1

Introduction

Chewing simulators are used for preclinical wear and fatigue testing or to simulate aging before an ultimate load test . According to FDA guidelines on good laboratory practice, most commonly used wear simulators have shortcomings in terms of control and regulation of force development . This could be one reason for the poor reproducibility and great variation of wear-testing results . For standardized testing and to achieve comparable results it is essential that the magnitudes of the forces generated by chewing simulators are exclusively defined by the test conditions, and that these are the same for every specimen.

The Willytec chewing simulator (Willytec/SD Mechatronik, Feldkirchen-Westerham, Germany) is a widely used weight-controlled chewing-simulation device . Although it has been reported that the forces generated by this chewing simulator are not well defined by the applied weights and are affected by the speed of descent of the countersample, this device seems to be a good compromise with regard to practicability, cost, and reliability . Another factor which may possibly effect contact forces in this and other chewing-simulation devices, has so far been neglected. Because of the dynamic mode of operation of this chewing simulator, we hypothesize that the contact force during the impact phase is not solely given by the test conditions (mass and velocity of the countersample), but also depends on the stiffness of the specimen. The objective of this study was, therefore, to investigate the effect of the specimen’s stiffness on the maximum contact forces for different test conditions (mass and velocity). Because a series of eight specimens can be tested simultaneously in the Willytec chewing simulator, possible differences between the test chambers of the chewing simulator were also of interest.

2

Materials and methods

The mode of operation of the Willytec chewing simulator ( Fig. 1 ) seems to be simple, and has been described in detail elsewhere . A rod loaded with extra weights (total mass m ) and an antagonist at the lower end is moved up and down by a crossbar. In our tests, the downward movement consisted of an acceleration on a distance of 2 mm, 4 mm way with a defined velocity <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='v’>vv
v
, and a deceleration on a distance of 2 mm. The impact of the antagonist on the specimen occurred at about half distance, i.e. during the phase with constant velocity. After the impact, rod and extra mass rest on the specimen as the crossbar moves further down. One cycle is completed when the antagonist is lifted from the specimen during the upward movement of the crossbar.

The Willytec chewing simulator.

Human enamel as well as four commonly used restorative dental materials differing in Young’s modulus were used to perform chewing simulation ( Table 1 ). For each restorative material, eight cylindrical disks (diameter 8 mm, height 2 mm, surface roughness R _a < 1 μm) were manufactured. For human enamel, almost planar sections of the buccal side of molars were used and trimmed approximately (deviations for height and diameter ±0.3 mm) to the same dimensions as the disks made of restorative dental materials. The enamel surface was not changed, i.e., grinding took place on all sides except the former tooth surface. All specimens were embedded in the specimen holders ( Fig. 2 ) with methacrylate (Technovit; Heraeus Kulzer, Hanau, Germany). Alumina spheres with a diameter of 4.5 mm and surface roughness R _a = 0.2 μm (Degussit; Friatec, Mannheim, Germany) were used as antagonists. These alumina spheres are also used in in vitro wear tests at our department.

Cylindrical disk (2 mm height, 8 mm diameter) embedded in the specimen holder with Technovit.

Force measurement with a very stiff sensor, placed between mass and specimen, would be a direct and accurate approach to measure the contact forces. However, if only one force sensor is available, the eight chambers have to be measured separately and due to the height of the force sensor only the investigated chamber could be loaded. To enable observation of the chewing simulator in its original state, i.e., no force sensor between mass and specimen, no readjustment when moving the sensor to the next chamber, and loading of all eight chambers simultaneously, the contact forces were not determined directly. Instead acceleration in the vertical direction (positive values in the direction of gravity) was measured at the upper ends of the rods. Preliminary tests showed that (a) periodic behavior occurred after 5–10 starting cycles, i.e., within each chamber a reproducible acceleration signal (<1% deviation of the signal magnitudes, identical shape) was measured for each impact, and (b) the recorded signal could be accurately reproduced after removing the sensor and placing it on the rod once more. With two accelerometers (B&K type 4383; Brüel & Kjaer GmbH, Bremen, Germany), the acceleration caused by impacts of a mass m = 5 kg moving with velocities v = 8, 15, 30, and 60 mm/s was measured for (1) all test chambers with the stiffest specimens, i.e., disks made of alumina, and for (2) the two test chambers showing the greatest deviation in (1) with the other specimens. In all tests, 100 cycles were performed and accelerations were recorded after 20 starting cycles to guarantee measurement of reproducible signals. The eigenfrequency of the accelerometers fixed to the rods was 20 kHz, thus stating the upper limit for accurate signal recording. Therefore, the output signal was recorded with a resolution of 5 μs (corresponds to a sampling frequency of 200 kHz).

In (1) the first accelerometer stayed on the rod of test chamber 1 (reference) and the second accelerometer was placed on the rods of test chamber 2 to test chamber 8, one after another. Therefore, all signals could be arranged on the same timescale with the acceleration signal of test chamber 1 as reference.

Estimation of the contact forces on the basis of the measured acceleration is explained in the following. Rigid body movement of the complete rod can be assumed as long as the length of the steel rod is small relative to the wavelength associated with the actual vibration frequency f . With a rod of length L = 0.4 m and a longitudinal wave speed c = 5400 m/s this assumption is valid for wavelengths λ = c / f > 10 L , i.e., frequencies f < c /(10 L ) = 1350 Hz. The contact force between antagonist and specimen, which is the only constraining force, is then given by F = − ma for rigid body movement. The measured acceleration signals were, therefore, low-pass-filtered at a frequency of 1000 Hz (<1350 Hz). The maximum contact force was therefore estimated as F _max = − ma _lf,max , where a _lf,max is the magnitude of the low-pass-filtered acceleration signal. This estimate is valid as long as the lower frequencies are dominant, i.e., higher frequencies can be neglected without causing a great error in contact force estimation. For this reason, the frequency spectrum of each acceleration signal was analyzed. With increasing high frequency part (which is neglected), an increasing error will be implemented in our estimation.

Since the influence of specimen stiffness and impact velocity were of interest, linear regression (SPSS 18.0, SPSS Inc., USA) was performed to test the dependence of relative force overshoot on Young’s modulus and impact velocity.

2

Materials and methods

The mode of operation of the Willytec chewing simulator ( Fig. 1 ) seems to be simple, and has been described in detail elsewhere . A rod loaded with extra weights (total mass m ) and an antagonist at the lower end is moved up and down by a crossbar. In our tests, the downward movement consisted of an acceleration on a distance of 2 mm, 4 mm way with a defined velocity <SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='v’>vv
v
, and a deceleration on a distance of 2 mm. The impact of the antagonist on the specimen occurred at about half distance, i.e. during the phase with constant velocity. After the impact, rod and extra mass rest on the specimen as the crossbar moves further down. One cycle is completed when the antagonist is lifted from the specimen during the upward movement of the crossbar.

The Willytec chewing simulator.

Human enamel as well as four commonly used restorative dental materials differing in Young’s modulus were used to perform chewing simulation ( Table 1 ). For each restorative material, eight cylindrical disks (diameter 8 mm, height 2 mm, surface roughness R _a < 1 μm) were manufactured. For human enamel, almost planar sections of the buccal side of molars were used and trimmed approximately (deviations for height and diameter ±0.3 mm) to the same dimensions as the disks made of restorative dental materials. The enamel surface was not changed, i.e., grinding took place on all sides except the former tooth surface. All specimens were embedded in the specimen holders ( Fig. 2 ) with methacrylate (Technovit; Heraeus Kulzer, Hanau, Germany). Alumina spheres with a diameter of 4.5 mm and surface roughness R _a = 0.2 μm (Degussit; Friatec, Mannheim, Germany) were used as antagonists. These alumina spheres are also used in in vitro wear tests at our department.

Cylindrical disk (2 mm height, 8 mm diameter) embedded in the specimen holder with Technovit.

Force measurement with a very stiff sensor, placed between mass and specimen, would be a direct and accurate approach to measure the contact forces. However, if only one force sensor is available, the eight chambers have to be measured separately and due to the height of the force sensor only the investigated chamber could be loaded. To enable observation of the chewing simulator in its original state, i.e., no force sensor between mass and specimen, no readjustment when moving the sensor to the next chamber, and loading of all eight chambers simultaneously, the contact forces were not determined directly. Instead acceleration in the vertical direction (positive values in the direction of gravity) was measured at the upper ends of the rods. Preliminary tests showed that (a) periodic behavior occurred after 5–10 starting cycles, i.e., within each chamber a reproducible acceleration signal (<1% deviation of the signal magnitudes, identical shape) was measured for each impact, and (b) the recorded signal could be accurately reproduced after removing the sensor and placing it on the rod once more. With two accelerometers (B&K type 4383; Brüel & Kjaer GmbH, Bremen, Germany), the acceleration caused by impacts of a mass m = 5 kg moving with velocities v = 8, 15, 30, and 60 mm/s was measured for (1) all test chambers with the stiffest specimens, i.e., disks made of alumina, and for (2) the two test chambers showing the greatest deviation in (1) with the other specimens. In all tests, 100 cycles were performed and accelerations were recorded after 20 starting cycles to guarantee measurement of reproducible signals. The eigenfrequency of the accelerometers fixed to the rods was 20 kHz, thus stating the upper limit for accurate signal recording. Therefore, the output signal was recorded with a resolution of 5 μs (corresponds to a sampling frequency of 200 kHz).

In (1) the first accelerometer stayed on the rod of test chamber 1 (reference) and the second accelerometer was placed on the rods of test chamber 2 to test chamber 8, one after another. Therefore, all signals could be arranged on the same timescale with the acceleration signal of test chamber 1 as reference.

Estimation of the contact forces on the basis of the measured acceleration is explained in the following. Rigid body movement of the complete rod can be assumed as long as the length of the steel rod is small relative to the wavelength associated with the actual vibration frequency f . With a rod of length L = 0.4 m and a longitudinal wave speed c = 5400 m/s this assumption is valid for wavelengths λ = c / f > 10 L , i.e., frequencies f < c /(10 L ) = 1350 Hz. The contact force between antagonist and specimen, which is the only constraining force, is then given by F = − ma for rigid body movement. The measured acceleration signals were, therefore, low-pass-filtered at a frequency of 1000 Hz (<1350 Hz). The maximum contact force was therefore estimated as F _max = − ma _lf,max , where a _lf,max is the magnitude of the low-pass-filtered acceleration signal. This estimate is valid as long as the lower frequencies are dominant, i.e., higher frequencies can be neglected without causing a great error in contact force estimation. For this reason, the frequency spectrum of each acceleration signal was analyzed. With increasing high frequency part (which is neglected), an increasing error will be implemented in our estimation.

Since the influence of specimen stiffness and impact velocity were of interest, linear regression (SPSS 18.0, SPSS Inc., USA) was performed to test the dependence of relative force overshoot on Young’s modulus and impact velocity.