DESC:TECHNICAL FIELD
Present disclosure relates to the field of testing and measurement devices. Particularly, but not exclusively, the present disclosure relates to a system and method for performing boundary lubrication studies and measuring tribological quantities. Further, the present disclosure also relates to an apparatus for testing lubricating properties of lubricants and/or the frictional and wear properties of materials.

BACKGROUND OF THE DISCLOSURE

Conventionally, while conducting tribological experiments for performing/determining boundary lubrication studies, experiments are formulated and performed in laboratory conditions such that, the associated experimental setup/machine simulates sliding characteristics present in actual working conditions. In laboratory conditions, motors and actuators may be employed to generate relative motion at the interface of interacting surfaces. Such relative motions between the interacting surfaces is opposed by friction force generated at the interface. Resistance to such relative motion, caused by the friction force, may be measured by using load cells.

However, there are two predominant problems associated with such conventional techniques of performing experiments. Firstly, the motors and/or actuators employed for generating relative motion have some inherent relative motion present therewithin. For instance, consider rotary motion generated by the motors and/or actuators. There exists a friction between interacting surfaces of the moving components of the motors and/or actuators, which affects frictional behavior at the interface being studied. The second problem lies on part of a measurement system associated with the experimental setup. For instance, in order to achieve high resolution in measured forces, stiffness of the load cell should be as low as possible. However, load cell includes some inherent stiffness associated therewithin, which adversely affects force measurements. Further, when the load cell is positioned in a system, the load cell itself applies a reaction force at the point of contact. Basically, the load cell offers a resistance to the motion due to its stiffness. Thus, the conditions simulated by the experimental setup is different in comparison with the actual conditions, due to addition of load cell/sensor stiffness and relative slip in the motors and/or actuators.

Further, another important aspect with regards to the load cell/sensor is its positioning or location of mounting in the experimental setup/machine. In order to accurately measure the friction force at the interface, the load cell/sensor should be placed as close as possible, to the motion being studied. The reason for such positioning is to minimize the effect of elasticity of the components present between the load cell/sensor and the motion being studied. Rigidity of structural member present between the interacting surfaces and the load cell/sensor influences the forces being measured. In other words, more rigid the structural member between the surface and the sensor, higher is the accuracy in the measured forces. Because of such higher rigidity, complete force will be transmitted to the load cell/sensor without much deformation of the intermediate structural member/components. Apart from the system stiffness, damping also plays a crucial role on the nature of the friction. Damping, inherently present in the experimental setup, causes additional energy loss in the system in addition to the frictional loss at the contact. In order to differentiate between the loss due to damping and loss due to friction, there should be a significant difference in their damping coefficients. Ideally, for a higher accuracy in frictional damping, the structural damping should be as low as possible. Therefore, it is important to have an under damped system.

The present disclosure is directed to overcome one or more limitations stated above or any other limitation associated with the conventional systems.

SUMMARY OF THE DISCLOSURE

One or more shortcomings of the conventional system are overcome by a system and a method as disclosed and additional advantages are provided through the system and the method as described in the present disclosure.

Additional features and advantages are realized through the techniques of the present disclosure.

In one non-limiting embodiment of the present disclosure, a tribometer for performing boundary lubrication studies and measuring tribological quantities is disclosed. The tribometer includes a first pendulum mounted on a first shaft accommodated in a first housing assembly. The tribometer further includes a second pendulum mounted on a second shaft accommodated in a second housing assembly. The second pendulum is positioned at a predetermined interval from the first pendulum. The first pendulum and the second pendulum are configured to swing independent of each other. The tribometer further includes a loading assembly coupled to free ends of the first pendulum and the second pendulum. The loading assembly is configured to provide a symmetrical loading condition between the free ends of the first pendulum and the second pendulum. The loading assembly includes a sample mounting unit adapted to provide a predetermined contact configuration between a sample and a surface contacting the sample. The loading assembly also includes at least one spring loading mechanism. The at least one spring loading mechanism includes a plurality of spring holders coupled to the sample mounting unit and to the free ends of the pendulum. The plurality of spring holders are configured to apply normal load at a point of contact between the sample and the surface contacting the sample. Further, a plurality of resilient members are configured to couple together the plurality of spring holders.

In an embodiment, the first housing assembly includes a first housing plate and a first bearing coupled to the first housing plate. The first bearing is also coupled to the first shaft accommodated in the first housing assembly. Further, the first housing assembly also includes a first and a second pendulum connectors for coupling the first pendulum to the first housing assembly.

In an embodiment, the second housing assembly includes a second housing plate and a second bearing coupled to the second housing plate. The second bearing is also coupled to the second pendulum shaft (also referred to as second shaft) accommodated in the second housing assembly. Further, the second housing assembly also includes a third and a fourth pendulum connectors for coupling the second pendulum to the second housing assembly.

In an embodiment, an encoder fixture is mounted on at least one of the first shaft and the second shaft. The encoder fixture is configured to measure angular position of at least one of the first pendulum and the second pendulum.

In an embodiment, a reader plate is coupled to at least one of the first shaft and the second shaft. The reader plate is mounted relative to the encoder fixture.

In an embodiment, the loading assembly includes a first adaptor, a second adaptor and a pendulum square for coupling of the plurality of spring holders to the sample mounting unit and to the free ends of the first pendulum and the second pendulum.

In an embodiment, the sample included in the sample mounting unit is a ball made of rigid material and the surface contacting the sample is at least one of a flat element made of rigid material.

In an embodiment, the sample mounting unit includes a ball holder including a first fastener for accommodating the ball made of rigid material. The sample mounting unit further includes a threaded member secured to the first fastener at one end and to a second fastener at an other end opposite the one end. The second fastener is fastened to the ball holder. A flat holder configured to accommodate the flat element. The flat holder is adapted to enable positioning of the ball and the flat element in a predetermined orientation relative to an axis of the sample mounting unit.

In an embodiment, the first pendulum and the second pendulum are mounted at a midpoint of the first shaft and the second shaft.

In another non-limiting embodiment of the present disclosure, a method for performing boundary lubrication studies and measuring tribological quantities is disclosed. The method includes mounting of a first pendulum onto a first shaft accommodated in a first housing assembly. The method further includes mounting of a second pendulum onto a second shaft accommodated in a second housing assembly. The second pendulum is positioned at a predetermined interval from the first pendulum. The method further includes coupling of a loading assembly to free ends of the first pendulum and the second pendulum. The loading assembly is configured to provide a symmetrical loading condition between the free ends of the first pendulum and the second pendulum. The method further includes providing a predetermined contact configuration between a sample and a surface contacting the sample by employing a sample mounting unit of the loading assembly. The method further includes applying normal load at a point of contact between the sample and the surface contacting the sample. The normal load at the point of contact is applied by employing a plurality of spring holders included in at least one spring loading mechanism of the loading assembly. The method further includes displacing the first pendulum and the second pendulum by a predefined angle relative to mean position of the first pendulum and the second pendulum. The method further includes determining total energy input to the first pendulum and the second pendulum during displacement of the first pendulum and the second pendulum by the predefined angle. The method also includes evaluating change in energy per unit sliding distance of the first pendulum and the second pendulum to determine energy dissipation and average friction in each swing cycle of the first pendulum and the second pendulum.

The foregoing summary is illustrative only and is not intended to be in any way limiting. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the drawings and the following detailed description.

BRIEF DESCRIPTION OF THE ACCOMPANYING FIGURES

The novel features and characteristics of the disclosure are set forth in the appended description. The disclosure itself, however, as well as a preferred mode of use, further objectives, and advantages thereof, will best be understood by reference to the following detailed description of an illustrative embodiment when read in conjunction with the accompanying figures. One or more embodiments are now described, by way of example only, with reference to the accompanying figures wherein like reference numerals represent like elements and in which:
Figure 1 is a schematic perspective view of a lateral force driven parallel pendulum tribometer, in accordance with an embodiment of the present disclosure.

Figure 2 is a schematic perspective view of a sample mounting unit, in accordance with an embodiment of the present disclosure.

Figure 3a is an exploded perspective view of a spring holder, in accordance with an embodiment of the present disclosure.

Figure 3b is a perspective view of the spring holder in an assembled state, in accordance with an embodiment of the present disclosure.

Figure 4 is a perspective view of a spring loading mechanism, in accordance with an embodiment of the present disclosure.

Figure 5 is a perspective view of a loading assembly, in accordance with an embodiment of the present disclosure.

Figure 6 is an exploded perspective view of the loading assembly, in accordance with an embodiment of the present disclosure.

Figure 7 is a perspective view of the loading assembly being mounted onto the pendulums, in accordance with an embodiment of the present disclosure.

Figure 8 is a perspective view of the pendulums being coupled to a housing, in accordance with an embodiment of the present disclosure.

Figure 9 is a perspective view of the housing mounted with pendulums, in accordance with an embodiment of the present disclosure.

Figure 10a is an exploded perspective view of a first housing assembly, in accordance with an embodiment of the present disclosure.

Figure 10b is a perspective view of the first housing assembly in an assembled state, in accordance with an embodiment of the present disclosure.

Figure 11a is an exploded perspective view of a second housing assembly, in accordance with an embodiment of the present disclosure.

Figure 11b is a perspective view of the second housing assembly in an assembled state, in accordance with an embodiment of the present disclosure.

Figure 12 illustrates a perspective view of the first and second housing assemblies mounted onto a top plate, in accordance with an embodiment of the present disclosure.

Figure 13 illustrates a perspective view of the top plate, in accordance with an embodiment of the present disclosure.

Figure 14 illustrates a schematic perspective view of the optical encoder, in accordance with an embodiment of the present disclosure.

Figure 15 illustrates a schematic view of the tribometer, with the pendulums being positioned in a stable configuration and in a deformed configuration, in accordance with an embodiment of the present disclosure.

Figures 16 and 17 is a schematic view of instantaneous position vectors of the contact points during sliding motion at the interface, in accordance with an embodiment of the present disclosure.

Figure 18 is a plot of angular position ? versus time for a calibration experiment, in accordance with an embodiment of the present disclosure.

Figure 19 is a plot of angular position ? versus time plot for sliding experiment, in accordance with an embodiment of the present disclosure.

Figure 20 is a plot of maximum amplitude in each cycle for the calibration experiment, with zero offset between the shafts, in accordance with an embodiment of the present disclosure.

Figure 21 is a plot of maximum amplitude in each cycle for dry contact, with 15mm offset between the shafts, in accordance with an embodiment of the present disclosure.

Figure 22 is a plot of angular velocity of rotation obtained by differentiating the ? with respect to time, in accordance with an embodiment of the present disclosure.

Figure 23 is a plot of comparison of angular velocity for the first pendulum and the second pendulum, in accordance with an embodiment of the present disclosure.

Figure 24 is a plot illustrating difference in angle between the first pendulum and the second pendulum, in accordance with an embodiment of the present disclosure.

Figure 25 is a plot of variation of sliding distance with time, in accordance with an embodiment of the present disclosure.

Figure 26 is a plot of sliding velocity versus time, in accordance with an embodiment of the present disclosure.

Figure 27 is a plot of variation of sliding distance and sliding velocity with time, in accordance with an embodiment of the present disclosure.

Figure 28 is a plot illustrating phase difference between sliding distance and sliding velocity, in accordance with an embodiment of the present disclosure.

Figure 29 is a spiral plot of sliding velocity versus the angular position (?, measured in degrees), in accordance with an embodiment of the present disclosure.

Figures 30a, 30b, 30c, and 30d are graphical plots of Angular position vs. Time response for 10 N normal load at point of contact between the ball and the flat (simply referred to as ‘point of contact’ hereinafter) for Hexadecane (HD), Hexadecane+1% Stearic acid (HDSA), 4T oil and Base oil (BO) lubricants, respectively, in accordance with an embodiment of the present disclosure.

Figures 31a, 31b, 31c, and 31d are graphical plots of Angular position vs. Time response for 20 N normal load at point of contact for Hexadecane (HD), Hexadecane+1% Stearic acid (HDSA), 4T oil and Base oil (BO) lubricants, respectively, in accordance with an embodiment of the present disclosure.

Figures 32a, 32b, 32c, and 32d are graphical plots of Angular position vs. Time response for 30 N normal load at point of contact for Hexadecane (HD), Hexadecane+1% Stearic acid (HDSA), 4T oil and Base oil (BO) lubricants, respectively, in accordance with an embodiment of the present disclosure.

Figures 33a, 33b and 33c are graphical plots of Normalized amplitude vs. Time for 10 N, 20 N, 30 N normal load at point of contact, in accordance with an embodiment of the present disclosure.

Figures 34a, 34b and 34c are graphical plots of reduction in maximum amplitude with number of cycles for 10 N, 20 N and 30 N normal load at point of contact, respectively, in accordance with an embodiment of the present disclosure.

Figures 35a, 35b and 35c are graphical plots of variation in energy dissipated per unit sliding distance in each cycle with number of cycles for different lubricants for 10 N, 20 N and 30 N normal load at point of contact, respectively, in accordance with an embodiment of the present disclosure.

Figures 36a, 36b and 36c are graphical plots of variation in energy dissipated per unit sliding distance in each cycle with maximum velocity for different lubricants for 10 N, 20 N and 30 N normal load at point of contact, respectively, in accordance with an embodiment of the present disclosure.

Figures 37a, 37b and 37c are graphical plots of Coefficient of Friction (CoF) vs. Maximum sliding velocity (Vmax) for 10 N, 20 N and 30 N normal load at point of contact, respectively, in accordance with an embodiment of the present disclosure.

Figures 38a and 38b are graphical plots of maximum velocity (Vmax) at transition from gross sliding to fretting, for 10 N normal load at point of contact, in accordance with an embodiment of the present disclosure.

Figure 39 is a graphical plot of transition from gross sliding towards fretting close to zero velocity at 30 N normal load at point of contact, in accordance with an embodiment of the present disclosure.

Figures 40a to 40f are graphical plots of percentage change in energy in the fretting transition regime plotted vs. Maximum velocity (Vmax) for various normal loads at point of contact, in accordance with an embodiment of the present disclosure.

Figure 41 is a graphical plot of Sliding velocity (in mm/s) vs. Angular position ? (in degrees), in accordance with an embodiment of the present disclosure.

Figure 42 illustrates color maps for 10 N normal load at point of contact, in accordance with an embodiment of the present disclosure.

Figure 43 illustrates color maps for 20 N normal load at point of contact, in accordance with an embodiment of the present disclosure.

Figure 44 illustrates color maps for 30 N normal load at point of contact, in accordance with an embodiment of the present disclosure.

Figure 45 illustrates rectangular color maps for 10 N normal load at point of contact, in accordance with an embodiment of the present disclosure.

Figure 46 illustrates rectangular color maps for 20 N normal load at point of contact, in accordance with an embodiment of the present disclosure.

Figure 47 illustrates rectangular color maps for 30 N normal load at point of contact, in accordance with an embodiment of the present disclosure.

Figure 48 is a flow chart of a method for performing boundary lubrication studies and measuring tribological quantities, in accordance with an embodiment of the present disclosure.

The figures depict embodiments of the disclosure for purposes of illustration only. One skilled in the art will readily recognize from the following description that alternative embodiments of the methods illustrated herein may be employed without departing from the principles of the disclosure described herein.

DETAILED DESCRIPTION

The foregoing has broadly outlined the features and technical advantages of the present disclosure in order that the detailed description of the disclosure that follows may be better understood. Additional features and advantages of the disclosure will be described hereinafter which form the subject of the description of the disclosure. It should also be realized by those skilled in the art that such equivalent systems, mechanisms, and methods which do not depart from the scope of the disclosure. The novel features which are believed to be characteristic of the disclosure, as to system and method of operation, together with further objects and advantages will be better understood from the following description, when considered in connection with the accompanying figures. It is to be expressly understood, however, that each of the figures is provided for the purpose of illustration and description only and is not intended as a definition of the limits of the present disclosure.

In the present document, the word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any embodiment or implementation of the present subject matter described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments.

While the disclosure is susceptible to various modifications and alternative forms, specific embodiment thereof has been shown by way of example in the drawings and will be described in detail below. It should be understood, however, that it is not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternative falling within the spirit and the scope of the disclosure.

The terms “comprises”, “comprising”, or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a method that comprises a list of steps does not include only those acts but may include other acts not expressly listed or inherent to such system and method thereof. In other words, one or more acts in the system and the method proceeded by “comprises… a” does not, without more constraints, preclude the existence of other acts or additional acts in the method.

Stribeck curve is a fundamental concept in the field of tribology derived by Richard Stribeck. The curve demonstrates that friction in fluid-lubricated contacts is a non-linear function of the contact load, the lubricant viscosity, and the lubricant entrainment speed. Particularly, the Stribeck curve shows relationship between coefficient of friction with product of relative velocity of sliding and viscosity of lubricant divided by the load per unit length. The Stribeck curve plotted for a particular lubricant describes the complete behavior of that lubricant. Further, lubrication mechanisms present in a tribo-system are broadly classified into 4 regimes, which are, boundary lubrication, mixed lubrication, elasto-hydrodynamic lubrication, and hydrodynamic lubrication regime. In the boundary lubrication, the chemistry of solid surface and the lubricant plays a major role, whereas in hydrodynamic lubrication regime, relative velocity and lubricant viscosity are dominant factors. Further, as the name indicates, in the mixed lubrication regime the imperative mechanisms are combinations of both boundary lubrication and hydrodynamic lubrication. Among the above-described lubrication regimes, the boundary lubrication regime is the least understood regime. Thus, in order to understand the operating lubrication mechanisms in different regimes of the Stribeck curve, it is important to measure the lubricant film thickness with higher accuracy. As described above, the boundary lubrication phenomenon is a complex phenomenon and its study requires the considerations of all the important factors in the sliding conditions. The present disclosure discloses a system and method for performing boundary lubrication studies and measuring tribological quantities.

Embodiments of the present disclosure disclose a lateral force driven parallel pendulum tribometer (simply referred to as ‘tribometer’ or ‘system’ or ‘test setup’ or ‘setup’ or ‘parallel pendulum machine’ or ‘machine’ hereinafter). The tribometer of the present disclosure has been configured as a high stiffness and highly under damped lateral force controlled tribometer. The tribometer has been configured such that, it is possible to achieve high resolution in sliding displacement at extremely low sliding speeds, which are the prerequisite conditions for achieving a boundary lubrication regime. Further, the tribometer has been configured to characterize effectiveness of lubricants under boundary lubrication conditions. The tribometer includes flexural members with associated stiffness, the flexural members being configured to store strain energy and release the strain energy upon actuation.

Henceforth, the present disclosure is explained with the help of figures of the tribometer and the components included in the tribometer. However, such exemplary embodiments should not be construed as limitations of the present disclosure, since the tribometer may be used with other types of pendulums, lubricants, contact types, actuators, and the like. A person skilled in the art can envisage various such embodiments without deviating from scope of the present disclosure.

Figure 1 is an exemplary embodiment of the present disclosure, which illustrates a schematic perspective view of a lateral force driven parallel pendulum tribometer (100). The tribometer (100) may include two pendulums mounted on two different shafts. The two pendulums may be mounted such that the two pendulums are separated by a predetermined interval therebetween. Both the pendulums are configured to swing independently. The pendulums may swing independently only in a free condition or in a no-load condition. The term ‘free condition’ or ‘no-load condition’ refers to absence of any load at free ends of the pendulum or when the free ends of the pendulum are not coupled to the loading assembly of the present disclosure. The free ends are those ends of the pendulum that are opposite to the ends that are coupled to a first shaft and a second shaft of the tribometer (100). Mutual dependence of motion between the two pendulums may be created by employing loading assembly including resilient members such as springs. The tribometer (100) may be configured to create a predetermined contact configuration while performing experiments for boundary lubrication studies. The tribometer (100) may be configured to create a ‘ball on flat contact’ type of contact configuration, while performing experiments for boundary lubrication studies. However, any other contact configuration required for performing experiments for boundary lubrication studies may also be created. During conduction of experiments, a ball (1) [shown in figure 2] may be mounted on a first pendulum (31a, as shown in figure 12) and a flat (6) may be mounted on a second pendulum (31b, as shown in figure 12). The second pendulum (31b) may be positioned at a predetermined interval from the first pendulum (31a). That is, the second pendulum (31b) is mounted at a distance (the predetermined interval) from the first pendulum (31a). Springs may be employed to apply normal load at the interface between the ball (1) and the flat (6). The term ‘normal load’ as used herein refers to a load/force that acts perpendicular (or ‘normal’) to the surface of an object, whereby exerting a normal stress. The first pendulum (31a) and the second pendulum (31b) may be displaced by a predefined angle relative to a mean position of the first pendulum (31a) and the second pendulum (31b). The term ‘mean position’ refers to the zero position of the first pendulum (31a) and the second pendulum (31b) that may be taken as a reference position i.e., 0 degrees. The first and second pendulums (31a, 31b) may be released from a given initial angle, to create a sliding motion at the interface between the ball (1) and the flat (6). Rotation of the first pendulum (31a) may be measured by a rotary encoder. The rotary encoder may be mounted on a shaft associated with one of the first pendulum (31a) and/or the second pendulum (31b). The rotary encoder may be configured to measure angular position of the pendulum it is mounted upon, as a function of time. Parameters such as frictional force and coefficient of friction may be calculated by measuring drop in angle of the pendulum in each cycle. The tribometer (100) may be configured to conduct experiments including different combinations of parameters. Various parameters that may be adjusted, varied and/or controlled to conduct experiments may include, but not limited to, normal load, frequency of oscillations, length of pendulum, amplitude of sliding and angle of release of the pendulum. Operational parameters and specifications of the tribometer (100) may be in the range as indicated in Table 1 shown below.

Sl. No. Specification Value/Range
1 Maximum speed of the pendulum 165 rpm
2 Rotary Encoder Resolution 0.79 arc seconds (0.000219 degrees)
3 DAQ rate 100kHz, 10MHz
4 Operating temperature Room temperature

Table 1: Tribometer specifications

Figure 2 illustrates a schematic perspective view of a sample mounting unit (10), in accordance with an embodiment of the present disclosure. The sample mounting unit (10) may be configured to create the ‘ball on flat contact’ type of contact configuration while performing experiments. The sample mounting unit (10) includes the ball (1) that may be held in a first ball holder nut (2) (also referred to as ‘first fastener’) of a ball holder (5). The ball holder (5) further includes a bolt (3) that may be fastened to the first ball holder nut (2) at one end and to a second ball holder nut (4) (also referred to as ‘second fastener’) at other end. The second ball holder nut (4) may also be fastened to the ball holder (5). The sample mounting unit (10) further includes the flat (6) that may be held in a flat holder (7). The flat holder (7) may be configured to accommodate the flat element (6) such that the flat holder (7) is adapted to enable positioning of the ball (1) and the flat element (6) in a predetermined orientation relative to an axis of the sample mounting unit (10). The axis of the sample mounting unit (10) may be positioned at the point of contact of ball (1, 17) and the flat (6, 16) and may be perpendicular to the loading direction. The flat holder (7) may include two slots such that, the two slots enable mounting of the flat holder (7) on a horizontal rod as well as on a vertical rod while keeping the sample (i.e., the ball (1) and the flat (6)) in a vertically upright position. The term ‘sample’ as used herein refers to the ball (1) and the phrase ‘surface contacting the sample’ refers to the flat element (6). The flat holder (7) may include a back plate (8) that enables fastening of the flat holder (7) to a shaft/rod mounted on a pendulum rod. The back plate (8) may include a tap adapted for a 4 mm grub screw. The grub screw enables positioning and fastening of the flat holder (7) at a desired location. Further, the ball holder (5) may also include a tap for grub screw that enables positioning and fastening of the ball holder (5) at a desired location.

Figure 3a illustrates an exploded perspective view of a spring holder (20), in accordance with an embodiment of the present disclosure. The spring holder (20) includes a frame (9) to which two spring hooks (14) are coupled or attached symmetrically. The two spring hooks (14) hold springs as illustrated in figure 4. The spring holder (20) further includes a slider (11) mounted on a lead screw (12). Upon rotation of the lead screw (12), the slider (11) moves back and forth accordingly, resulting in stretching of the springs attached to the hooks (14). Such movement of the slider (11) and the stretching of the springs attached to the hooks (14) results in application of normal load at the point of contact between the ball (1) and the flat (6) (simply referred to as ‘point of contact’ hereinafter). Therefore, the magnitude of normal load applied at the contact hence depends on the stiffness of the springs used to apply load. Accordingly, the tribometer (100) of the present disclosure enables conduction of experimental tests over a wide range of normal loads. Further, figure 3b illustrates a perspective view (30) of the spring holder (20) in an assembled state, in accordance with an embodiment of the present disclosure.

Figure 4 illustrates a perspective view of a spring loading mechanism (40), in accordance with an embodiment of the present disclosure. The spring loading mechanism (40) includes a first spring holder (20a) including a back plate (8a), a frame (9a), a slider (11a), a lead screw (12a) and a washer (13a). The spring loading mechanism (40) further includes a second spring holder (20b) [which may be considered to have constructional features that are diametrically similar to the first spring holder (20a)]. However, for the purpose of clarity, various parts of the second spring holder (20b) are provided with different referral numerals] including the frame (9b), the slider (11b), the lead screw (12b) and the washer (13b). The first spring holder (20a) and the second spring holder (20b) may be coupled together by a pair of springs (15a and 15b). A flat specimen (16) may be mounted on the back plate (8a) and may be in contact with a ball specimen (17) mounted on the second spring holder (20b).

Figure 5 illustrates a perspective view of a loading assembly (50), in accordance with an embodiment of the present disclosure. The loading assembly (50) is configured to create mutual dependence of motion between the two pendulums (31a and 31b). The figure illustrates positioning of the spring holder frames (9) in the loading assembly (50). Further, figure 6 illustrates an exploded perspective view (60) of the loading assembly (50), in accordance with an embodiment of the present disclosure. The loading assembly (50), as depicted in figure 6, includes a first adaptor (18), a second adaptor (19) and a pendulum square (21) for coupling of the spring holder frames (9) to other components that are included in the loading assembly (50) and for mounting of the loading assembly (50) onto the pendulum. The loading assembly (50) may include four spring holder frames (9). Normal load may be applied at the point of contact between the ball specimens (17) and the flat specimens (16), with the help of springs (15a and 15b). Two spring holder frames (9) may be positioned/mounted on each of two horizontal rods holding the ball and flat assembly (i.e. sample mounting unit 10). Two spring holder frames (9) may be mounted in the front of the ball (1, 17) and two spring holder frames (9) may be mounted at the rear of the flat (6, 16). Such positioning or mounting of the spring holder frames (9) may result in symmetrical loading at the point of contact between the ball (1, 17) and the flat (6, 16). A loading is considered to be symmetric with respect to an axis in its plane, if the reflection of the loading about the axis is identical to the loading itself. The term ‘symmetrical loading’ as used herein refers to a condition in which the reflection of the loading is identical to a plane/axis at the point of contact of ball (1, 17) and the flat (6, 16). The plane/axis at the point of contact of ball (1, 17) and the flat (6, 16) may be perpendicular to the loading direction. The loading direction may be parallel to the plane/axis of swing of pendulums (31a, 31b). Initially, contact between the ball (1, 17) and the flat (6, 16) may be made and normal load may be applied with the help of four springs (i.e., two sets of 15a and 15b).

Figure 7 illustrates a perspective view (70) of the loading assembly (50) being mounted onto the pendulums, in accordance with an embodiment of the present disclosure. The loading assembly (50) may be mounted onto the pendulums by employing, but not limited to, the first adaptor (18), the second adaptor (19) and the pendulum square (21). Further, figure 8 illustrates a perspective view (80) of the pendulums (mounted with the loading assembly (50)) being coupled to a housing, in accordance with an embodiment of the present disclosure. Figure 9 illustrates a perspective view (90) of the housing which is depicted in an assembled condition.

Figure 10a illustrates an exploded perspective view of a first housing assembly (110), in accordance with an embodiment of the present disclosure. The first housing assembly (110) includes a first housing plate (22a), a first bearing (23a) coupled to a first pendulum shaft (also referred to as ‘first shaft’ hereinafter) (24a), and a first and a second pendulum connectors (25a and 25b) for coupling the pendulum to the first housing assembly (110). The first housing assembly (110) further includes an encoder fixture (26) and a readhead or a reader plate (27) which may be connected to the first pendulum shaft (24a). Further, figure 10b illustrates a perspective view (120) of the first housing assembly (110) in an assembled state.

Figure 11a illustrates an exploded perspective view of a second housing assembly (130), in accordance with an embodiment of the present disclosure. The second housing assembly (130) includes a second housing plate (22b), a second bearing (23b) coupled to a second pendulum shaft (also referred to as ‘second shaft’ hereinafter) (24b), and a third and a fourth pendulum connectors (25c and 25d) for coupling the pendulum to the second housing assembly (130). Further, figure 11b illustrates a perspective view (140) of the second housing assembly (130) in an assembled or workable state

Figure 12 illustrates a perspective view (150) of the first and second housing assemblies (110, 130) mounted onto a top plate (28), with the first and second pendulum (31a, 31b) hanging downwardly. Figure 13 illustrates a perspective view (160) of the top plate (28), in accordance with an embodiment of the present disclosure. In the embodiment, both the first and second housing assemblies (110, 130) may be constructed from a single piece of metal so as to avoid any temporary joints in their basic construction. In order to mount the shafts (24a, 24b) on the housing (110, 130), two rectangular columns (29) of the dimensions 50x10x72mm may be cut out from a single block of Aluminum. The rectangular columns (29) may have co-axial holes of diameter 22mm to enable mounting of roller bearings. Two roller bearings (23a, 23b) of inner diameter 10mm and outer diameter 2mm are coupled to the ends of the shafts (24a, 24b) as shown in the figures 10a, 10b, 11a and 11b. The above-described assembly of the shafts (24a, 24b) and the bearings (23a, 23b) may be mounted onto the housing assemblies (110, 130). The roller bearings (23a, 23b) may be fastened at their locations with the help of grub screws mounted on a top face of the rectangular column (29) as shown in the figure. All the components of the loading assembly (50) being mounted onto the pendulums may be onto the top plate (28) by means of the first and second housing assemblies (110, 130). As illustrated in the figure, the first housing assembly (110) is coupled to a first pendulum (31a) and the second housing assembly (130) is coupled to the second pendulum (31b).

In an embodiment, the pendulums (31a, 31b) may be positioned at the center of the shafts (24a, 24b). The encoder fixture (26) may be held at an end of the shaft (24a, 24b). The dimensions of the shafts (24a, 24b) may be optimized to have minimum deflection, that may be caused by the weight of the pendulum (31a, 31b) and by the weight other assemblies that are mounted onto the pendulum (31a, 31b). The first pendulum (31a) and the second pendulum (31b) may be mounted at a midpoint of the first shaft (24a) and the second shaft (24a), to have minimum deflection, that may be caused by the weight of the pendulum (31a, 31b) and by the weight other assemblies that are mounted onto the pendulum (31a, 31b). In the embodiment, the total weight of pendulum (31a, 31b) in combination with the weight of other assemblies mounted onto the pendulum (31a, 31b) may be 5 kilograms (kg). By considering a factor of safety (FoS) of 2, the pendulum shafts (24a, 24b) may be structurally designed for a normal load of 10 kg. Further, conventionally, bearings (23a, 23b) are coupled to the shafts through pressing operation. It is important to note that, pressing operation may induce deformation and bending in the shafts if not done with precision. Such deformation and bending should be avoided, as a load cell and/or a sensor may be mounted on one end of the shaft and hence adequate care needs to be taken during loading. In addition, bending in shafts will cause misalignment in the positioning of the load cell and/or sensor. In the embodiment, in order to prevent such bending, the shafts (24a, 24b) may be designed as stepped shafts, as illustrated in figures 10a and 11a. In the embodiment, the sensor may be a non-contact type sensor that does not affect the stiffness of the system.

In an embodiment, angular measurements may be made by employing a non-contact type optical encoder. The optical encoder may be a rotary encoder configured to perform angular position measurements. Figure 14 illustrates a schematic perspective view of the optical encoder (170), in accordance with an embodiment of the present disclosure. The encoder (170) includes a scale, a reader head, and a green spacer (32). The scale of the encoder (170) includes markings that are spaced with a fixed distance therebetween. In case of a rotary encoder, the markings are fixed angle apart. The distance between two consecutive markings on the scale gives the resolution of the sensor. When in motion, the position of these markings is measured by the reader head of the encoder (170). The resolution of the rotary encoder (170) that is employed in the tribometer may be 0.79 arc seconds (0.000219 degrees). Further, since the scale at which the measurements are performed is minute in nature, the alignment of the reader head is relative to the scale and hence becomes extremely important. This is an important factor to be considered while designing the shafts (24a, 24b) of the pendulum (31a, 31b).

In an embodiment, while conducting experiments with the tribometer (100), the stable positions of the pendulums (31a, 31b) may be at zero position. The zero position may be taken as a reference position i.e. 0 degrees. Further, since both the pendulums (31a, 31b) are constrained to move together, displacing the first pendulum (31a) by an angular position ?1 results in displacement of the second pendulum (31b) by a different angle ?2. The difference in the angular positions of both the pendulums (31a, 31b) depends on the separation (distance) between the shafts (24a, 24b) on which pendulums (31a, 31b) are mounted. While conducting experiments, the point of contact will always lie between the two pendulums (31a, 31b). However, in order to maintain the symmetry of the setup and to avoid any mass imbalance, the point of contact may be always brought exactly at the center of two pendulum shafts (24a, 24b). This is done by adjusting the position of the two adaptors (18, 19) which are holding the ball assembly and the flat assembly. In the tribometer (100) including double pendulum motion, the driving force may be gravitational force. The configuration of the tribometer (100) enables achieving of different sliding distance for same energy. Accordingly, with such configuration of the tribometer (100), the sliding speeds can be varied, while keeping the sliding displacement constant. Further, by achieving a greater number of peaks in the displacement response, higher resolution can be achieved in measurement of tribological parameters.

Kinematic and dynamic analysis:
Figure 15 illustrates a schematic view of the tribometer (100), with the pendulums being positioned in a stable configuration (180) and deformed configuration (190), in accordance with an embodiment of the present disclosure. Points O and O’ are the respective points about which the first pendulum (31a) and the second pendulum (31b) are rotating. Flat (6, 16) has been attached to the first pendulum (31a) and the ball (1, 17) has been attached to the second pendulum (31b). Point P is the point of contact between ball (1, 17) and the flat (6, 16). This is the stable or mean configuration of the pendulums (31a, 31b). When we displace the first pendulum (31a) by an angle ?, there is a relative sliding at the interface of the ball (1, 17) and the flat (6, 16) and the point of contact P slides relative to the flat (6, 16). Therefore, the angular displacements of the pendulums (31a, 31b) will result in a linear motion at the interface. During this process of rotating the first pendulum (31a) by angle ?, the second pendulum (31b) will be displaced by a certain angle which is not equal to ?. This is due to the geometry of the setup. The intuitive feel of this can be got by observing the fact that when the second pendulum (31b) is at angle of 90 degrees, the first pendulum (31a) is at angle lesser than 90 degrees. This difference in the angles of two pendulums (31a, 31b) depends upon the separation between the pendulum rotation axes. Therefore, the separation between the point O and O’ is an important parameter in the experiment. Not only this separation dictates the difference in the angles of the two pendulums (31a, 31b), it also determines the magnitude of sliding as a function of ? during the sliding motion. For a given angle, if we compare the sliding distance for a given angular position ?, the larger the separation between the pendulum axes, the higher is the sliding distance at the sliding interface.

Figure 16 and Figure 17 illustrates a schematic view (200, 210, 220, 230) of instantaneous position vectors of the contact points during sliding motion at the interface, in accordance with an embodiment of the present disclosure. Particularly, figures 16 and 17 illustrate functional relationship between sliding distance and sliding velocities as a function of angular position ?, in the form of a vector diagram. Again, O and O’ are the axis of rotation and are fixed at their locations. The point of contact can be identified as the coincident points P1 and P2, where P1 lies on flat (6, 16) and P2 lies on the ball (1, 17) at this instant of time. The position vector of the point of contact on flat (6, 16) from O is OP1. Similarly, the position vector of point of contact on ball from the axis of rotation O’ is given by O'P2. In order to analyze the motion of the point of contact, let us construct a line which is parallel to flat (6, 16), passing through the center of the ball (1, 17) at T and intersecting the line OO’ at a point Q. The line OQ is defined in such a way that it always remains perpendicular to the length of the first pendulum (31a). When the pendulum rotates by ?, the angle between OQ’ and horizontal line joining OO’ is also ?. Since the angle of rotation is known to us, we have the exact location of Q’ at any instant of time. In order to locate the position of point of contact, we have the following two paths to reach the point of contact. Vector from O to P is the direct vector position of the point of contact. The same contact point can also be reached by following the position vectors OQ’, Q’O’, O’T and TP. Since, the position vector of point Q’ is known to us, we can simplify the analysis just by consider the closed vector loop Q’O’T. In the closed vector loop Q’O’T, let us define the vectors in the following ways.
Q’O’=A ?, O’T=B ?, Q’T=C ?.
Therefore, we can write
A ?+B ?=C ?
1

We can write the vectors in terms of their magnitude and directions. Vectors A ?, B ? and C ? can be written as A ?=AA ^, B ?=BB ^ and C ?=CC ^ where A ^, B ^ and C ^ are the unit vectors in the direction of vectors A ?, B ? and C ?. If we identify the known and unknown quantities of this vector loop, we have the following conditions:
A ? is completely known as the position of point Q’ is known at all times.
The direction of vector C ? is known to us at all times as it is always parallel to the pendulum 1.
The magnitude of vector B ? is known to us as it comes from the geometry of pendulum 2. The centre point of the ball is always at a fixed distance from the point of rotation of pendulum 2.
Therefore, the unknown quantities in the vector loop are the magnitude of the vector C ? and direction of vector B ?. If we determine these two unknown quantities as a function of ?, we can determine the sliding distance and sliding velocities at the point of contact.
We can use Chase’s method to solve for the unknowns. The procedure and the steps to find the unknowns are discussed below.
The coordinate system is defined as shown in the Error! Reference source not found.. Z axis defined in the direction perpendicular to the plane and is positive in the direction coming out of the plane. i ^, j ^ and k ^ are the unit vectors along the x, y and z directions respectively.
The objective is to eliminate one of the unknowns from the equation and solve for the other unknown quantity. So, if we take the dot product of equation 1, with a vector ?toC ?, the dot product is zero. So, we choose a vector C ^×k ^ and take its dot product with equation 1. We get
A ?.(C ^×k ^)+B ?.(C ^×k ^)=C ?.(C ^×k ^)
2

Since (C ^×k ^) is perpendicular toC ?, therefore
C ?.(C ^×k ^ )=0
3

The remaining non-zero terms of the equations gives us
A ?.(C ^×k ^ )+B ?.(C ^×k ^ )=0 4

The above equation can be written in terms of magnitudes and directions of the vector B ? as
A ?.(C ^×k ^ )+BB ^.(C ^×k ^ )=0
5

Let ? be the angle between B ^ and(C ^×k ^ ), we can write
B ^.(C ^×k ^ )=cos?
6

Therefore
cos?=(-A ?.(C ^×k ^ ))/B
7

Now, let us define a new coordinate system with C ^ and (C ^×k ^ ) as the basis (as they are orthonormal), B ^ can be written as
B ^=cos? (C ^×k ^ )+sin? C ^
8

Where, sin?=±v(1-cos^2?? ). Therefore,
sin?=±v(1-((-A ?.(C ^×k ^ ))/B)^2 ) 9

This gives us
sin?=±1/B v(B^2-(-A ?.(C ^×k ^ ))^2 )
10

Therefore, the equation 8 can be written as
B ^= (-A ?.(C ^×k ^ ))/B (C ^×k ^ )±1/B v(B^2-(-A ?.(C ^×k ^ ))^2 ) C ^
11

Multiplying equation 11 by the magnitude of B ?, which known to us, we get the complete vector as
B ?=[-A ?.(C ^×k ^ )] (C ^×k ^ )±[v(B^2-(-A ?.(C ^×k ^ ))^2 )] C ^
12

In order to find the C ?, substitute the value of B ? from equation 12 into 1, we get
C ?=A ?+[-A ?.(C ^×k ^ )] (C ^×k ^ )±[v(B^2-(-A ?.(C ^×k ^ ))^2 )] C ^
13

This can be simplified to
C ?=[A ?.C ^±v(B^2-(-A ?.(C ^×k ^ ))^2 )] C ^
14

Writing the vectors a ?, A ?, C ? and r ? in the form of components along
a ?=a cos? i ^+a sin? j ^
A ?=(h-a cos?) i ^-a sin? j ^
C ^=sin? i ^ -cos? j ^
r ?=-rcos? i ^-rsin? j ^
The following are evaluated as
C ^×k ^=-cos? i ^-sin? j ^
A ?.(C ^×k ^ )=a-hcos?
Therefore, substituting the above expressions in equation 12 and 14 we have
B ?=[-(hcos?-a)cos?±(v(B^2-(a-hcos?)^2 ))sin?] i ^+[-(hcos?-a)sin?±(v(B^2-(a-hcos?)^2 ))cos?] j ^
15

C ?=[hsin?±(v(B^2-(a-hcos?)^2 ))]sin? i ^-[hsin?±(v(B^2-(a-hcos?)^2 ))]cos? j ^
16

Sliding displacement calculation:
During the pendulum motion, the length of the vector C ? changes as the ball slides relative to the flat surface. The magnitude of the displacement at the interface can be calculated by measuring the change in length of the vector C ? relative to its magnitude at mean position of the pendulums.
Sliding displacement is given by the equation
x=(|C| ) ?-C_0
x=hsin?±(v(B^2-(a-hcos?)^2 ))-C_0 17

Where c_o is the magnitude of the vector C ? at ?=0.
Sliding velocity calculation:
In the given figure, (OQ') ?=a ?, (Q'T) ?=C ? , (TP_1 ) ?=r ?,( O'T) ?=B ? , (?TP?_2 ) ?=r ?, (Q'O') ?=A ?.
Therefore,
(OP_1 ) ?=(OQ') ?+(Q'T) ?+(TP_1=) ?
(O'P_2 ) ?=(O'T) ?+(TP_2 ) ?

Or,
(OP_1 ) ?=a ?+C ?+r ?
(O'P_2 ) ?=B ?+r ?

(OP_1 ) ?=[acos?+hsin^2 ?±(v(B^2-(a-hcos?)^2 ))sin?-rcos?] i ^+[asin?-hsin? cos?±(v(B^2-(a-hcos?)^2 ))cos?-rsin?] j ^
18

(O'P_2 ) ?=[(a-hcos?)cos?±(v(B^2-(a-hcos?)^2 ))sin?-rcos?] i ^+[(a-hcos?)sin?±(v(B^2-(a-hcos?)^2 ))cos?-rsin?] j ^
19

The velocity of point P1 is perpendicular to (OP_1 ) ? and velocity of P2 is perpendicular to (O'P_2 ) ?. Velocities of point P1 and P2 are indicated by VP1 and VP2 in the figure.
These velocities are resolved in two components, one along the direction of sliding and another perpendicular to the direction of sliding. These directions are indicated by the unit vectors t ^ and n ^ respectively.
If (?_1 ) ?=?_1 k ^ is the angular velocity of pendulum 1 and (?_2 ) ?=?_2 k ^ is the angular velocity of the second pendulum (31b), then velocities of point P1 and P2 are VP1 and VP2 which are given by
(VP_1 ) ?=(?_1 ) ?×(OP_1 ) ?

(VP_2 ) ?=(?_2 ) ?×(O'P_2 ) ?
20

From figure, the components of unit vectors along normal and tangential direction in the given coordinate system are given by
n ^=cos? i ^+sin? j ^

t ^=sin? i ^-cos? j ^
21

In order to maintain the contact between the mating parts during the motion, the components of the VP1 and VP2 along n ^ should be same. This is the necessary condition.
Therefore,
(VP_1 ) ?.n ^=(VP_2 ) ?.n ^
22

This condition yields the value of ?_2 as,
?_2=?_1 [-cos?(OP_1y )+sin?(OP_1x)]/[-cos?(O'P_2y )+sin?(O'P_2x)]
23

OP_1y, OP_1x , O'P_2x and O'P_2y are the components of the vectors (OP_1 ) ? and (O'P_2 ) ?
(OP_1 ) ?=[OP_1x ] i ^+[OP_1y ] j ^

(O'P_2 ) ?=[O'P_2x ] i ^+[O'P_2y ] j ^
24

given by equation 19.
Once ?_2 is determined, the velocity VP2 can be calculated using equation 20.
(VP_1 ) ?=?_1 (-OP_1y ( i) ^+OP_1x j ^ )

(VP_2 ) ?=?_2 (-O'P_2y ( i) ^+O'P_2x j ^ )
25

Therefore, the relative velocity of ball and flat along the tangential direction at the interface is the velocity of sliding. It is given by
(V_s ) ?=((VP_1 ) ?.t ^-(VP_2 ) ?.t ^ ) t ^
26

Where
(VP_1 ) ?.t ^=-?_1 OP_1y sin?-?_1 OP_1x cos?
(VP_2 ) ?.t ^=-?_2 O'P_2y sin?-?_2 O'P_2x cos?
Method to calculate friction from the data
Energy dissipation in the system: During the entire motion of the double pendulum (tribometer (100)) setup, the only external force acting on the system is gravitational force. When the pendulum is taken to initial angle ?1, energy is stored in the system in the form of potential energy. This potential energy has two components which are gravitational potential energy and potential energy stored in the springs used for applying normal load. During the sliding motion, the spring extends, and the extension depends upon the sliding amplitude at the interface. Consequently, some amount of energy is stored in the springs. When the pendulum is released, the potential energy is converted to the kinetic energy. If there are no dissipative forces present in the system, this conversion of energy from potential to kinetic and vice versa will continue indefinitely and the maximum angular position at the extremes will remain same each time. However, this is not the case. During the motion, energy is getting dissipated mainly due to two reasons. One is the air drag which opposes the motion of the pendulum and second one is the friction at the rolling and the sliding interfaces. Energy dissipation due to friction is occurring at the roller bearings (23a, 23b) by which the pendulums are suspended and sliding the sliding at the interface of ball and flat contact. This energy dissipation leads to reduction in the amplitude of oscillations in each cycle. This energy dissipation is related to friction force in order to determine the energy lost due to frictional dissipation.

Further, bearing friction is calculated by doing a calibration experiment. In order to find out the bearing friction, it is necessary to eliminate the sliding friction at the ball-flat interface. The sliding friction will be zero when there is no sliding at the interface. The sliding distance at the interface can be adjusted by adjusting the distance between two shafts. When the two shafts are coaxial, the sliding distance at the interface becomes zero and hence the sliding friction component is also zero. Therefore, the drop in the maximum angular position in each cycle is due to the frictional energy loss in the bearings (23a, 23b). Bearings are often lubricated using greases in order to reduce the wear of the moving elements. Bearings of different makes may have different grades of greases and the damping behavior depends upon the grease present in the bearings (23a, 23b). Also, the stress needed to shear the greases is higher than the dry rolling friction. Therefore, this grease is removed from the bearings (23a, 23b). Oil in the bearing (23a, 23b) is removed by cleaning the bearing (23a, 23b) with hexane.

Calibration and results
Calibration and sliding experiments are conducted for 15 degrees initial angle of release. In calibration experiment, the pendulum shafts (24a, 24b) are coaxial. In sliding experiment, the separation between the axes of the two pendulums is 15mm. The data is recorded at 100 kHz sampling frequency. Figure 18 shows the response of angular position ? with time for calibration experiment, with zero offset between the pendulum shafts (24a, 24b). Figure 19 shows angular position ? versus time plot for sliding experiment, for dry contact and with 15mm offset between the pendulum shafts (24a, 24b). The sliding experiment is conducted under dry condition. As can be observed, the time taken to completely stop the motion in a calibration is much higher than the sliding experiment. In calibration experiments there are 1200 cycles whereas the dry sliding experiments for 10 N normal load has only 120 cycles. The envelope of slope of the response also gives important information about the nature of damping. If we have viscous damping in the system, there is an exponential decay in the amplitude. In case of dry friction, the amplitude decay is linear. The friction in the system can be a combination of both the viscous and dry friction components as well.

The envelope of the ?max vs. Time data is plotted by plotting the maximum theta in each cycle as a function of time as shown in figures 20 and 21. Particularly, figure 20 illustrates a plot of maximum amplitude in each cycle for the calibration experiment, with zero offset between the shafts. Figure 21 illustrates a plot of maximum amplitude in each cycle for the dry contact, with 15mm offset between the shafts. Difference in the nature of the damping can be clearly observed in both the cases shown in figures 20 and 21. The angular velocity of rotation is obtained by differentiating the ? with respect to time as shown in figure 22. Figure 23 illustrates comparison of angular velocity for first pendulum (31a) and second pendulum (31b). Figure 24 illustrates that the difference in angle between the first pendulum (31a) and second pendulum (31b) is minor. Figure 25 illustrates variation of sliding distance with time, while figure 26 illustrates a plot of sliding velocity versus time. Further, figure 27 illustrates variation of sliding distance and sliding velocity with time. ?_2 is calculated from ?_1 using equations/relations 17 to 23. The comparison of the two curves shows the marginal difference between the angular velocities of the two pendulums. However marginal, this difference has been considered in all the calculations which are done subsequently.

The sliding velocity of the interface is calculated by using equation 17. The maximum amplitude of the sliding distance in the first cycle is 3.83mm and the maximum velocity of sliding at the interface is 13mm/s. As the sliding continues, the sliding distance reduces in the same manner of angular displacement. Between sliding distance and sliding velocity, there exists a phase difference of 90 degrees as can be observed in figure 28. Further, this sliding velocity can be plotted with the angular position to get the phase diagram as shown in the figure 29. That is, figure 29 is a spiral plot of sliding velocity versus the angular position (?, measured in degrees). As we are going to discuss in the later results, qualitative assessment of the lubricants effectiveness can be done efficiently just by mere observation this plot.

Details of Experiment
As described earlier, sliding experiments are conducted for 15 degrees initial angle of release. In calibration experiment, the pendulum shafts (24a, 24b) are coaxial. In sliding experiment, the separation between the axes of the two pendulums is 15mm. Data is recorded at 100 kHz sampling frequency. Further, experiments are conducted using four different lubricants. These lubricants are Hexadecane (HD), Hexadecane+1% Stearic Acid (HDSA), commercial 4T oil and Base Oil (BO). Contact configuration at the interface is Ball-Flat contact with ball having a diameter of 6.35mm. The sample included in the sample mounting unit may be a ball made of rigid material such as steel. The surface contacting the sample may be at least one of a flat element made of rigid material such a steel. The material for the Flat element is SS316L (SS316L is a type of metallic alloy of stainless steel that is austenitic and contains nickel and molybdenum, which make it corrosion resistant) and the ball (sample) is made up of hardened steel. Experiments are conducted for three different normal loads 10 N, 20 N and 30 N. These loads correspond to the Hertzian contact pressures of 1387 MPa, 1747 MPa and 2000 MPa respectively.

Results and discussions
Angular position vs. Time response
Optical encoder is configured to measure angular position of at least one pendulum as a function of time. The angular position may be measured for at least one of the first pendulum (31a) and the second pendulum (31b). Figures 30a, 30b, 30c, and 30d depict variation of angular position with time for given lubricants for 10 N normal load applied at point of contact between ball and the flat. The lubricants employed in study are (a) Hexadecane (HD), (b) Hexadecane+1% Stearic acid (HDSA), (c) 4T oil (4T) and (d) Base oil (BO). It can be observed from Figures 30a, 30b, 30c, and 30d that for all the lubricants, the Angular position vs. Time response can be divided into two regions. We call the first of the two regions as region 1 where there is large reduction in amplitude in each cycle. In region 2, there is a lower reduction in amplitude as compared to region 1. Such existence of two regions and a clear demarcation between them was found to be absent in the angular position vs. time response of the calibration experiment (in which there was no sliding at the interface).

Further, a graphical plot of displacement in terms of angular position vs. time response for 20 N and 30 N is shown in Figure 31 and Figure 32, respectively. As can be observed for 10 N normal load applied at point of contact, the length of region 1 is maximum for HDSA followed by 4T, HD and BO in the same order. This indicates the rate of loss of energy due to friction is lowest for HDSA and the oscillation continues for larger number of cycles. Further, this means BO has highest energy dissipation rate. A similar trend is observed for the lubricants at 20 N and 30 N normal load. However, the number of cycles in region 1 and region 2 reduced continuously as the normal load is increased.

In order to find out the reason for presence of two regions (1 and 2) in the sliding experiments, as a first step, the amplitude of transition between region 1 and region 2 is noted down. Table 2 shows the values of amplitude of transition (in degrees) from region 1 to region 2 for different lubricants for different loads.

Lubricant Normal load
10 N 20 N 30 N
HD 0.1521 0.2496 0.3081
HDSA 0.1061 0.1422 0.2057
4T 0.1294 0.1870 0.6414
BO 0.1876 0.3597 0.9490

Table 2: Region 1 to Region 2 Transition Amplitude (TA) (in degrees)

Relation between the amplitude of sliding and the angular position helps us to determine the sliding displacement amplitude at the transition from region 1 to region 2. Furthermore, Table 3 gives us the values of the transition amplitudes for various lubricants in terms of sliding distance at the interface in mm.

Lubricant Normal load
10 N 20 N 30 N
HD 0.0398 0.06535 0.08661
HDSA 0.0277 0.03723 0.05385
4T 0.0338 0.04895 0.16790
BO 0.04911 0.09410 0.24854

Table 1: Region 1 to Region 2 Transition Amplitude (TA) (in mm)

Since the amplitude of sliding at transition is less than 1mm, we estimate the contact radius between the ball and the flat for the given loads of 10 N, 20 N and 30 N using Hertzian contact equations, as detailed in
Table 2.
Normal load Hertzian contact pressure(max) (MPa) Contact length ‘2a’(mm) Contact radius ‘a’(mm)
10 N 1387 0.117 0.0585
20 N 1747 0.148 0.0740
30 N 2000 0.169 0.0845

Table 2: Contact length using Hertzian equations
As a next step, we calculate the ratio of the transition amplitude to the contact radius as detailed in
Table 3.
Lubricant Normal load
10 N 20 N 30 N
HD 0.68 0.88 1.025
HDSA 0.47 0.50 0.637
4T 0.57 0.66 1.98
BO 0.84 1.27 2.941

Table 3: Transition amplitude to contact radius ratio

As can be clearly seen from
Table 3, for different lubricants, the transition amplitudes are of the same order as the contact radius and are comparable. The minimum value of this ratio is 0.47 which occurs for HDSA for 10 N normal load. The ratio has a maximum for BO at 30 N normal load.
An important conclusion which can be made from the above discussions is that the region 1 of the displacement-time response is the region of gross sliding. In this region the displacement amplitudes are much larger than the length of the contact radius. However, as the energy is continuously dissipated by the friction at the ball flat interface, there is continuous reduction in displacement amplitude and the contact goes from the gross sliding towards the region 2 which is the region where fretting takes place. In this region, the sliding amplitudes are comparable (of the same order as) the contact radius evaluated using Hertzian equation. In conclusion, the region 1 is the sliding region and the region 2 is the fretting region of the amplitude response.

The maximum amplitude in each cycle for different lubricants is normalized and plotted for the different normal loads as shown in Figures 33a-33d. Also, we plot the number of cycles in sliding region and fretting region which gives us an estimate of the performance of lubricants under these different sliding conditions.

Referring to Figure 33a, for 10 N normal load the total time taken for completion of the experiment and total number of cycles is higher. It can be seen that, as the normal load is increased, the point of transition to fretting region shifts towards a lower number of cycles. The number of cycles in an experiment is dictated by the average friction in each cycle. Higher the average frictional force in a cycle, higher will be the energy dissipation. This will lead to a higher reduction in the amplitude of oscillation and the total number of points will be reduced. This can be clearly observed in Figure 33 (c) for BO and 4T oil where number of points are less and discretely visible. Also, it can be observed that the length of sliding region reduces, and the length of the fretting region increases as the normal load is increased.

In addition to the above, since the reduction in amplitude in one complete cycle is directly proportional to the average frictional force in that cycle, difference in maximum amplitude in each cycle is plotted as shown in Figures 34a, 34b and 34c. It can be observed from Figures 34a-34c that for 30 N normal load, the reduction amplitude is maximum for HD followed by 4T oil, HD and HDSA in the reducing order. Particularly, for HD and BO, the change in amplitude first increases to a maximum value and then reduce to lower values. For 4T oil also there is rise and then fall in amplitude reduction values. However, for HDSA, ?Amplitude (in degrees) value reduces continuously. Similar trend is observed for the experiments done at reduced normal loads of 10 N and 20 N. However, the reduction in amplitude is lower for lower normal loads as compared to higher normal loads. This indicates that at lower normal loads, lesser energy is dissipated due to the interfacial friction and the experiment continues for a longer duration of time. Thus, the reduction in amplitude is a direct indication of the average friction in that cycle. Since there is a non-linear relation between the reduction in amplitude and reduction in energy of the system, we find out the average frictional force in a cycle from the change in energy per unit sliding distance in one cycle of pendulum oscillation. The method to determine the friction is discussed in the following section.

Method to determine the effectiveness of the lubricant in the boundary lubrication regime
Method to determine the effectiveness of the lubricant in the boundary lubrication regime
?E/x helps us to evaluate the Co-efficient of Friction (CoF) in the boundary lubrication region. Accordingly, points to be considered to find out the effectiveness of the lubricants are as follows:
– Total energy input at the beginning of the experiment is same for all experiments.
– Change in Energy per unit sliding distance in each cycle is an indication of the average friction in that cycle.
– Total number of cycles taken to stop the pendulum motion (which also indicate the total time taken to dissipate the input energy).

Change in Energy per unit sliding distance:

Change in energy of the system per unit sliding distance at the interface helps us to evaluate the average CoF in the boundary lubrication regime. In all experiments, Total energy input at the beginning of the experiment is same. This input energy is dissipated by the average frictional force at the interface. The change in energy per unit sliding distance in each cycle is an indication of the average friction in that cycle. This energy difference in a cycle is when divided by the total sliding distance in that cycle, gives the average frictional force. The variation of frictional force with number of cycles and is shown in Figures 35a, 35b and 35c.

For all lubricants, delta E per unit sliding distance follows the same trend as the reduction in amplitude curve. For HD, there is increase and reduction in delta E per unit sliding distance before the contact goes into fretting region. This indicates a higher average friction for HD when compared to 4T and BO. The frictional force is minimum HDSA. Here it can be observed that for HDSA (all loads), the change in energy per unit sliding distance continuously reduces with the number of cycles. However, this is not the case with the BO, HD and 4T oil. Especially for the BO, it can be observed clearly that for 20 N and 30 N normal loads, there is a reduction and increase in the ?E/x values in the sliding regime. This indicates that the average frictional force reduces and increases again in the sliding regime (1). This gives us an estimate of the fluctuations in the average frictional force with the number of cycles. These fluctuations can be clearly observed in BO, HD and 4T oil for 30 N normal load and HD and BO for 20 N normal loads.

Since the frictional force is in a tribo-system depends on the velocity of sliding at the interface, we plot the ?E/x values with maximum velocity Vmax in each cycle as shown in Figures 36a, 36b and 36c. An important observation that can be made from Figures 36a-36c is that the density of points in the curves for different normal load. The number of points in a curve for the given lubricant is highest for 10 N normal load. Increase in normal load increases the energy dissipation due to friction. Therefore, if we observe for the BO, at 10 N normal load there is a larger number of points as compared to 20 N and 30 N normal load. Similar trend is observed for all the oils. Moreover, if we have a look at 30 N normal load, the energy dissipation per unit sliding is minimum for HDSA (large number of data points compared to BO 30 N). As the average friction force increases, the curve shifts upwards, and the number of points reduces. Thus, this upward shifting of the curve and the reduction in the number of data points is attributed to lower effectiveness of the lubricant. Thus, a relative comparison of the lubricant effectiveness can be made by observing this plot of change in energy per unit sliding distance.
The coefficient of friction (CoF) is calculated by taking the ratio of the change in energy per unit sliding distance with the normal load. Since normal load is constant for an experiment, the CoF curve follows the same trend as that of energy dissipated per unit sliding distance vs. maximum sliding velocity (Vmax), as shown in Figure 37.

It can be observed from Figure 37 that, in general, average CoF values are higher at larger sliding velocities when there is gross sliding between the ball and flat. As the sliding velocity at the interface reduces and the contact goes from gross sliding towards fretting, the average CoF value varies according to the average energy dissipated per unit sliding distance in a cycle and reduces to a very small value. For a given normal load, BO has highest average CoF of all the lubricants followed by HD, 4T oil and HDSA respectively. Moreover, from Figure 37, it can be observed that for HDSA, the average CoF values are higher at lower normal loads and average CoF values reduces as we increase the normal loads. On the other hand, for BO and 4T oil, the average CoF increases as we increase the normal loads. This indicates that HDSA is more effective as a boundary lubricant even at higher loads however BO and 4T oil are less effective than HDSA. As the energy is dissipated continuously during sliding and the amplitude of oscillation reduces and the contact goes into fretting condition, this would lead to the development of the stick region between the ball and flat.

Further, if we have a look at the plot of energy dissipated per unit sliding distance with the maximum sliding velocity (as shown in Figure 38) (for 10 N normal load), we can observe that the transition from sliding towards fretting happens at higher Vmax for HD. HD is followed by BO, 4T oil and HDSA in the reducing order of the velocity of transition towards fretting. The same trend is followed by the oils for 20 N normal load. However, for 30 N normal loads, the velocity of transition is highest for BO followed by HD. For rest of the oils, the order remains the same.

In this regard, if we observe the maximum sliding velocity Vmax at the transition to fretting, for higher normal loads, this transition takes place at higher sliding velocity for all the lubricants, as shown in Figure 39. Of all the oils, HDSA has the lowest velocity at transition to fretting. The larger difference at lower velocities is a clear indication of the effectiveness of Stearic acid in Hexadecane as a boundary lubricant. A closer look at the point of dip clearly indicates that the transition to fretting happens at a lower velocity. This means that the transition to a region with a stick region happens at a lower velocity which is a good indication of the ‘effectiveness’ of a boundary lubricant. The average CoF in a cycle is calculated by calculating the energy dissipated at contact per unit sliding distance in that cycle. As the number of oscillations continues, the maximum energy available at the beginning of each cycle is lower than the maximum energy at the beginning of the previous cycle. This potential energy at the beginning of each cycle keeps on reducing.

When the contact operates in the fretting regime, the amplitude of oscillation is less than 1mm. It is important to note here that although the initial energy available at the beginning of each cycle reduces with number of cycles, the total sliding distance in a cycle also reduces. Thus, we get very low values of average CoF in the fretting regime. A better way to understand the friction in fretting regime is to calculate the percentage change in energy in each in the fretting regime. Figures 40(a), (c) and (e) shows the variation of percentage change in energy in each cycle plotted with the corresponding Vmax in each cycle for 10 N, 20 N and 30 N normal loads respectively. We can observe that, as we move from higher sliding velocities to lower sliding velocities, the percentage change in energy values increases continuously in the sliding regime. As the contact goes into fretting, there is development of stick zone at the ball and flat contact. And the energy is dissipated in two ways: (1) the energy dissipated due to slipping at the edges of the ball and flat contact and (2) the energy dissipated due to the elastic and plastic deformation of the surfaces in the stick region of the contact. As the amplitude of oscillation reduces continuously, the amount of slipping at the contact edge reduces and the contribution of the elastic-plastic deformation in the stick region increases. If we zoom in the plots for percentage change in energy close to the transition region, we observe that the percentage change in energy values increases to a higher value before transitioning to fretting regime. For BO and HD, the transition towards the fretting takes place at a lower value of percentage change in energy and at higher sliding velocities. For HDSA, this transition happens at a higher value of percentage change in energy but at lower sliding velocities. This indicates that the formation of the Stick region for HDSA is delayed and happens at lower sliding velocities and sliding amplitudes as compared to other lubricants. Thus, HDSA is more effective than other oils if we consider the sliding contacts at lower velocities. As the normal load at the contact is increased, the point of transition shifts towards higher velocities indicating the formation of the Stick region at higher amplitudes, as shown in Figures 40 (b), (d) and (f). The percentage change in energy values increases in the fretting regime again because even though the energy dissipation does not vary large, there is consider reduction in the available energy at the beginning of each cycle in fretting. Thus, the denominator of the fraction used to calculate percentage change in energy reduces leading to increase in percentage change in energy dissipated.

Qualitative assessment of Lubricants using color maps
In order to ease the process of interpreting the plots in order to determine how effective a lubricant is, sliding velocity at the interface is plotted as a function of theta. If friction in a cycle is more, there will be large decrement in the delta A value. Therefore, depending on the value of either delta A or delta E per unit sliding distance, we can assign different colors which indicate the value of friction in that cycle. For example, if the difference in delta A is higher, all the points in that cycle are plotted using red color which indicates higher friction. Similarly, different ranges of delta A are assigned different colors. In the following plots, red color indicates higher friction and green color indicates least friction. Orange and yellow are the intermediate cases.
Salient features of Circular color plots:
The qualitative assessment of a lubricant can be done easily by observing the sliding velocity vs. theta plot.
Sliding velocity vs. theta graph is spiral.
If the friction in each cycle is higher, then the amplitude reduction will be higher.
Higher the percentage of green color and lower the percentage of red color indicates that the given lubricant has a better effectiveness in boundary lubrication regime.

Figure 41 depicts a circular graphical plot of Sliding velocity (in mm/s) versus Angular position ? (in degrees). Figures 42, 43 and 44 depict circular color maps for 10 N, 20 N and 30 N normal load at point of contact, respectively. If we compare HD and HD+SA results for 10 N, 20 N and 30 N cases, it can be clearly seen that the percentage of green color is higher in HD+SA. Therefore, Hexadecane with 1% Stearic acid is a better boundary lubricant when compared to pure Hexadecane. Dry sliding shows a very large percentage of red color indicating the higher friction during the sliding. Moreover, the spacing between the two contours of also indicates the extent of energy lost. Higher the spacing, higher the energy lost. Therefore, we can see for dry condition, we have higher number of cycle when compared to 30 N normal load. Thus, the density of color gives us the information about the number of cycles under dry or lubricated contacts. Therefore, using the above plots, the effectiveness of a lubricant in the boundary lubricant regime can be compared and qualitative assessment can be done conveniently.

Rectangular color plots
Circular color maps give us the information regarding the energy dissipation in a lubricant and the effectiveness of different lubricants with respect to each other. It can be used for firsthand comparison of different lubricants. However, it is difficult to observe the fretting zone due to its smaller region in the circular maps. The information regarding the effectiveness of lubricants in fretting regime can however be encoded in the rectangular color plots as shown in Figure 45.

Rectangular color plots are obtained by normalizing the Amplitude vs. Time response of different lubricants. Here, the color maps are generated on the basis of normal loads. That is one set of color maps will be generated for each normal load. In order to generate a set of color maps, firstly the two regions of the sliding and the fretting are demarcated. The sliding region of every lubricant is normalized to a value of 1. The fretting regions of different lubricants are scaled on the basis of energy dissipated per unit sliding values at the transition from sliding to fretting. Smaller the transition amplitude to fretting smaller will be the height of the fretting region.

In contrast to circular maps, the sliding and fretting regions are color coded separately in sliding and fretting regimes. This is done on the basis of the values of energy dissipated per unit sliding distance, as shown in Figure 45(e). Similar to the circular maps, we assign different colors to different intervals of energy dissipated per unit sliding in sliding regime. Red indicates higher dissipation and green indicates lower values of energy dissipation per unit sliding. This color mapping is then applied to the sliding regime of the normalized response. Similarly, the fretting region is also color coded on the basis of energy dissipated per unit sliding from red color to green color. Figure 45, Figure 46, and Figure 47 shows the rectangular color maps for 10 N, 20 N and 30 N normal loads, respectively.

To summarize, the direct inspection of the rectangular color plots gives us the following information:
Larger the length of the rectangular region: indicates more number of cycles.
Smaller the transition amplitude to fretting: Smaller the height of the fretting region
Larger the green color in a particular region (for a given normal load): Better the lubricant as compared to others in that region.
Larger red color in a region: less effective the lubricant.
In addition to the color gradient, there are certain alternate bands of colors repeating. For example, in BO 30 N normal load, there are alternate bands of orange and yellow colors in the fretting regime. This banding in the rectangular plots indicates the variation in friction with number of cycles/ sliding velocity.

Figure 48 illustrates a flow chart of a method (300) for performing boundary lubrication studies and measuring tribological quantities, by employing the tribometer (100) of the present disclosure.

The order in which the method (300) is described is not intended to be construed as a limitation, and any number of the described method blocks may be combined in any order to implement the method (300). Additionally, individual blocks may be deleted from the method (300) without departing from the scope of the subject matter described herein.

As depicted at block 301, the method (300) includes mounting of a first pendulum (31a) onto a first shaft (24a) accommodated in a first housing assembly (110).

As depicted at block 302, the method (300) further includes mounting of a second pendulum (31b) onto a second shaft (24b) accommodated in a second housing assembly (130). The second pendulum (31b) is positioned at a predetermined interval from the first pendulum (31a).

As depicted at block 303, the method (300) further includes coupling of a loading assembly (50) to free ends of the first pendulum (31a) and the second pendulum (31b). The loading assembly (50) is configured to provide a symmetrical loading condition between the free ends of the first pendulum (31a) and the second pendulum (31b).

As depicted at block 304, the method (300) further includes providing a predetermined contact configuration between a sample and a surface contacting the sample by employing a sample mounting unit (10) of the loading assembly (50).

As depicted at block 305, the method (300) further includes applying normal load at a point of contact between the sample and the surface contacting the sample. The normal load at the point of contact is applied by employing a plurality of spring holders (20) included in at least one spring loading mechanism (40) of the loading assembly (50).

As depicted at block 306, the method (300) further includes displacing the first pendulum (31a) and the second pendulum (31b) by a predefined angle relative to mean position of the first pendulum (31a) and the second pendulum (31b).

As depicted at block 307, the method (300) further includes determining total energy input to the first pendulum (31a) and the second pendulum (31b) during displacement of the first pendulum (31a) and the second pendulum (31b) by the predefined angle.

As depicted at block 308, the method (300) also includes evaluating change in energy per unit sliding distance of the first pendulum (31a) and the second pendulum (31b) to determine energy dissipation and average friction in each swing cycle of the first pendulum (31a) and the second pendulum (31b).

The tribometer (100) of the present disclosure may be used in industries for qualitative assessment of the lubricants in the boundary lubrication conditions. The time required for conduction of experiment by employing the tribometer (100) is of short duration and hence, enables in faster testing. Moreover, the method of determining the effectiveness just by comparing the color maps gives a quicker way to evaluate and compare different lubricants to a layman. The tribometer (100) has been configured to be based on a stiffness based design, in which all the components are designed in such a way that we have high stiffness system. The exclusion of the actuator stiffness and the sensor stiffness reduces their effects at the contact interface. This allows us to capture the sliding events at the interface using rotary encoder with higher accuracy and precision. Various parameters such as pendulum length, separation between the pendulums and angle of release, different sliding velocities can be obtained at the interface. Therefore, the boundary lubrication regime and stick-slip phenomenon can be studied using the tribometer (100) under lower sliding velocity conditions (close to zero velocity).

In addition to the above, key features of the tribometer (100) are high stiffness, low damping, and geometry/constructional configuration. The tribometer (100) of the present disclosure is configured as a highly stiff and a highly under damped system. Configuring the tribometer (100) to be highly stiff and highly under damped, allows us to reduce the effect of these parameters (i.e. stiffness and damping) on the actual frictional interactions and their measurements. Further, such configuration enables us to study the nature of the actual interactions especially at lower velocities, close to zero velocity. Additionally, there are many systems that include combined rolling and sliding friction components. One example of such system is the hip joints. The configuration of the tribometer (100) permits us to vary the sliding and rolling components by varying the different parameters such as pendulum separation and the angle of release (?). Specifically, by progressively reducing the pendulum separation distance, the sliding distance and sliding velocities can be changed for the same energy input. In the tribometer (100), a revolution of the pendulum shaft (24a, 24b) by 0.79 arc seconds results in about 50nm sliding at the interface. Therefore, we get a high resolution of the sliding distance which allows us to study the asperity interactions.

EQUIVALENTS:

With respect to the use of substantially any plural and/or singular terms herein, those having skill in the art can translate from the plural to the singular and/or from the singular to the plural as is appropriate to the context and/or application. The various singular/plural permutations may be expressly set forth herein for sake of clarity.

While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting.
Referral Numerals
Particulars Numeral
Ball or sample 1
First ball holder nut or first fastener 2
Bolt or threaded member 3
Second ball holder nut or second fastener 4
Ball holder 5
Flat element or Flat specimen 6
Flat holder 7
Back plate 8, 8a
Frame 9, 9a, 9b
Slider 11, 11a, 11b
Lead screw 12, 12a, 12b
Washer 13, 13a, 13b
Spring hook 14
Spring or resilient member 15a, 15b
Flat specimen 16
Ball specimen 17
First adaptor 18
Second adaptor 19
Spring holder 20
First spring holder 20a
Second spring holder 20b
Pendulum square 21
First housing plate 22a
Second housing plate 22b
First bearing 23a
Second bearing 23b
First pendulum shaft or first shaft 24a
Second pendulum shaft or second shaft 24b
First pendulum connector 25a
Second pendulum connector 25b
Third pendulum connector 25c
Fourth pendulum connector 25d
Encoder fixture 26
Readhead plate or reader plate 27
Top plate 28
Column 29
First pendulum 31a
Second pendulum 31b
Green spacer 32
Sample mounting unit 10
Spring holder 20
Perspective view of the spring holder 30
Spring loading mechanism 40
Loading assembly 50
Exploded perspective view of the loading assembly 60
Perspective view of the loading assembly mounted onto the pendulums 70
Perspective view of the pendulums coupled to the housing 80
Perspective view of the housing mounted with pendulums 90
Tribometer or Lateral force driven parallel pendulum tribometer 100
First housing assembly 110
Perspective view of the first housing assembly 120
Second housing assembly 130
Perspective view of the second housing assembly 140
Perspective view of first and second housing assemblies 150
Perspective view of the top plate 160
Optical encoder/Rotary encoder 170
Schematic view of the tribometer with pendulums positioned in a stable configuration 180
Schematic view of the tribometer with pendulums positioned in a deformed configuration 190
Schematic view of instantaneous position vectors of the contact points during sliding motion at the interface 200, 210, 220, 230
Method flowchart 300
Flow chart blocks 301-308

,CLAIMS:We claim:
1. A tribometer (100) for performing boundary lubrication studies and measuring tribological quantities, comprising:
a first pendulum (31a) mounted on a first shaft (24a) accommodated in a first housing assembly (110);
a second pendulum (31b) mounted on a second shaft (24b) accommodated in a second housing assembly (130), wherein the second pendulum (31b) is positioned at a predetermined interval from the first pendulum (31a);
wherein the first pendulum (31a) and the second pendulum (31b) are configured to swing independent of each other; and
a loading assembly (50) coupled to free ends of the first pendulum (31a) and the second pendulum (31b), wherein the loading assembly (50) is configured to provide a symmetrical loading condition between the free ends of the first pendulum (31a) and the second pendulum (31b);
wherein the loading assembly (50) comprises:
a sample mounting unit (10) adapted to provide a predetermined contact configuration between a sample (1, 17) and a surface (6, 16) contacting the sample; and
at least one spring loading mechanism (40), comprising:
a plurality of spring holders (20) coupled to the sample mounting unit (10) and to the free ends of the pendulum (31a, 31b), wherein the plurality of spring holders (20) are configured to apply normal load at a point of contact between the sample (1, 17) and the surface (6, 16) contacting the sample; and
a plurality of resilient members (15a, 15b) coupling together the plurality of spring holders (20).

2. The tribometer (100) as claimed in claim 1, wherein the first housing assembly (110) comprises:
a first housing plate (22a);
a first bearing (23a) coupled to the first housing plate (22a) and to the first shaft (24a) accommodated in the first housing assembly (110); and
a first and a second pendulum connectors (25a, 25b) for coupling the first pendulum (31a) to the first housing assembly (110).

3. The tribometer (100) as claimed in claim 1, wherein the second housing assembly (130) comprises:
a second housing plate (22b);
a second bearing (23b) coupled to the second housing plate (22b) and to the second shaft (24b) accommodated in the second housing assembly (130); and
a third and a fourth pendulum connectors (25c, 25d) for coupling the second pendulum (31b) to the second housing assembly (130).

4. The tribometer (100) as claimed in claim 1, wherein an encoder fixture (26) is mounted on at least one of the first shaft (24a) and the second shaft (24b), and wherein the encoder fixture (26) is configured to measure angular position of at least one of the first pendulum (31a) and the second pendulum (31b).

5. The tribometer (100) as claimed in claim 4, wherein a reader plate (27) is coupled to at least one of the first shaft (24a) and the second shaft (24b) and wherein the reader plate (27) is mounted relative to the encoder fixture (26).

6. The tribometer (100) as claimed in claim 1, wherein the loading assembly (50) comprises a first adaptor (18), a second adaptor (19) and a pendulum square (21) for coupling of the plurality of spring holders (20) to the sample mounting unit (10) and to the free ends of the first pendulum (31a) and the second pendulum (31b).

7. The tribometer (100) as claimed in claim 1, wherein the sample (1, 17) included in the sample mounting unit (10) is a ball (1, 17) made of rigid material and the surface (6, 16) contacting the sample (1, 17) is at least one of a flat element (6, 16) made of rigid material.

8. The tribometer (100) as claimed in claim 7, wherein the sample mounting unit (10) comprises:
a ball holder (5) including a first fastener (2) for accommodating the ball (1, 17) made of rigid material;
a threaded member (3) secured to the first fastener (2) at one end and to a second fastener (4) at an other end opposite the one end, wherein the second fastener (4) is fastened to the ball holder (5); and
a flat holder (7) configured to accommodate the flat element (6), wherein the flat holder (7) is adapted to enable positioning of the ball (1, 17) and the flat element (6, 16) in a predetermined orientation relative to an axis of the sample mounting unit (10).

9. The tribometer (100) as claimed in claim 8, wherein the first pendulum (31a) and the second pendulum (31b) are mounted at a midpoint of the first shaft (24a) and the second shaft (24b), respectively.

10. A method (300) for performing boundary lubrication studies and measuring tribological quantities, the method (300) comprising:
mounting (301), a first pendulum (31a) onto a first shaft (24a) accommodated in a first housing assembly (110);
mounting (302), a second pendulum (31b) onto a second shaft (24b) accommodated in a second housing assembly (130), wherein the second pendulum (31b) is positioned at a predetermined interval from the first pendulum (31a);
coupling (303), a loading assembly (50) to free ends of the first pendulum (31a) and the second pendulum (31b), wherein the loading assembly (50) is configured to provide a symmetrical loading condition between the free ends of the first pendulum (31a) and the second pendulum (31b);
providing (304), a predetermined contact configuration between a sample (1, 17) and a surface (6, 16) contacting the sample (1, 17) by employing a sample mounting unit (10) of the loading assembly (50);
applying (305), normal load at a point of contact between the sample (1, 17) and the surface (6, 16) contacting the sample (1, 17), by employing a plurality of spring holders (20) included in at least one spring loading mechanism (40) of the loading assembly (50);
displacing (306), the first pendulum (31a) and the second pendulum (31b) by a predefined angle relative to mean position of the first pendulum (31a) and the second pendulum (31b);
determining (307), total energy input to the first pendulum (31a) and the second pendulum (31b) during displacement of the first pendulum (31a) and the second pendulum (31b) by the predefined angle; and
evaluating (308), change in energy per unit sliding distance of the first pendulum (31a) and the second pendulum (31b) to determine energy dissipation and average friction in each swing cycle of the first pendulum (31a) and the second pendulum (31b).