Development of a pendulum machine for measuring contact lens friction

Abstract

The lubrication ability of a contact lens is one of its most essential properties because high friction on an eyelid causes discomfort during blinking. Friction measurements allow assessment of lubrication ability. So far, several apparatuses have been developed to measure contact lens friction. However, thus far, ocular physiological conditions including sliding speed and area have been imperfectly realised. Herein, a pendulum‐type friction tester was developed for the assessment of contact lenses under physiological conditions. A high sliding speed of 90 mm/s was achieved thanks to the short oscillation period of the small pendulum. Physiologically, the sliding surface on a contact lens was realised at the fulcrum of the pendulum. The coefficient of friction for the interaction between a contact lens and plastic hemisphere was directly calculated from the decay in potential energy during the free libration of the pendulum. Friction coefficient of a commercially available contact lens in saline solution, 0.1% and 0.3% HA solutions were 0.036, 0.039 and 0.050, respectively. These results were reliable because they ranged within the low levels reported by previous studies. It was shown that the present pendulum machine represents a major advancement in the realisation of physiologically realistic contact lens friction measurement.

INTRODUCTION

A contact lens is a device for visual correction. Today, a huge number of people worldwide wear contact lenses. Many of them, however, complain of discomfort after daily use []. To improve user comfort, many types of materials have been developed for contact lenses of different designs. Moreover, a variety of eye drops are available for the care of contact lens users.

As reported previously, contact lens friction during blinking causes discomfort to the user. Furthermore, high friction between the lens and eyelid can be the cause of lid wiper epitheliopathy []. Therefore, lubrication is essential for contact lenses. To assess this contact lens property, friction measurements are useful. A number of investigations into contact lens friction have been carried out []. When measuring friction to assess a contact lens, the physiological environment of an ocular surface must be reproduced (Figure ). Chemical conditions, including the material properties that are essential for the boundary lubrication, have been sufficiently realised in such investigations. The mechanical conditions essential for the fluid film lubrication, however, have not been adequately reproduced because of apparatus limitations. The contact pressure on the cornea is similar to that experienced by the underside of the eyelid []. In the literature studies, the contact areas have been, however, much narrower than those of real eyelids because of the use of flat counter surfaces. In addition, the sliding directions used have been linear, differing from the sliding that occurs on real eyelids. Moreover, the maximum sliding speed of around 120 mm/s during blinking motions [] cannot be reached in the laboratory because the sliding area is too small to allow acceleration to these speeds.

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Herein, the authors present an improved method to measure contact lens friction. Specifically, in this study an implementation of the pendulum method is adopted, a standard friction-measurement method. Circular sliding can be achieved by setting the contact lens specimen at the fulcrum of the pendulum. In addition, a wide circular area from the surface of a hemisphere that resembles an ocular surface can be realised on the counter surface. The friction coefficient was directly calculated from the decay in potential energy during the free libration of the pendulum. Some commercially available contact lenses were tested within different types of eye-drop solutions. The reliability of this measurement was evaluated by comparing the results with those of previous studies in the literature. Furthermore, it was found that the sliding speed was limited to 90 mm/s because of the size of the pendulum.

METHODS

Pendulum machine theory

A list of the relevant parameters for a general pendulum machine is provided in Table . A pendulum-type friction-tester is assembled from a frame and a weight, with a device to fix the specimen and a supporting base (Figure ). The friction measurement involves two circular surfaces that are slid across each other during the free libration of the pendulum frame. From the energy balance between frictional loss and the decrease in the potential energy of the pendulum, the coefficient of friction f can be calculated via the following Equation . 1 $f=\frac{l\cdot \mathrm{\Delta }\theta }{4r}$

TABLE 1 Pendulum machine parameter nomenclature

Specific Properties	State Variables
Friction coefficient	F	Sliding speed	v (m/s)
Sliding radius	r (m)	Inclination angle	θ (rad)
Length from fulcrum to gravity centre	$l$ (m)	Decay in amplitude	Δθ (rad)
Effective length of pendulum	L (m)	Angular velocity	ω (rad/s)
Inertia moment	I (kg m2)	Contact pressure	p (Pa)
Pendulum mass	M (g)	Libration period	T (s)
Lubricant viscosity	μ (Pa s)

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In Equation (), f is the friction coefficient, Δθ [rad] is the amplitude decay per libation cycle, l [m] is the distance between the centre of gravity and the fulcrum of the pendulum, and r [m] is the radius of the sliding surfaces. The angular amplitudes are detected by the use of an electric inclinometer [] or by direct reading like as in the present study.

When assessing lubrication properties, various environmental conditions should be controlled. The relevant physical parameters are force, pressure, speed, and the shape and size of the sliding area. The chemical parameters are the material properties of the sliding surfaces and lubricant, including its viscosity. These parameters should be given values that allow simulation of the actual environments of the object being assessed. The sliding speed v (m/s) is equal to the product of the angular velocity ω (rad/s) and the radius of curvature of the specimen r (m). 2 $v=r\omega$

Meanwhile, the angular velocity during the motion of a pendulum is approximately sinusoidal during one cycle of libration. 3 $\omega =\theta \sin \left(\frac{2\pi t}{T}\right)$

In Equation (), θ is the amplitude and T (s) is the period of the motion. Thus, the maximum sliding velocity v_max is given as follows. 4 $v_{\max }=\frac{2\pi r\theta }{T}$

The libration period T can be expressed as a function of the effective pendulum length L (m). 5 $T=2\pi \sqrt{\frac{L}{g}}$

Thus, the maximum sliding speed can also be expressed as follows: 6 $v_{\max }=r\theta \sqrt{\frac{g}{l}}$

Rearranging Equation (), the relationship between the effective length and maximum speed is also written as 7 $l=\frac{g{r}^2{\theta }^2}{v_{\max }^2}$

In Equations , $g$ is the acceleration due to gravity, 9.8 m/s². The radius of curvature of a standard contact lens r is approximately 10 mm. The amplitude θ cannot exceed π/6 rad because of the inclination limit of the pendulum frame, to avoid contact between the pendulum and the fixing device.

The sliding speed during the downward blink of an eyelid is, however, >100 mm/s []. When a value for sliding radius r is selected such that it is similar to the curvature of a contact lens (10 mm), a length $l$ of 27 mm is required to achieve this sliding speed. This length is only twice the diameter of a contact lens. Moreover, the distance between the fulcrum and gravitation centre l is smaller than the effective length L of the pendulum body, as shown in the following equation. 8 $L=l+\frac{I}{Ml}\ge l$

In Equation (), I is the moment of inertia of the pendulum and M is its mass. Therefore, a very small pendulum should be designed for measuring contact lens friction. If a heavy material is used for the pendulum frame, the moment of inertia and effective length are large, and therefore the sliding speed is low. Thus, a light material must be selected for the pendulum frame.

Pendulum machine for contact lens friction measurement

After consideration of the above-mentioned factors, the authors designed and built a pendulum machine to measure contact lens friction (Figure ). The shape and width of the sliding area are those of a complete contact lens itself, set at the fulcrum of the pendulum. The counter surface is a dome of polyethylene terephthalate (PET) with an internal radius of 10 mm (Figure ). The lower surface of the dome was finished with an average roughness of 0.3 μm.

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Pressure is applied to the specimen by the pendulum weight. Typical values of contact pressure on the entire eyelid have been reported to be in the range of 1–5 kPa []. The total load on the contact lens area (radius, typically 7 mm) required to realise this pressure is 0.15–0.77 N. Thus, the pendulum should weigh 16–79 g. However, the fact that disturbances during pressure measurements could make the values higher should be considered. Thus, the weight of the pendulum should be low as possible (Table ).

TABLE 2 Designed pendulum parameters

Design parameters
Mass: m		17.2 g
Sliding radius: r		10 mm
Length to the gravitational centre: $l$		27 mm
Actually measured values
Period: T		0.36 s
Equivalent radius: L		32 mm
Estimated maximum speed: Vmax		91 mm/s

The main frame of the pendulum is a wire made from a super elastic alloy (0.8 φ Ni-Ti alloy, ACTMENT Co. Japan), which is light and strong. The lens was bonded onto an acrylic hemisphere (radius of curvature, 9.5 mm) with silicon paste, as shown in Figure . The hemisphere was fixed to the pendulum frame by a T-shaped polypropylene pipe. The dome was connected to an aluminium ring base. The total weight of the main part of the pendulum was measured to be 17.2 g. The distance between the fulcrum centre and the centre of gravity was measured to be 27 mm (Figure ). A natural libration period of 0.364 s was measured for the pendulum. The equivalent radius was estimated using Equation () to be 32 mm. Using Equation (), the maximum sliding speed was estimated as 90 mm/s for the initial swing of the pendulum.

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The measuring system, as shown in Figure , was completed by the addition of a protractor to the back wall, behind the pendulum, a lever for the initial swing, and a digital video camera (CX370 V, Sony Co., Japan). During the free libration, the position of the marker on the protractor scale was recorded by the video camera. After the measurement, the amplitude of each libration was obtained from the movie, by replaying the pendulum motion. The angles corresponding to the turning point of each oscillation during the free libration were read from the movie screenshots on the monitor display, as shown in Figure . The decay in amplitude per cycle Δθ was calculated from the regression curve of the change in the turning-point angle (Figure ).

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Specimens and measurements

A commercially available daily disposable-type contact lens made of poly(2-hydroxyethyl methacrylate) (Narafilcon A, ACUVUE Trueye, Johnson & Johnson, United States) was used as the specimen. The radius of the base curve was 9.0 mm and the outer diameter was 14.2 mm. The average pressure due to the pendulum weight 17.2 g loaded on the contact lens surface was estimated to be 1.1 kPa because the (Figure ).

Before undergoing the friction test, the contact lens was rinsed with saline solution to remove any residual packing solution. The fixing device was cleaned with pure alcohol before the contact lens was bonded to the acrylic hemisphere.

The free libration commenced as soon as the contact lens was placed on the PET-dome counter surface. The pendulum frame was pulled to the hook by a string. An initial amplitude of π/6 rad was set by the position of the hook. Free swinging motion began after the pendulum was released from the hook. On occasions when the libration orientation was unstable, the measurement was re-started after securing the specimen position.

The specimen contact lenses were soaked in lubricant, which filled the PET dome. Three types of eye drops were used as the lubricant with different percentages of hyaluronic acid (HA): 0% (saline solution), 0.1%, and 0.3%. For each of these experimental conditions, 0.4 ml of solution was added to the lens. For comparison, measurements were also made in nothing (‘No lubricant’ condition); in this case, the lens surface was wiped dry after saline washing. The average molecular weight of HA is 1 MDa. The viscosity of each lubricant was measured using an Ubbelohde viscometer (SU, Sibata, Japan). The measured viscosity values for the saline, HA 0.1%, and HA 0.3% solutions were 0.92 mPa s, 3.13 mPa s, and 27.66 mPa s, respectively.

Ten specimens were used for each experimental condition (n = 10). All measurements were performed in a room in which the temperature and humidity were maintained at constant levels of 25.3 ± 0.6°C and 56 ± 3.5%, respectively.

RESULTS

In all the measurements it was observed that the angle at the turning point of the oscillation monotonically decreased (Figure ). The change in this angle was not, however, linear with oscillation number and was instead fitted to a quadratic function (Figure ). The decay in oscillation amplitude Δθ can be read from this fitted curve. The decay in amplitude gradually decreased with the progress of the libration. The friction coefficient, which was calculated using Equation (), decreased with the decay in amplitude. This change in the tribological conditions with the decay amplitude results from the change in sliding speed (4). A relationship between sliding speed and friction coefficient is apparent in Figure . However, high sliding speeds are required to realise the physiological conditions. Therefore, the authors used the average decay in amplitude for the initial five libration cycles as the result of the friction measurement.

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Thus, the measured coefficient of friction for the lens was 0.036 ± 0.003 (mean ± SD) in saline solution (0% HA). The corresponding values for 0.1% and 0.3% HA solutions were 0.039 ± 0.003 and 0.050 ± 0.007, respectively (Figure ). For the dry contact lens (no lubricant), the value was 0.055 ± 0.004.

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DISCUSSION

Over the past 2 decades, ever more sophisticated and effective applications of friction measurements have been employed to assess the lubrication ability of contact lenses [, ]. The measured coefficient of friction values for poly(2-hydroxyethyl methacrylate) contact lenses similar to those used herein vary widely, ranging from 0.02 to 0.3 (Table ). An exact value for this parameter remains unknown. However, it can be estimated that the resistance of the measurement system has been usually high to detect small friction coefficient of contact lenses. Therefore, low friction coefficient values are expected to be reliable. However, friction coefficients in the range of 0.03–0.04 were detected in these measurements using the pendulum method. These values are sufficiently low and therefore can be considered to be reliable. Thus, the reliability of the proposed method using the pendulum machine is confirmed.

TABLE 3 Literature contact lens friction measurement results

First Author	Rennie AC	Dunn AC	Roba M	Zhou Bo	Samsom M	Sterner O
Year	2005	2008	2011	2011	2014	2016
Machine	Tribometer	Tribometer	Tribometer	Tribometer	Torque meter	Tribometer
Counter shape	Flat plate	Flat plate	Flat plate	Flat plate	Pipe section	Flat plate
Counter material	Glass	Cell layer	Mucin-coated glass	Plastics	Glass	Glass
Motion	Straight	Straight	Straight	Straight	Round	Straight
Maximum speed	6 mm/s	0.3 mm/s	10 mm/s	0.1–5 mm/s	0.1–50 mm/s	0.1 mm/s
Pressure or load	10–40 mN	0.5 mN	2.7–6.7 kPa	0.5–100 mN	13–16 kPa	0.25–4 mN
Lubricant	Packing solution	Growth media	Tear-like fluid	Buffered saline	Additive PG4	Packing solution with additives
Specimen	Etafilcon A	Silicone-based hydrogel	Narafilcon A	Senofilcon-A	Narafilcon A	Senofilcon-A, et al.
Friction coefficient	0.05–0.07	0.03	0.032, SD 0.013	0.1	0.1–0.3	0.02

It was demonstrated in previous studies that the friction coefficient is dependent on the sliding speed []. This dependency was also seen in the results of the present study (Figure ). In addition, a speed of >100 mm/s, which is the speed of the human eyelid, is necessary to assess the lubrication ability of contact lenses. However, the sliding speed was limited to very low values in the previous studies [, , ], because commercially available tribometers, which have strokes that are too short to achieve high speeds, were used.

Using the proposed method, a maximum sliding speed of 90 mm/s was achieved for the pendulum that was developed. The sliding speed changes sinusoidally during each cycle of the motion of a pendulum. This motion resembles the blink of the eyelid, which is favourable for the accurate assessment of lubrication ability. The frame rate of the video camera used here was 30 fps. The maximum error for reading of the running-point amplitude value was estimated at 1%; the sinusoidal oscillation cycle has a period of 0.36 s. It may be appreciated that this sliding speed is significantly higher than those utilised in previous studies. Nonetheless, further acceleration is necessary to reproduce the speed of the blinking motions of the human eyelid. However, there is a specific sliding-speed limit for the pendulum machine.

The effective pendulum length is larger than the distance between the fulcrum and the gravitational centre, as shown by Equation (). However, the decay in amplitude Δθ increases with the friction coefficient f [see Equation ()]. When L is 32 mm and r is 10 mm, which is the case for the proposed pendulum machine, Δθ is given as follows: 9 $\mathrm{\Delta }\theta >1.25f$

On the other hand, the maximum initial amplitude is π/6 rad. Therefore, the total libration cycle n is as follows: 10 $n<0.42/f$

On the other hand, at least three libration cycles are necessary to complete the measurement of Δθ. The maximum friction coefficient that can be measured is 0.14. Fortunately, every friction coefficient obtained herein was lower than this value. The friction coefficients of some contact lenses, however, exceeded the value of 0.2 []. When measuring friction under such lubricating conditions, a larger pendulum is necessary to realise sufficient cycles of libration. The sliding speed in this case would inevitably be reduced. Fortunately, low-performance contact lenses can be assessed under any conditions, as they are different to physiological ones.

Despite its importance in lubrication, the effect of lubricant viscosity was not discussed in previous studies. Lubricant viscosity influences only the fluid film formation. During this period, the shape of the sliding surface is an important factor. When a tribometer is used for measurement of friction, the sliding surface is, however, very different from the actual eyelid surface that interacts with the contact lens. In addition, for the torque-meter measurements of Samson et al. [], only ring-like surfaces underwent sliding. In contrast, herein, the entire contact lens surface slid across a hemisphere. This sliding area is the same as that occurring in the physiological condition. Thus, this in vitro comparison of lubricants can be applied to the assessment of eye-drops.

Hyaluronic acid is generally used as the moisturising ingredient in eye drops. A lubricating effect is also expected for HA []. However, in the present results, HA was not demonstrated to possess lubrication properties. Rather, it was found that the viscosity of HA might increase the friction, as shown in Figure . The effects of viscosity on the frictional resistance were also observed through the speed dependency of the latter (Figure ).

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The material of the counter surface is an important factor in the assessment of lubrication ability. Actual eyelid materials, however, cannot be used for friction measurements. Mucin-coated glass, cell sheets, and plastic have all been used []. A clear difference between these materials was not reported for friction-measurement experiments. The polyethylene terephthalate hemisphere used herein could be a more appropriate material because this polymer surface is similar to cell membranes. Further modification of the counter surface could be helpful for the assessment of the lubrication abilities of contact lenses.

CONCLUSION

The authors developed a pendulum machine to assess the lubrication ability of contact lenses. Force, pressure, shape, and area were all selected to reproduce the physiological conditions. The counter surface material and lubricant can be selected for specific purposes. The sliding speed reached 90 mm/s, which is much higher than the corresponding values for previous studies but lower than the speeds of physiological eyelid motion. It was found, theoretically, that the sliding speed is limited by the size of the pendulum, with physiologically realistic high speeds becoming possible only for unfeasibly small pendulums.

ACKNOWLEDGMENTS

The authors would like to sincerely thank Dr. Kazuhiro Yoshida PhD for technical assistance with the experiments.

References

Efron, N., et al.: Lid wiper epitheliopathy. Prog Retin Eye Res. 53, 140–174 (2016). [DOI: https://dx.doi.org/10.1016/j.preteyeres.2016.04.004]