CN106053270A - Experiment device and method for measuring Young modulus of metal wire according to simple harmonic vibration - Google Patents

Abstract

The invention discloses an experiment device and method for measuring the Young modulus of a metal wire according to simple harmonic vibration, relates to a Young modulus measuring device and method, and aims to solve the problems that in the conventional university physical experiments, the experiment principle for measuring metal wire Young modulus is single and abstract, and the telescope is hard to adjust. The device comprises a crossbeam, which is arranged on the upper end of a support. An upper clamping head and a force sensitive sensor are arranged on the middle of the crossbeam. Two ends of a metal wire are respectively connected to the force sensitive sensor and a lower clamping head. The lower clamping head and a metal frame are fixed together, and an iron block is fixed in the metal frame. An electromagnet device is arranged under the metal frame. A measuring device is composed of a Hall element, a measurement controller, a Hall voltage amplifying device, and a digital oscilloscope. The period of Hall voltage waveform with periodic changes is measured by the digital oscilloscope to obtain the period of a metal wire spring oscillator that performs simple harmonic vibration, and finally the period of metal wire spring oscillator is substituted into a formula to calculate the Young modulus of the metal wire. The provided method is suitable for measuring the Young modulus of a metal wire.

Description

A kind of experimental provision and method surveying tinsel Young's modulus according to simple harmonic oscillation

Technical field

The present invention relates to a kind of Experiment of College Physics device, be specifically related to a kind of according to simple harmonic oscillation survey tinsel Young The experimental provision of modulus and method.

Background technology

Under external force, the change of shape that solid is occurred, referred to as deformation.It can be divided into elastic deformation and plastic deformation Two classes.External force removes the complete restorable deformation of energy of rear object, referred to as elastic deformation.If the external force mistake being added on object Greatly, so that after external force is removed, object can not restore to the original state completely, and leaves residual deformation, the most referred to as plastic deformation.In this reality In testing, only study elastic deformation.To this end, the size of external force should be controlled, with ensure this external force remove after object resilient. Simplest deformation is bar-like object (or tinsel) by the elongation after external force and shortening.If an a length of L of object, sectional area is S, Along its length after force F, object elongation (or shortening) is Δ L.Ratio F/S is the active force in unit are, is referred to as stressing, Which determine the deformation of object；Ratios delta L/L is the specific elongation of object, referred to as strain, and it represents the size of object deformation.Press According to Hooke's law, the elastic limit internal stress at object is directly proportional to strain, proportionality coefficientIt is referred to as Young Modulus.

Experiment shows, Young's modulus is unrelated with the size of external force F, length L of object and sectional area S, and is solely dependent upon rod The material of (or tinsel).Young's modulus is to describe an important mechanics parameter of solid material elastic deformation ability, is selected One of foundation of mechanical component material, is parameter conventional in engineering.No matter it is elastomeric material, such as various metal materials, Or fragile material, such as glass, pottery etc., or other various new materials, such as fiberglass, carbon fibre composite etc., for Ensure the use of normal safe, will measure their Young's modulus.For a long time, the Young's modulus measuring material is generally adopted Use static stretch method, typically carry out on universal testing machine.This method load is big, and loading velocity is slow, there is relaxation mistake Journey, can increase measurement error, and be difficult to fragile material measure, and measures also inconvenient under condition of different temperatures.20th century The eighties, there are people's laser-holographic interferometry and laser speckle photography method that the Young's modulus of the carbon composite of aerospace field is entered Row is measured, and carrys out the impact on Young's modulus of the research material defect with this, achieves good effect.The nineties in 20th century, power Learn Young's modulus measuring method i.e. hang wire flexural resonance method to recommend to perform as national technical standard.This method can be Measure the Young's modulus of various material in the range of bigger high/low temperature, and certainty of measurement is higher.Static method except static stretch method, Also have static twist method, the method for Static bending etc.；Dynamic method except lateral resonance, also longitudinal resonance, torsional resonance etc..Additionally also Wave speed measurement method can be used, utilize continuous wave or impulse wave to measure Young's modulus.

Although kinetics Young's modulus measuring method i.e. hang wire flexural resonance method has many good qualities, but due to theory Formula is complicated, and principle is the most readily understood, and equipment is the most more complicated, and experiment difficulty is big, therefore in Experiment of College Physics at present frequently with Static stretch method surveys tinsel Young's modulus, measures Chroococcus minutus Δ L wiry according to optical lever amplification principle, in recent years Also there are the some other more advanced micro-displacement measurement method of employing, such as current vortex sensor method, Michelson interference Instrument method, optical fibre displacement sensor method etc. measure Chroococcus minutus Δ L wiry, thus calculate tinsel Young's modulus. At present in Experiment of College Physics, the experimental project of Module by Stretching silk Young's modulus is primarily present following deficiency:

One, generally uses static stretch method to survey tinsel Young's modulus, and principle is more single.

Its two, according to optical lever amplification principle, the amplification system consisted of optical lever, telescope and scale measures metal The Chroococcus minutus of silk, although method is ingenious, but principle is more abstract, the most readily understood, and telescopical regulation difficulty is bigger, Points for attention are the most, and directly utilize telescope to carry out observing measurement by human eye, are very easy to fatigue, easily by data Mistake, affect the accuracy of measurement result.

Its three, general use counterweight to apply pulling force to tinsel, calculate pulling force with the nominal mass of counterweight inaccurate, thus Affect the accuracy of experimental result.

Summary of the invention

In order to overcome the above-mentioned deficiency of prior art, the present invention proposes a kind of according to simple harmonic oscillation survey tinsel Young's modulus Experimental provision and method, experimental principle of the present invention is easily understood, and wire spring oscillator is done simple harmonic quantity and shakes by described experimental provision Dynamic cycle T, is converted to the cycle T of periodically variable Hall voltage, through Hall voltage amplifying device by Hall element After amplification, waveform shows on digital oscilloscope, observes the waveform of Hall voltage, measures its cycle T, and experimental phenomena is straight See, observe with measure more convenient.The wire spring oscillator using electromagnet apparatus to make iron block and tinsel constitute does simple harmonic quantity Vibration, easy to operate.Measure pulling force size suffered by tinsel by force-sensing sensor, and measure display screen by force-sensing sensor Show, can conveniently monitor pulling force suffered by tinsel, it is to avoid exceed elastic limit；By surveying wire spring oscillator lower end institute The gravity suffered by object of system, and then obtain its quality m, accurately facilitate.

The present invention solves the experimental provision of the foundation simple harmonic oscillation survey tinsel Young's modulus that its technical problem is used: Being included on bracket base and arrange support, pedestal upper end arranges crossbeam, arranges upper grip and force-sensing sensor, metal in the middle of crossbeam Silk one end is connected with upper grip and force-sensing sensor, and the other end is connected with lower chuck, and lower chuck and a metal framework are fixed on one Rise, fix an iron block inside metal framework, electromagnet apparatus is set below metal framework.Force-sensing sensor is quick with power by interface Sensor measurement controller is connected, and force-sensing sensor is used for measuring pulling force size suffered by tinsel, and can pass through force-sensing sensor Measurement display screen shows.Electromagnet apparatus is used for applying pulling force in iron block to tinsel by magneticaction, then discharges, So that the iron block being fixed together and metal framework do simple harmonic oscillation under tinsel effect, and electromagnet apparatus work can be passed through Make current adjusting knob regulation pulling force size.The identical four blocks of Magnet of specification are symmetrically disposed in metal framework side, can Moving up and down with metal framework, Hall element is made up of Hall element, two blocks of Magnet and Hall element Mersure Controler, Hall Element is arranged on fixture, and fixture is rack-mount, and fixture can move to change position along support, and Hall element passes through interface It is connected with Hall element Mersure Controler, can be big by electric current in Hall element operating current adjusting knob regulation Hall element Little, the Hall voltage at Hall element two ends can be shown by Hall element voltage display screen, Hall element Mersure Controler Being connected with Hall voltage amplifying device by interface, Hall voltage amplifying device is connected with digital oscilloscope by interface, numeral The waveform of the Hall voltage after being amplified by Hall voltage amplifying device can be shown by oscillograph, observes and surveys Amount.

The experimental provision survey tinsel Young's modulus surveying tinsel Young's modulus according to simple harmonic oscillation of the present invention Experimental technique, the detailed process of the method comprises the following steps:

Step one, by observe bracket base level gauge, the bracket base leveling serew on adjusting pole base, make support Base level；

Step 2, along support movable clamp, make Hall element be positioned at Magnet three and the centre of Magnet four, by Hall element Size of current regulation suitable, observe the Hall voltage size at Hall element two ends, carefully adjust the position of Hall element, make suddenly Your voltage is zero, and now Hall element is located just at Magnet three and the middle of Magnet four；

Step 3, make electromagnet apparatus work, apply pulling force in iron block to tinsel by magneticaction, by regulation electricity Magnet arrangement operating current, makes pulling force size to fit, then makes electromagnet apparatus quit work, so that the ferrum being fixed together The wire spring oscillator that block and metal framework and tinsel are constituted starts to do simple harmonic oscillation, drives at iron block and metal framework Under, Magnet three and Magnet four do simple harmonic oscillation the most up and down, and the magnetic induction suffered by Hall element the most periodically becomes Change, so that the Hall voltage at Hall element two ends the most periodically changes；

Step 4, this periodically variable Hall voltage are after Hall voltage amplifying device amplifies, and waveform is in numeral oscillography Show on device, observe the waveform of Hall voltage, measure its cycle T, the iron block being i.e. fixed together and metal framework and gold The wire spring oscillator belonging to silk composition does the cycle T of simple harmonic oscillation；

Step 5, make wire spring oscillator stop vibration, treat stable after, measure tinsel institute by force-sensing sensor By pulling force size, and shown by force-sensing sensor measurement display screen, it is simply that the thing of wire spring oscillator lower end direct bearing Gravity suffered by body, and then its quality m can be obtained；

Step 6, measure length L wiry between force-sensing sensor and lower chuck with meter ruler, measure tinsel with micrometer Diameter d, and calculate its sectional area

Step 7, by length L wiry, sectional area S, quality m of wire spring oscillator lower end direct bearing object, and Wire spring oscillator does the cycle T of simple harmonic oscillation and substitutes into formulaYoung's modulus Y wiry can be obtained.

Theoretical basis according to simple harmonic oscillation survey tinsel Young's modulus:

If an a length of L of tinsel, sectional area is S, and Young's modulus is Y, applies pulling force F, wire elongation along its length Amount is the active force in unit are for Δ L, ratio F/S, is referred to as stressing, which determines deformation wiry；Ratios delta L/L is Specific elongation wiry, referred to as strain, it represents the size of tinsel deformation.According to Hooke's law, in elasticity wiry Limit internal stress is directly proportional to strain, proportionality coefficient i.e. Young's modulus Y, i.e.

$\frac{F}{S}=Y\·\frac{\mathrm{\Δ}L}{L}---\left(1\right)$

(1) formula is become

$F=\frac{YS}{L}\·\mathrm{\Δ}L---\left(2\right)$

According to (2) formula as, this tinsel can be regarded a coefficient of elasticitySpring.This wire spring is erected Directly hanging, the object that a mass is m is fastened in lower end, then wire spring and this object constitute a wire spring oscillator, and giving should System applies certain pulling force, then discharges, then in the vertical direction is done simple harmonic oscillation by object, and its cycle can be by spring oscillator Period Formula is obtained, i.e.

$T=2\mathrm{\π}\sqrt{\frac{m}{k}}---\left(3\right)$

By the coefficient of elasticity of wire spring(3) formula of substitution, can do simple harmonic oscillation by this wire spring oscillator Time cycle be

$T=2\mathrm{\π}\sqrt{\frac{Lm}{YS}}---\left(4\right)$

According to (4) formula, Young's modulus Y wiry can be obtained, i.e.

$Y=\frac{4{\mathrm{\π}}^{2}Lm}{T^{2}S}---\left(5\right)$

According to (5) formula, as long as measuring length L wiry, sectional area S, the object that wire spring oscillator lower end is fastened Quality m, and cycle T when wire spring oscillator does simple harmonic oscillation, it is possible to substitute into formula and obtain Young wiry Modulus Y.

The invention has the beneficial effects as follows:

One, the present invention proposes a kind of new method surveying tinsel Young's modulus according to simple harmonic oscillation, and the method is with logical Frequently with the static stretch method surveying tinsel Young's modulus to there is essence different, and the experimental principle of the method institute foundation The simplest, it is simply that common mass-spring model, high school physics class just has been directed to correlation formula, in course of University Physics also There is detailed analysis, be easily understood.If this invention be incorporated in Physical Experiments, it is remarkably contributing to abundant university thing Reason experiment content, the thinking of open student, the initiative spirit of training student, strengthen student and use knowledge to solve the energy of problem flexibly Power.

Its two, the present invention propose according to simple harmonic oscillation survey tinsel Young's modulus experimental provision the most uncomplicated, Improve a little on the basis of existing experimental provision, be easier to realize.

Its three, wire spring oscillator is done the cycle T of simple harmonic oscillation by the experimental provision that the present invention proposes, and is passed by Hall Sensor is converted to the cycle T of periodically variable Hall voltage, and after Hall voltage amplifying device amplifies, waveform is in numeral oscillography Showing on device, observing the waveform of Hall voltage, measure its cycle T, experimental phenomena is directly perceived, observe with measure more convenient.

Its four, the experimental provision that the present invention proposes uses electromagnet apparatus to make the wire spring that iron block and tinsel are constituted Oscillator does simple harmonic oscillation, easy to operate.

Its five, the experimental provision that the present invention proposes measures pulling force size suffered by tinsel by force-sensing sensor, and leads to Cross force-sensing sensor measurement display screen to show, can conveniently monitor pulling force suffered by tinsel, it is to avoid exceed elastic limit；Pass through Survey the gravity suffered by object of wire spring oscillator lower end direct bearing, and then obtain its quality m, accurately facilitate.

Accompanying drawing explanation

The present invention is further described with embodiment below in conjunction with the accompanying drawings.

Accompanying drawing is the structural representation of the present invention.

1. crossbeam in figure, 2. upper grip, 3. force-sensing sensor, 4. support, 5. bracket base leveling serew, 6. bracket base Level gauge, 7. bracket base, 8. force-sensing sensor Mersure Controler, 9. force-sensing sensor measures display screen, 10. force-sensing sensor Zeroing knob, 11. force-sensing sensors measurement startup buttons, 12. tinsels, 13. lower chucks, 14. metal frameworks, 15. iron blocks, 16. electromagnet apparatus, 17. electromagnet apparatus operating current adjusting knobs, 18. electromagnet apparatus switch keys, 19. Magnet one, 20. Magnet two, 21. Magnet three, 22. Magnet four, 23. Hall elements, 24. Hall element Mersure Controlers, 25. Hall element electricity Pressure display screen, 26. Hall element Mersure Controler switch keys, 27. Hall element operating current adjusting knobs, 28. Hall electricity Pressure amplifying device, 29. digital oscilloscopes, 30. digital oscilloscope display screens, 31. digital oscilloscope switch keys, 32. fixtures.

Detailed description of the invention

In figure, arranging support 4 on bracket base 7, support 4 upper end arranges crossbeam 1, arrange in the middle of crossbeam 1 upper grip 2 and Force-sensing sensor 3, tinsel 12 one end is connected with upper grip 2 and force-sensing sensor 3, and the other end is connected with lower chuck 13, lower folder 13 are fixed together with a metal framework 14, and metal framework 14 is internal fixes an iron block 15, arranges electricity below metal framework 14 Magnet arrangement 16.Force-sensing sensor 3 is connected with force-sensing sensor Mersure Controler 8 by interface, and force-sensing sensor 3 is used for measuring Pulling force size suffered by tinsel 12, and can be shown by force-sensing sensor measurement display screen 9.Electromagnet apparatus 16 is used for leading to Cross magneticaction and apply pulling force in iron block 15 to tinsel 12, then discharge, so that the iron block 15 being fixed together and metal Framework 14 does simple harmonic oscillation under tinsel 12 acts on, and can regulate pulling force by electromagnet apparatus operating current adjusting knob 17 Size.The specification i.e. Magnet 1 of identical four blocks of Magnet, Magnet 2 20, Magnet 3 21 and Magnet 4 22 are symmetrically disposed in The side of metal framework 14, can move up and down with metal framework 14, and Hall element is by Hall element 23, Magnet 3 21, Magnet 4 22 and Hall element Mersure Controler 24 form, Hall element 23 is arranged on fixture 32, and fixture 32 is arranged on support 4, Fixture 32 can move to change position along support 4, and Hall element 23 is connected with Hall element Mersure Controler 24 by interface, can Size of current in Hall element 23 is regulated, the Hall electricity at Hall element 23 two ends by Hall element operating current adjusting knob 27 Pressure can be shown by Hall element voltage display screen 25, and Hall element Mersure Controler 24 is put with Hall voltage by interface Big device 28 is connected, and Hall voltage amplifying device 28 is connected with digital oscilloscope 29 by interface, and digital oscilloscope 29 can be by The waveform of the Hall voltage after being amplified by Hall voltage amplifying device 28 is shown, enterprising at digital oscilloscope display screen 30 Row is observed and is measured.

Specific experiment operating procedure is:

(1) by observing bracket base level gauge 6, the bracket base leveling serew 5 on adjusting pole base 7, support is made Base 7 level.

(2) along support 4 movable clamp 32, Hall element 23 is made to be positioned at Magnet 3 21 and the centre of Magnet 4 22, by suddenly It is suitable, by Hall element voltage display screen that size of current in Hall element 23 is regulated by your element manipulation current adjusting knob 27 The 25 Hall voltage sizes observing Hall element 23 two ends, further along support 4 movable clamp 32, carefully adjust Hall element 23 Position, making Hall voltage is zero, and now Hall element 23 is located just at Magnet 3 21 and the middle of Magnet 4 22.

(3) make electromagnet apparatus 16 work by electromagnet apparatus switch key 18, given in iron block 15 by magneticaction Tinsel 12 applies pulling force, and observes pulling force size suffered by tinsel 12, by regulation by force-sensing sensor measurement display screen 9 The operating current of electromagnet apparatus operating current adjusting knob 17 regulating magnet device 16, makes pulling force size to fit, then leads to Crossing electromagnet apparatus switch key 18 makes electromagnet apparatus 16 quit work, so that the iron block 15 being fixed together and metal frame The wire spring oscillator that frame 14 is constituted with tinsel 12 starts to do simple harmonic oscillation, under iron block 15 and metal framework 14 drive, Magnet 3 21 and Magnet 4 22 do simple harmonic oscillation the most up and down, and the magnetic induction suffered by Hall element 23 is the most periodically Change, so that the Hall voltage at Hall element 23 two ends the most periodically changes.

(4) this periodically variable Hall voltage is after Hall voltage amplifying device 28 amplifies, and waveform is at digital oscilloscope Show on 29, digital oscilloscope display screen 30 observed the waveform of amplified Hall voltage, measure its cycle T, The wire spring oscillator that the iron block 15 being i.e. fixed together and metal framework 14 and tinsel 12 are constituted does the week of simple harmonic oscillation Phase T.

(5) make wire spring oscillator stop vibration, after waiting to stablize, measure tinsel 12 institute by force-sensing sensor 3 By pulling force size, and shown by force-sensing sensor measurement display screen 9, it is simply that the thing of wire spring oscillator lower end direct bearing Gravity suffered by body, and then its quality m can be obtained.

(6) measure length L of tinsel 12 between force-sensing sensor 3 and lower chuck 13 with meter ruler, measure metal with micrometer The diameter d of silk 12, and calculate its sectional area

(7) by length L of tinsel 12, sectional area S, quality m of wire spring oscillator lower end direct bearing object, Yi Jijin Belong to silk spring oscillator and do the cycle T substitution formula of simple harmonic oscillationYoung's modulus Y wiry can be obtained.

Above the present invention is set forth, but the most conditional intention of embodiment that the present invention is introduced, not Deviating from the range of present subject matter, the present invention can have multiple changing and modifications.

Claims (2)

1. the experimental provision surveying tinsel Young's modulus according to simple harmonic oscillation, it is characterised in that it is included in bracket base On support is set, pedestal upper end arranges crossbeam, arranges upper grip and force-sensing sensor, tinsel one end and upper grip in the middle of crossbeam And force-sensing sensor is connected, the other end is connected with lower chuck, and lower chuck and a metal framework are fixed together, inside metal framework Fix an iron block, electromagnet apparatus is set below metal framework；Force-sensing sensor measures control by interface with force-sensing sensor Device is connected, and force-sensing sensor is used for measuring pulling force size suffered by tinsel, and can be shown by force-sensing sensor measurement display screen Out；Electromagnet apparatus is used for applying pulling force in iron block to tinsel by magneticaction, then discharges, so that being fixed on one The iron block played and metal framework do simple harmonic oscillation under tinsel effect, and can pass through electromagnet apparatus operating current adjusting knob Regulation pulling force size；

The identical four blocks of Magnet of specification are symmetrically disposed in metal framework side, can move up and down with metal framework, Hall Sensor is made up of Hall element, two blocks of Magnet and Hall element Mersure Controler, and Hall element is arranged on fixture, and fixture is pacified Being contained on support, fixture can move to change position along support, and Hall element passes through interface and Hall element Mersure Controler phase Even, can be by size of current in Hall element operating current adjusting knob regulation Hall element, the Hall electricity at Hall element two ends Pressure can be shown by Hall element voltage display screen, and Hall element Mersure Controler amplifies dress by interface with Hall voltage Putting connected, Hall voltage amplifying device is connected with digital oscilloscope by interface, and digital oscilloscope can will pass through Hall voltage The waveform of the Hall voltage after amplifying device amplification shows, observes and measures.

The experimental provision survey tinsel Young mould surveying tinsel Young's modulus according to simple harmonic oscillation the most according to claim 1 The experimental technique of amount, it is characterised in that the detailed process of the method comprises the following steps:

Step one, by observe bracket base level gauge, the bracket base leveling serew on adjusting pole base, make bracket base Level；

Step 2, along support movable clamp, make Hall element be positioned at Magnet three and the centre of Magnet four, by the electricity in Hall element Stream size adjustment is suitable, observes the Hall voltage size at Hall element two ends, carefully adjusts the position of Hall element, makes Hall electricity Pressure is zero, and now Hall element is located just at Magnet three and the middle of Magnet four；

Step 3, make electromagnet apparatus work, apply pulling force in iron block to tinsel by magneticaction, pass through regulating magnet Device operating current, makes pulling force size to fit, then makes electromagnet apparatus quit work so that the iron block being fixed together and The wire spring oscillator that metal framework is constituted with tinsel starts to do simple harmonic oscillation, under iron block and metal framework drive, and magnetic Ferrum three and Magnet four do simple harmonic oscillation the most up and down, the cyclically-varying the most therewith of the magnetic induction suffered by Hall element, from And make the Hall voltage at Hall element two ends the most periodically change；

Step 4, this periodically variable Hall voltage are after Hall voltage amplifying device amplifies, and waveform is on digital oscilloscope Show, observe the waveform of Hall voltage, measure its cycle T, the iron block being i.e. fixed together and metal framework and tinsel The wire spring oscillator constituted does the cycle T of simple harmonic oscillation；

Step 5, make wire spring oscillator stop vibration, treat stable after, measure tinsel institute tension by force-sensing sensor Power size, and shown by force-sensing sensor measurement display screen, it is simply that the object institute of wire spring oscillator lower end direct bearing The gravity being subject to, and then its quality m can be obtained；

Step 6, measure length L wiry between force-sensing sensor and lower chuck with meter ruler, with micrometer measure wiry directly Footpath d, and calculate its sectional area

Step 7, by length L wiry, sectional area S, quality m of wire spring oscillator lower end direct bearing object, and metal Silk spring oscillator does the cycle T of simple harmonic oscillation and substitutes into formulaYoung's modulus Y wiry can be obtained.