Dynamic force contactor, providing a dynamic force, and calibrating a force sensor to be traceable to the international system of units

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First Claim
1. A dynamic force contactor to provide a dynamic force, the dynamic force contactor comprising:
 a magnet that provides a magnetic field;
an electrical conductor that communicates an alternating current perpendicular to the magnetic field, the alternating current from the electrical conductor in combination with the magnetic field from the magnet providing a Lorentzian force;
an armature disposed proximate to the magnet, the electrical conductor disposed on the armature such that the armature reciprocates in a reciprocating direction relative to the magnet in response to the Lorentzian force and that produces the dynamic force; and
a dynamic force mediator in communication with the electrical conductor and the armature such that;
the dynamic force mediator monitors an alternating voltage across the electrical conductor;
the dynamic force mediator monitors an alternating current through the electrical conductor; and
the dynamic force mediator monitors a reciprocation velocity of the armature.
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Abstract
A dynamic force contactor includes: a magnet that provides a magnetic field; an electrical conductor that provides an electric field perpendicular to the magnetic field, the electric field from the electrical conductor in combination with the magnetic field from the magnet providing a Lorentzian force; an armature disposed proximate to the magnet, the electrical conductor disposed on the armature such that the armature reciprocates in a reciprocating direction relative to the magnet in response to the Lorentzian force and that produces the dynamic force; and a dynamic force mediator in communication with the electrical conductor and the armature such that: the dynamic force mediator monitors an alternating voltage across the electrical conductor; the dynamic force mediator monitors an alternating current through the electrical conductor; and the dynamic force mediator monitors a reciprocation velocity of the armature.
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LINEAR ELECTROMAGNETIC MACHINES  
Patent #
US 20110037327A1
Filed 01/23/2009

Current Assignee
Phillip Raymond Michael Denne

Sponsoring Entity
Phillip Raymond Michael Denne

Active torque bias system and controls  
Patent #
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Filed 05/16/2002

Current Assignee
The Timken Company

Sponsoring Entity
The Timken Company

Direct current homopolar machine  
Patent #
US 5,587,618 A
Filed 04/13/1995

Current Assignee
George D. Hathaway

Sponsoring Entity
George D. Hathaway

Linear reciprocating electrical generator  
Patent #
US 4,500,827 A
Filed 06/11/1984

Current Assignee
Mario J. Pasichinskyj, Thomas D. Merritt

Sponsoring Entity
Mario J. Pasichinskyj, Thomas D. Merritt

Medical apparatus system having optical fiber load sensing capability  
Patent #
US 8,182,433 B2
Filed 09/28/2005

Current Assignee
St. Jude Medical International Holding S.a r.l.

Sponsoring Entity
Endosense SA

16 Claims
 1. A dynamic force contactor to provide a dynamic force, the dynamic force contactor comprising:
 a magnet that provides a magnetic field;
an electrical conductor that communicates an alternating current perpendicular to the magnetic field, the alternating current from the electrical conductor in combination with the magnetic field from the magnet providing a Lorentzian force;
an armature disposed proximate to the magnet, the electrical conductor disposed on the armature such that the armature reciprocates in a reciprocating direction relative to the magnet in response to the Lorentzian force and that produces the dynamic force; and
a dynamic force mediator in communication with the electrical conductor and the armature such that;
the dynamic force mediator monitors an alternating voltage across the electrical conductor;
the dynamic force mediator monitors an alternating current through the electrical conductor; and
the dynamic force mediator monitors a reciprocation velocity of the armature.  View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
 a magnet that provides a magnetic field;
1 Specification
The application claims priority to U.S. Provisional Patent Application Ser. No. 62/558,101 filed Sep. 13, 2017, the disclosure of which is incorporated herein by reference in its entirety.
This invention was made with United States Government support from the National Institute of Standards and Technology (NIST), an agency of the United States Department of Commerce. The Government has certain rights in the invention. Licensing inquiries may be directed to the Technology Partnerships Office, NIST, Gaithersburg, Md., 20899; voice (301) 3019752573; email tpo@nist.gov; reference NIST Docket Number 16033US1.
Disclosed is a dynamic force contactor to provide a dynamic force, the dynamic force contactor comprising: a magnet that provides a magnetic field; an electrical conductor that provides a current perpendicular to the magnetic field, the current in the electrical conductor in combination with the magnetic field from the magnet providing a Lorentzian force; an armature disposed proximate to the magnet, the electrical conductor disposed on the armature such that the armature reciprocates in a reciprocating direction relative to the magnet in response to the Lorentzian force and that produces the dynamic force; and a dynamic force mediator in communication with the electrical conductor and the armature such that: the dynamic force mediator monitors an alternating voltage across the electrical conductor; the dynamic force mediator monitors an alternating current through the electrical conductor; and the dynamic force mediator monitors a reciprocation velocity of the armature.
Disclosed is a process for providing a dynamic force, the process comprising: disposing the armature of the dynamic force contactor in contact with a structure to which the dynamic force is applied; providing electrical power to the electrical conductor, the electrical power comprising a timevarying amplitude; and reciprocating the armature at the reciprocation velocity in response to providing electrical power to the electrical conductor to provide the dynamic force to the structure.
Disclosed is a process for calibrating a force sensor to be traceable to the international system of units (SI), the process comprising: disposing the armature of the dynamic force contactor in contact with a structure to which the force sensor under calibration is disposed; providing electrical power to the electrical conductor, the electrical power comprising a timevarying amplitude; reciprocating the armature at the reciprocation velocity in response to providing electrical power to the electrical conductor; providing the dynamic force to the structure; measuring the alternating voltage; determining the alternating current through the electrical conductor; determining the reciprocation velocity of the armature; determining the dynamic force from the reciprocation velocity, the alternating voltage, and the alternating current; and determining a calibration response for the force sensor to calibrate the force sensor to be traceable to the SI.
The following description should not be considered limiting in any way. With reference to the accompanying drawings, like elements are numbered alike.
A detailed description of one or more embodiments is presented herein by way of exemplification and not limitation.
It has been discovered that a dynamic force contactor can be a portable dynamic force standard that provides a mechanical dynamic force so that the dynamic force applied to a structure can be determined through electrical and mechanical measurements. Advantageously, the dynamic force contactor is a portable apparatus for dynamic force calibration that dynamically calibrates a force sensor in an environmental setting in which the force sensor resides or is applied. The dynamic force contactor overcomes challenges in measuring dynamic force such as a dynamic calibration response of the force sensor that can change and that can depend upon an application setting.
Trade, commerce, and test of materials and engineering structures involve a determination of force in areas such as commercial weight of goods (e.g., produce and raw materials), aerospace structures (e.g., aerodynamic drag forces and reaction forces in landing gear), crash testing of vehicles, machining and manufacturing processes, and the like. The force can be measured with a conventional force sensor that often outputs a voltage that represents an applied force. The output voltage and a sensor calibration response provide a force value for each value of the output voltage of the conventional force sensor to determine the applied force. The dynamic force contactor described herein provides traceability of the calibration response of the conventional force sensor through a measurement of voltage, current, and reciprocation velocity to the International System (SI) of Units.
The dynamic force contactor provides and determination of dynamic force, wherein conventional national and international force calibration procedures that determine the calibration response of conventional force sensor determine static force where the applied force is constant and does not change with time. Unexpectedly, the dynamic force contactor dynamically calibrates the force sensor even when the force changes in time. The dynamic force contactor overcomes problems with calibrating a force sensor dynamically that include a dynamic calibration response of the force sensor that changes depending on the application setting in which the force sensor is used. Moreover, the dynamic force contactor provides accurate dynamic force measurements and calibrates the force sensor for making accurate dynamic force measurements.
Dynamic force contactor 200 provides dynamic force 252. In an embodiment, with reference to
In an embodiment, with reference to
In an embodiment, with reference to
In an embodiment, with reference to
In an embodiment, with reference to
In an embodiment, with reference to
Dynamic force contactor 200 produces dynamic force 252 and dynamic force signal 250. Dynamic force contactor 200 includes magnet 210 that produces magnetic field 212, which interacts with alternating current 226 within electrical conductor 214 to produce Lorentzian force 218. Lorentzian force 218 moves armature 230 in reciprocating direction 228 and applies dynamic force 252 to structure 266. Dynamic force 252 is measured using dynamic force mediator 232 by measuring alternating voltage 224, alternating current 226, and reciprocation velocity 222. In an embodiment, magnet 210 is a permanent or electric magnet. In an embodiment, magnet 210 is a rare earth permanent magnet.
Magnet 210 produces magnetic field 212, also referred to as magnetic field 212, that has a magnetic field strength from a nanoTesla to tens of Tesla, specifically from 0.01 Tesla to 10 Tesla, and more specifically from 0.1 Tesla to 2 Tesla. In an embodiment, magnetic field 212 is produced by a rare earth permanent magnet.
Electrical conductor 214 is disposed in magnetic field 212 and communicates alternating current 226. In an embodiment, electrical conductor 214 can be a single or multiturn coil of wire. Lorentzian force 218 is generated from electrical conductor 214 interacting with magnetic field 212. Secondary electrical conductor 220 is disposed in magnetic field of secondary magnet 242 and generates a force that moves armature 230 along reciprocating direction 228. Reciprocation velocity 222 is a velocity of armature 230 along reciprocating direction 228. Alternating voltage 224 is the voltage across electrical conductor 214. Alternating current 226 is the current flowing through electrical conductor 214. Reciprocating direction 228 is a primary direction along which armature 230 reciprocates. Armature 230 reciprocates and applies dynamic force 252 to structure 266.
Dynamic force mediator 232 can include a circuit that is used to measure alternating voltage 224, alternating current 226, and reciprocation velocity 222. In an embodiment, with reference to
Housing 234 houses all or some components that generates or measures dynamic force 252. Accelerometer 236 measures acceleration of housing 234. The acceleration is used to calculate displacement or velocity of housing 234. Light source 238 can be used with light detector 240 to determine relative motion of armature 230 and housing 234. Light detector 240 can be used with light source 238 to determine relative motion of armature 230 and housing 234. Secondary magnet 242 can be used with secondary electrical conductor 220 to generate motion of armature 230. Coupler 244 provides a physical link between secondary electrical conductor 220 and secondary magnet 242 to armature 230. Magnetic field guide 246 is a high permeability material that shapes magnetic field 212 so that it interacts with electrical conductor 214. Armature guide 248 constrains motion of armature 230 along reciprocating direction 228. Dynamic force signal 250 is a signal that is proportional to dynamic force 252, which is calculated from alternating voltage 224, alternating current 226, and reciprocation velocity 222 optionally with a correction. Dynamic force 252 is a timevarying force applied to structure 266. Handle 254 is member by dynamic force contactor 200 is held with a hand or mount. Flange 260 mechanically supports flexure 292 and is attached to housing 234. Current source 262 generates alternating current 226. Shunt resistor 264 measures alternating current 226. Structure 266 can include force sensor 268, which can be calibrated with dynamic force contactor 200. Force sensor 268 is a forceindicating instrument disposed on structure 266 and can be calibrated with dynamic force contactor 200. Unknown force signal 270 is a signal from force sensor 268 that is calibrated with dynamic force contactor 200. Support material 272 mechanically reinforces magnetic field guide 246. Optical cavity mirror 278 is a mirror disposed on an optical cavity that measures displacement and reciprocation velocity 222 of armature 230. Fiber optic 280 transmits light from optical cavity mirror 278 to optical signal 286 output. Wire 282 communicates alternating voltage 224 and alternating current 226. Supply current 284 generates alternating current 226. Optical signal 286 is an output of the optical cavity from fiber optic 280. Strain gage 288 measures strain of shear web 290 that indicates force applied to force sensor 268. Shear web 290 deflects when a force is applied to the sensor. Flexure 292 constrains the primary motion of armature 230 along reciprocating direction 228. Direct light 294 is light emitted from light source 238 and can be detected directly or indirectly by light detector 240. Reflected light 296 is light from light source 238 that is reflected from armature 230 and detected by light detector 240. Enclosure 298 covers dynamic force mediator 232. Terminal 300 is an access location wherein alternating voltage 224 is measured.
It should be appreciated that various components of dynamic force contactor 200 can be made from a metal, plastic, glass, ceramic, polymer, composite, and the like or a combination thereof. Materials of construction selected for the components should not interfere with operability of dynamic force contactor 200.
Dynamic force contactor 200 can be made in various ways. In an embodiment, a process for making dynamic force contactor 200 includes disposing electrical conductor 214 proximate to magnet 210 and in magnetic field 212 so that alternating current 226 of electrical conductor 214 is oriented perpendicular to magnetic field 212, wherein electric field 216 in combination with magnetic field 212 from magnet 210 provide Lorentzian force 218; disposing armature 230 proximate to magnet 210 such that electrical conductor 214 is disposed on armature 230, wherein armature 230 reciprocates in reciprocating direction 228 relative to magnet 210 in response to Lorentzian force 218 and wherein armature 230 produces dynamic force 252; and disposing dynamic force mediator 232 in communication with electrical conductor 214 and armature 230 such that dynamic force mediator 232 monitors alternating voltage 224 across electrical conductor 214, alternating current 226 through electrical conductor 214, and reciprocation velocity 222 of armature 230. The process for making dynamic force contactor 200 also can include disposing magnet 210, electrical conductor 214, armature 230, and dynamic force mediator 232 in housing 234. The process for making dynamic force contactor 200 also can include disposing accelerometer 236 on armature 230; disposing light source 238 on housing 234 or armature 230; disposing light detector 240 on housing 234 or armature 230; disposing secondary electrical conductor 220 opposing electrical conductor 214 such that magnet 210 is interposed between second electrical conductor 220 and electrical conductor 214; disposing magnetic field guide 246 proximate to magnet 210 to provide a selected shape of magnetic field 212 in which electrical conductor 214 is disposed; disposing armature guide 248 proximate to the armature 230 to provide linear motion in reciprocating direction 228 of armature 230; providing housing 234 with flange 260, rostrum 256, caudal member 258, and handle 254; or disposing enclosure 298 on dynamic force mediator 232 elements of dynamic force contactor 200 as shown in
Dynamic force contactor 200 can be made by combining: a magnet (e.g., an electromagnet or permanent magnet); an electrical conductor (e.g., metallic wire); light and rigid material of high electrical resistivity; a resistor; a fast voltage measuring circuit (e.g., a voltmeter); material of high magnetic permeability; material of sufficient strength and rigidity to support the magnet, electrical conductor, and light rigid material; a flexure spring; an accelerometer; and an AC electrical power source (e.g., a signal generator, amplifier, and the like). With reference to
Electrical conductor 214 is disposed to pass through magnetic field 212 in series to conduct a current perpendicular to magnetic field 212. Two sections of electrical conductor 214 passing through magnetic field 212 can be identical. Electrical conductor 214 can be two seriallyconnected coils that are disposed in one of the two radial magnetic fields 212. One sections of electrical conductor 214 in magnetic field 212 (e.g., magnetic field 212) is supported on light and rigid material that supports electrical conductor 214 and transmits force on electrical conductor 214 to external structure 266 or force sensor 268. This piece of material move independently with respect to magnetic field 212 except for support by flexure springs, which locate electrical conductor 214 within magnetic field 212 and are mounted for freedom along a selected axis of operation, e.g., reciprocating direction 228, and provide restraint with respect motion transverse to reciprocating direction 228. Accelerometer 236 can be disposed on the light rigid material to measure reciprocation velocity 222. A portion of electrical conductor 214 disposed in a second area of magnetic field 212 can be rigidly mounted to support material 272. A resistor can be connected in series with electrical conductor 214 and the power source. The voltage measurement circuits can be electrically connected across the resistor to measure alternating current 226. Voltage measurement circuits can be connected across each of the two sections of electrical conductor 214 located in magnetic field 212 to measure voltage.
The resistor, voltage measuring circuit, magnetic field guide 246, or combination thereof can be mechanically connected to remaining components to form a selfcontained device. Control electronics can be integrated in dynamic force contactor 200 such that dynamic force signal 250 is an analog or digital signal indicative of force. An integrated, visible display, e.g., an LCD, or touch screen, can display force. It is contemplated that the resistor or the second magnetic field 212 and associated section of electrical conductor 214 passing therethrough can be physically separated and mechanically decoupled from dynamic force contactor 200.
Dynamic force contactor 200 has numerous advantageous and unexpected benefits and uses. In an embodiment, a process for providing dynamic force 252 includes disposing armature 230 of dynamic force contactor 200 in contact with structure 266 to which dynamic force 252 is applied; providing electrical power to electrical conductor 214, the electrical power including a timevarying amplitude; and reciprocating armature 230 at reciprocation velocity 222 in response to providing electrical power to electrical conductor 214 to provide dynamic force 252 to structure 266.
The process for providing dynamic force 252 further can include measuring the alternating voltage 224, alternating current 226, and the reciprocation velocity 222 which are used to calculate the Lorentzian force 218. In an embodiment, the velocity can be determined with the optical cavity mirror 278 or a light source 238 and light detector 240. Additionally, the acceleration of the housing can be measured with an accelerometer 236, which can be used to apply necessary corrections to the measurements.
In the process for providing dynamic force 252, disposing armature 230 of dynamic force contactor 200 in contact with structure 266, and current source 262 generates alternating current 226 in electrical conductor 214, which interacts with magnetic field 212 to produce a Lorentzian force 218.
In the process for providing dynamic force 252, providing electrical power to electrical conductor 214 can be provided by a current source that is external or internal to dynamic force contactor 200.
In the process for providing dynamic force 252, reciprocating armature 230 at reciprocation velocity 222 can be measured by an optical interferometric technique that can include optical cavity mirror 278. The velocity can also be measured using light source 238 and light detector 240.
In an embodiment, a process for operating dynamic force contactor 200 includes connecting the movable piece of light material supporting electrical conductor 214, e.g., to structure 266 or force sensor 268, such as by contacting armature 230 to structure 266 or fastening dynamic force contactor 200 to structure 266 (wherein a fastener such as a bolt is included in the light material); energizing the electrical power source and providing a selected timevarying waveform to electrical conductor 214; measuring timevarying voltage U1(t) measured across resistor R; determining current flowing in electrical conductor 214 as I(t)=U1(t)/R; and from measurements of voltage across electrical conductor 214 disposed in magnetic field 212, U2(t) and U3(t), determining alternating voltage 224 U(t) induced by motion of first section of electrical conductor 214 as U(t)=U2(t)−U3(t); determining force generated by current flowing through electrical conductor 214 as F(t)=I(t) V(t)/U(t), wherein this force is equal to the force applied to structure 266, F_{app}(t), plus any force F1(t) to accelerate electrical conductor 214 and supporting material and accelerometer 236 as well as force F2(t) that deflects the mounting flexures such that the force generated is F_{app}(t)=F(t)−F1(t)−F2(t). When flexures have negligible stiffness in the direction of motion, F2(t) can be ignored. The process also can include calculating F1(t) from acceleration A(t) measured by accelerometer 236, and known mass M of moving electrical conductor 214, support structure, and accelerometer 236. The process can include determining F_{app}(t)=I(t) V(t)/U(t)−M A(t), wherein, if mass M or acceleration A(t) is sufficiently small, F1(t) is negligible, and F_{app}(t)=I(t) V(t)/U(t).
Dynamic force contactor 200 also can be used to calibrating a force sensor to be metrologically traceable to the international system of units (SI). As used herein, “metrologically traceable” refers to a property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty. In this regard, metrological traceability herein accords with the International Vocabulary of Metrology—Basic and General Concepts and Associated Terms, VIM, 3rd edition, JCGM 200:2008, also published as ISO Guide 99 by ISO (ISO/IEC Guide 9912:2007, International Vocabulary of Metrology—Basic and General Concepts and Associated Terms, VIM (2008). As used herein, “calibration” refers to an operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication. It is contemplated that a calibration can be expressed by a statement, calibration function, calibration diagram, calibration curve, calibration table, and the like and can include an additive or multiplicative correction of the indication with associated measurement uncertainty.
In an embodiment, with reference to
In the process for calibrating force sensor 268 to be traceable to the SI, disposing armature 230 of dynamic force contactor 200 is placed in contact with structure 266 and dynamic force 252 is applied.
In the process for calibrating force sensor 268 to be traceable to the SI, providing electrical power to electrical conductor 214 can be performed with current source 262 that generates alternating current 226 in electrical conductor 214, which interacts with magnetic field 212 to produce Lorentzian force 218.
In the process for calibrating force sensor 268 to be traceable to the SI, reciprocating armature 230 at reciprocation velocity 222 can be measured using optical interferometric techniques that can include optical cavity mirror 278. The velocity can also be measured with light source 238 and light detector 240.
In the process for calibrating force sensor 268 to be traceable to the SI, providing dynamic force 252 to structure 266 can be done by using current source 262 to generate alternating current 226 in electrical conductor 214, which interacts with magnetic field 212 to produce Lorentzian force 218.
In the process for calibrating force sensor 268 to be traceable to the SI, measuring alternating voltage 224 can be done across terminal 300 with a voltmeter that is traceable to the SI, which can be integrated with dynamic force contactor 200 or can be a separate instrument.
In the process for calibrating force sensor 268 to be traceable to the SI, determining alternating current 226 through electrical conductor 214 can be done by using shunt resistor 264 in dynamic force mediator 232.
In the process for calibrating force sensor 268 to be traceable to the SI, determining reciprocation velocity 222 of armature 230 can be measured using optical interferometric techniques that can include optical cavity mirror 278. The velocity can be measured using light source 238 and light detector 240.
In the process for calibrating force sensor 268 to be traceable to the SI, determining dynamic force 252 from reciprocation velocity 222, alternating voltage 224, and alternating current 226 can be calculated using Kibble'"'"'s method, described below.
In the process for calibrating force sensor 268 to be traceable to the SI, determining a calibration response S for force sensor 268 can be done by determining dynamic force 252 applied by dynamic force contactor 200 using Kibble'"'"'s method and by measuring unknown force signal 270. The calibration response is calculated as S=F/O, wherein F is the Fourier Transforms of dynamic force 252, and O is the Fourier transforms of unknown force signal 270.
Dynamic force contactor 200 and processes disclosed herein have numerous beneficial uses, including providing an SI traceable, dynamic force to be simultaneously realized and measured in an environment inside or outside of a laboratory setting, which transfers calibration to a force transducer in its application setting.
Moreover, dynamic force contactor 200 and processes herein have numerous advantageous properties. In an aspect, dynamic force contactor 200 can have a smaller uncertainty than conventional transfer standards. Moreover, dynamic force contactor 200 can calibrate a force transducer to a higher bandwidth than conventional products.
Dynamic force contactor 200 and processes herein unexpectedly provide and measure dynamic force using electrical quantities as a primary standard up to high mechanical frequencies in contrast to conventional transfer standards that are secondary standards.
The articles and processes herein are illustrated further by the following Examples, which are nonlimiting.
Here, dynamic force contactor 200 is a portable dynamic force standard device that generates a mechanical force so that an applied force can be determined through electrical and mechanical measurements. Dynamic force contactor 200 is a portable, dynamic force calibrator that can be used to dynamically calibrate force sensors in the application setting in which they are used. This device overcomes challenges in measuring dynamic forces, namely that a force sensor'"'"'s dynamic calibration response changes depending on the application setting in which it is used.
Dynamic force contactor 200 produces a Lorentz force generated by currentcarrying wire 214 in magnetic field 212 to apply dynamic force 252 to force sensor 268 that can be used to dynamically calibrate force sensor 268 in its application setting. As shown in
With reference to
Dynamic force mediator 232, e.g., as shown in
In this manner, dynamic force contactor 200 determines dynamic force 252. It is contemplated that electrical conductor 214 can be a coil disposed in a uniform radial magnetic field 212 generated by magnet 210 that can be a permanent magnet. Timevarying alternating current 226 I(t) in electrical conductor 214 generates a timevarying axial force on electrical conductor 214 according to
F(t)=BLI(t), (1)
where B is the radial magnetic field and L is the length of electrical conductor 214 in the field. The BL product is determined by measuring alternating voltage 224 U(t) across electrical conductor 214 and reciprocation velocity 222 v(t) of electrical conductor 214 relative to magnetic field 212,
The voltage drop U_{tot}(t) across electrical conductor 214 is the sum
U_{tot}(t)=U(t)+U_{R}(t), (3)
where U_{R }(t) is the drop due to the resistance of electrical conductor 214 (including lead lengths to measurement points) and can be corrected for or rendered negligible.
The force F given by [1] is applied to electrical conductor 214 and is applied to systemundertest (F_{app}) less the force F_{inet }used to accelerate the inertia of armature 230 (electrical conductor 214 plus any additional material in which electrical conductor 214 is embedded) and any parasitic forces F_{par }acting on armature 230 due to connected wires, suspension, and air drag.
F=F_{app}+F_{inet}+F_{par} (4)
The force F_{inet }is given by the product of mass and acceleration of armature 230,
F_{inet}=∫a(r)ρ(r)dr, (5)
where a(r) is the local acceleration and ρ(r) is the local density. The acceleration a can be measured using an accelerometer or interferometer. The mass of armature 230 (and potentially mass distribution) can be known during use of dynamic force contactor 200. Armature 230 can be connected via flexures. Flexible wires can interconnect to electrical conductor 214. For smallamplitude motion of armature 230, F_{par }can be negligible.
With regard to SI traceable measurement or calibration with dynamic force contactor 200, measurement of accelerometer output, voltage of shunt resistor 264, and alternating voltage 224 of electrical conductor 214 can be performed by an external instrument or by a component integrated into dynamic force contactor 200 such as dynamic force mediator 232. Similarly, current source 262 can be an onboard battery or capacitance.
It is contemplated that dynamic force contactor 200 can include different geometries or types of electrical conductor 214 or magnet 210, different ways of measuring reciprocation velocity 222 (including optical methods, such as interferometric measurements in different interferometer configurations), determination of BL product by calculation, different ways of measuring or estimating acceleration of armature 230 and inertial correction, closedloop operation (e.g., feedback on force, velocity, displacement, acceleration, current, voltage or strain amplitudes), handheld vs mechanicallysupported configurations, variations on the force waveforms applied (sine, pulse, chirp, step, random, etc.), various means of measuring or calculating F_{par}, using airbearing support of armature 230 to minimize F_{par}, using inductive or capacitive coupling of the current into electrical conductor 214 to eliminate a wire link between electrical conductor 214 and housing 234, type of wire used for a coil of electrical conductor 214, measuring alternating current 226 other than a sensing resistor, and the like.
Alternating current 226 I(t) can be measured, e.g., by placing an known resistance in series with electrical conductor 214 and measuring alternating voltage 224 across electrical conductor 214. Alternating voltage 224 U_{tot}(t) can be measured by a voltmeter, and alternating current 226 v(t) can be measured by an optical interferometer such as the FabryPerot interferometer, or by accelerometers attached to armature 230 and housing 234. This measurement may be done simultaneously with application of dynamic force 252 and measurement of alternating current 226 or performed in a separate step.
A size of dynamic force contactor 200 can be selected for a particular application and be small enough to be conveniently portable so that dynamic force contactor 200 can apply known forces to calibrate force measurement systems in various locations and configurations. In other words, dynamic force contactor 200 is ported to a working measurement system. It is contemplated, without limitation, that a practical volume and mass for portability of dynamic force contactor 200 is approximately 2 m^{3 }and 50 kg respectively but dynamic force contactor 200 that are smaller in both metrics by an order of magnitude or more are contemplated. An amplitude of can be, e.g., from 1 mN to 1 kN. An applied bandwidth of which can be from 1 mHz to 50 kHz. An uncertainty within this amplitude and bandwidth can be from 0.01% to 10%.
Here, equations are numbered starting again with equation 1, and dynamic force contactor 200 is a portable dynamic force primary standard that uses Lorentz force on a currentcarrying wire in a magnetic field to generate a known force. The device has a size that is effective (e.g., small enough) to be conveniently portable to be used to apply known forces to calibrate force measurement systems in various locations and configurations. The device is taken to the working measurement system and not the other way around although the working measurement system can be taken to the device. With reference to
F(t)=BLI(t), [1]
wherein B is the radial magnetic field, and L is the length of the coil in the field. I(t) is measured, e.g., by placing an accuratelyknown resistance in series with the coil and measuring the voltage drop across it. The BL product is determined by measuring the voltage drop U(t) across the coil and the velocity v(t) of the coil relative to the magnetic field,
BL=U(t)/v(t) [2]
The voltage drop Utot(t) across the coil is the sum
Utot(t)=U(t)+UR(t) [3]
wherein UR(t) is the drop due to the resistance of the coil (including lead lengths to measurement points) and can be corrected for or rendered negligible.
U_{tot}(t) can be measured by a connected voltmeter, and v(t) can be measured by an optical interferometer such as the FabryPerot interferometer shown in
The force F given by equation [1] is applied to the coil and applied to systemundertest (F_{app}) less the force F_{inet }used to accelerate the inertia of the armature (coil plus any additional material in which the coil is embedded) and any parasitic forces F_{par }acting on the armature due to connected wires, suspension, and air drag.
F=F_{app}+F_{inet}+F_{par} [4]
The force F_{inet }is given by the product of mass and acceleration of the armature,
F_{inet}=∫a(r)ρ(r)dr [5]
wherein a(r) is the local acceleration and ρ(r) is the local density. The acceleration a may be measured using an attached accelerometer or an interferometer. The armature mass (and potentially mass distribution) is a previouslydetermined quantity taken to be known during use of the portable standard. As shown in
With reference to
Here, equations are numbered starting again with equation 1, and methods are described that generate high frequency (approximately 10 kHz) SItraceable (International System of Units) dynamic forces using Kibble (watt) balances. Differences between static and highfrequency Kibble balances are discussed. Three potential configurations of Kibble balances for dynamic force metrology, and their relative benefits and drawbacks, are presented. The configurations can be used to design primary dynamic force standards based on Kibble'"'"'s approach that can be used to calibrate force measurement systems in situ. Such standards can be embedded into engineering structures to provide accurate reference force values.
The Kibble or watt balance provides an accurate experimental method for relating macroscopic values of mechanical quantities (e.g., force, mass, acceleration) to electrical quantities (e.g., voltage, current, resistance). Measurements of Planck'"'"'s constant using such balances are a basis for the proposed redefinition of the kilogram. A number of different configurations of Kibble balances have been developed or proposed for static measurements. Our device uses the Kibble balance principle to realize SItraceable (traceable to the International System of Units) forces with frequencies exceeding 10 kHz and uncertainties at or below the percent level.
Traceable dynamic force standards are used for calibrating and testing the accuracy of force measurements in a wide variety of applications, such as material testing, aerodynamic wind tunnel measurements, and automotive crash testing, to name a few. Generally, standards with expanded uncertainties at the level of approximately 1% are used for such applications. Laboratory primary standards have been developed, but uncertainties of such primary systems in the fewpercent range have so far been restricted to frequencies less than 5 kHz. Furthermore, the dynamic sensitivity of an assembled force measurement system is not the same as that of the isolated force sensor, reducing the utility of exsitu calibration of force sensors for dynamic force measurements. Portable or embedded dynamic force standards are needed to calibrate force measurement systems in their operational installations. One such portable dynamic standard is a calibrated force sensor that can be struck against the force measurement system that is to be calibrated, resulting in a common force applied to both devices. By measuring the response of each device, the calibration of the portable standard can be transferred to the application force measurement system. A portable transfer standard of this sort, namely an instrumented hammer, has been calibrated with an uncertainty of less than 2.1% (k=2) up to 5 kHz. However, a portable calibrated force sensor is a secondary standard, as it must itself be traceably calibrated against a primary reference. The dynamic force contactor 200 here is a portable primary standard based on the Kibble principle although dynamic force contactor 200 can be a secondary standard based on a calibration of magnetic field integral against a force standard. Moreover, dynamic force contactor 200 can be integrated into a structure to generate known dynamic forces at a location that is not externally accessible, e.g., including integration with a force transducer as a composite device.
In Kibble balances, a mechanical force (in balances designed to measure mass or Planck'"'"'s constant this is typically the local gravitational force on a mass) is balanced by a Lorentz force
=−I(()×())=−I (1)
where I is the uniform current flowing along a wire (usually in the form of a coil) of length L and differential length element dl, immersed in magnetic field of flux density B. The accurate determination of the value of this BL integral is the main challenge in applying the Lorentz force law for accurate measurements. Kibble evaluated BL from induced voltage UE generated across the wire when it is moved at velocity V through the magnetic field,
U_{g}=·(()×())=· (2)
Thus, measuring voltage UE, velocity V, and current I gives the force F in the direction of BL with magnitude F according to:
where θ is the angle between the BL and V vectors, and BL≡UE/V is the magnitude of BL. For a remainder of the Example, vector notation is dropped and reference is made to magnitudes F, U, V, and BL.
Demonstrated relative uncertainties of SItraceable dynamic forces that have bandwidths in the 1 kHz to 5 kHz range are a few percent. The dynamic force contactor 200 has a percentlevel uncertainty and operates at frequencies up to 10 kHz or above. This contrasts with static Kibble balances that determine Planck'"'"'s constant or realize mass with relative uncertainties at the level of 1×10^{−6}.
With the electrical current I(t) varying at kilohertz frequencies, dynamic impedances, particularly coil inductances, are critical. Similarly, the realized Lorentz force may not be the force applied to the target structure because of mechanical filtering effects. The difference between the applied force F_{app }and the force realized by equation (1) F is shown in
F_{app}=F−m_{a}{umlaut over (x)}_{a}−k_{f}(x_{a}−x_{b})−c_{f}({dot over (x)}_{a}−{dot over (x)}_{b}), (5)
where F is the force realized by equation (1), Fapp is the force applied to the structure, ma is the lumpedparameter mass of the armature, kf is the stiffness of the flexures, and xa and xh are the respective positions of the armature and housing of the device. The second term on the righthand side is a correction of the realized force F due to the inertia of the armature, the third term is a correction for the flexure stiffness, and the last term accounts for dissipation from the flexures. This model assumes that the armature has an internal fundamental resonance frequency that is much higher than the frequency range of interest. If the dynamics of the armature significantly affect the response, then a higherorder model, such as a three DOF system (shown in
A difference between static and dynamic operation is the ability to operate in a simultaneous mode in the dynamic case, wherein current, voltage, and velocity are measured at the same time. Thus, BL can be measured at any instant of time. Time variation of BL, due, e.g., to coil motion in a nonuniform B field, is not a source error. The uncertainty associated with BL can depend upon measured values of UE and V, which are functions of time.
Configurations dynamic force contactor 200 as Kibble balance dynamic force standards are discussed with regard to a portable dynamic force standard, but configurations can be inserted into a measurement system such as that shown in
With regard to a single coil with dynamically calibrated BL configuration, a single coil disposed in a magnetic field generates a known force. Here, BL is calibrated in a first measurement, and during subsequent use of the device, the current I is measured to determine force via equation (1). The calibration of BL can be done by using an external device to translate or oscillate the armature with the coil open circuited, while measuring V and UE. The calibration of BL can also be performed with the coil stationary, using a statically calibrated force transducer or deadweights to measure the applied force generated by a measured current I and using equation (1). Here, the Kibble principle plays no role, and the device is just a calibrated voice coil actuator.
An exemplary design is shown in
An advantage is the simplicity of the force measurement, as the prior calibration of the BL product avoids making measurements of voltage UE and velocity V during the force realization. The value of the BL product can be characterized as a function of coil position, as well as angular rotations, and can contribute to uncertainty of the realized force. As such, a magnet and coil geometry that subjects the coil to a highly uniform and radial magnetic field, such as employed in high precision Kibble balances, can be used. Likewise, slower temporal variation of the BL product, e.g., due to the effect of temperature changes, can contribute to uncertainty.
With regard to a dual coil with dualmode (nonsimultaneous) operation, a dynamic extension of Kibble balances is used for static highprecision applications, wherein the measurements of V (t), U(t), and I(t) are performed in separate phases, with a second coil being used to drive the force generation coil at an optimal velocity in the BLproduct determination phase. This configuration has the advantage that incorporating the drive mechanism into dynamic force contactor 200 makes it easier to calibrate the BL product closer in time and under similar conditions (e.g., the same temperature) as when the force is realized. Moreover, the BL product can be measured before and after the force realization to check for any changes. Although this mitigates slow temporal variations in the BL product, the spatial dependence can be characterized. An armature structure is shown in
With regard to dual coil with singlemode (simultaneous) operation, simultaneous measurement with a bifilar coil reduces resistive voltage drop. Dynamic force contactor 200 can include two nominallyidentical coils with approximately equal complex impedances Z_{coil1 }and Z_{coil2}. The two coils are arranged in series so that the same current flows through each coil, resulting in approximately equal resistive and inductive voltage drops. Coil 1 includes the armature of the device, is suspended by flexures, and oscillates under action of the Lorentz force on the current in the radial magnetic field, developing induced voltage UE. Coil 2 is fixed and develops no induced voltage. Thus, the voltage drops across the coil are largely canceled by a differential measurement, leaving only the induced voltage drop across coil 1. The induced voltage UE is determined from the difference between the measured voltages U1 and U2 as,
U_{g}=U_{1}−U_{2}−ΔU_{Z12}, (6)
where ΔU_{Z12}=IΔZ_{12 }corrects for impedance mismatch between the two coils. The coils are disposed in matched magnetic fields that are achieved by symmetrical construction and selection of matched permanent magnets. Application of the magnetic field to the second coil matches operating points on the nonlinear permeability curves of the pole pieces. Furthermore, both coils are mounted in the device body, which minimizes temperature difference between the two core assemblies that might cause differential magnetization of the permanent magnets and differential permeability of the cores. An alternative design disposed the second coil outside of dynamic force contactor 200, connected by a cable.
With regard to estimated uncertainty, the force uncertainty of dynamic force contactor 200 can depend on values of measured quantities, which can depend on Kibble balance design and mechanical properties of the system to which the balance is coupled.
An uncertainty of the AC current measurement has an expected relative uncertainty of approximately 0.5% at 10 kHz for current amplitudes in the 0.1 A to 1 A range. Another contribution is internal dynamics of the armature. The armature can have a fundamental longitudinal internal resonance above 10 kHz such that the force correction due to the internal dynamics is below 10%. We can calculate such corrections with approximately 5% uncertainty, resulting in an overall uncertainty contribution of approximately 0.5%. Spatial and temporal variation of the magnetic field will contribute to the uncertainty for configurations in
Dynamic force transducers can be designed based off the above description. Devices discussed here have the advantage of being selfcalibrating and can be installed in the host measurement structure and then calibrated in that setting. The dynamic force contactor 200 can be integrated into conventional force transducers, as shown in
Additionally, dynamic force contactor 200 that includes active feedback control to generate a current to balance or compensate for an applied force by keeping the armature at a fixed position is shown in
The dynamic force contactor 200 provides Kibble balances for dynamic force metrology that provide primary dynamic forces directly to a system of interest. Uncertainties on the dynamic force output from dynamic force contactor 200 are smaller than conventional force standards. The dynamic force contactor 200 can be constructed at different scales for applications at various force amplitude scales. For dynamic force contactors 200 that have armatures and coils with sufficiently small mass, e.g., less than approximately 100 grams, bandwidths up to 10 kHz occur. For a oneNewton sinusoidal standard, uncertainties at the percent level or better occur.
Here, equations are numbered starting again with equation 1, and dynamic force contactor 200 is described as being a dynamic force standard based on principles of the Kibble (watt) balance. The dynamic force contactor 200 provides lowuncertainty traceable dynamic forces over a wide frequency range. The dynamic force contactor 200 determines force from simultaneous measurement of voltage, velocity and current. The dynamic force contactor 200 can operate with only a current measurement, based on a calibrated BL integral. For a dynamic force contactor 200 that produces a 10newton force amplitude, an uncertainty below 1% can be achieved for operating frequencies exceeding 10 kHz. This dynamic force contactor 200 provides an accuratelyknown dynamic force for calibration of systems for measuring dynamic forces such as forces varying as fast as or faster than the settling time of the force measurement system.
The dynamic force contactor 200 generates SItraceable forces up to high frequencies with uncertainties at or below the percent level. At this level of uncertainty, it is believed that measures and corrections taken in Kibble balances designed for extremeaccuracy measurements are unnecessary, and high operating frequency achieves percentlevel uncertainty.
Traceable dynamic force standards are needed for calibrating and testing the accuracy of force measurements in a wide variety of applications, such as material testing, aerodynamic wind tunnel measurements, and automotive crash testing. Conventional primary standards are not easily applied to force measurement systems in the field. A dynamic sensitivity of an assembled force measurement system is not the same as that of the isolated force sensor, limiting the utility of external calibration of force sensors for dynamic force measurements. The dynamic force contactor 200 overcomes these problems and provides a portable dynamic force standard to calibrate force measurement systems in their operational installations. A conventional calibrated force sensor that can be struck against the force measurement system that is to be calibrated results in a common force applied to both devices, but this conventional device is a secondary standard because it must be traceably calibrated, allowing transfer of the calibration from a primary standard to a working system. In contrast, the dynamic force contactor 200 herein advantageously is a primary standard that can be used to directly calibrate so that it can be a secondary standard.
In Kibble balances, a mechanical force in balances designed to measure mass or Planck'"'"'s constant this is typically the gravitational force is balanced by a Lorentz force
=−()⊗I()d=I, (1)
where I is the current flowing in a wire (usually in the form of a coil) of length L and differential length element , immersed in magnetic field of flux density . The accurate determination of the value of this integral is the main challenge in application of the Lorentz force law to accurate calibration, and Kibble evaluated this from the induced voltage U generated across the wire when it is moved at velocity V through the magnetic field,
U=·()⊗()d=·. (2)
The dynamic force contactor 200 has an axial force component, e.g., the component present in a geometry. Thus, measuring voltage U, axial velocity component V and current I gives the axial force magnitude F according to
where the timedependence of the physical quantities has been explicitly indicated. At an angular frequency ω,
where {tilde over (F)}, Ũ, Ĩ and {tilde over (V)} are complex amplitudes. The dynamic force contactor 200 can operate based on these relations.
An alternative to using the dynamic force contactor 200 as a Kibble balance (i.e., using equation 3 or 4 of this Example) is to calibrate the integral (e.g., using a static force measurement) and then use equation (1) with only a current measurement. Such a calibration can be performed at DC, using a statically calibrated force transducer or deadweights. While such a prior measurement of the integral removes the need to make accurate measurements of voltage U and velocity V, it introduces effects of spatial variation of the integral as a function of coil position and of temporal variation of the integral due for example to the effect of temperature changes. Nevertheless, with dynamic force contactor 200 to provide a sufficiently spatially uniform integral it can be an attractive mode of operation for force uncertainty at the 1% level. Attention is paid to Kibble balance operation, i.e., operation based on equations (3) and (4). Furthermore, sinusoidal force waveforms are involved, and the dynamic force contactor 200 can be a force calibration tool.
Table 1 provides values of device parameters and operating dynamic variables over the frequency range 10 Hz to 10 kHz for dynamic force contactor 200.
An example design of dynamic force contactor 200 is shown in
A resistive and inductive voltage drops across the coil can occur. A bifilar coil can eliminate the resistive voltage drop but not the inductive voltage drop. While the resistive and induced voltages are 90 degrees out of phase, allowing phasesensitive detection to separate them, the inductive voltage drop is 180 degrees out of phase with the induced voltage and not separable. The dynamic force contactor 200 can include two nominally identical coils with approximately equal resistances R_{coil1}, R_{coil2 }and approximately equal inductances _{coil1}, _{coil2}. The two coils are arranged in series so that the same current flows through each coil, resulting in approximately equal resistive and inductive voltage drops. Coil 1 is disposed proximate to the armature of, is suspended by flexures, and oscillates under action of Lorentz force on the current in the radial magnetic field, developing induced voltage U. Coil 2 is fixed and develops no induced voltage. Thus, the inductive and resistive voltage drops across the coils are largely cancelled by a differential measurement, leaving the induced voltage drop across coil 1.
The induced voltage U is related to the measured voltage U_{meas }by
U=U_{meas}−ΔU_{R}−Δ, (5)
and the applied force F is related to the coil current I and measured voltage U_{meas }by
wherein ΔU_{R}=I(R_{coil1}−R_{coil2}) is the residual resistive voltage drop; Δ=i2πfI(_{coii1}−_{coil2}) is the residual inductive voltage drop at excitation frequency f; F_{inet }is the force required to accelerate the armature inertia, and F_{par }is the parasitic force applied to the armature by support flexures, connected wires, and air drag.
The coils are subjected to matched radial fields, achieved by symmetrical construction and selection of matched permanent magnets; the application of the radial field to the second inductor is done in order to match the operating points on the nonlinear permeability curves of the inductor cores. Furthermore, the coils are mounted together in the housing of dynamic force contactor 200, which minimizes temperature differences between the two core assemblies and which would otherwise create differential magnetization of the permanent magnets and permeability of the cores. Alternatively, the second coil could be disposed external to dynamic force contactor 200 and connected to dynamic force contactor 200 by a cable.
An electrical model of dynamic force contactor 200 is shown in
wherein ΔZ is the impedance difference between the coils and i=√{square root over (−1)}. In the limit that C_{1 }and C_{2 }go to zero, ΔZ reduces to ΔR+iωΔL where ΔR≡R_{2}−R_{1 }and Δ≡_{2}−_{1}. In practice, a process for calibrating the impedance difference ΔZ(ω) includes holding coil 1 fixed (in addition to coil 2) so that U=0 V, for which case ΔZ=U_{meas}/I. If temporary clamping of coil 1 is less rigid than the permanent fixation of coil 2, a small current value can be used in this calibration to minimize motion of coil 1 due to deformation of the clamping mechanism. The capacitances across the coils result in a difference between the current I_{1 }in coil 1, which generates the force F, and the total (measured) current I
and in a difference between the currents in the two coils, I_{1 }and I_{2},
With calibration of ΔZ(ω), which includes the capacitances C_{1 }and C_{2}, this current difference is not a source of error in the determination of U. However, capacitances C_{1}, C_{2}, and C_{L }introduce error into the measurement of the forcegenerating current I_{1}. Additionally, _{L }will introduce a (frequencydependent) phase offset between the measured current I and the force generating current I_{1}. For the remainder of this Example, neglect capacitances and _{L }such that Equation (6) becomes
U_{meas}=U+I(ΔR+iωΔ). (10)
Mechanical behavior of dynamic force contactor 200 can be determined by the mechanical system to which it is coupled, e.g., a system under test (SUT). A mechanical model of the device coupled to an SUT with an internal degree of freedom is shown in
A number of degrees of freedom of SUT may vary from zero up to tens or higher, and quantitative mechanical properties (e.g., mode resonant frequencies and quality factors) can vary from one SUT to another. The model shown in
The equations of motion for x_{s}, the displacement of the SUT, x_{1}, the displacement of the armature, and x_{b}, the displacement of the device body, are
m_{1}{umlaut over (x)}_{1}+b_{a}({dot over (x)}_{1}−{dot over (x)}_{s})+k_{a}(x_{1}−x_{s})=F (11)
(m_{2}+m_{s}){umlaut over (x)}_{s}−b_{a}({dot over (x)}_{1}−{dot over (x)}_{s})+b_{s}{dot over (x)}_{s}−k_{a}(x_{1}−x_{s})+k_{s}x_{s}=0 (12)
m_{b}{umlaut over (x)}_{b}=F_{R}−F (13)
Solving these in the frequency domain gives
The quantities plotted in
The induced voltage U is proportional to the relative velocity V (equation (2)) plotted in
In
wherein φ_{meas }is the phase of U_{meas}. Alternatively, since U and velocity V are in phase,
wherein φ_{V }is the phase of the measured velocity. Thus, determining the amplitude of U requires (equation 18) knowing the phase of U_{meas }with respect to the current I, or (equation 19) knowing the phases of U_{meas }and V with respect to the current I. This would be provided for example by synchronous sampling of U_{meas }and I (and V in the case of equation (19)).
The expressions for the phase φ_{U }of U corresponding to equations (18) and (19) respectively are
The equality of the righthand sides of equations (20) and (21) can be used as a check of the accuracy of measurements and validity of assumptions. Equivalently to (21), the total phase of the righthand side of equation (19) should be zero.
At sharp antiresonances in the bodyarmature relative motion, the relative velocity and induced voltage vanish, and large uncertainties result from using the fully insitu Kibble balance method. At such operating points the force can be determined by the “quasi insitu” approach of extracting the integral (using equations 2 and 5) from the measurements of current, velocity and voltage at other frequencies, and then using equation 1 to determine the force at and around the antiresonance, with an uncertainty contribution from the possible variation of the effective integral with operating point.
Extracting the amplitude of the induced voltage U from the amplitude of the measured voltage U_{meas }requires a phase measurement, the minimum requirement being a measurement of φ_{meas}, the phase of the measured voltage relative to the excitation current. In a force calibration of a SUT, it will often be desired to know the phase of an output signal from the SUT with respect to the force F_{app }applied to it. It may appear that to determine the Lorentz force F (amplitude and phase) applied to the armature by the magnetic field using equation (3) or (4), that the relative phases of U, I and V must be measured. However, since the current I is in phase with F, and the induced voltage U is in phase with the relative velocity V, F=UI/V=U∥I/V and only the amplitudes of the three input quantities are measured to give the amplitude of F. The phase of F (with respect to the current I) is zero. To determine the force F_{app }applied to the SUT, corrections to F for the armature inertia and parasitic forces are applied as indicated by equation (6), and these will in general include a phase correction.
In addition to measuring the phase of U_{meas }with respect to the excitation current, additional phase measurement in determining the phase response of the SUT output signal is that of the SUT output signal with respect to the excitation current. Analytical knowledge of the phase difference between F and F_{app }can occur at some frequencies.
A location of resonant features can vary from one SUT to another. The achieved force uncertainty as a function of frequency can dependent on mechanical properties of the SUT can be determined in the calibration as a function of the electrical and mechanical measurements made.
With regard to uncertainty, equation (6) is repeated here as equation (22) for convenience.
Quantities measured during operation of dynamic force contactor 200 include voltage U_{meas}(t) across the coils, voltage U_{s}(t) across a currentmeasuring shunt resistance, relative velocity V(t) of the armature with respect to the body, acceleration a_{B}(t) of the body, and operating frequency ω. Quantities that are characterized offline are the residual differential resistance ΔR and inductance Δ, the currentmeasuring shunt resistance Rs, the armature and body masses m_{1}, m_{2 }and m_{b}, and the stiffness K of the armature support flexures. The current I(t) is determined as I=U_{s}/R_{s}. The inertial offset F_{inet}(t) due to the armature acceleration is determined as F_{inet}=m_{1 }a_{1}+m_{2 }a_{2}=m_{1}(iωV+a_{B})−m_{2}ω^{2}X_{S}(ω). The parasitic restoring force of the flexures is calculated as K X(t), where the relative displacement X(t) of the armature with respect to the body is determined as X(t)=V(t)/ω. We do not correct for additional parasitic forces (e.g. due to wires and air), but treat these as an uncertainty δF_{par2 }equal to an estimated upper bound for such forces. Rewriting the measurement equation in terms of these quantities gives
Assuming these measurements to be uncorrelated, the uncertainty in the applied force is given as
In operation of dynamic force contactor 200, X_{S}(ω) can be calculated from a model (X_{1}(ω) is determined from the measured V(ω) and a_{B}(ω), to which the modeled X_{S}(ω)−X_{1}(ω) given by equations (14) and (15) is added). Thus δX_{S }in equation (24) has many contributions. The second column of Table 2 lists expressions for sensitivity coefficients in equation (22), and the third column of Table 2 lists a range of the corresponding force uncertainty contributions for the system modeled.
The largest contribution to the force uncertainty over most of the frequency range 10 Hz to 10 kHz is due to the uncertainty in the sensing resistance used to measure the current. The uncertainty in this resistance is estimated as 0.2%, including the effects of temperaturesensitivity of the resistance. Apart from reducing the uncertainty of the resistance, this uncertainty contribution can be lowered by operating the device at a higher force level, and hence a higher relative velocity V.
The dynamic force contactor 200 is a highbandwidth force standard that can be coupled to working force measurement systems. Although an exemplary 10 N force amplitude was used in this Example, dynamic force contactor 200 can operate at other frequencies, e.g., up to ˜10 kHz, and dynamic force contactor 200 can be sized for different force amplitudes and frequency ranges. It is contemplated that dynamic force contactor 200 can be disposed temporarily or permanently into a mechanical system, e.g., a body that is rigidlycoupled into the mechanical system in which the force measurement is being made. Although this Example describes operation of dynamic force contactor 200 at a fixed Lorentz force amplitude, achieved by holding the excitation current amplitude fixed, alternatively, a different quantity could be held constant. Feedback from SUT acceleration to the supply current could be used to keep the SUT displacement amplitude constant to avoid damage.
While one or more embodiments have been shown and described, modifications and substitutions may be made thereto without departing from the spirit and scope of the invention. Accordingly, it is to be understood that the present invention has been described by way of illustrations and not limitation. Embodiments herein can be used independently or can be combined.
Reference throughout this specification to “one embodiment,” “particular embodiment,” “certain embodiment,” “an embodiment,” or the like means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of these phrases (e.g., “in one embodiment” or “in an embodiment”) throughout this specification are not necessarily all referring to the same embodiment. Furthermore, particular features, structures, or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.
All ranges disclosed herein are inclusive of the endpoints, and the endpoints are independently combinable with each other. The ranges are continuous and thus contain every value and subset thereof in the range. Unless otherwise stated or contextually inapplicable, all percentages, when expressing a quantity, are weight percentages. The suffix “(s)” as used herein is intended to include both the singular and the plural of the term that it modifies, thereby including at least one of that term (e.g., the colorant(s) includes at least one colorants). “Optional” or “optionally” means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where the event occurs and instances where it does not. As used herein, “combination” is inclusive of blends, mixtures, alloys, reaction products, and the like.
As used herein, “a combination thereof” refers to a combination comprising at least one of the named constituents, components, compounds, or elements, optionally together with one or more of the same class of constituents, components, compounds, or elements.
All references are incorporated herein by reference.
The use of the terms “a” and “an” and “the” and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. “Or” means “and/or.” Further, the conjunction “or” is used to link objects of a list or alternatives and is not disjunctive; rather the elements can be used separately or can be combined together under appropriate circumstances. It should further be noted that the terms “first,” “second,” “primary,” “secondary,” and the like herein do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. The modifier “about” used in connection with a quantity is inclusive of the stated value and has the meaning dictated by the context (e.g., it includes the degree of error associated with measurement of the particular quantity).