Determination of Surface Mechanical Properties Using a Hertzian Contact and Ultrasound Sensor J. Armendariz, A. Baltazar, C. Treesatayapun Robotics and Advanced Manufacturing Program, CINVESTAV, Unidad-Saltillo, Coahuila, Mexico
Abstract— Nondestructive monitoring of contact properties for biological and engineering materials is important in several engineering areas. Also, in robotics, manipulation of fragile objects requires precise determination of instantaneous contact area and forces with minimum intrusion. In this paper, a contact probe based on hertzian contact and ultrasonic energy transmission for characterization of surface properties is proposed. The probe is built from a solid semi-spherical head which is sonified from the top by an ultrasonic transducer with a center frequency of 1 MHz. Force range was 0-23N and displacements as small as 0.05 millimeters were reached with a proposed automatic control system. A quasi-static spring model to describe the interfacial properties at contact is studied. The results indicate that due to its high sensitivity, the probe could be used for measurements of surface mechanical response.
based on Hertzian contact and ultrasonic energy transmission for characterization of these surface properties is proposed. II.
DESIGN OF THE PROBE BASED ON HERTZIAN CONTACT AND ULTRASOUND
The main element of the structure design of the probe (Fig. 1) is a solid semi-spherical head which is sonified from the top by an ultrasonic transducer with center frequency of 1MHz and 19mm diameter. The transducer is used to generate an ultrasonic pulse inside the semi-sphere which sonifies the contact surface. The spherical shape of the probe allows analyzing the contact based on Hertz.
Keywords- instant contact; ultrasound; force estimation; surface properties
I.
INTRODUCTION
The appropriate knowledge of contact properties and force sensing are unquestionable requirements for grasping and handling materials in robotic manipulation. In previous years, several methods have been proposed to address this problem, including: proximity sensors for detecting materials in manipulation tasks [1], piezoelectric elements for localizing transient events between position and force control [2], tactile sensors to determine the shape and texture of surfaces [3], and estimation of friction coefficient between the robot end-effector and the grasped object by means of force sensors for determining optimal grasping forces [4]. Recently, the study of the human hand has drawn the attention of researchers in the field of robotic grasping and control [5] due to the inherent information that a dexterous human hand can provide about the contact, the friction, the increased contact area behavior, and the great sensitivity of touch [6, 7]. Meanwhile, the contact mechanic has been investigated by using ultrasound for describing the real contact area and its shape [8, 9]. The ultrasonic technique is used due to its high sensitivity for detecting changes on the signal response when two materials are brought into contact [10], and the possible application for estimating mechanical properties on the test surface [11, 12]. In this paper, hertz theory and ultrasound are combined for presenting a new method for measuring elastic and non-elastic response of materials with low yield modulus. The aim of this work is to investigate the possibility of using a semi-spherical probe illuminated at the contact by ultrasound to sense mechanical properties of materials. To accomplish this, a probe
Figure 1. Force probe based on hertzian contact and ultrasound, and probe dimensions.
An ultra thin force sensor (0.203mm) manufactured by Tekscan Inc. was integrated in the probe, which is used for estimating the elastic modulus of the test material when it is unknown; otherwise this sensor is not needed and the force is measured based on the hertzian model and ultrasound, used by the force sensor proposed. Fig. 2 shows the physical probe. INTEGRATED FORCE SENSOR
TRANSDUCER SENSOR STRUCTURE
SPHERICAL SHAPE SENSOR BASED ON HERTZIAN CONTACT
Figure 2. The physical probe based on hertzian contact and ultrasound.
The semi-spherical shape of the probe allows analyzing the contact between the test surface and the probe by measuring the amplitude of the reflected ultrasonic signal. If the interface is Plexiglas-air, almost all of the energy (99.995%) is reflected back to the transducer but if the probe makes contact with the material, part of it is transmitted into the test material. An example of the time domain signal response from the Plexiglas
E-mail addresses:
[email protected] (J. Armendariz),
[email protected] (A. Baltazar),
[email protected] (C. Treesatayapun).
To be published in IEEE Ultrasonics Symposium 2010
The probe design complies with the Hertz theory. It follows the assumption that each body can be considered as an elastic half-space loaded over an small elliptic region (in this case circular) and the dimension of such contact region at the interface is small compared with the dimensions of the bodies in contact, such that allows stresses and strains at contact can be treated independently of those coming from the geometry, method of attachment, or the boundaries of each solid [13, 14]. III.
EXPERIMENTS
The probe is integrated in a robotic system of four degrees of freedom (3 prismatic and 1 angular) developed and integrated in our laboratory. The drivers and user interface were developed in LabVIEW; this includes positioning the force probe, to control sending and receiving of ultrasonic pulses by using PCI Local Bus compliant device (PDA14), and performing the required signal processing. Once the reflected pulse is received by the PDA14 and passed to the PC, signal processing including a fast Fourier transform (FFT) is carried out to obtain the amplitude frequency spectrum of the test pulse. 0.4
Voltage [V]
0.2
0
-0.2
-0.4
0
1
2 Time [sec]
3
4 -5
x 10
Figure 3. Signal using a Plexiglas sphere.
Interface Plexiglas-air Amplitude [dB]
semi-sphere/air interface is shown in Fig. 3. Time and frequency domain analysis of echo-pulses signals could then be used for monitoring of signal amplitude variations. It is expected that the contact of the probe with the test surface would produce amplitude decreasing of the reflected signal. In the probe´s design the acoustic impedance mismatch at the interface was kept small (plexiglas-sample test). Thus, the instant contact could be monitored with the proposed ultrasonic sensor. After initial contact it is clear that the amount energy leaking into the test surface will be proportional to the contact area.
35 First time touching contact
30
25 0.2
0.6 0.8 Frequency [MHz]
1
1.2
Figure 5. The initial contact was determined by observing the drop in reflected ultrasonic energy.
A. Detection of Instantaneous Contact Preliminary experiments showed that the slight probe contact with the test surface produces amplitude reduction of the reflected signal (Fig. 4). This is because the acoustic impedance mismatch at the interface (plexiglas-elastometer or tomato fruit) is small. Therefore, it indicates that instant contact which otherwise is extremely difficult to monitor based only on the force sensor could be detected with the proposed probe. The initial contact was determined by observing the drop in reflected ultrasonic energy from the tip of contact allowing a very high sensitivity at the onset of contact (Fig. 5), and displacements as small as 0.05 millimeters were reached with a proposed intelligent control system based on fuzzy rules [15]. In order to verify the accuracy and the error when the first contact point is sensed, experiments were performed to compare the experimental contact radii and those predicted from hertzian contact. The experiments were carried out on a piece of Plasticine. Due to its plastic deformation, after applying and removing pressure by the probe, a permanent circular mark over the Plasticine is left (Table 1). Experimental radius was measured by a digital vernier. A good agreement between Hertz and real experiments was found. B. Detection of Normal Contact To determine normal contact in relation to the surface, it is necessary to analyze the amplitude variation when the angle varies. Thereby, normal contact is achieved when the drop in the reflected signal is a maximum; this is because a greater amount of energy is concentrated in the center of the probe (Fig. 6). TABLE I.
Figure 4. a) First contact point is detected when by observing the drop in reflected ultrasonic energy, b) displacement in the normal direction, where , and it is controlled by the robotic system.
0.4
EXPERIMENTAL CONTACT RADIUS COMPARED WITH HERTZ ON A PIECE OF PLASTICINE
Displacement [mm]
Radius predicted by Hertz [mm]
Experimental radius [mm]
Error [%]
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
3.16 4.47 5.48 6.32 7.07 7.75 8.37 8.94
3.25 4.65 5.73 6.64 7.60 8.29 8.78 9.37
2.7000 3.8250 4.4118 4.7500 6.9600 6.5633 4.7072 4.5442
To be published in IEEE Ultrasonics Symposium 2010
C. Estimation of the Elastic modulus Estimation of the elastic modulus is achieved by controlling the normal displacement in relation to the surface in combination with the Hertz theory. As we mentioned above, the probe structure integrates an ultra thin force sensor to allow measuring the reaction force; this value is used as data input in the Hertz theory (as described below) for estimating surface elastic modulus on the test material. It is important to mention that if the elastic modulus of the test surface is known, this force sensor is not needed and the force is measured by the proposed probe based on the hertzian contact and ultrasound. D. Force Contact Estimation The role of ultrasonic sonification of the contact area is twofold: first, it provides an effective method to detect the onset of contact due to its high sensitivity at contact; and second, it presents an alternative method to monitor applied force (pressure) especially for very low loads where the force sensor sensitivity is compromised. In the performed experiments, the normal displacement δ in relation to the surface was controlled with a robotic system and it was used as data input on the Hertz theory to estimate the normal contact force. As it was mentioned, the sensor is based on hertzian contact, and thereby, the shape of the area of contact and how it grows in size with increasing load can be predicted by Hertz [2] as a function of approach (), applied force (F), radius of curvature of the spherical probe (R), radius of the contact region (a) and the combined elastic modulus of the indenter and the specimen (E*). The area can be expressed as where
1/2 a R .
or
1/2 16 F 3RE*2 , 9
( Z1Z 2 )2 K 2 ( Z1 Z 2 )2 ( Z1Z 2 )2 K 2 ( Z1 Z 2 )2
The experiments were performed on the elastometer and analyzed by using the quasi-static spring model. By using (3) as the fitting curve in the numerical algorithm least square method, the results in Fig. 11 show good agreement for small displacements. The model fits well for displacements less than 0.3 mm. But for higher values, the model does not agree with results. The discrepancy could be related to the boundary conditions between the sphere and the test material. However, further analysis is needed.
(1)
No contact
The contact was carried out between the interface Plexiglas-elastometer and a tomato fruit. Fig. 7 shows the contact force as a function of displacement, on the elastometer. The area is a circle of radius a, and its circular shape is kept as the force is applied on the elastometer. As it can be noticed, the elastic modulus estimated by the proposed probe is in good agreement with the experimental results obtained by using the ultra thin force sensor. After the first contact point is detected, the signal amplitude decreases as a function of contact force (contact area increase) and therefore more ultrasonic energy is transmitted through the touching area. This is used to characterize the calibration curve between the signal amplitude of the ultrasonic reflection versus the applied load (Fig. 8).
3°
35
(2)
where , R, and E* are known parameters. The pressure distribution is a maximum at the center of contact and tends to zero at the edge of the contact circle. Therefore, outside the circular contact region the pressure is assumed zero.
(3)
where is the angular frequency of the wave ( ), Z is the impedance of each material in contact, and Re is the reflection coefficient.
4°
The contact force can be calculated as a function of the contact radius or as a function of the approach by 4 E*a3 F 3R
Re
Amplitude [dB]
R
E. Analysis of the quasi-static spring model In order to represent the contact properties of two media, Tattersall [16] proposed a model where the interfacial forces are represented by a density of springs between them, and the strength of the coupling is denoted by a constant K, as
2°
Normal contact
30
1°
25 20 0.2
0.4
0.6 0.8 1 Frequency [MHz]
1.2
1.4
Figure 6. Amplitude variation for different angles in relation to the surface. 25 Hertz theory data2 Experimental data data3
20
Force [N]
Acontact a
2
Similar experiments were conducted on a whole tomato fruit sample. Fig. 9 shows the contact force as a function of displacement. It can be seen that the ultra thin force sensor cannot measure forces lower than 2 Newton, but the force sensor proposed based on hertzian contact and ultrasound can measure forces under that threshold. This can be reached because the onset of the contact point is detected effectively. The calibration curve between the ultrasonic amplitude and the applied load is depicted in Fig. 10.
15
Load
Force probe based on hertzian contact and ultrasound
10 Unload 5 Force Sensor integrated 0
0
0.1
0.2
0.3
0.4 0.5 0.6 Displacement [mm]
0.7
0.8
0.9
1
Figure 7. The applied load increases as a function of displacement. The dashed lines show the experimental data measured by the ultra thin force sensor. The full line shows the result obtained with Hertz by using the elastic modulus estimated by the sensor based on hertzian contact and ultrasound (elastometer).
To be published in IEEE Ultrasonics Symposium 2010
Ultrasonic Amplitude [dB]
40 Hertz theory data2 Experimental Data data3
Force probe based on hertzian contact and ultrasound
38 36
Unload 34 32
Force Sensor integrated
30
Load 0
5
10
15
20
25
two media was described. The onset of contact was determined by observing the amplitude change of the ultrasonic signal from the tip of contact with very high sensitivity. Elastic modulus was determined by Hertz theory. The limit of the quasi-static spring model to describe the interfacial spherical contact was determined to be correct only at a few millimeter displacements after initial contact. It was concluded that the developed probe could be applied for measurements of surface mechanical response where a high sensitivity to contact is required.
Force [N]
Figure 8. After the first contact point is detected, the signal amplitude decreases as a function of contact force and therefore more ultrasonic energy is transmitted through the touching area (elastometer). 5 Hertz theory
Force [N]
4
Load
REFERENCES
data2 Experimental data data3
3
[1]
Force probe based on hertzian contact and ultrasound
[2]
2
Unload
1
0
ACKNOWLEDGMENT This work was partially supported by CONACyT Mexico, Grants SEP-CONACyT #58951 and #84791.
[3]
Force Sensor integrated
0
0.1
0.2
0.3
0.4 0.5 0.6 Displacement [mm]
0.7
0.8
0.9
1
Figure 9. The contact force as a function of displacement. After the load was removed, plastic deformation was observed. This is related to low yield modulus and the visco-elastic behavior of the sample fruit tomato.
[4]
[5]
Ultrasonic Amplitude [dB]
39 Hertz theory data2 Experimental Data data3
Force probe based on hertzian contact and ultrasound
38
[6]
[7]
37 Force Sensor integrated 36
[8]
Unload 35
34
Load
[9] 0
0.5
1
1.5
2
2.5 Force [N]
3
3.5
4
4.5
5
Figure 10. The calibration curve between the ultrasonic reflection versus the applied load (tomato). 0
Reflection Coefficient [dB]
[11]
0.05 mm
-5
[10]
0.1 mm 0.2 mm
0.3 mm
-10
[12]
0.4 mm
-15
0.5 mm
-20 0.6 mm
[13]
-25 -30
[14]
-35
[15] 5.5
6
6.5
7 7.5 Frequency [Hz]
8
8.5
9 5
x 10
Figure 11. Experimental data (continuous lines) compared with the quasistatic spring model (dotted).
IV.
CONCLUSIONS
[16]
R. Volpe, R. Ivlev, “A survey and experimental evaluation of proximity sensors for space robotics”, IEEE Int. Conf. on Robotics and Automation, 4, 1994, 3466-3473. J.S. Son, E.A. Monteverde, R.D. Howe, “A tactile sensor for localizing transient events in manipulation”, IEEE Int. Conf. Robotics Automation, San Diego, CA, 1994, 471-476. R.A. Russell, S. Parkinson, “Sensing surface shape by touch”, IEEE Int. Conf. Robotics Automation, Atlanta, GA, 1993, 423-428. M.R. Tremblay, M.R. Cutkosky, “Estimating friction using incipient slip sensing during manipulation task”, IEEE Int. Conf. Robotics Automation, Atlanta, GA, 1993, 429-434. I. Kao, F. Yang, “Stiffness and contact mechanics of soft fingers in grasping and manipualtion”, IEEE Trans. on Robotics and Automation, 20(1), 2004. L. Biagiotti, F. Lotti, C. Melchiorri, G. Vassura, “Mechatronic design of innovative fingers for anthropomorphic robot”, IEEE Int. Conf. on Robotics and Automation, Seoul, 2003. T. Inoue, S. Hirai, “Elastic model of deformable fingertip for softfingered manipulation”, IEEE Transactions on Robotics, Vol.22, No.6, pp. 1273-1279, Dec., 2006. R.S. Dwyer-Joyce, A.M. Quinn, B.W. Drinkwater, “An experimental procedure for mapping hertzian contacts”, Int. Conf. on Tribology, Beijing, 2001. M. Pau, F. Aymerich, F. Ginesu, “Distribution of contact pressure in wheel-rail contact area”, Tribology International, 253, 2003. R.S. Dwyer-Joyce, B.W. Drinkwater, “In situ measurement of contact area and pressure distribution in machine elements”, Tribology letters, Vol. 14, No. 1, 2003. R.S. Dwyer-Joyce, N. Hankinson, “Ultrasonic measurement of the elastic properties of soft surface coatings”, Tribology International, Vol. 39, No.4, pp. 326-331, 2005. A. Baltazar, S. Rokhlin, C. Pecorari, “On the relation between ultrasonic and micromechanical properties of contacting rough surfaces”, J. Mech. Phys. Solids, Vol. 50 , 1397-1416, 2002. A.C. Fischer-Cripps, Introduction to Contact Mechanics, Springer Science, New York, 2007. K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985. J. Armendariz, C. Treesatayapun, A. Baltazar, “Development of an estimated force feedback controller based on hertzian contact and ultrasound”, IEEE Robotic and sensors environments, Phoenix, AZ, 2010, in press. H.G. Tattersall, “The ultrasonic pulse-echo technique as applied to adhesion testing”, J. Phys. D: Appl. Phys. 6, 819, 1973.
A sensor based on ultrasonic reflected signals to determine instantaneous contact area and force on the interface between
To be published in IEEE Ultrasonics Symposium 2010
