CN101109694B - Method for predicting low frequency damping of titanium-nickel shape memory alloy - Google Patents

Abstract

The invention provides a predicting method for the low-frequency damp of a Ti-Ni shape memorizing alloy, which is characterized in that the operation procedures are: the intrinsic damp spectral line of Ti-Ni shape memorizing alloy under the frequency is calculated in quantitative way; the instantaneous damp spectral line of Ti-Ni shape memorizing alloy under the frequency is determined; the intrinsic damp spectral line is subtracted from the total damp spectral line to get the instantaneous damp spectral line; the instantaneous damp spectral line is predicated under other frequency, and instantaneous damp DT(Omega 2) is worked out under other frequency Omega 2; the damp spectral line is predicated under other frequency; the intrinsic damp spectral line is added with the predicated instantaneous damp spectral line of other frequency, so the predicated damp spectral line of other frequency is obtained, the relative error of the peak value of the damp spectral line is 3.1-3.3%. For the method, for predicting the damp of the Ti-Ni alloy under other frequency, it is only necessary to measure the damp under a frequency at a constant temperature rate of the Ti-Ni alloy. The method is simple and reliable, of high accuracy, convenient, rapid and high efficient.

Description

The Forecasting Methodology of the low frequency damping of Ti-Ni marmem

Technical field

The invention belongs to the quantitative analysis tech of the damping of marmem, belong to the method for the low frequency damping of predicted titanium nickel shape memory alloy especially.

Background technology

At present, marmem is owing to have the shockproof occasion of vibration damping that reasonable damping capacity has been applied to buildings such as bridge etc., and potential application has fields such as bullet resistant material, tennis racket.The high damping of marmem and the low temperature damping characteristic of martensite and martensite phase transformation or reverse transformation process mutually are closely related.Ti-Ni marmem has than the better damping capacity of the Ni-based marmem of other titaniums and is subjected to more concern.

The damping method of measuring Ti-Ni marmem has dynamic mechanical analysis instrument method (DMA), rocks method etc.Usually, need measure damping under conditions such as different vibration frequencies, different intensification or rate of temperature fall, therefore, this work is numerous and diverse, expends great amount of manpower and material resources.The present invention carries out quantitative test calculating to the damping spectral line of certain frequency of the Ti-Ni marmem of measuring, determines intrinsic damp and transient state damping, predicts the damping of other frequencies on this basis.This method precision height, speed are fast, time saving and energy saving, convenient and swift.

Summary of the invention

The object of the present invention is to provide a kind of Forecasting Methodology of Ti-Ni marmem low frequency damping, this method is by determining intrinsic damp and the transient state damping under the Ti-Ni marmem frequency earlier; Obtain transient state damping under other frequencies according to the quantitative relationship between the transient state damping under the different frequency then; At last intrinsic damp and the transient state damping addition of being obtained just can be obtained the damping under other frequencies.

The technical scheme that adopts is:

The Forecasting Methodology of the low frequency damping of Ti-Ni marmem may further comprise the steps:

1, determine the intrinsic damp of Ti-Ni marmem:

The damping of marmem can be divided into intrinsic damp, transient state damping and phase transformation damping.Wherein intrinsic damp (is D _I(T)) be martensite and austenite separately the mixed number of damping mutually, relevant with the microstructure of two-phase.And the transient state damping (is D _T(T)), be to produce in the temperature change process only in heating or cooling, the transient state damping is zero when constant temperature.The phase transformation damping (is D _P(T)) with martensite and austenite between phase transformation relevant.Usually, the phase transformation damping is very little, can ignore.

For the martensite reverse transformation be martensite to the austenite phase transformation process, martensite transfor mation is that austenitic volume fraction can be expressed as:

$f\left(T\right)={\∫}_{T_s}^T{D}_T\mathrm{\ωdT}/{\∫}_{T_s}^{T_f}{D}_T\mathrm{\ωdT}---\left(1\right)$

Here T _sBe lower than the martensite reverse transformation and begin temperature, T _fBe higher than martensite reverse transformation end temp, ω is the vibration frequency of sample.Integration J (T) and J (T _f) definition be respectively

$J\left(T\right)={\∫}_{T_s}^T(D-D_1)\mathrm{\ωdT}={\∫}_{T_s}^T{D}_T\mathrm{\ωdT}+{\∫}_{T_s}^T{D}_P\mathrm{\ωdT}---\left(2\right)$

$J\left(T_f\right)={\∫}_{T_s}^{T_f}(D-D_1)\mathrm{\ωdT}={\∫}_{T_s}^{T_f}{D}_T\mathrm{\ωdT}+{\∫}_{T_s}^{T_f}{D}_P\mathrm{\ωdT}---\left(3\right)$

Utilize formula (1), can obtain following formula:

$J\left(T\right)=f\left(T\right){\∫}_{T_s}^{T_f}{D}_T\mathrm{\ωdT}+{\∫}_{T_s}^T{D}_P\mathrm{\ωdT}---\left(4\right)$

J(T)/J(T _f)＝f(T)+Δf(T) (5)

Wherein

$\mathrm{\Δf}\left(T\right)=\frac{{\∫}_{T_s}^T{D}_P\mathrm{\ωdT}-\frac{J\left(T\right)}{J\left(T_f\right)}{\∫}_{T_s}^{T_f}{D}_P\mathrm{\ωdT}}{{\∫}_{T_s}^{T_f}{D}_T\mathrm{\ωdT}}$

Δ f (T) is very little under high-temperature speed and low-frequency condition, can ignore.At this moment, can obtain following relational expression:

J(T)/J(T _f)≈f(T) (6)

And D _I(T) can think the mixed number of damping of martensite attitude and Ovshinsky figure damping, promptly

D _I(T)＝f(T)D _a+[1-f(T)]D _m (7)

Intrinsic damp can adopt following alternative manner to calculate:

Choose initial arbitrarily intrinsic damp function (D _I) _Initially, this function must be between Ovshinsky figure damping value and martensite attitude damping value.

Calculate D-(D _I) _Initially), integration J (T) and J (T _f), can calculate volume fraction f (T) by formula (6).Intrinsic damp (the D that can make new advances by following formula _I) ₁:

(D _I) ₁＝f(T)D _a+[1-f(T)]D _m (8)

By (D ₁) ₁, carry out the intrinsic damp difference of iterative computation before and after iteration, i.e. (D _I) _I-1With (D _I) _iBetween the absolute value of difference less than certain setting value, as 10 ^-6, 10 ^-7Deng.At last, obtain accurate intrinsic damp.

Total damping is deducted the mixed number that intrinsic damp then obtains transient state damping and phase transformation damping easily.Because the phase transformation damping is very little, so this mixed number can be similar to and thinks the transient state damping value.

2, determine the transient state damping of the Ti-Ni marmem under other frequencies.

The transient state damping of marmem and the pass between vibration frequency are:

D _T∝1/ω ⁿ (9)

N is the coefficient less than 1.Ti-Ni marmem heats up or rate of temperature fall during less than 7 ℃ of part clocks in the frequency range of 1～10Hz, and can get the n value behind over-fitting is 0.725.Pass between the transient state damping of different frequency is:

$\frac{D_T\left({\mathrm{\ω}}_1\right)}{D_T\left({\mathrm{\ω}}_2\right)}={\left(\frac{{\mathrm{\ω}}_2}{{\mathrm{\ω}}_1}\right)}^{0.4}---\left(10\right)$

Therefore, if the transient state damping D under known certain frequency _T(ω ₁), just can obtain transient state damping D under other frequencies according to formula (10) _T(ω ₂)

3, predict the damping of the Ti-Ni marmem under other frequencies.

Because intrinsic damp is relevant with martensite and Ovshinsky figure's damping and microstructure, so the intrinsic damp of the marmem under the different frequency is identical.

Transient state damping addition with the intrinsic damp and the step 2 of the determined Ti-Ni marmem of step 1 are obtained just can obtain the damping spectral line under the different frequency.

The Forecasting Methodology of the low frequency damping of Ti-Ni marmem of the present invention, its job step is:

(1) the temperature scanning damping spectral line under certain vibration frequency of measuring Ti-Ni marmem requires constant heating or cooldown rate T '≤7 ℃/minute.Vibration frequency 1≤ω≤10Hz.

(2) the intrinsic damp spectral line of the Ti-Ni marmem under this frequency of quantitative Analysis.Detailed process is: choose initial arbitrarily intrinsic damp function (D _I) _Initially, this function must be between Ovshinsky figure damping value and martensite attitude damping value.Calculate (D-(D _I) _Initially), calculate integration

With

According to formula J (T)/J (T _f) ≈ f (T) obtains phase transformation volume fraction f (T), by formula (D _I) ₁=f (T) D _a+ [1-f (T)] D _mCalculate intrinsic damp (D _I) ₁, calculate (D-(D then _I) ₁), carry out iterative computation, the intrinsic damp difference before and after iteration, i.e. (D _I) _I-1With (D _I) _iThe absolute value of difference less than certain setting value, as 10 ^-5Deng.At last, can obtain accurate intrinsic damp.Precision is 5 * 10 ^-5In.

(3) determine the transient state damping spectral line of the Ti-Ni marmem under this frequency.From total damping spectral line, deduct the intrinsic damp spectral line, just can obtain transient state damping spectral line.

(4) predict transient state damping spectral line under other frequencies.According to the quantitative relationship between the transient state damping of different frequency

Suppose the frequencies omega that calculates ₁Under the transient state damping be D _T(ω ₁), then can obtain other frequencies omega ₂Under transient state damping D _T(ω ₂).

(5) predict damping spectral line under other frequencies.With the transient state damping spectral line addition under the intrinsic damp spectral line that calculates and other frequencies of being predicted, the damping spectral line under other frequencies that promptly obtain being predicted.The relative error of the peak value of damping spectral line is about 3.1-3.3%.

This method only need to measure Ti-Ni alloy in the damping of certain frequency under the steady temperature speed with regard to the damping under measurable other frequencies, simple and reliable, precision is high, convenient and swift, efficient is high.

Description of drawings

Fig. 1 is the Ti of measuring _50.2Ni _49.8(at.%) the damping spectral line of marmem (vibration frequency is 8Hz).

Fig. 2 is the Ti that calculates _50.2Ni _49.8The intrinsic damp spectral line of marmem (vibration frequency is 8Hz).

Fig. 3 is the Ti that calculates _50.2Ni _49.8The transient state damping spectral line of marmem (vibration frequency is 8Hz).

Fig. 4 is the Ti of prediction _50.2Ni _49.8The transient state damping spectral line (vibration frequency is respectively 1Hz) of marmem.

Fig. 5 is the Ti that obtains with experiment of prediction _50.2Ni _49.8The damping spectral line of marmem (vibration frequency is 1Hz).

Embodiment

Embodiment one

With 106.5 ℃ of peak temperatures is example, and as shown in Figure 1, vibration frequency is that 106.5 ℃ total damping value under the 8Hz condition is 0.01976134.

Obtaining vibration frequency according to formula 1-8 through iterative computation is that 106.5 ℃ intrinsic damp value under the 8Hz condition is 0.00220895.

The total damping value is deducted the intrinsic damp value, and to obtain vibration frequency be that 106.5 ℃ transient state damping value under the 8Hz condition is 0.01755239.

Obtaining vibration frequency according to formula 10 is that 106.5 ℃ prediction transient state damping value under the 1Hz condition is 0.07926483.

With frequency is that 106.5 ℃ intrinsic damp value and vibration frequency under the 8Hz condition is that 106.5 ℃ the prediction total damping value that 106.5 ℃ prediction transient state damping value addition under the 1Hz condition obtains under the 1Hz condition is 0.08147378.And 106.5 ℃ prediction total damping value under the 1Hz condition that experiment records is 0.08650012, and relative error is about 5.8%.

Embodiment two

With 60 ℃ of peak temperatures is example, and as shown in Figure 1, vibration frequency is that 60 ℃ total damping value under the 8Hz condition is 0.00490419179.

Obtaining vibration frequency according to formula 1-8 through iterative computation is that 60 ℃ intrinsic damp value under the 8Hz condition is 0.00409991.

The total damping value is deducted the intrinsic damp value, and to obtain vibration frequency be that 60 ℃ transient state damping value under the 8Hz condition is 0.00017816.

Obtaining vibration frequency according to formula 10 is that 60 ℃ prediction transient state damping value under the 1Hz condition is 0.00080455.

With frequency is that 60 ℃ intrinsic damp value and vibration frequency under the 8Hz condition is that 60 ℃ the prediction total damping value that 60 ℃ prediction transient state damping value addition under the 1Hz condition obtains under the 1Hz condition is 0.00490446.And 60 ℃ prediction total damping value under the 1Hz condition that experiment records is 0.00532001, and relative error is about 7.8%.

Claims (1)

1. the Forecasting Methodology of the low frequency damping of Ti-Ni marmem is characterized in that job step is:

Temperature scanning damping spectral line under certain vibration frequency of a, measuring Ti-Ni marmem requires constant heating or cooldown rate T '≤7 ℃/minute, vibration frequency 1≤ω≤10Hz;

The intrinsic damp spectral line of the Ti-Ni marmem under b, this frequency of quantitative Analysis, detailed process is: choose initial arbitrarily intrinsic damp function (D _I) _Initially, this function must calculate (D-(D between Ovshinsky figure damping value and martensite attitude damping value _I) _Initially), calculate integration With

T _sBegin temperature, T for being lower than the martensite reverse transformation _fFor being higher than martensite reverse transformation end temp, according to formula J (T)/J (T _f) ≈ f (T) obtains phase transformation volume fraction f (T), by formula (D _I) ₁=f (T) D _a+ [1-f (T)] D _mCalculate intrinsic damp (D _I) ₁, calculate (D-(D then _I) ₁), carry out iterative computation, the intrinsic damp difference before and after iteration, i.e. (D _I) _I-1With (D _I) _iThe absolute value of difference less than 10 ^-5, obtaining accurate intrinsic damp at last, precision is 5 * 10 ^-5In; Wherein D is a total damping, D _aAnd D _mBe respectively austenite damping and martensite damping;

C, determine the transient state damping spectral line of the Ti-Ni marmem under this frequency from total damping spectral line, to deduct the intrinsic damp spectral line, obtain transient state damping spectral line;

D, predict the transient state damping spectral line under other frequencies, according to the quantitative relationship between the transient state damping of different frequency

Suppose the frequencies omega that calculates ₁Under the transient state damping be D _T(ω ₁), then can obtain other frequencies omega ₂Under transient state damping D _T(ω ₂);

E, predict the damping spectral line under other frequencies, with the transient state damping spectral line addition under the intrinsic damp spectral line that calculates and other frequencies of being predicted, damping spectral line under other frequencies that promptly obtain being predicted, under 60 ℃ of specific peak temperatures, determine the transient state damping value of vibration frequency 8Hz, the total damping value of predicting vibrational frequencies 1Hz in view of the above again obtains the prediction total damping value of 60 ℃ of peak temperatures under the 1Hz condition and the relative error of experiment value, is about 7.8%.

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