CN105810053A - Experimental device and method for measuring Young's modulus of steel wire through resonance phenomenon - Google Patents

Abstract

The invention discloses an experimental device and an experimental method for measuring Young's modulus of a steel wire through a resonance phenomenon, and relates to a Young's modulus measuring device and a measuring method. The invention aims at solving the problem that experiments of College Physics are relatively simple and abstract in principle of measuring the Young's modulus of the steel wire at present, and the problem that a telescope is relatively difficult to regulate. According to the device, a cross beam is arranged at the upper end of a bracket; an upper chuck and a vibration exciter are arranged in the middle of the cross beam; two ends of the steel wire are connected to the vibration exciter and a lower chuck; the lower chuck is fixed to an iron block; a vibration pickup device is arranged at the lower part of the iron block; the vibration exciter is connected to a signal source; and the vibration pickup device is connected to an amplifier and an oscilloscope. According to the method disclosed by the invention, a sinusoidal signal is converted into mechanical vibration by virtue of the vibration exciter, so that a spring vibrator of the metal wire is subjected to forced vibration, the vibration is converted into an electric signal by virtue of the vibration pickup device, the frequency of the sinusoidal signal is regulated, the intrinsic frequency of the spring vibrator of the metal wire is obtained when the maximal waveform amplitude is achieved, and the intrinsic frequency is introduced to a formula, so that the Young's modulus of the steel wire is calculated. The experimental device and the experimental method disclosed by the invention are suitable for measuring the Young's modulus of the steel wire.

Description

A kind of experimental provision utilizing covibration to survey tinsel Young's modulus and method

Technical field

The present invention relates to a kind of Experiment of College Physics device, be specifically related to a kind of experimental provision utilizing covibration to survey tinsel Young's modulus and method.

Background technology

Under external force, the change of shape that solid occurs, it is called deformation.It can be divided into elastic deformation and plastic deformation two class.External force removes the complete restorable deformation of energy of rear object, is called elastic deformation.If the external force being added on object is excessive, so that after external force removes, object can not restore to the original state completely, and leaves residual deformation, is just referred to as plastic deformation.In this experiment, elastic deformation is only studied.For this, it should control external force size, 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 object length is L, sectional area is S, and along its length after force F, object elongation (or shortening) is Δ L.Ratio F/S is the active force in unit are, is called and stresses, and which determines the deformation of object；Ratios delta L/L is the specific elongation of object, is called strain, and it represents the size of object deformation.According to Hooke's law, the elastic limit internal stress at object is directly proportional to strain, proportionality coefficientIt is called Young's modulus.

Experiments show that, Young's modulus is unrelated with the size of external force F, the length L and sectional area S of object, and is solely dependent upon the material of rod (or tinsel).Young's modulus is to describe an important mechanics parameter of solid material elastic deformation ability, is one of foundation selecting 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., in order to ensure the use of normal safe, their Young's modulus will be measured.For a long time, the Young's modulus measuring material generally adopts static stretch method, is typically on universal testing machine and carries out.This method load is big, and loading velocity is slow, there is relaxation process, can increase measurement error, and fragile material is not easily measured, and measures also inconvenient under condition of different temperatures.The eighties in 20th century, 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 measured, carry out the impact on Young's modulus of the research material defect with this, achieve good effect.The nineties in 20th century, kinetics Young's modulus measuring method and hang wire flexural resonance method recommend to perform as national technical standard.This method can measure the Young's modulus of various material within the scope of bigger high/low temperature, and certainty of measurement is higher.Static method, except static stretch method, also has static twist method, the method for Static bending etc.；Dynamic method, except lateral resonance, also has longitudinal resonance, torsional resonance etc..It can in addition contain use wave speed measurement method, utilize continuous wave or impulse wave to measure Young's modulus.

Although kinetics Young's modulus measuring method and hang wire flexural resonance method have many good qualities, but owing to theoretical formula is complicated, principle is not readily understood, equipment is also more complicated, experiment difficulty is big, therefore Experiment of College Physics at present surveys tinsel Young's modulus frequently with static stretch method, Chroococcus minutus Δ L wiry is measured according to optical lever amplification principle, also there is the some other more advanced micro-displacement measurement method of employing in recent years, such as current vortex sensor method, Michelson's interferometer method, optical fibre displacement sensor method etc. measures Chroococcus minutus Δ L wiry, thus calculating tinsel Young's modulus.In current Experiment of College Physics, the experimental project of Module by Stretching silk Young's modulus is primarily present following deficiency:

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

They are two years old, according to optical lever amplification principle, the amplification system consisted of optical lever, telescope and scale measures Chroococcus minutus wiry, although method is ingenious, but principle is more abstract, not readily understood, telescopical adjustment difficulty is relatively larger, and points for attention are relatively more, and utilize telescope to carry out observing measurement either directly through human eye, it is very easy to fatigue, it is easy to data mistaken, affect the accuracy of measurement result.

Its three, being generally adopted counterweight and apply pulling force to tinsel, calculating pulling force with the nominal mass of counterweight inaccurate, thus affecting 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 experimental provision utilizing covibration to survey tinsel Young's modulus and method, experimental principle of the present invention is easily understood, described experimental provision utilizes vibrator that the sinusoidal signal that sine signal source exports is converted to the mechanical vibration of same frequency, pass to the wire spring oscillator being made up of iron block and tinsel, wire spring oscillator is made to make longitudinal forced vibration, this vibration is converted to the signal of telecommunication through vibration pickup, after being amplified by amplifier, waveform shows on analog oscilloscope, by regulating the frequency of the sinusoidal signal of sine signal source output, until wave-shape amplitude is maximum, the frequency of the sinusoidal signal of now sine signal source output is exactly resonant frequency, the namely natural frequency f of wire spring oscillator, experimental phenomena is directly perceived, observe more convenient with measurement.

This invention address that the experimental provision that covibration surveys tinsel Young's modulus that utilizes of its technical problem is: include arranging support on bracket base, pedestal upper end arranges crossbeam, upper grip and vibrator are set in the middle of crossbeam, tinsel one end is connected with upper grip and vibrator, the other end is connected with lower chuck, and lower chuck and an iron block are fixed together.Vibrator is connected with sine signal source by interface, and sinusoidal signal voltage amplitude and the frequency size of sine signal source output can be continuously adjusted by knob, and can show on a display screen.The sinusoidal signal that sine signal source exports is converted to the mechanical vibration of same frequency by vibrator, passes to the wire spring oscillator being made up of iron block and tinsel, makes wire spring oscillator make longitudinal forced vibration.Iron block is arranged below vibration pickup, and iron block contacts gently with vibration pickup, and vibration pickup is arranged on fixture, and fixture is rack-mount, and fixture can move to change position along support.The mechanical vibration of the wire spring oscillator that iron block is constituted with tinsel are converted to the signal of telecommunication by vibration pickup, vibration pickup is connected with amplifier by interface, amplifier is connected with analog oscilloscope by interface, the waveform of the signal of telecommunication after being amplified by amplifier can be shown by analog oscilloscope, carries out observing and measures.

The experimental technique of tinsel Young's modulus surveyed by the experimental provision utilizing covibration to survey tinsel Young's modulus of the present invention, and 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 iron block contact gently with vibration pickup；

Step 3, it is suitable that the sinusoidal signal voltage amplitude exported by sine signal source regulates, by regulating the frequency that sinusoidal signal frequency coarse adjustment knob is gradually increased the sinusoidal signal of sine signal source output, the sinusoidal signal that sine signal source exports is converted to the mechanical vibration of same frequency by vibrator, pass to the wire spring oscillator being made up of iron block and tinsel, wire spring oscillator is made to make longitudinal forced vibration, this vibration is converted to the signal of telecommunication through vibration pickup, after being amplified by amplifier, waveform shows on analog oscilloscope, when the frequency of sinusoidal signal of sine signal source output is away from the natural frequency of wire spring oscillator, iron block is almost motionless or vibration is very faint, on analog oscilloscope only small almost without the waveform of the signal of telecommunication or wave-shape amplitude；When the frequency of the sinusoidal signal of sine signal source output moves closer to the natural frequency of wire spring oscillator, based on resonance principle, the Oscillation Amplitude of iron block is gradually increased, and the wave-shape amplitude of analog oscilloscope power on signal is gradually increased；

Step 4, on analog oscilloscope display screen, observe the waveform of this signal of telecommunication, by regulating sinusoidal signal frequency fine tuning knob, carefully regulate the frequency size of the sinusoidal signal of sine signal source output further, until the wave-shape amplitude of this signal of telecommunication is maximum, the frequency now read from sinusoidal signal frequency display screen is exactly resonant frequency, the namely natural frequency f of wire spring oscillator；

Step 5, measure the quality m of wire spring oscillator lower end direct bearing object with balance, measure length L wiry between vibrator and lower chuck with meter ruler, measure diameter d wiry with micrometer, and calculate sectional area wiry

Step 6, by length L wiry, sectional area S, wire spring oscillator lower end direct bearing object quality m, and wire spring oscillator natural frequency f substitute into formulaYoung's modulus Y wiry can be obtained.

Covibration is utilized to survey the theoretical basis of tinsel Young's modulus:

If a metal filament length is L, sectional area is S, and Young's modulus is Y, applies tensile force f along its length, and wire elongation amount is Δ L, and ratio F/S is the active force in unit are, is called and stresses, and which determines deformation wiry；Ratios delta L/L is specific elongation wiry, is called strain, and it represents the size of tinsel deformation.According to Hooke's law, it is directly proportional to strain at elastic limit internal stress wiry, proportionality coefficient and Young's modulus Y, namely

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

(1) formula is become

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

According to (2) formula, it is possible to this tinsel to be regarded as a coefficient of elasticitySpring, this wire spring is vertically hung, the object that a mass is m is fastened in lower end, then wire spring and this object constitute a wire spring oscillator, apply certain pulling force to this system, then discharge, then in the vertical direction is done simple harmonic oscillation by object, its cycle can be obtained by the Period Formula of spring oscillator, namely

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

The natural frequency of wire spring oscillator is can be obtained fom the above equation

$f=\frac{1}{T}=\frac{1}{2\mathrm{\π}}\sqrt{\frac{k}{m}}---\left(4\right)$

By the coefficient of elasticity of wire spring(4) formula of substitution, can obtain

$f=\frac{1}{2\mathrm{\π}}\sqrt{\frac{YS}{Lm}}---\left(5\right)$

According to (5) formula, Young's modulus Y wiry can be obtained, namely

$Y=\frac{4{\mathrm{\π}}^2{f}^{2}Lm}{S}---\left(6\right)$

Applied vibration source acts on wire spring oscillator, makes wire spring oscillator make longitudinal forced vibration.When the frequency in applied vibration source is not equal to the natural frequency of wire spring oscillator, wire spring oscillator vibrates hardly or Oscillation Amplitude is only small；When the frequency in applied vibration source is equal to the natural frequency of wire spring oscillator, based on resonance principle, the Oscillation Amplitude of wire spring oscillator will increase suddenly.Measure the frequency f in now applied vibration source, i.e. the natural frequency f of wire spring oscillator.Measure length L wiry, sectional area S, the quality m of the object of wire spring oscillator lower end direct bearing, it is possible to according to formula (6), obtain Young's modulus Y wiry.

The invention has the beneficial effects as follows:

One, the present invention proposes a kind of new method surveying tinsel Young's modulus based on resonance principle, it is different that the method also exists essence from the static stretch method surveying tinsel Young's modulus generally adopted in Physical Experiments, and the experimental principle of the method institute foundation is very simple, it is exactly common mass-spring model and resonance principle, high school physics class just has been directed to correlation formula, course of University Physics also has detailed analysis, is easily understood.If being therefore incorporated in Physical Experiments by this invention, being remarkably contributing to abundant Experiment of College Physics content, the thinking of open student, the initiative spirit of training student, strengthening student and using knowledge problem-solving ability flexibly.

Its two, the present invention propose utilize covibration survey tinsel Young's modulus experimental provision also uncomplicated, the basis of existing experimental provision is improved a little, be easier realization.

They are three years old, the experimental provision experimental provision that the present invention proposes utilizes vibrator that the sinusoidal signal that sine signal source exports is converted to the mechanical vibration of same frequency, pass to the wire spring oscillator being made up of iron block and tinsel, wire spring oscillator is made to make longitudinal forced vibration, this vibration is converted to the signal of telecommunication through vibration pickup, after being amplified by amplifier, waveform shows on analog oscilloscope, by regulating the frequency of the sinusoidal signal of sine signal source output, until wave-shape amplitude is maximum, the frequency of the sinusoidal signal of now sine signal source output is exactly resonant frequency, the namely natural frequency f of wire spring oscillator, experimental phenomena is directly perceived, observe more convenient with measurement.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the present invention is further described.

Accompanying drawing is the structural representation of the present invention.

1. crossbeam in figure, 2. upper grip, 3. vibrator, 4. support, 5. bracket base leveling serew, 6. bracket base level gauge, 7. bracket base, 8. sine signal source, 9. sinusoidal signal frequency display screen, 10. sinusoidal signal frequency coarse adjustment knob, 11. sinusoidal signal frequency fine tuning knob, 12. sinusoidal signal voltage amplitude display screen, 13. sinusoidal signal voltage amplitude adjusting knob, 14. the interface between vibrator and sine signal source, 15. tinsel, 16. lower chuck, 17. ferrum block, 18. vibration pickup, 19. fixture, 20. amplifier, 21. analog oscilloscope, 22. analog oscilloscope display screen, 23. analog oscilloscope switch key.

Detailed description of the invention

In figure, including arranging support 4 on bracket base 7, support 4 upper end arranges crossbeam 1, in the middle of crossbeam 1, upper grip 2 and vibrator 3 are set, tinsel 15 one end is connected with upper grip 2 and vibrator 3, and the other end is connected with lower chuck 16, and lower chuck 16 and an iron block 17 are fixed together.Vibrator 3 is connected with sine signal source 8 by the interface 14 between vibrator with sine signal source, the sinusoidal signal voltage amplitude of sine signal source 8 output can pass through sinusoidal signal voltage amplitude adjusting knob 13 and continuously adjust, and can show on sinusoidal signal voltage amplitude display screen 12；Sinusoidal signal frequency size can pass through sinusoidal signal frequency coarse adjustment knob 10 and sinusoidal signal frequency fine tuning knob 11 continuously adjusts, and can show on sinusoidal signal frequency display screen 9.The sinusoidal signal that sine signal source 8 exports is converted to the mechanical vibration of same frequency by vibrator 3, passes to the wire spring oscillator being made up of iron block 17 and tinsel 15, makes wire spring oscillator make longitudinal forced vibration.Iron block 17 is arranged below vibration pickup 18, and iron block 17 contacts gently with vibration pickup 18, and vibration pickup 18 is arranged on fixture 19, and fixture 19 is arranged on support 4, and fixture 19 can move to change position along support 4.The mechanical vibration of the wire spring oscillator that iron block 17 and tinsel 15 are constituted are converted to the signal of telecommunication by vibration pickup 18, vibration pickup 18 is connected with amplifier 20 by interface, amplifier 20 is connected with analog oscilloscope 21 by interface, the waveform of the signal of telecommunication after being amplified by amplifier 20 can be shown by analog oscilloscope 21, carries out observing and measures.

Specific experiment operating procedure is:

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

(2) along support 4 movable clamp 19, iron block 17 is made to contact gently with vibration pickup 18.

(3) by sinusoidal signal voltage amplitude adjusting knob 13 and sinusoidal signal voltage amplitude display screen 12, the sinusoidal signal voltage amplitude exported by sine signal source 8 regulates suitable.By regulating the frequency that sinusoidal signal frequency coarse adjustment knob 10 is gradually increased the sinusoidal signal of sine signal source 8 output, the sinusoidal signal that sine signal source 8 exports is converted to the mechanical vibration of same frequency by vibrator 3, pass to the wire spring oscillator being made up of iron block 17 and tinsel 15, make wire spring oscillator make longitudinal forced vibration.This vibration is converted to the signal of telecommunication through vibration pickup 18, and after being amplified by amplifier 20, waveform shows on analog oscilloscope 21.When the frequency of sinusoidal signal is away from the natural frequency of wire spring oscillator, iron block 17 is almost motionless or vibration is very faint, only small almost without the waveform of the signal of telecommunication or wave-shape amplitude on analog oscilloscope 21；When the frequency of sinusoidal signal moves closer to the natural frequency of wire spring oscillator, based on resonance principle, the Oscillation Amplitude of iron block 17 is gradually increased, and the wave-shape amplitude of analog oscilloscope 21 power on signal is gradually increased.

(4) on analog oscilloscope display screen 22, observe the waveform of this signal of telecommunication, by regulating sinusoidal signal frequency fine tuning knob 11, carefully regulate the frequency size of the sinusoidal signal of sine signal source 8 output further, until the wave-shape amplitude of this signal of telecommunication is maximum, the frequency now read from sinusoidal signal frequency display screen 9 is exactly resonant frequency, the namely natural frequency f of wire spring oscillator.

(5) measure the quality m of wire spring oscillator lower end direct bearing object with balance, measure the length L of tinsel 15 between vibrator 3 and lower chuck 16 with meter ruler, measure the diameter d of tinsel 15 with micrometer, and calculate sectional area wiry

(6) the length L of tinsel 15, sectional area S, the quality m of wire spring oscillator lower end direct bearing object and the natural frequency f of wire spring oscillator are substituted into formulaYoung's modulus Y wiry can be obtained.

Above the present invention is set forth, but the not conditional intention of embodiment that the present invention introduces, and without departing substantially from the scope of present subject matter, the present invention can have multiple changing and modifications.

Claims (2)

1. one kind utilizes the experimental provision that covibration surveys tinsel Young's modulus, it is characterized in that, it includes arranging support on bracket base, pedestal upper end arranges crossbeam, upper grip and vibrator are set in the middle of crossbeam, tinsel one end is connected with upper grip and vibrator, and the other end is connected with lower chuck, and lower chuck and an iron block are fixed together；Vibrator is connected with sine signal source by interface, sinusoidal signal voltage amplitude and the frequency size of sine signal source output can be continuously adjusted by knob, and can show on a display screen, the sinusoidal signal that sine signal source exports is converted to the mechanical vibration of same frequency by vibrator, pass to the wire spring oscillator being made up of iron block and tinsel, make wire spring oscillator make longitudinal forced vibration；

Iron block is arranged below vibration pickup, iron block contacts gently with vibration pickup, vibration pickup is arranged on fixture, fixture is rack-mount, and fixture can move to change position along support, and the mechanical vibration of the wire spring oscillator that iron block is constituted with tinsel are converted to the signal of telecommunication by vibration pickup, vibration pickup is connected with amplifier by interface, amplifier is connected with analog oscilloscope by interface, and the waveform of the signal of telecommunication after being amplified by amplifier can be shown by analog oscilloscope, carries out observing and measures.

2. the experimental technique of tinsel Young's modulus surveyed by the experimental provision utilizing covibration to survey tinsel Young's modulus according to claim 1, 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 iron block contact gently with vibration pickup；

Step 3, it is suitable that the sinusoidal signal voltage amplitude exported by sine signal source regulates, by regulating the frequency that sinusoidal signal frequency coarse adjustment knob is gradually increased the sinusoidal signal of sine signal source output, the sinusoidal signal that sine signal source exports is converted to the mechanical vibration of same frequency by vibrator, pass to the wire spring oscillator being made up of iron block and tinsel, wire spring oscillator is made to make longitudinal forced vibration, this vibration is converted to the signal of telecommunication through vibration pickup, after being amplified by amplifier, waveform shows on analog oscilloscope, when the frequency of sinusoidal signal of sine signal source output is away from the natural frequency of wire spring oscillator, iron block is almost motionless or vibration is very faint, on analog oscilloscope only small almost without the waveform of the signal of telecommunication or wave-shape amplitude；When the frequency of the sinusoidal signal of sine signal source output moves closer to the natural frequency of wire spring oscillator, based on resonance principle, the Oscillation Amplitude of iron block is gradually increased, and the wave-shape amplitude of analog oscilloscope power on signal is gradually increased；

Step 4, on analog oscilloscope display screen, observe the waveform of this signal of telecommunication, by regulating sinusoidal signal frequency fine tuning knob, carefully regulate the frequency size of the sinusoidal signal of sine signal source output further, until the wave-shape amplitude of this signal of telecommunication is maximum, the frequency now read from sinusoidal signal frequency display screen is exactly resonant frequency, the namely natural frequency f of wire spring oscillator；

Step 5, measure the quality m of wire spring oscillator lower end direct bearing object with balance, measure length L wiry between vibrator and lower chuck with meter ruler, measure diameter d wiry with micrometer, and calculate sectional area wiry

Step 6, by length L wiry, sectional area S, wire spring oscillator lower end direct bearing object quality m, and wire spring oscillator natural frequency f substitute into formulaYoung's modulus Y wiry can be obtained.