power ( P ) is not measured directly, but must be calculated from torque ( τ ) and angular velocity ( ω ) values or force ( F ) and linear velocity ( v ): Division by a conversion constant may be required, depending on the units of measure used. For imperial or U.S. customary units, For metric units, A dynamometer consists of an absorption (or absorber/driver) unit, and usually includes

5251-549: The first edition of Dynamo-Electric Machinery . Thompson motivates the term as follows: Just as the Newtonian definition of force is that which produces or tends to produce motion (along a line), so torque may be defined as that which produces or tends to produce torsion (around an axis). It is better to use a term which treats this action as a single definite entity than to use terms like " couple " and " moment ", which suggest more complex ideas. The single notion of

5340-415: The force exerted by the dyno housing in attempting to rotate. The torque is the force indicated by the scales multiplied by the length of the torque arm measured from the center of the dynamometer. A load cell transducer can be substituted for the scales in order to provide an electrical signal that is proportional to torque. Another means to measure torque is to connect the engine to the dynamo through

5429-611: The force is variable over a three-dimensional curve C , then the work is expressed in terms of the line integral: W = ∫ C F ⋅ d r = ∫ Δ t F ⋅ d r d t   d t = ∫ Δ t F ⋅ v d t . {\displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {r} =\int _{\Delta t}\mathbf {F} \cdot {\frac {d\mathbf {r} }{dt}}\ dt=\int _{\Delta t}\mathbf {F} \cdot \mathbf {v} \,dt.} From

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5518-410: The force to the axis of the level. An absorbing dynamometer acts as a load that is driven by the prime mover that is under test (e.g. Pelton wheel ). The dynamometer must be able to operate at any speed and load to any level of torque that the test requires. Absorbing dynamometers are not to be confused with "inertia" dynamometers, which calculate power solely by measuring power required to accelerate

5607-523: The formula is valid for any general situation. In older works, power is sometimes called activity . The dimension of power is energy divided by time. In the International System of Units (SI), the unit of power is the watt (W), which is equal to one joule per second. Other common and traditional measures are horsepower (hp), comparing to the power of a horse; one mechanical horsepower equals about 745.7 watts. Other units of power include ergs per second (erg/s), foot-pounds per minute, dBm ,

5696-468: The friction discs is attached to the load through a coupling. A piston pushes the stack of friction discs and steel plates together creating shear in the oil between the discs and plates applying a torque. Torque can be controlled pneumatically or hydraulically. Force lubrication maintains a film of oil between the surfaces to eliminate wear. Reaction is smooth down to zero RPM without stick-slip. Loads up to hundreds of thermal horsepower can be absorbed through

5785-568: The infinitesimal linear displacement d s {\displaystyle \mathrm {d} \mathbf {s} } is related to a corresponding angular displacement d θ {\displaystyle \mathrm {d} {\boldsymbol {\theta }}} and the radius vector r {\displaystyle \mathbf {r} } as d s = d θ × r {\displaystyle \mathrm {d} \mathbf {s} =\mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} } Substitution in

5874-586: The instantaneous speed – not on the resulting acceleration, if any). The work done by a variable force acting over a finite linear displacement s {\displaystyle s} is given by integrating the force with respect to an elemental linear displacement d s {\displaystyle \mathrm {d} \mathbf {s} } W = ∫ s 1 s 2 F ⋅ d s {\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} \mathbf {s} } However,

5963-399: The magnetic field strength to control the amount of braking. The electromagnet voltage is usually controlled by a computer, using changes in the magnetic field to match the power output being applied. Sophisticated EC systems allow steady state and controlled acceleration rate operation. A powder dynamometer is similar to an eddy current dynamometer, but a fine magnetic powder is placed in

6052-731: The maximum performance of a device in terms of velocity ratios determined by its physical dimensions. See for example gear ratios . The instantaneous electrical power P delivered to a component is given by P ( t ) = I ( t ) ⋅ V ( t ) , {\displaystyle P(t)=I(t)\cdot V(t),} where If the component is a resistor with time-invariant voltage to current ratio, then: P = I ⋅ V = I 2 ⋅ R = V 2 R , {\displaystyle P=I\cdot V=I^{2}\cdot R={\frac {V^{2}}{R}},} where R = V I {\displaystyle R={\frac {V}{I}}}

6141-612: The most common absorbers used in modern chassis dynos. The EC absorbers provide a quick load change rate for rapid load settling. Most are air cooled, but some are designed to require external water cooling systems. Eddy current dynamometers require an electrically conductive core, shaft, or disc moving across a magnetic field to produce resistance to movement. Iron is a common material, but copper, aluminum, and other conductive materials are also usable. In current (2009) applications, most EC brakes use cast iron discs similar to vehicle disc brake rotors, and use variable electromagnets to change

6230-416: The most useful technologies in small (200 hp (150 kW) and less) dynamometers. Electric motor / generator dynamometers are a specialized type of adjustable-speed drive . The absorption/driver unit can be either an alternating current (AC) motor or a direct current (DC) motor. Either an AC motor or a DC motor can operate as a generator that is driven by the unit under test or a motor that drives

6319-403: The motoring dynamometer is sized for motoring. A typical size ratio for common emission test cycles and most engine development is approximately 3:1. Torque measurement is somewhat complicated since there are two machines in tandem - an inline torque transducer is the preferred method of torque measurement in this case. An eddy-current or waterbrake dynamometer, with electronic control combined with

6408-683: The particle's position vector does not produce a torque. The magnitude of torque applied to a rigid body depends on three quantities: the force applied, the lever arm vector connecting the point about which the torque is being measured to the point of force application, and the angle between the force and lever arm vectors. In symbols: τ = r × F ⟹ τ = r F ⊥ = r F sin ⁡ θ {\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \implies \tau =rF_{\perp }=rF\sin \theta } where The SI unit for torque

6497-414: The path C and v is the velocity along this path. If the force F is derivable from a potential ( conservative ), then applying the gradient theorem (and remembering that force is the negative of the gradient of the potential energy) yields: W C = U ( A ) − U ( B ) , {\displaystyle W_{C}=U(A)-U(B),} where A and B are

6586-481: The power absorption unit is configured to provide a set braking force torque load, while the prime mover is configured to operate at whatever throttle opening, fuel delivery rate, or any other variable it is desired to test. The prime mover is then allowed to accelerate the engine through the desired speed or RPM range. Constant force test routines require the PAU to be set slightly torque deficient as referenced to prime mover output to allow some rate of acceleration. Power

6675-414: The power involved in moving a ground vehicle is the product of the aerodynamic drag plus traction force on the wheels, and the velocity of the vehicle. The output power of a motor is the product of the torque that the motor generates and the angular velocity of its output shaft. Likewise, the power dissipated in an electrical element of a circuit is the product of the current flowing through

6764-421: The power of large naval engines. Water brake absorbers are relatively common today. They are noted for their high power capability, small size, light weight, and relatively low manufacturing costs as compared to other, quicker reacting, "power absorber" types. Their drawbacks are that they can take a relatively long period of time to "stabilize" their load amount, and that they require a constant supply of water to

6853-444: The power train of a vehicle directly from the drive wheel or wheels without removing the engine from the frame of the vehicle), is known as a chassis dyno . Dynamometers can also be classified by the type of absorption unit or absorber/driver that they use. Some units that are capable of absorption only can be combined with a motor to construct an absorber/driver or "universal" dynamometer. Eddy current (EC) dynamometers are currently

6942-580: The product of a torque on a shaft and the shaft's angular velocity. Mechanical power is also described as the time derivative of work. In mechanics , the work done by a force F on an object that travels along a curve C is given by the line integral : W C = ∫ C F ⋅ v d t = ∫ C F ⋅ d x , {\displaystyle W_{C}=\int _{C}\mathbf {F} \cdot \mathbf {v} \,dt=\int _{C}\mathbf {F} \cdot d\mathbf {x} ,} where x defines

7031-488: The pulse length τ {\displaystyle \tau } such that P 0 τ = ε p u l s e {\displaystyle P_{0}\tau =\varepsilon _{\mathrm {pulse} }} so that the ratios P a v g P 0 = τ T {\displaystyle {\frac {P_{\mathrm {avg} }}{P_{0}}}={\frac {\tau }{T}}} are equal. These ratios are called

7120-477: The quickest load change ability, just slightly surpassing eddy current absorbers. The downside is that they require large quantities of hot oil under high pressure and an oil reservoir. The hydraulic dynamometer (also referred to as the water brake absorber) was invented by British engineer William Froude in 1877 in response to a request by the Admiralty to produce a machine capable of absorbing and measuring

7209-528: The rate of change of force is yank Y {\textstyle \mathbf {Y} } and the rate of change of position is velocity v {\textstyle \mathbf {v} } , the expression can be further simplified to: P = r × Y + v × F . {\displaystyle \mathbf {P} =\mathbf {r} \times \mathbf {Y} +\mathbf {v} \times \mathbf {F} .} The law of conservation of energy can also be used to understand torque. If

7298-506: The required force lubrication and cooling unit. Most often, the brake is kinetically grounded through a torque arm anchored by a strain gauge which produces a current under load fed to the dynamometer control. Proportional or servo control valves are generally used to allow the dynamometer control to apply pressure to provide the program torque load with feedback from the strain gauge closing the loop. As torque requirements go up there are speed limitations. The hydraulic brake system consists of

7387-570: The rotor is thus cycled around its B-H characteristic, dissipating energy proportional to the area between the lines of that graph as it does so. Unlike eddy current brakes, which develop no torque at standstill, the hysteresis brake develops largely constant torque, proportional to its magnetising current (or magnet strength in the case of permanent magnet units) over its entire speed range. Units often incorporate ventilation slots, though some have provision for forced air cooling from an external supply. Hysteresis and Eddy Current dynamometers are two of

7476-744: The torque and angular velocity of the input and T B and ω B are the torque and angular velocity of the output. If there are no losses in the system, then P = T A ω A = T B ω B , {\displaystyle P=T_{\text{A}}\omega _{\text{A}}=T_{\text{B}}\omega _{\text{B}},} which yields the mechanical advantage M A = T B T A = ω A ω B . {\displaystyle \mathrm {MA} ={\frac {T_{\text{B}}}{T_{\text{A}}}}={\frac {\omega _{\text{A}}}{\omega _{\text{B}}}}.} These relations are important because they define

7565-875: The torque and the angular displacement are in the same direction, then the scalar product reduces to a product of magnitudes; i.e., τ ⋅ d θ = | τ | | d θ | cos ⁡ 0 = τ d θ {\displaystyle {\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}=\left|{\boldsymbol {\tau }}\right|\left|\mathrm {d} {\boldsymbol {\theta }}\right|\cos 0=\tau \,\mathrm {d} \theta } giving W = ∫ θ 1 θ 2 τ d θ {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \,\mathrm {d} \theta } The principle of moments, also known as Varignon's theorem (not to be confused with

7654-424: The type of absorption/driver unit. One means for measuring torque is to mount the dynamometer housing so that it is free to turn except as restrained by a torque arm. The housing can be made free to rotate by using trunnions connected to each end of the housing to support it in pedestal-mounted trunnion bearings. The torque arm is connected to the dyno housing and a weighing scale is positioned so that it measures

7743-414: The unit under test. When equipped with appropriate control units, electric motor/generator dynamometers can be configured as universal dynamometers. The control unit for an AC motor is a variable-frequency drive , while the control unit for a DC motor is a DC drive . In both cases, regenerative control units can transfer power from the unit under test to the electric utility. Where permitted, the operator of

7832-733: The vectors into components and applying the product rule . But because the rate of change of linear momentum is force F {\textstyle \mathbf {F} } and the rate of change of position is velocity v {\textstyle \mathbf {v} } , d L d t = r × F + v × p {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} +\mathbf {v} \times \mathbf {p} } The cross product of momentum p {\displaystyle \mathbf {p} } with its associated velocity v {\displaystyle \mathbf {v} }

7921-909: The velocity v can be expressed as the product: P = d W d t = F ⋅ v {\displaystyle P={\frac {dW}{dt}}=\mathbf {F} \cdot \mathbf {v} } If a constant force F is applied throughout a distance x , the work done is defined as W = F ⋅ x {\displaystyle W=\mathbf {F} \cdot \mathbf {x} } . In this case, power can be written as: P = d W d t = d d t ( F ⋅ x ) = F ⋅ d x d t = F ⋅ v . {\displaystyle P={\frac {dW}{dt}}={\frac {d}{dt}}\left(\mathbf {F} \cdot \mathbf {x} \right)=\mathbf {F} \cdot {\frac {d\mathbf {x} }{dt}}=\mathbf {F} \cdot \mathbf {v} .} If instead

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