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Design and Implementation of Diaphragm

Type Pressure Sensor in a Direct Tire

Pressure Monitoring System (TPMS) forAutomotive Safety Applications

Ambarish G. MohapatraDept. of Applied Electronics and Instrumentation

Silicon Institute of Technology

Bhubaneswar, IndiaEmail: [email protected]

Abstract:Correct tire pressure is a critical factor in the safe operation and performance of a motor vehicle. Over inflatedtires often result in unnecessary tire wear, reduced gas mileage and less than optimal vehicle performance aswell as vehicle safety. A tire pressure monitoring system (TPMS) monitors air pressure and temperature in thetires of a motor vehicle, and that generates a signal indicative of the tire pressure and temperature in each of thetires to increase the vehicle performance and safety. Present work is based on the design of tire pressuremonitoring system which includes pressure sensor, an RF-communication unit, signal processing unit anddisplay unit. To sense the changes in inflation pressure, a diaphragm based pressure sensor was designed to beused in pressure measurement of the tube. The inflation pressure was transmitted to the receiver side using ISM(Industrial, Scientific and Medical) band at 433.92MHz and ASK (Amplitude-Shift Keying) modulationscheme. The pressure sensor was tested at room temperature as well as at elevated temperature of 33°C - 70°C.Finally, the collected data was analyzed and different sensor characteristics were found out.

Keywords: TPMS, Automotive safety, Pressure Sensor, Microcontroller, RF communication, ISM band, ASK.

1. Introduction

Tire Pressure Monitoring System (TPMS) plays a vital role in automotive safety applications [2]. This system is based on direct method of tire pressure measurement. This system contains a direct tire pressure monitoring principle, RF communication link and a display unit for monitoring the pressure of the tire. The pressure sensor used here was a piezoresistive type pressure sensor. The sensor was a circular diaphragm type pressure sensor and a strain gauge was bonded on one face of the diaphragm which was taken as reference pressure(atmospheric pressure) and other side was connected to the input pressure valve. A strain gauge is based on

piezoresistive principle so the resistance of the strain gauge will show a change. In a full bridge strain gaugeconfiguration the output voltage of the bridge will change with the change in strain gauge resistance. A/Dconverter is used to get digital data and was then transmitted to a central receiver to display the inflation pressure.

Ambarish G. Mohapatra / International Journal of Engineering Science and Technology (IJEST)

ISSN : 0975-5462 Vol. 3 No. 8 August 2011 6514

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Fig. 1. Basic block diagram of a Tire Pressure Monitoring System (TPMS)

In a tire pressure monitoring system the RF link plays a major role in sending data to the receiver unit near thedriver side. The transmission of data is done by a suitable packet format containing pressure sensor data.

Transmission and reception of sensor data: The sensor data was transmitted to a central receiver unit with aspecific serial ID and displayed in an LCD driver. The transmission and reception of data was done over ISM

band at a frequency of 433.92MHz [3]. The transmitted data was arranged in a header of preamble, sensor IDand pressure data. The display driver used was made by using a microchip PIC16F877A microcontroller and anLCD. The data encoding method used in this project is based on PWM format with TE (basic pulse element)

time of 400 s μ [Figure 2].

Fig. 2. Data encoding format

The transmitter data header

Preamble Sensor ID Sensor data

Fig. 3. Transmitter data header

Preamble: The preamble is a series of 31 logic ‘1’ bits followed by a single logic ‘0’ bit. The preamble allows

the receiver to recognize the RF transmission as a valid transmitted message. The preamble also allows thereceiver to synchronize to the RF message, thereby compensating for any oscillator inaccuracies within thetransmitter. The transmitter preamble bits can be varied based on the system requirements. Longer preamble bitlengths may be appropriate where receiver quiescent current is an issue. Shorter preamble bit lengths may beappropriate where transmitter battery usage is a concern. In either case, it is purely a trade-off between receiver quiescent current and battery power consumed by the transmitter device.

Sensor ID: The 32bit transmitter ID is used to uniquely identify each transmitter. A frame of 32 bits insures thatthere is a very low probability that any two transmitters will have the same ID.Sensor Data: The pressure in kg/cm

2was obtained putting the received unsigned value in the putting the

received unsigned value in the equation found by calibrating the sensor using the tire with different input pressure levels.



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2. System Configuration and Experimental Procedure

In the TPM system we have used following major component to monitors the internal pressure of anautomobile's tire.

a. Pressure sensor b. Associated signal conditioning unitc. Transmitter Unit

d. RF Receiver Unite. Liquid Crystal Display driver circuit

2.1. Design of diaphr agm type pressure sensor

The sensor used in this work was made using a special purpose diaphragm strain gauge bonded on a circular diaphragm. The sensor was designed using the equation 1.

2

22)1(

)82.0( Et

PR

V

E ν −=

Δ(1)

In the above equation the output voltage per volt of excitation is generally chosen to be 2mV/V for almost allthe strain gauge based transducers.

Table 1. Assumed sensor design parameters. Parameters Values chosen

V

E Δ

2 mV/V

E (Young’s modulus)AL 0.7E6 kg/cm2

P (Maximum pressure) 2.5 kg/cm2

ν (Poisson’s ratio) 0.3

R (Radius of thediaphragm)

1.5 cm

By putting the above parameters, the thickness of the diaphragm obtained as:t = 0.54mm

During design of the circular diaphragm pressure transducer two types of strain distributions were taken intoconsideration

• Circumferential Strain

• Radial Strain

Radial strain

Circumferential

strain

According to the strain distribution profile in the diaphragm [Figure 4] below at any input pressure the

circumferential strain T ε is always positive and maximum value at r=0. The radial strain Rε is positive in some

regions but negative in others and maximum negative value at r=R 0.

)23r 20

(R 28Et

)2 ν3p(1

ε R −−

=

)

2

r

2

0(R 28Et

)2

ν3p(1

T−

−=

ε



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Fig. 4. Strain distribution profile in the circular diaphragm

Under the action of the pressure the diaphragm deflects and changes from a flat circular plate to a segment of a

large radius shell. As a consequence, the strain in the diaphragm is nonlinear with respect to the applied pressure[15]. Acceptable linearity can be maintained by limiting the deflection of the diaphragm. The designconsideration of diaphragm pressure transducer contains two major parameters.

• Deflection of the diaphragm

• Natural frequency of the diaphragm (considered only for dynamic pressure measurement)

2.2. Deflection of the diaphragm:

The center deflection Wc of the diaphragm can be expressed as equation [2]

3

24

16

)1(3

Et

PRWc

ν −= (2)

The sensor output will be linear if Wc < t/4 at maximum pressure. As a general rule, the deflection of the

diaphragm at the center must not be greater than the diaphragm thickness for perfect linearity condition and thedeflection should be limited to one quarter the diaphragm thickness.

2.3. Natur al f requency of the diaphragm (for dynamic measurement):

In order to faithfully respond to dynamic pressures, the resonant frequency of the diaphragm must beconsiderably higher than the highest applied frequency. Depending strongly upon the degree of damping in thediaphragm strain gauge assembly and in the fluid in contact with the diaphragm, the resonant frequency should be at least three to five times as high as the highest applied frequency [15]. The subject of proper design for accurate dynamic response is too complex and extensive to be included here. However, for transducers subjectto high frequencies or to sharp pressure wave fronts involving high-frequency components, careful

consideration must be given to frequency response, both in terms of amplitude and phase-shift. The undamped

resonant frequency of a rigidly clamped diaphragm can be expressed using U.S. Customary Units as equation[3].

)1(

469.022

0ν γ −

= gE

R

t f n In Hz (3)

Where g = acceleration of gravity (386.4 in/sec2)

γ =weight density (lbs/in3)

The above equation [3] can be expressed as SI Unit as the equation [4] expressed below.

)1(

469.022

0ν ρ −

= E

R

t f n

In Hz(4)

Where ρ = mass density (g/cm2)



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The sensor used here was designed and calibrated for 0 to 2.5 kg/cm2

static pressure variation. By applying theabove equation for diaphragm deflection the deflection at the center of the diaphragm is 0.31346 cm, which ismore than the maximum center deflection of a square diaphragm at 2.5 kg/cm2.

2.4. Modeling of circular diaphragm:

The strain profile distribution of the diaphragm was also studied using finite element analysis (FEM) and partialderivative equation (PDE) method. Some of the analysis results are mentioned below.

Fig. 5. Total displacement (in meter) of the circular diaphragm Fig. 6. Mesh stucture of the circular diaphragm

Fig. 7. Strain energy density J/m3 of the circular diaphragmFig. 8. Stress distribution profile of the circular diaphragm

Here a special-purpose diaphragm strain gauge was mounted on one side of the diaphragm which was exposedto atmospheric pressure as a reference pressure and other side is exposed to tire inflation tire pressure. The linear gauge configuration [Figure 9] functions in the same manner as the circular configuration with only minor differences in total gauge output. The main advantages of using a linear design are ease of installation (lesssurface area to bond) and generally lower gauge cost. The diaphragm pressure transducer is small, easy tofabricate, and inexpensive, and has a relatively high natural frequency. The diaphragm type pressure sensor

designed in this project [Figure 10].

Fig. 9. Stress distribution profile of the circular diaphragm Fig. 10. Stress distribution profile of the circular diaphragm



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2.5. Cali brati on of pressure sensor: The designed pressure sensor was calibrated using a dead weight pressure gauge tester (which makes use of therelationship between pressure acting on the known area of a vertically free floating piston producing a force

balanced by known dead weights) and the input-output relationship was also found out.

2.6. Design of associated signal conditi oning cir cuit: The signal conditioning circuit was designed to amplify the sensor output voltage to match the resolution of themicrocontroller and to nullify the offset voltage of the strain gauge bridge circuit. The signal conditioning circuitwas made according to the specifications listed below.

Table 2. Signal conditioning circuit parameters.

Input parameter Source signal Signal conditioning

Input pressure range 0 – 2.5kg/cm2

Parameter: voltageRange: 14.4 mV – 26.6 mV

Parameter: Voltage, linear Range: 0 – 1.5 V

The bridge output voltage was given to a high input impedance circuit to minimize the loading effect. Theoutput voltage from the unity follower configuration was given to a differential amplifier to nullify the bridgeoffset voltage.

Fig. 11. Diaphragm type pressure sensor. Fig. 12. Pressure sensor connected to a tire.

Fig. 13. Signal conditioning unit and transmitter circuitconnected to a tire. Fig. 14. Transmitter and receiver circuits used in this work.

Fig. 15. Strain distribution profile in the circular diaphragm Fig. 16. Strain distribution profile in the circular diaphragm



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Fig. 17. Receiver unit and display circuit ready for online

measurement.

Fig. 18. Receiving data were monitored in a PC and stored for further analysis.

3. Results and Discussions

The system was designed to measure maximum tire pressure of 2.5kg/cm2 or 35.55psi. The system wasconfigured to transmit the tire pressure value continuously to a central receiver. The transmitter was also tested

with 54sec transmission delay to minimize the transmitter battery power dissipation. The output of the sensor was displayed in the central receiver using an LCD. Whenever the pressure will go above 2.5kg/cm2

and below2.2kg/cm

2, the warning LED was configured to blink with a warning sound using a buzzer. Different outputs of

the sensor with different input tire pressure levels were taken at both room temperature (33°C) and also at anelevated temperature to find out different static characteristics of the sensor. Different sensor characteristicswere also studied by analyzing the sensor outputs with respect to the input pressure levels.

Table. 3. Input tire pressure levels (kg/cm2) Vs Sensor output voltage (volts)

Pressure

(kg/cm2)

Output-

1(volts)

Output-

2(volts)

Output-

3(volts)

Output-

4(volts)

Output-

5(volts)

Output-

6(volts)

Output-

7(volts)

Out

put-

8(vo

lts)

0 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.00

6

0.2 0.066 0.060 0.066 0.067 0.068 0.066 0.066 0.067

0.4 0.180 0.178 0.182 0.178 0.180 0.179 0.180 0.17

8

0.6 0.300 0.297 0.300 0.296 0.300 0.297 0.300 0.29

6

0.8 0.416 0.416 0.420 0.416 0.420 0.416 0.416 0.41

6

1.0 0.530 0.530 0.531 0.530 0.530 0.531 0.530 0.53

2

1.2 0.657 0.658 0.658 0.659 0.658 0.658 0.659 0.65

8

1.4 0.749 0.748 0.749 0.747 0.749 0.750 0.749 0.74

7

1.6 0.859 0.859 0.859 0.859 0.859 0.859 0.859 0.859

1.8 0.959 0.959 0.959 0.959 0.959 0.959 0.959 0.959

2.0 1.060 1.060 1.060 1.061 1.060 1.060 1.062 1.06

0

2.2 1.165 1.165 1.165 1.165 1.165 1.165 1.166 1.16

6

2.5 1.355 1.355 1.355 1.355 1.355 1.355 1.355 1.35

5

3.1. Sensor character istics: From the input to the output, a sensor may have several conversion steps before it produces an electrical signal.For instance, pressure inflicted in the tire first results change in strain in the diaphragm, which, in turn, causes

deflection, which, in turn, results in an overall change in resistance in the strain gauge bonded on the diaphragm.This change in resistance will cause unbalance in the strain gauge bridge circuit, which, in turn, results in output

voltage change in the bridge circuit. From the input pressure and output voltage readings different sensor characteristics can be found out. The sensor characteristics studied in this project are listed [Table. 4].



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Table.4 Sensor Characteristics

Transfer function Repeatability

Full-scale input Resolution

Full-scale output Accuracy

Sensitivity Calibration error

Hysteresis Environmental factor (temperature)

3.2. Transfer function: An ideal or theoretical output stimulus relationship exists for every sensor. If the sensor is ideally designed and

fabricated with ideal materials by ideal workers using ideal tools, the output of such a sensor would alwaysrepresent the true value of the stimulus. The ideal function may be stated in the form of a table of values, agraph, or a mathematical equation. An ideal (theoretical) output–stimulus relationship is characterized by the so-called transfer function. This function establishes dependence between the electrical signal S produced by thesensor and the stimulus s: S =f (s). That function may be a simple linear connection or a nonlinear dependence,(e.g., logarithmic, exponential, or power function). In many cases, the relationship is one-dimensional (i.e., theoutput versus one input stimulus). A one-dimensional linear relationship is represented by the equation [5]

S =a +bs [5]

Where a is the intercept (i.e. the output signal at zero input signal) and b is the slope, which is sometimes called

sensitivity. S is one of the characteristics of the output electric signal used by the data acquisition devices as thesensor’s output. It may be amplitude, frequency, or phase, depending on the sensor properties.Logarithmic function:

S =a +b ln s [6]

Exponential function:

S =aeks [7]

Power function:

S =a0 +a1s [8]

Where k is a constant number.

A sensor may have such a transfer function that none of the above approximations fits sufficiently well. In thatcase, a higher-order polynomial approximation is often employed.

In this project by considering the input tire pressure levels and the corresponding output voltages, a linear

transfer function was obtained as the equations (9 and 10) written below. The function established between theelectrical signal S produced by the sensor and the stimulus‘s’ is given by: S=f(s)Theoretical calculation:

S= 0.4524*s [9]

Practical calculation: [From the graph as in Figure 19]

S= 0.55*s - 0.021 [10]

Fig. 19. Graph between input pressure [kg/cm2] Vs S/C output voltage [V]



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3.3. Full -scale input: A dynamic range of stimuli which may be converted by a sensor is called a span or an input full-scale (FS). Itrepresents the highest possible input value that can be applied to the sensor without causing an unacceptably

large inaccuracy. For the sensors with a very broad and nonlinear response characteristic, a dynamic range of theinput stimuli is often expressed in decibels, which is a logarithmic measure of ratios of either power or force(pressure). It should be emphasized that decibels do not measure absolute values, but a ratio of values only. Adecibel scale represents signal magnitudes by much smaller numbers, which, in many cases, is far more

convenient.By definition, decibels are equal to 10 times the log of the ratio of powers.

1

2log101 P

P dB =

[11]

In a similar manner, decibels are equal to 20 times the log of the force, pressure, current, or voltage.

1

2log201S

S dB =

[12]

In this project the sensor was designed according to the sensor design equation (1) for the maximum input tire pressure level of 2.5kg/cm

2. Means the sensor can sense a pressure range of 0 to 2.5kg/cm

2. Hence the highest

possible input value that can be applied to the designed sensor without causing an unacceptably large inaccuracyis 2.5kg/cm2.

Full-scale input = 2.5kg/cm2

= 35.55psi

3.4. Ful l-scale output: Full-scale output (FSO) is the algebraic difference between the electrical output signals measured withmaximum input stimulus and the lowest input stimulus applied.

Full-scale output = 1.131 volts [Theoretical]

= 1.355 volts [Practical]

3.5. Sensitivity: Sensitivity is a measure of the change in output of an instrument for a change in input. Generally speaking, highsensitivity is desirable in an instrument because a large change in output for a small change in output implies

that a measurement may be taken easily. Sensitivity must be evaluated together with other parameters, such aslinearity of output to input, range and accuracy. The value of the sensitivity is generally indicated by the transfer

function. Thus, when a pressure transducer output 0.55V per kg/cm2

, the sensitivity is 0.55V/kg/cm2

. Thesensitivity of the sensor was found out by plotting a graph between input tire pressure levels and output voltagereadings from the sensor.

Sensitivity = 0.45V/kg/cm2 [Theoretical]

= 0.55V/kg/cm2 [Practical]

3.6. Hysteresis:

Hysteresis error is a deviation of the sensor’s output at a specified point of the input signal when it isapproached from the opposite directions (Figure. 16). For example, a displacement sensor when the objectmoves from left to right at a certain point produces a voltage which differs by 20 mV from that when the object

moves from right to left. If the sensitivity of the sensor is 10 mV/mm, the hysteresis error in terms of displacement units is 2 mm.

Fig. 20. Measurement of Hysteresis error Fig. 21. Hysteresis calculation



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In these work two sets of readings, both in forward and backward directions were plotted as in Figure 21 and themaximum deviation was found out as 0.02kg/cm2.

Hysteresis = 0.02kg/cm2 [Theoretical]

3.7. Repeatability: A repeatability (reproducibility) error is expressed as the maximum difference between output readings asdetermined by two calibrating cycles [Figure.18), unless otherwise specified. It is usually represented as % of (Full-Scale) FS:

%100×Δ

= FS

r δ [13]

Possible sources of the repeatability error may be thermal noise, build-up charge, material plasticity, and so on.

Fig. 22. Repeatability error Fig. 23. Repeatability error calculation

Therefore by taking two sets of readings (RUN1 and RUN2), the repeatability error was found out as the graph(Figure. 19).

From the graph the deviation found out as ∆ = 0.02 from 1st and 2nd run.Repeatability error = (0.02/2.5)*100 = 0.8 %.

3.8. Resolution: The resolution (R) is the smallest increments of stimulus which can be sensed.

Resolution (R) = 0.0355Kg/cm2

0.50509psi

Where R is the smallest increments of stimulus which can be sensed

3.9. Accuracy: The deviation [Figure 24] can be described as a difference between the value which is computed from the outputvoltage and the actual input value.

Fig. 24. Accuracy error calculation

At 2.5kg/ cm2

output voltage = 1.355 VPressure = Full-scale output/Sensitivity

= (1.355/0.4524)= 2.99 kg/cm2

Error = 2.99 – 2.5 = 0.495 kg/cm2

% Error =100

5.2

495.0×

= 19.80% [Inaccuracy]



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4. Conclusion

The automobile Tire Pressure Monitoring System (TPMS) helps the driver to be conscious about the change intire inflation pressure. The system was designed successfully and also tested with different tire pressure levels at

different environmental conditions. The pressure sensor was designed using a self temperature compensateddiaphragm type strain gauge, operating temperature range of -75°C to +95°C, tested at a temperature range of 33°C – 70°C. The pressure data was successfully transmitted with a new transmission scheme to minimize the power consumption and maximize the transmitter battery life.

Acknowledgments

The authors thank to Dr. R. N. Pal, retired Professor IIT Kharagpur, India and his team for their help inconducting experiments with tire pressure monitoring system (TPMS). We also thank Prof. A.K.Tripathy,Silicon Institute of Technology, Orissa for his assistance in the research work in the laboratory.

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[5]. Song, H.J.; Colburn, J.S.; Hsu, H.P.; Wiese, R.W.; “Development of Reduced Order Model for Modeling Performance of Tire Pressure

Monitoring System”, IEEE 64th Vehicular Technology Conference, 2006. VTC-2006 Fall. 2006, Page(s): 1 – 5.[6]. Yulan Zhou; Yongsheng Chai; Yahong Lin; Kun Wang; “An application of multi-sensor information fusion in Tire Pressure

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[7]. Kukshya, V.; Song, H.J.; Hsu, H.P.; Wiese, R.W.; “Impact of Inter-Vehicular Interference on the Performance of Tire PressureMonitoring Systems”, IEEE 66th Vehicular Technology Conference, 2007. VTC-2007 Fall. 2007, Page(s): 778 – 781.

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About the authorAmbarish G. Mohapatra received the M.Tech. degree in Sensor System Technologyfrom Vellore Institute of Technology, VIT University, Vellore, India, in 2008 and theBachelor in Electronics and Communication Engineering (ECE) from NationalInstitute of Science and Technology (NIST), Berhampur, Inida, in 2004.

He is currently pursuing the Doctor of Science in Technology degree and is working asAssistant Professor in Silicon Institute of Technology, Bhubaneswar, India. He hasnumber of national and international papers in the field of sensing and control, where

his interests are sensors and transducers, MEMS, wireless sensor network andBiomedical signal processing.



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