1 Introduction

The majority of rolling or sliding element bearings, cams, and gears in use today are grease lubricated. However, grease is a complex multi-phase material as compared with Newtonian liquid lubricants. The effects of temperature, speed, and pressure on grease film thickness are well known, but the related mechanisms are not well understood [1, 2]. Many experimental investigations on grease have shown that the film behaviors depend on base oil viscosity, soap type and concentration, and most importantly, inlet lubricant supply [3–6]. However, most of these understandings of grease lubrication are restricted to steady-state conditions.

In practical cases, many moving-elements are working under transient conditions. Glovnea and Spikes [7] measured oil film thickness during reversal of entrainment in cyclically accelerated/decelerated motion, and the comparison of experimental results with an existing theoretical model showed that the measured minimum film thickness at the side of the contact was higher than the calculated value. Sugimura [8] suggested that the elastohydrodynamic film thicknesses under transient conditions deviated from those under steady-state conditions. Glovnea [9] found that when a sudden entrainment speed step was applied, the film thickness showed damped oscillations for about 30 ms before stabilizing at the steady-state value.

Taking into consideration that many grease lubricated moving-elements operate in oscillatory or intermittent fashion, the microoscillation can occur (the amplitude is close to the diameter of the Hertzian contact area) due to the presence of inertia. In this case, moving-elements may suffer from fretting wear [10]. Kaneta et al. [11, 12] mentioned that a decrease in amplitude influenced oil film collapse, and then led to wear. McColl’s work [13] indicated that the grease lubricant was capable of providing an effective shield around the fretting interface but was easily squeezed out of the main contact area. Zhou et al. [14] suggested that the ratio of the displacement amplitude to the radius of the Hertzian contact area was the most important parameter to affect the coefficient of friction using grease lubricant. These investigations are only concerned with the condition of the film formation under oscillation and the performance of the grease under fretting conditions.

Microoscillation is a typical case of transient motion. The entrainment velocity is always changing, and the amplitude of the microoscillation is very small, so the speed has to be very low. The newly formed lubricant film cannot flood the entire contact area. The theory of elastohydrodynamic lubrication could not apply to the case under microoscillation; therefore, it is essential to examine the behaviors of grease under microoscillation. The aim of the present study is to provide the basic characteristics of the grease film behaviors in the point contact area during reciprocating microoscillation through direct observations of the grease film using the technique of relative optical interference intensity.

2 Experimental Conditions

The technique of relative optical interference intensity was used to study the film formation and motion of the grease lubricant under microoscillation. The technique was originally developed for measuring thin fluid lubricant film thickness and profiles [15–17] and can be extended to measure the film thickness of grease under the oscillation condition [18]. A schematic diagram of the experimental measurement system and microoscillation is shown in Fig. 1, where L is amplitude, which represents the moving distance of the contact area, and D represents the diameter of the Hertzian contact area. In tests, in order to observe the behaviors of grease film in the contact area, the amplitude of the microoscillation was less than the diameter of the Hertzian contact area.

Fig. 1
figure 1

Schematic diagram of the experimental apparatus and the microoscillation: a Schematic diagram of the experimental apparatus. b Schematic diagram of the microoscillation

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The contacting pairs are composed of a precision 7/8 inch diameter steel ball (Young’s modulus E = 210 GPa and Poisson’s ratio ν = 0.3) and a glass disk (E = 77.6 GPa and ν = 0.17) with a diameter of 180 mm and a thickness of 15 mm. The ball is loaded against the underside of the disk which is coated with a semi-reflecting chromium layer. The active surface roughness values (R a) of the balls and the disk are about 5 and 2 nm, respectively.

The tests were conducted under rolling and sliding microoscillation conditions. In the case of the rolling microoscillation condition, the glass disk was driven by the programmable motor through a synchronous belt, and the steel ball was driven by the traction force transmitted through the contact point. For the sliding microoscillation condition, the steel ball was fixed, and pure sliding between the contact surfaces occurred. The controllable speed range of the programmable motor is from 0.0001 to 3 rev/s, and the acceleration/deceleration range is from 0.01 to 1280 rev/s2. The disk rotation angle per step of the programmable motor is 0.01 degree.

The lithium grease was used as the lubricant in the tests, and its properties are listed in Table 1. The refractive index of the test grease is 1.435. All the tests were conducted at a temperature 25 ± 1 °C. Under the rolling condition, the ball and the disk were loaded together with an applied load of 22 N, which corresponded to a maximum Hertzian pressure of 0.497 GPa and a contact diameter of 0.292 mm. While under the sliding condition, the load was 14 N, providing a maximum Hertzian pressure of 0.423 GPa and a contact diameter of 0.252 mm. The tests were conducted at constant acceleration/deceleration of 0.44 m/s2. The relationship between the maximum oscillation velocity and the oscillation amplitude can be expressed as:

$$ V_{ \max } = \sqrt {aL} $$
(1)

where V max is the maximum oscillation velocity, a is the acceleration, and L is the oscillation amplitude.

Table 1 Physical parameters of the grease lubricant in the test
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As shown in Fig. 2, the tests were performed in two steps [19]. In the first step, the ball impacted the grease layer on the surface of the disk. As the two surfaces approached, the grease in the range of contact area cannot move out of the contact area in time, and some grease entrapped in the contact area [20–22]. The entrapped grease was marked by broken line in the central contact area. In the second step, the glass disk was driven by the motor in microoscillation. Before tests, the disk, the ball, and all the relevant parts of the apparatus were thoroughly cleaned with acetone and isopropanol in an ultrasonic bath.

Fig. 2
figure 2

The steps of the tests

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3 Experimental Results

3.1 Behaviors of Grease Film During One Cycle Under the Rolling Microoscillation

The formation and distribution of the grease film in the central contact area can be seen from the set of interferograms in Fig. 3, and the two arrows indicate the motion directions. The zero entrainment positions occurred just at the instants of 0 T and 1/2 T in one cycle. Figure 3a–f corresponds to the first half period and the others correspond to the other half period. During the first half period, the entrainment inlet is on the left side of the contact area. It can be seen that the entrapped grease is carried by a tow effect of the moving surfaces to the outlet. The shape of the entrapped grease remains almost unchanged before it reaches the outlet zone. In addition, the new grease film moves into the contact area. Then, a crescent-shaped grease film occurs. Such a phenomenon was also observed by Kaneta et al. [23]. After reversal, the initial inlet becomes the outlet. The entrapped grease and the crescent-shaped grease film are carried by the tow effect of moving surfaces to the new outlet which can be seen from Fig. 3f–j. The shapes of the entrapped grease and the newly formed grease film remain almost unchanged before they arrive at the outlet edge, and the new grease film formed in the new inlet region.

Fig. 3
figure 3

Interferograms during one cycle under the rolling microoscillation (load is 22 N, amplitude is 0.122 mm)

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Figure 4 shows the film profiles along the rolling direction at zero entrainment velocity instants (i.e., the instants of 0, 1/2, and 1 T). As can be seen, the film thickness profile of the entrapped grease remains almost unchanged when it moves in the contact area along the rolling direction, and the maximum film thicknesses of the entrapped grease does not change obviously in one cycle.

Fig. 4
figure 4

The film thickness profiles along the rolling direction at the instants of 0, 1/2, and 1 T

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3.2 Behavior of Grease Film During One Cycle Under the Sliding Microoscillation

When the ball was kept fixed and the disk was driven by the motor, a series of interferograms were taken and given in Fig. 5, and the corresponding film thickness profiles along the sliding direction at the zero entrainment velocity in one cycle are shown in Fig. 6. The crescent-shaped grease film occurs gradually from the inlet, very similar to that find in the cases under the rolling conditions. However, a remarkable phenomenon appears. Under the sliding microoscillation, there are relative displacements in the sliding direction at the working interface between the ball and the glass disk in the contact area. As shown in Fig. 5, the entrapped grease is carried by the moving surface from the inlet side to the outlet side, and the shape of the entrapped grease remains almost unchanged before it moves out of the contact area. Because the steel ball is fixed, the position of the entrapped grease on the ball in the contact area is always changing. It can be deduced that relative motion occurs possibly near the grease/ball interface.

Fig. 5
figure 5

Interferograms during one cycle under the sliding microoscillation (load is 14 N, sliding amplitude is 0.176 mm)

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Fig. 6
figure 6

The film thickness profiles along the sliding direction at the instants of 0, 1/2, and 1 T

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As can be seen from Fig. 6, the film thickness profile of the entrapped grease remains almost unchanged when it moves in the contact area along the sliding direction, and the maximum film thicknesses of the entrapped grease decreases slightly in one cycle.

4 Discussion

4.1 Occurrence of Relative Motion in Central Contact Area

Under the sliding microoscillation condition, relative motion has been observed at the grease/ball interface. However, it cannot be confirmed that whether relative motion occurs near the grease/disk interface. In order to investigate the relative motion between the glass disk and the entrapped grease, a reference line was scratched on the working surface of the glass disk. A series of interferograms showing the grease film behavior in the contact area corresponding to the rolling condition and the sliding condition are shown in Figs. 7a and 8a, respectively. The reference line is marked by the broken line.

Fig. 7
figure 7

The movement of the entrapped grease under the rolling microoscillation (load is 14 N, rolling amplitude is 0.176 mm): a Interferograms in one cycle. b The displacement variation of the disk surface, ball surface, and entrapped grease in the contact region

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Fig. 8
figure 8

The movement of the entrapped grease under the sliding microoscillation (load is 14 N, rolling amplitude is 0.176 mm): a Interferograms in one cycle. b The displacement variation of the disk surface, ball surface, and entrapped grease in the contact region

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In the case of rolling microoscillation, as shown in Fig. 7a, there is no relative displacement between the glass disk and the entrapped grease. The shape of the entrapped grease remains almost unchanged while moving in the Hertzian contact area. The displacements of the disk, the ball, and the entrapped grease in one cycle are plotted in Fig. 7b. It can be seen that the displacement of the entrapped grease is the same as that of the glass disk during one cycle. It can be deduced that the relative motion does not occur between the glass disk and the entrapped grease under the rolling microoscillation.

However, in the case of sliding microoscillation, the reference line moves faster than the entrapped grease, and the shape of the entrapped grease has no obvious change while moving in the Hertzian contact area, as shown in Fig. 8a. The displacements of the disk, the entrapped grease, and the ball in one cycle are plotted in Fig. 8b. It can be seen that the displacement of the entrapped grease is smaller than that of the disk. Therefore, it can be deduced that the relative motions occur at the two interfaces of the grease/disk and the grease/ball at the same time under the sliding microoscillation.

How does the relative motion occur in the contact area by using grease under the sliding microoscillation? In the contact area, the viscosity of the grease increases with the contact pressure. The variation of the grease viscosity can be expressed by:

$$ \eta = \eta_{0} e^{ap} $$
(2)

where η is the viscosity of the grease at a given pressure, η 0 is the viscosity of the grease at the atmospheric pressure, e is the constant of 2.718, α is the pressure/viscosity coefficient, and p is the applied pressure. The Herschel–Bulkley flow model was used by Kauzlarich and Greenwood [24] to describe the inlet rheology of grease:

$$ \tau = \tau_{\text{cg}} + \eta \gamma^{n} $$
(3)
$$ \tau_{\text{cg}} = \tau_{0} e^{ap} $$
(4)

where τ is the shear stress, τ cg is the critical yield shear stress that the grease can sustain, that is, the grease will flow when the shear stress exceeds the τ cg in the contact area, γ is the shear rate, and n is a constant (<1), τ 0 is the yield shear stress of the grease at the atmospheric pressure.

In order to obtain the contact pressure in the entrapped region, the finite element method was used to calculate the pressure in the entrapped grease. The method was based on the following assumptions:

  1. 1.

    The entrapped grease in the contact area was considered as a rigid body.

  2. 2.

    The shape of the entrapped grease abode by the cosine function, and the entrapped grease was just at the center of the contact area.

  3. 3.

    The contact stress that can deform the disk and ball in the contact area is close to the pressure in the entrapped grease.

In this way, the shape of the entrapped grease can be expressed by:

$$ h = h_{0} \cos \theta = h_{0} \left( {\cos {\frac{\pi x}{{2r_{0} }}}} \right) $$
(5)

where h is the entrapped grease film thickness, h 0 is the maximum entrapped grease film thickness (h 0 = 200 nm), x is the distance from one point to the center point of the contact area, and r 0 is the radius of the entrapped grease (r 0 = 48 μm).

Figure 9 shows the schematic diagram of finite element model. The pressure distribution in the contact area is shown in Fig. 10. It can be seen that the pressure increased rapidly in the entrapped grease region as compared with other regions in the Hertzian contact area. The mean pressure of the entrapped grease region is about 0.85 GPa in the sliding tests. As shown in Fig. 11, the critical yield shear stress of the grease at atmospheric pressure is 244 Pa. According to Eq. 4, the critical yield shear stress of the entrapped grease is 32.3 GPa. If the entrapped grease flows under the sliding microoscillation condition, the coefficient of friction exceeds 115. In fact, the coefficient of friction in point contact by using grease is about 0.1. It at least implies that the grease in the contact area can be considered as a solid material in a glassy state [25, 26]. In tests, with the disk sliding, the entrapped grease can hardly flow due to the large critical yield shear stress. Only when the shear stress exceeds the critical yield shear stress of the grease/disk interface or the grease/ball interface, the relative motion can occur.

Fig. 9
figure 9

The schematic diagram of the finite element model

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Fig. 10
figure 10

The distribution of the pressure in the contact region

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Fig. 11
figure 11

Rheological curve of the grease

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4.2 Formation and Motion of Grease Film in Central Contact Area

In this part, the behaviors of the newly formed grease film will be discussed. The process of the formation and motion of the grease film in rolling condition is shown in Fig. 12. The film thickness profiles correspond to the given positions (section plane) on the interferograms. The processes of the formation and the motion of the grease film in sliding condition are shown in Fig. 13. As can be seen from Figs. 12a and 13a, once the grease film formed in the inlet region, the film thickness profile is almost unchanged during moving in the contact area [8]. The film thickness is affected considerably by the fluctuation of the entrainment velocity under microoscillation [27, 28]. After reversal, as shown in Figs. 12b and 13b, the formed grease film moves to the outlet, and the film thickness profile of the formed grease film remains largely unchanged before the formed grease film enter the outlet zone.

Fig. 12
figure 12

Process of the grease film formation/disrepair in the rolling microoscillation: a Formation of the grease film. b Disrepair of the formed grease film

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Fig. 13
figure 13

Process of the grease film formation/disrepair in the sliding microoscillation: a Formation of the grease film. b Disrepair of the formed grease film

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The maximum width of the newly formed grease film coincides with the amplitude of the microoscillation under the rolling condition. However, the maximum width of the newly formed grease film is smaller than the amplitude of the microoscillation under the sliding condition, and it is due to the occurrence of relative motion between the formed grease film and the working surfaces [9, 19].

4.3 Variation of the Grease Film Thickness Under Microoscillation

It is always assumed that sufficient grease is present in the inlet to form the grease film. In fact, the film formation characteristic is also influenced by the lubricant supply to the contact area. The rheological properties of grease are complex and dependent on both the shear rate and the duration of shearing [6]. At a low shear rate, the grease behaves as a plastic solid and does not flow until a critical yield stress has been reached. Thus, once the grease has been pushed to either side of the rolling/sliding track by the passage of the ball, it would not be a spontaneous flow back to replenish the inlet immediately. Therefore, the inlet of the contact area is only partially filled and the film thickness is reduced from the fully flooded value. Then, starvation occurs rapidly near the inlet region and the grease film thickness drops. It can be seen from Fig. 14, the newly formed maximum grease film thickness decreases during the repeated microoscillation. Obviously, the supply of the grease lubricant to the contact area plays an important role in determining the grease film thickness. In fact, under microoscillation, it is not easy to supply the contact area with the grease and finally the contact area is in a lubricant starved condition. Thereby, with the repeated microoscillation, the number of the grease lubricant molecules entering into the contact area decreases and the grease film thickness drops gradually. Once little grease lubricant is present in the contact area, lubricating failure happens. Consequently, the friction should increase and the surface could be damaged easily.

Fig. 14
figure 14

The variations of the formed maximum film thickness with the repetition of microoscillations

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5 Conclusion

The behaviors of the grease film in the contact area in a microoscillation process have been investigated. Experimental results indicate that the grease film is formed in the inlet region, and its thickness profile remains almost unchanged in one cycle during motion in the contact area. A crescent-shaped film has been observed in the contact area. In the case of the rolling microoscillation condition, the crescent-shaped grease film and the entrapped grease film are carried by the two moving surfaces at the same velocity. However, in the case of the sliding microoscillation condition, relative motions occur both at the two interfaces of the grease/ball and the grease/disk. Under the same microoscillation amplitude, the maximum width of the crescent-shaped film without the relative motion is larger than that with the relative motion. During repetition of microoscillations, the crescent-shaped grease film thickness drops gradually, and ultimately the lubrication failure would occur.