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Implementation of Force Sensor with Multi Strain Gauges for

Enhancing Accuracy and Precision

Y. C. Kim, Y. S. Ihn, H. R. Choi, S. M. Lee, and J. C. Koo

Abstract A force sensor using strain gauges is widely usedin many mechanical measuring systems. A method of measuringforce and contact point using two gauges is available althoughit rather limited to extension of micro scale measurement. Inorder to overcome this limitation and to maximize a precisionof the strain gauge sensor, sensor structure was optimized.Also, we used Kalman filtering for increasing an accuracy. Itsignificantly increase the signal to noise ratio and stability of thesensor. This force sensor using strain gauges will be applied todiverse fields such as inspecting a micro system or manipulatingsmall devices.

I. INTRODUCTION

The foundation of robotic industrial automation is basedon development of high performance actuators and sensors.

The need for sensors with high performance, small size,

high precision, and low price has increased with the de-

velopment of high performance robots with sophisticated

movement(e.g., humanoid) and the precision of semicon-

ductor and display equipment. It is essential that force

sensors can be tactile to manipulate fragile or transformable

objects precisely, and protect people and industrial equip-

ment. F. Beyeler et al. studied a micro-gripper with inte-

grated force sensor having maximum resolution of 70nNusing piezoelectric element, and K. Kim et al. studied

a micro-electromechanical system(MEMS)-based capacitive

force sensor having resolution of 33.2 nN. [1], [2]. Inthese case, the developed sensor has a very sophisticated

level of resolution; however, its drawback is high cost.

Menciassi et al. studied micro-gripper using force sensors

with a resolution of 1mNusing semiconductor strain gauges[3]. In this case, there is a limit of resolution due to the

influence from the outside such as noise and temperature.

However, because of its reasonable price, it is widely used

as a load cell or 6-axis F/T sensor. Some researchers have

studied development of sensors using strain gauges in various

fields. Arai et al. made a micro gripper for precise manip-

ulation [4]. His integrated piezo-resistive force sensor was

fabricated by micro-machining techniques. The resolution of

this force sensor was about 100 N. Bicchi et al. studiedthe contact sensing problem [5]. Methods of looking for

contact position and evaluating the force and moment at

the interface had been mentioned in their research. The

optimal position problem had been considered for a one-

dimensional(1-D) model with one and two strain gauges

Y. C. Kim, Y. S. Ihn, H. R. Choi, and J. C. Koo are with School ofMechanical Engineering, Sungkyunkwan University, Suwon, Korea

S. M. Lee is with Division of Applied Robot Technology, Korea Instituteof Industrial Technology, Ansan, Korea

All correspondences are to be sent to Prof. Koo at jckoo@skku.edu

[6], [7]. These studies mainly focused on characteristic of

strain gauges in order to improve accuracy and precision

of the sensor. In contrast, we principally focused on post-

processing by filtering, and on the structure of the sensor.

Resolution was increased using optimization of the sensor

structure based on the contact sensing problem. Precision

and accuracy was improved by applying the Kalman filtering

process to an experimental result. In this study, we developed

a theoretical approach to force measurement method and

the Kalman filtering process as described in Section 2.

In Section 3, the detailed optimization procedure of the

force sensor structure and implementation of measurementhardware system are decribed, and the performance of the

force sensor is estimated. In Section 4, we describe our

experimental results. In Section 5, we give our conclusions

and describe future work.

II. THEORETICAL BACKGROUND

A. Measuring Force

Our goal is to develop a force sensor using strain gauges

based on a calibration process between two strain values to

measure force value. Strain gauges 1,2 and 3 are attached

to a sensor structure made copper plate at fixed point x1,x2and x3. When sensor structure is deformed by contacting

other objects, strain value is measured through a strain gaugeamplifier. Because we know strain the value, the position of

each gauge, and the material properties of the copper plate,

force data is calculated using the following equations:

1 =My

EI =

h

2EIF(x x1) (1)

2 =My

EI =

h

2EIF(x x2) (2)

3 =My

EI =

h

2EIF(x x3) (3)

F1 = bh2

6(x2 x1)(E11 E22) (4)

F2 = bh2

6(x3 x1)(E11 E33) (5)

It has been located each at 1 , 2 and 3 on optimalposition from fixed section in order to get more sensitivity

information. Before it measures a force, the strain values at

each position can be calculated using equation (1),(2) and

(3) . These values were transformed using equation (4) and

(5). We estimated fused value through measured signal F1,

192978-1-4244-7102-7/10/$26.00 2010 IEEE

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F2 for more credible result. (h : thickness of beam, I : themoment of inertia, E : the modulus of elasticity, xn : theposition attached strain gauge from fixed section)

B. Kalman Filtering

A Kalman filter is an efficient infinite impulse response

filter, and is used to estimate the state of a dynamic system

using the observation values of error covariance through

an infinite cycle loop. The algorithm has several advan-

tages. First, it is simple because it is a recursive filter that

estimates the state from a series of noise measurements.

Second, astringency is distinguished more effectively than

other filters, and filtering can be processed in the time

domain. Third, it can be applied to diverse system models

because the algorithm is considered observation process with

variables. However, the Kalman filter has a weak point in

that requires a large quantity of calculations compared to a

least mean square(LMS) filter or recursive least square(RLS)

filter. A step for increasing sensor resolution is required to

filtering process to eliminate noise from measured original

data. The noises are caused by a characteristic of the sensor

or by analog-to-digital converting(ADC)process(these noises

are called measurement noise). Another noise,called process

noise, is caused by inaccuracy of the system model due to

a limitation that considering a large number of variables is

impossible(therefore, the model is no complete). Therefore,

the difference between predictions of the state of these part

is considered as noise. The noises are assumed to be a

gaussian model that is possible to express the characteristics

of noise by using value of mean and variance. The Kalman

filtering process is shown in Fig.1. And figure 2 show

an algorithm of the Kalman filtering process using MAT-

LAB/SIMULINK(The MathWorks, Inc.). Figure 3 shows a

simple model of our sensor, and the theoretical model isexpressed as follows:

amFk

k

=

0 1

mK

2T2 1

amFk

k1

+

1

m

0

Fs+wk

yk=

0 1 am

Fk

k

+ vk

(6)

III. SENSOR AND ALGORITHMA. Design of Sensor

A strain gauge is a device used to measure the defor-

mation of an object. Foil strain gauges are used in many

situations, but this is not enough to measure small forces.

For measurements of small strain, semiconductor gauges, so

called piezoresistors, are often preferred over foil gauges. A

semiconductor gauge usually has a larger gauge factor than a

foil gauge. Semiconductor gauges tend to be more sensitive

to temperature changes,are more fragile than foil gauges,

and result in much larger output for a given stress. Due to

Fig. 1. Kalman Filtering Process

Fig. 2. Kalman Filter algorithm (MATLAB/SIMULINK)

Fig. 3. System modeling

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TABLE I

THE STRAIN VALUES FOR DIFFERENT TYPES OF NOTCHES

Model Strain value (104)No-notch 0.2367

V-notch 0.3687

Rectangul ar-not ch 0.5741

Semicircle-notch 0.4268

these properties, they tend to be used in miniature sensor

designs. To increase the sensitivity of a strain gauge sensor,

efficient design of the sensor structure have to required on

gauge attachment points. First design of the structure made

from steel was very simple shaped but this tip can relatively

operate large contact force without considering optimized

gauges position. But next improved sensor made from copper

was changed structure to get some sensitive information.

We were tried to analysis and test among changing feasible

materials(e.g., stainless, aluminum, copper) then the copper

is so good in the result of analysis on equal applied force.

And structure is designed that could minimize the effect on

errors caused inner and outer environment and also could

maximize the sensitivity of sensor. The beam is made of thin

and flexible material that can easily bend even under a weak

force. Therefore, we designed an efficient beam structure that

used a notch formation at gauge attachment points. It would

be designed the fixed plate and notch of sensor beam. The

fixed plate could minimize a moving of sensor beam and

notch of sensor beam has to concentrate a stress form applied

force on optimized position. We considered three type of the

notch: V-shaped, rectangular, and semicircular. These three

models were verified using FE Analysis. According to the

strain values shown in Table I, the rectangular notch had

better than it about 1.5 times. Figure 4 shows the final modelused this study.

Fig. 4. Design of the sensor

Design of modeling, at second step, was considered that

the fixed plates are attached a rubber for hold harder and

the cover prevents plastic deformation of the copper plate

or damage to the gauges, and has electromagnetic shielding

and grounding to reduce noise. The size of the new model

was 85mm20mm15mm (length width height), and the

size of the inner beam part with the semiconductor strain

gauges was 60mm12mm4mm (length width height).

The tip was made from tungsten,used enhancing strain value

by increasing moment, with a diameter 0.1mm and length25mm. Each strain gauge was located at optimal positionfrom a fixed section for greater sensitivity. But the design

of the outer cover, at third step, was modified to enlarge the

inner space that could be allowed movement of the sensor

structure and tip.

B. System Setup

Figure 5 shows our experimental setup. To minimize

vibration by excitation transmitted from the floor, a vibra-

tion isolation table was used. To eliminate noise from the

environment (e.g. air flow, electric waves, and temperature),

we used a copper cover for shielding and to prevent plastic

deformation of the sensor structure. The experimental proce-

dure is following some steps. First step, the sensor tip contactto fixed object or specimen measured weight by other device.

Second, the strain value generated by the deformation of

the sensor structure was switched to a force signal using

calibration equation. To filter the signal from noise, two

sensor signals were optimized by the Kalman filtering pro-

cess. For this process, we used LABVIEW software(National

Instrument) and MATLAB/SIMULINK for the algorithm in

post-processing.

Fig. 5. Experiment System

IV. EXPERIMENTALR ESULTFigure 6 (left) shows measuring force value during 60

seconds, and the loading force over 2040s without filtering.

The signal shown is not clear due to noise. The noise causes

lower resolution, and thus it was impossible to measure force

at the micro-level. To overcome this limitation, a filtering

process is required. At each 20s and 40s interval, the impulse

of the moment occurred due to momentary contact with

the object. First, we analyzed the characteristic frequency

of the noise through fast Fourier transform (FFT) analysis,

and observed the peak point of the noise at a frequency

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of 25 Hz. Therefore, we were simply the convergence of

the results using low pass filtering (LPF) to compare with

the fusion from the Kalman filtering. Figure 6 (right) is a

result from Kalman filtering. LPF has a cut-off frequency

limitation, and does not have a fast response time at the

bandwidth of very low level frequencies. However, the results

from Kalman filtering showed that there was no loss of data,

and had a rapid response time. Therefore, we were able to

verify the results, as shown in Fig. 6, that the noise was

effectively eliminated and the sensor had a high resolution.

To compare the accuracy of the two methods, we conducted

a quantitative analysis thorough repeated experiments. The

figure 7 show that the results from Kalman filtering have

more high accuracy.

Fig. 6. Original Data(Left) and Kalman Filtering Data(Right)

Fig. 7. Comparison Results by KF and LPF

V. CONCLUSIONS

A. Conclusions

In this study, we proposed two methods for increasing asensitivity of the force sensor, one is the Kalman filtering

process. Through the filtering, we obtained reliable data and

effectively eliminated noise. Another method is a mechanical

design for optimizing a structure shape. We optimized the

sensor structure for enhancing a sensitivity using a notch

to concentrate strain, well-flexible material for maximizing

a deformation, and a rigid tip for additional moment force.

Therefore, we acquired precise measurable micro-level data

and obtained high-resolution data. Using this two methods,

we verified that fabricated sensor has a sensitivity of about

0.11mV/N. Force sensors using strain gauges are notwidely used in the field of micro measurement despite having

a cost advantage. However, fabricated sensor in this study is

possible applying for the micro system, we expect that the

strain gauge sensor will be widely applied in areas such as

industrial robots and sensors/actuators.

VI. ACKNOWLEDGMENTS

This research is financially supported by the Ministry of

Knowledge Economy(MKE) and Korea Institute for Ad-

vancement in Technology (KIAT) through the Workforce

Development Program in Strategic Technology, and by the

Ministry of Knowledge Economy(MKE) and Korea Evalu-

ation Institute of Industrial Technology(KEIT) through the

Industrial Technology Development Projects.

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