Xing－h(huán)ong ZHANG，Lei QIU?，Xin CHEN，Tao HE，Shu－xiang LIU2 Chongqing Key Laboratory of Time-grating Sensing and Advanced Testing Technology，Chongqing University of Technology，Chongqing 400054，China

2 Vehicle Engineering Department，Sichuan Engineering Technical College，Deyang 618000，China

Study on the precision ultrasonic densimeter*

Xing－h(huán)ong ZHANG1，Lei QIU?1，Xin CHEN1，Tao HE1，Shu－xiang LIU21Chongqing Key Laboratory of Time-grating Sensing and Advanced Testing Technology，Chongqing University of Technology，Chongqing 400054，China

2Vehicle Engineering Department，Sichuan Engineering Technical College，Deyang 618000，China

To settle some problem s on the traditionaldensity measurement instrumentagainstactualapp lication，a high precision ultrasonic densimeter is designed on the basis of the ultrasonic wave propagation characteristics.The high resolution and fast signa l collection circuit and the digital subdivision algorithms which are used tomake themeasurementof the ultrasonic wave propagation time reach nanosecond and ensure the measurement resolution of the ultrasonic densimeter better than 0.000 01 ×103kg/m3.The distributed measuring probes are installed oppositely at the ektexine of the vesselwhich is contained the measured medium.The distributed structure design is help ful to im prove the accuracy of the measurement result.

Ultrasonic wave，Density measurements，Echo signal，Digital subdivision

*Project supported by the Natural Science Foundation of Chongqing(Grant No.cstc2012jjA70004 and cstc2012 jjA40062)，the National Natural science Foundation of China(Grant No.51275551)，and the Graduate Innovation Fund of Chongqing University of Technology(Grant No.YCX2013206).

Xing－h(huán)ong ZHANG，Professor.? LeiQIU，E－mail:qiulei@2013.cqut.edu.cn

1.Introduction

Density is one of physical quantities ofmaterial properties.The density measurement embodies the measurement level of our country and is widely used in the field of technology，agriculture，industry and our daily life［1］.

Several kinds of densimeters are used in the industry，such as vibration liquid densimeter，capacitive liquid densimeter and ray density sensor，but in the practical application these traditional densimeters all have some deficiencies.For examples，the vibration liquid densimeter and the capacitive liquid densimeter have the characteristic of low cost and wide measurement rang，but the low measurement accuracy and difficultmaintenance;the ray densimeter can realize non－contact measurement，but also has the disadvantage about radiation hazards［2］.

In recent years，with the rapid development of the high technology，a new thought of the density measurement is proposed based on the ultrasonic technology［3］.The ultrasonic technology can realize the density measurement with the non－contact and continuity［4］.The ultrasonic density sensors have promising application prospects，which can complete the dynamic measurement of density with high precision［5］.

2.The principle of ultrasonic densimeter

The densitymeasurement by using the ultrasonic technology is based on the relationship between the ultrasonic propagation characteristic and the media density.The ultrasonic wave propagation velocity changes with the variation of media density when propagating in the media.Themedia density can be measured indirectly through the propagation velocity measurement of the ultrasonic wave in themedia.

The ultrasonic densimeter adopts the distributed structure，that is，the multiple probes are installed oppositely at the ektexine of the vessel.The ultrasonic wave pass through themeasured media and propagate between the probes.The installation schematic of three pairs probes is shown in Figure 1.

In the Figure1，the core part of the probe is the piezoelectric transducer which can convert the analog signal tomechanical vibration and transmit the ultrasonic wave.Also，it can convert the mechanical vibration generated by the ultrasonic to the analog signal［6］.There are three pairs probes(E11and E21，E12and E22，E13and E23)to be installed at the ektexine of the vessel oppositely.The installation position of the probes are lower than the height of the measured media.The transducers E11，E12，E13are used to transmit the ultrasonic wave signals，while the transducers E21，E22，E23are used to receive the ultrasonic wave signals.

Figure 1.The installation schematic of probes

During the density measurement，the driving signals of ultrasonic wave stimulate the transducers E11，E12，E13transmit the ultrasonic wave，and the corresponding transducers E21，E22，E23convert the received ultrasonic wave signals to the electrical signals.The digital subdivision and the interpolation algorithm are used to data processing to obtain several density values.Finally，we get the result by averaging the several density values.

3.Structure composition of the ultrasonic densimeter

The principle diagram of ultrasonic densimeter is shown in Figure 2.The ultrasonic densimeter is composed of the ultrasonic wave transmitting transducer group(E11，E12，E13)，the ultrasonic wave receiving transducer group(E21，E22，E23)，the central processing unit(CPU)，the field programmable gate array(FPGA)，the analog to digital conversion circuit，the amplifier circuit，the filter circuit，the power amplification circuit，the digital to analog conversion circuit，the channel switching circuit，the display circuit，and the keyboard.Three pairs ultrasonic wave transducers are installed oppositely at the ektexine of the vessel which is filled up with media.

FPGA starts to drive the transmitting transducer group and sample the output signals of the receiving transducer group after receiving the commands from CPU.The digital signals，generated by the signal generator constructed in the FPGA，are converted to the analog signals through the D/A circuit.After the wave amplifying，the analog signals drive the transmitting transducers to transmit the ultrasonic wave one by one.The electrical signal，converted by the receiving transducers from the mechanical vibration，are filtered and amplified by the filter circuit and the amplifier circuit，then the processed electrical signal is transmitted to the analog to digital conversion circuit.

Figure 2.The principle diagram of ultrasonic densimeter

The A/D circuit converts the received signal to digital electrical signal，and stores the data in the RAM constructed in the FPGA.The CPU calculates the ultrasonic wave propagation time between the two oppositely installed transducers on the basis of the data stored in the FPGA.Then a density value can be gotten on the base of the relationship between the propagation time and density.

The channel switching circuit switches the new channel，and the driving circuit drives another transducer.The new density value is calculated by transmitting and receiving the ultrasonic wave between the transducers.At last，the CPU calculates the arithmetic mean of the several density values and gets the final result.

4.The ultrasonic driving signal and the echo signal

The function of the driving circuit is generating the driving signal which can stimulate the transducer transmit the ultrasonic wave.Under the control of the CPU，the signal generator constructed in the FPGA generates the digital sine waves.The digital sine waves are converted to the analog signal through waveform transform by the D/A conversion circuit，the filter circuit and the amplifier circuit.The schematic diagram of ultrasonic driving signal is shown in Figure 3.

Figure 3.The ultrasonic wave driving signal

The ultrasonic wave driving signal is composed of eight sine waves whose frequency is 1 MHz.The number ofwaveform and the frequency are based on a comprehensive analysis.The frequency of ultrasonic wave signal is the same to the frequency of driving signal.If the frequency of ultrasonic wave is higher，themeasurement resolution of the propagation time is better，but the propagation distance of ultrasonic wave is shorter because of the energy attenuation.

The echo signal processing circuit process the echo signal received and calculate the propagation time.The number of the driving signal waveform is setas eight to ensure the accuracy of propagation time measurement.With the emission and stopped of the driving signal，the echo signal present periodic change that the amplitude firstly increases and then decreases.In the echo signal，the maximum amplitude waveform is the characteristic wave，the zerocrossing of the characteristic wave is the feature point.The schematic diagram of the ultrasonic wave echo signal is shown in the Figure 4.

5.The precisionmeasurement of the propagation time

The key to ensure the precision measurement of media density is the high precision propagation time measurement of ultrasonic wave.As long as the time is measured accurately，the high precision density measurement can be realized.

The propagation time of ultrasonic wave is the time difference between corresponding points of the echo signal and the driving signal［7］.The key issue of precisemeasurement of propagation time is to determine the starting point time and the end point time.The propagation time is easy to be computed and implemented as long as the starting point and the end point are determined.The starting point is accurately determined by the hardware circuit，therefore，the accuracy of propagation time is dependent on the determination of the end point［8］.The schematic diagram of propagation time is shown in Figure 5.

Figure 4.The ultrasonic wave echo signal

Figure 5.The ultrasonic wave propagation time

The zero－crossing pointof the eighth waveform is set as the starting time，then the end point of the propagation time is the zero－crossing point of the characteristic wave，namely the feature point P0.The sampling frequency of A/D is fA/D，the time difference between two adjacent point is tA/D;the number of the sampling points from the first point to point P is N，the sampling value of point P is V1，the corresponding time is t1;the sampling value of point P1is V2，the time difference between P and P0is t2，the corresponding time of the point P0is tend，the starting time of the ultrasonic wave propagation time is tstart，the propagation time is t.

In the small area near the zero－crossing point，the wave curve of sine wave is close to the linear.The t2can be calculated on the basis of the linear interpolation method

6.The resolution analysis of density measurement

According to the principle of the density measurement on the basis of the ultrasonic technology，we can know that themeasurement accuracy of density is related to the propagation time.Therefore，the precision measurement of propagation time is very important.Because the starting point of propagation time can be determined accurately，the propagation time is measured as long as the end time can be determined accurately.

As known from the equation，the resolution of the end time is

The frequency of echo signal is 1 MHz;the resolution of the A/D chip is 10 bits，the sampling frequency of the chip is 16 MHz，then the amplitude of signal can be divided into 1 024 parts，there are 8 points can be sampled during half cycle.The waveform from positive maximum to negative maximum is seen as the linear.It is obviously known that

But，during the half period from positive maximum to negativemaximum，the curve slope near the zero－crossing point ismuch larger than the slope near the peak，then

The starting time can be accurately determined，then the resolution ofmeasured time is depended on the resolution of the end time［9］.From the equation(8)，the resolution of measured time is less than 0.488 ns.The distance between two oppositely installed transducers is a constant value，under the certain temperature，there are three density values been calculated.The final density is obtained through performing arithmetic average value of the density values.

For instance，when the temperature is 25℃，the density of water is 0.997 0 ×103kg/m3，and the propagation velocity of ultrasonic wave is1 497 m/s，while the density of alcohol is 0.789 0 ×103kg/m3and the propagation velocity of ultrasonic wave is 1 207 m/s.If the propagation distance is 0.3 m，at the 25℃，the ultrasonic wave propagation time in the water is 2.004 0 ×10－4s while 2.485 5 ×10－4s in the alcohol.The time difference is 4.8149 ×10－5s.If the propagation time is less than 4.814 9 ×10－9s，the resolution of measured density better than 0.000 021 ×103kg/m3can be realized.In the design，the ultrasonic densimeter can realize 0.488 ns timemeasurement，then themeasured density resolution can reach 0.000 01 ×103kg/m3.

7.Conclusion

Considering the defects of the conventional densimeters，the new thought is used to design a densimeter—ultrasonic densimeter.The ultrasonic densimeter has two features:

1)The ultrasonic densimeter adopts the distributed structure，the three pairs probes are oppositely installed at the ektexine of the vessel.The special structure forms a multiple channel measure system.The final result is obtained through processing the three density values with arithmetic average value method.The distributed structure design makes the resultmore close to the real value.

2)The digital subdivision interpolation algorithm and the A/D conversion circuit ensure the ultrasonic wave propagation time can be measured accurately.That fast－data－processing hardware circuit based on the FPGA makes the density measurement real－time.

From the analysis result，the designed ultrasonic densimeter can realize the resolution of timemeasurement better than 0.488 ns.It makes the measure－ment resolution of the ultrasonic densimeter reach 0.000 01 ×103kg/m3.

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精密超聲波密度計研究*

張興紅1，邱 磊?1，陳 鑫1，何 濤1，劉淑香2

1.重慶理工大學(xué)時柵傳感及先進(jìn)檢測技術(shù)重慶市重點實驗室，重慶 400054
2.四川工程職業(yè)技術(shù)學(xué)院 車輛工程系，四川德陽 618000

針對傳統(tǒng)的密度測量儀器存在的不足，根據(jù)超聲波的傳播特性設(shè)計了一種超聲波密度計。通過超聲波波速的測量來實現(xiàn)密度計的高精度測量。利用高分辨率、快速的信號采樣電路以及數(shù)字細(xì)分算法使超聲波傳播時間的測量達(dá)到ns級，為密度測量的分辨率優(yōu)于0.000 01×103kg/m3提供了保障。采用分布式多聲道結(jié)構(gòu)有利于密度測量精度的提高。

超聲波;密度測量;回波信號;數(shù)字細(xì)分算法

TP216

10.3969/j.issn.1001－3881.2014.24.008

2014－08－30