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Grease film variation in reciprocating sliding motion
Tribology International 114 (2017) 373–388
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Grease film variation in reciprocating sliding motion a,⁎
a
a
Jing Wang , Xianghua Meng , Shanshan Wang , Qian Zou a b
MARK
b
School of Mechanical Engineering, Qingdao Technological University, Huangdao Campus, 266520 Qingdao, China School of Engineering and Computer Science, Oakland University, Rochester, MI 48309, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: Grease lubrication Reciprocating motion Grease starvation Sliding
In this study, optical interferometry experiments were carried out to investigate the grease film distribution over long working periods in sliding reciprocating motion. In the experiments, the ball was stationary while the glass disk was sliding in a triangular wave or a rectangular wave. Due to the existence of the thickener fiber, in the first several working periods, the variations of the film shape in the first and second stokes are different. With the increase of the period, the starvation effect gradually emerges, together with the occurrence of the grease replenishment. Thus the variations of the grease film in both strokes are similar. For the same sliding speed vmax, the replenishment is more drastic for a rectangular wave and the minimum film thickness is a little thicker.
1. Introduction Reciprocating motions widely exist in engineering and is an important branch of transient elastohydrodynamic lubrication (EHL). It can be found in contacts such as gear teeth, cam and its follower, rolling element bearings etc. Due to the reversal of motion, the outlet cavitation zone in one stroke becomes the inlet starvation zone in the beginning of the next stroke, making the problem more complex. In 1972, Petrousevitch et al. [1] explored the oil shape and film thickness in reciprocation motion theoretically and experimentally. Hooke et al. [2] derived the dimensionless film thickness formula for reciprocating motion numerically. Their results were validated by Sugimura et al. [3] experimentally using an ultra-thin film optical interferometric technique. Wang et al. [4] simulated the line contact reciprocating motion and revealed the mechanism of the oil film formation and its characteristics. Later Wang et al. [5] compared experimental and theoretical results under short stroke reciprocating motions in point contacts and obtained good agreement. They found that the influence of reverse oil starvation increased with the increase of the working frequency. Izumi et al. [6] pointed out the film thickness in reciprocating motion was thinner than that in unidirectional motion because of the oil starvation caused by the reversal of the surfaces. Li et al. [7,8] conducted an experimental investigation to explore the grease film behaviour of point contact lubrication during micro-oscillation in the case of pure rolling or pure sliding and spotted a critical entraining speed in their experiments. They found that when the entraining velocity was lower than the critical value, the thickener fiber played a vital role in the grease film formation while the film thickness was far
⁎
higher than the theoretical predicted value. With the increase of the entraining velocity, the thickener fiber was pushed out of the contact so that the variation of the film thickness coincided with the theoretically predicted values. Sudeep et al. [9] studied the effect of surface texture on the traction force in reciprocating motion and found around 30% off of the traction force. Grease lubrication has been studied by many researchers. Cann and Lubrecht [10] found that the loading-unloading process would contribute to lubricant replenishment. For better understanding of replenishment, some researchers found that lateral vibration [11], temperature [12], centrifugal force [13,14] and surface tension [15] would also promote grease reflowing back to the contact. Ali et al. [16] introduced an innovative mechanism by channeling the lubricant towards the centerline of the over rolled track to reduce or overcome the negative effects of starved lubrication in concentrated contacts. Huang et al. [17] showed that slide/roll ratio contributed to replenishing the contact by transferring more grease to the vicinity of the contact to form a larger lubricant reservoir. Recently, they [18] found that the higher oil bleeding ratio of grease, the larger re-formed lubricant reservoir would be. Cyriac et al. [19] and Misty et al. [20] studied the effect of a mixture of water in grease on the lubrication performance. Cyriac et al. [21] experimentally explored the influence of the thickener particle size and concentration on the grease EHL film thickness and found that the film thickness increases with the increase in the particle size and concentration at medium speed. Zhang [22] explored the lubrication characteristics of lithium grease mixed with glycerinum in point contacts on a ball-on-disk test rig by optical interferometric technique. She found that at very low speed, due to the existence of thickener fiber, the grease
Correspondence to: School of Mechanical Engineering, Qingdao Technological University, Huangdao Campus, 777 Jialingjiang Road, 266520 Qingdao, China. E-mail address: [email protected] (J. Wang).
http://dx.doi.org/10.1016/j.triboint.2017.04.049 Received 15 January 2017; Received in revised form 7 April 2017; Accepted 27 April 2017 0301-679X/ © 2017 Elsevier Ltd. All rights reserved.
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film thickness was thicker than that using the base oil as lubricant. However, at higher speed, the grease film thickness was at the same level as the base oil film thickness. Laurentis et al. [23] experimentally measured the friction coefficients and film thickness of a series of commercial bearing greases and their bled oils. They reported that for lithium greases, a quite thick film was formed at low speed, which was much higher than that of their corresponding base oil film. There existed a "critical entraining velocity", above which the film thickness became nearly the same as that of the base oil. Gonçalves et al. [24] revealed the similar behaviour on a ball-on-disc test rig with optical interferometry using polymer greases. The aim of the present study is to explore the basic behaviour of the grease lubrication film over long working periods. In the experiments, the steel ball is stationary while the glass disk is sliding in reciprocating motion in the form of a triangular wave or a rectangular wave.
the charge coupled device (CCD) used in the experiments, the working period is set as 1 s. The steel ball was loaded against the underside of the glass disk with a force of F=30 N. One working period of reciprocating motion consists of two strokes. Based on an isothermal assumption, the Reynolds equation is written as
∂(ρh ) ∂(ρh ) ∂ ⎛ ρh3 ∂p ⎞ ∂ ⎛ ρh3 ∂p ⎞ ⎜ ⎟+ ⎜ ⎟=12ue +12 ∂x ⎝ η ∂x ⎠ ∂y ⎝ η ∂y ⎠ ∂x ∂t
In oil lubricated reciprocating motion [4,5], the variation of oil film ∂(ρh ) ∂(ρh ) is controlled by wedge term (12ue ∂x ) and squeeze term (12 ∂t ). Around the stroke end, the squeeze term is dominant so that an entrapped oil film is formed with the inlet film thickness thinner than that at the outlet. Thereafter, with the increase of the entraining velocity, the wedge effect is enhanced so that the entrapped oil film is transported by the entraining velocity to the outlet, and a wedge shaped oil film is formed. Then with the further increase of the entraining velocity, the film thickness is lifted gradually, the wedge-shaped oil film is moved out of the contact, and the maximum central film thickness occurs a little later than at the stroke center. When the entraining velocity is reduced, the film thickness decreases with the decrease of the wedge effect. The squeeze effect becomes dominant again and at last an entrapped oil film is formed at the stroke end. The variation of the film thickness in the two strokes is completely same, except their different directions. The outlet cavitation zone formed in one stroke works as the inlet starvation zone in the next stroke after the moving direction is reversed. Under lower entraining velocity, the influence of oil starvation is trivial while the influence increases with the increase in working frequency [4,5]. When the starvation effect is significant, the existence time of the starvation in the two stroke should be the same if the vibration of the test rig, the measurement errors etc. are removed.
2. Experimental methods Experiments were conducted using a ball-on-disk apparatus, and the technique of relative optical interference intensity was used to study the film thickness and motion of the grease lubrication under reciprocating motion. The contacting pairs were composed of a 25.4 mm diameter steel ball and a glass disk with a diameter of 150 mm and a thickness of 15 mm. One side of the glass disk was coated with a Cr-layer approximately 20 nm thick to facilitate partial reflection. All the tests were conducted under a controlled laboratory environment with a constant room temperature of 23 °C.The properties of the steel and glass were reported in Table 1. Either the glass disk or the steel ball has its driving system. Each includes a Mitsubishi AC servo motor, a high precision speed reducer and coupling etc.. The servo motor is programmable with a nominal power output of 400 W. A red point light source with a wavelength of 630 nm was used in the experiments. Images were collected with an image capture card (OK-LV20A) and a black-white camera (OKAM1130) produced by Beijing JoinHope Image Technology Ltd. The OK camera employs LVDS(low voltage differential signaling) digital output technique. In this study, optical interferometry experiments were carried out when the ball is stationary while the glass disk was moving in the form of a triangular wave or a rectangular wave, as shown in Fig. 1. With T the working period, for triangular wave, A=0.25; while for rectangular wave, A=0.5, the stroke length L reads
L = Avmax T
3.1. Triangular wave Fig. 2 gives the optical interferograms and mid-section film profiles along the entraining direction in the first period for vmax=20 mm/s， L=5 mm. In Figs. 2(a)-(e) for the first stroke, the inlet is at the left side while in Figs. 2(g)-(l) for the second stroke, the outlet is at the right side. The same applies to Figs. 3, 4, 7, 8. At startup time instant, the steel ball is loaded against the glass disk and the grease with thickener fiber lumps in the contact, shown as in Fig. 2(a). Due to the thickener fiber, the contact grease film thickness is thick and unevenly distributed. With the increase of the entraining velocity, the glass disk leaves the first location at the stroke end, some of the thickener is pushed out of the contact during the process so that the film thickness is reduced very much, as shown in Fig. 2(b). In Fig. 2(c) there is very little thickener fiber left in the contact so that the film thickness becomes much lower. In Fig. 2(d), the entraining velocity gets its maximum and the film thickness is obviously increased. Due to the decrease of the entraining velocity, it is seen that the film thickness drops at the inlet part, as shown in Fig. 2(e). In Fig. 2(f), at the stroke end, a wedgeshaped film thickness is formed, different from the common entrapped film shape at stroke end of oil lubricated reciprocating motion [4,5]. In the beginning of the reverse stroke, like what is shown in Fig. 2(g), the outlet cavitation zone in Fig. 2(f) becomes an inlet starvation region, which does not influence the film thickness because of the low entraining speed. The very low entraining velocity results in a reduced inlet film thickness and thus a small entrapment appears in Fig. 2(g). Once the wedge-shaped oil film formed at the stroke end leaves the contact, the film thickness takes on a new wedge-shape, as shown in Fig. 2(h). The film thickness is increased in the stroke center (Fig. 2(i)) and then decreased (Fig. 2(j)). Around the end of this period, the glass disk resumes to the previous location where some of the thickened fiber remains, the thick irregular film thickness is formed in Figs. 2(k) and 2(l). Moreover, the amount of the thickener fiber in Fig. 2(l) is less than
(1)
The lithium grease of Centoplex 3 was used as the lubricant in the tests. Centoplex 3 is multi-purpose grease based on oxidation-resistant mineral oil and lithium soap. Due to the good resistance to work under normal temperatures and loads, this grease can be used for long-term lubrication, and its properties are listed in Table 2. Before all the tests, the disk, the ball and all the relevant parts of the apparatus were thoroughly cleaned with alcohol and acetone. 3. Results and discussions The experiments were performed under sliding condition where the glass disk was rotating and the ball was stationary. By the limitation of Table 1 Properties of ball and disk materials. Properties
Steel (ball)
Glass (disk)
Young's modulus (GPa) Poisson's ratio Density (kg/m3) Thermal conductivity（W/m K） Specific heat（J/kg K）
210 0.3 7850 46 470
81 0.208 2510 1.11 840
(2)
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Fig. 1. The variation of glass disc velocity.
is repelled out of the contact gradually. At the “startup stroke end”, the central film thickness is reduced gradually. At the “end stroke end”, the 5 central film profiles coincide with one another. For the 5th working period, the influence of the thickener fiber on the central film thickness around the “startup stroke end” is slight. From Fig. 5(a), it is seen that during 0.15 T≤t≤0.85 T, the central film thickness increases and then decreases with the variation of the entraining velocity in a triangular wave, similar to the central film thickness variation in oil lubrication [4,5]. In Fig. 5(b), the central film thickness for the 20th, 50th, 70th working period nearly coincide with one another and similar to the curves in Fig. 5(a) except those during 0.0 T≤t≤0.1 T and 0.9 T≤t≤0.1 T. Moreover, the central film thickness at the “startup stroke end” has fallen to the level of that at the “end stroke end”. The results during 0.0 T≤t≤0.1 T or 0.5 T≤t≤0.6 T correspond to the time period when the wedge-shaped film formed at the beginning of the stroke end passes through the contact. In Fig. 5(b), the inlet grease starvation zone by the reverse motion exerts no influence on the central film thickness. Fig. 5(c) shows the results for the working periods N=100, 200, 300, 400 and 500, respectively. The curve for the 100th working period is nearly the same as that of 70th working period. The other 4 curves fluctuate around that of the 100th working period. The authors suppose that the fluctuation is caused by the replenishment of the grease from the side reservoirs back to the sliding track. It should also be noted that for 0.15 T≤t≤0.33 T or 0.65 T≤t≤0.8 T for the curve of N=400 or for 0.15 T≤t≤0.36 T or 0.65 T≤t≤0.82 T for the curve of N=500, obvious drop is found, illustrating the significance of the grease starvation. The following film thickness rise validates the grease replenishment effect. In Fig. 5(d), the 5 curves are similar again with only smaller fluctuations, representing the decreased effect of replenishment. During 0.15 T≤t≤0.4 T or 0.65 T≤t≤0.85 T, the central film thickness is also reduced. Fig. 6 shows the variation of the minimum film thickness for vmax=20 mm/s，L=5 mm. Around the “startup stroke end” (0 T≤t≤0.1 T or 0.9 T≤t≤1 T) in Fig. 6(a), only the minimum film thickness of the 1st and 2nd is higher than the rest 3 curves due to the existence of the thickener fiber. During 0.1 T≤t≤0.9 T, the 5 curves nearly coincide with one another. Similar to the variation of the central film thickness, after the wedge-shaped oil film leaves the contact, the minimum film thickness faces an increase and then a decrease in each stroke. And the variation is in the same tendency as those for N=3, 4, 5 in Fig. 6(a). In Fig. 6(b), the 3 curves nearly coincide with each other. In Fig. 6(c), the fluctuations are drastic and there is an obvious film thickness reduction during 0.15 T≤t≤0.35 T or 0.6 T≤t≤0.85 T after N=400 by the obvious effect of grease starvation. In Fig. 6(d), the grease starvation becomes significant but the fluctuations become less significant than those in Fig. 6(c) due to the decrease effect of replenishment. The minimum film thickness for 0.5 T≤t≤0.7 T is generally higher for that during 0.0 T≤t≤0.2 T. The reason of the difference may come from the uneven grease distribution and therefore the uneven replenishment of the grease.
Table 2 Grease properties. Grease Base oil Thickener Applicable temperature range (℃) Cone penetration (25 ℃ 0.1 mm) Base oil viscosity (40 ℃ mm2/s) Base oil viscosity (100 ℃ mm2/s) Dropping point DIN ISO 2176 (℃) NLGI grade
Centoplex 3 Mineral oil Lithium soap −15 to 150 220–250 100 10 > 190 3
that in Fig. 2(a), so the film thickness in Fig. 2(l) is thinner. In oil lubricated reciprocating motion, the entrapped film shape at one stroke end is the same as that of the other, except their opposite direction. However, the film shape in Fig. 2(f) is different from Fig. 2(a) and (l), it is the feature of grease reciprocating lubrication. In order to interpret the lubrication phenomena easily in the following, 0 T is named as “startup stroke end” and 1/2 T is “end stroke end”. Fig. 3 gives the optical interferograms and mid-section film profiles in the 100th period for vmax=20 mm/s，L=5 mm. In this period, the thickener fiber has basically disappeared. In Fig. 3(a)，the “startup stroke end”，although there is slight reduction in the film thickness at the periphery of the contact area, the grease film still takes on a wedge shape with the dominance of the squeeze effect, like what is shown in Fig. 2(f). This film shape is the same as shown in that in Fig. 3(f) at the “end stoke end”, but in opposite direction. That is to say, the variation of the grease film has become similar to.that in oil lubricated contact. By comparison of Figs. 2 and 3, after 99 working periods, there is obvious film thickness reduction around the stroke end. At the beginning of each stroke, the outlet starvation region in the previous stroke becomes a much more obvious inlet starvation region. It can be seen that the existence time of the starvation area is also longer than that in Fig. 2. But compared with the mid-section film profiles in Fig. 2, the effect of grease starvation is negligibly small. Fig. 4 gives the optical interferograms and mid-section film profiles in the 1000th period for vmax=20 mm/s，L=5 mm. After long working periods, the degree of grease starvation becomes very severe. In each stroke, the grease starvation exists even longer and the starvation area is larger. By the joint effect of entraining velocity and grease starvation, the film thickness in the contact decreases and fluctuates irregularly. In Fig. 4(c), (d) and (i), (j)，the contact becomes parched by the severe grease starvation. Fig. 5 shows the variations of central film thickness over a number of selected working periods，vmax=20 mm/s，L=5 mm with N is the number of the working periods. Fig. 5(a) is for 1st, 2nd, 3rd, 4th and 5th working period. Around the “startup stroke end” in the 1st period, the central film thickness is relatively thick due to the existence of the thickener fiber. It is also thicker than that at the “end stroke end” and that at 1T. With the increase of the working period, the thickener fiber
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Fig. 2. Interferograms and mid-section film thickness during the first cycle under the motion of triangular wave (vmax=20 mm/s，L=5 mm).
is thicker and the fluctuation of the film thickness is more obvious. Especially for the 1st working period, a very shallow entrapment is found at the “end stroke end”. In Fig. 7(a), for the first 5 working periods, again, around the “startup stroke end”, i.e.,0.0 T≤t≤0.1 T and
Fig. 7 shows the variations of central film thickness in a number of selected working periods for vmax=40 mm/s，L=10 mm. The optical photos are not given because the variation of the grease film is similar as those for vmax=20 mm/s，L=5 mm. The differences are that the film 376
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Fig. 3. Interferograms and mid-section film thickness during the 100th cycle under the motion of triangular wave (vmax=20 mm/s，L=5 mm).
0.9 T≤t≤1.0 T, the grease film thickness is thick due to the existence of the thickener fiber. During 0.1 T≤t≤0.9 T,the 5 curves coincide with one another. In Fig. 7(b), the central film thickness for N=20 is nearly the same as that of N=5 except the portion around the “startup stroke
end”. Grease starvation happens earlier at N=50 during 0.25 T≤t≤0.3 T and 0.65 T≤t≤0.8 T and grows severer during 0.1 T≤t≤0.45 T and 0.55 T≤t≤0.8 T for N=70. In Fig. 7(c), the starved effect for N=100 is much severer than that of N=70. Although there are rises and falls in
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Fig. 4. Interferograms and mid-section film thickness during the 1000th cycle under the motion of triangular wave (vmax=20 mm/s，L=5 mm).
the distribution of the central film thickness in Fig. 7(c), the general tendency is to level off. In Fig. 7(d), it is seen that for N=600, 700, 800, 900 and 100, all 5 curves are identical to be a straight line. That is to say, from N=600, the variation of the entraining velocity exerts no influence on the central film thickness. Fig. 8 shows the variations of minimum film thickness for
vmax=40 mm/s，L=10 mm. Similar to the variations in Fig. 7, the grease starvation becomes obvious since N=50 and the minimum film thickness at last turns to a constant horizontal line since N=600 over one working period, irrespective of the variation of the entraining velocity. Fig. 9 demonstrates the optical interferograms and mid-section film 378
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Fig. 5. The central film thickness under the motion of triangular wave (vmax=20 mm/s，L=5 mm).
shape occurs in the rest pictures. At the “end stroke end” shown in Fig. 9(f), the grease film takes on a wedge shape with a shallow entrapped film, similar to what was found in reciprocating oil lubrica-
profiles in the 1st period for vmax=200 mm/s， L=50 mm. It is seen that except for Figs. 9(a) and 9(l), at the “startup stroke end”, where the film thickness is quite thick because of the thickener fiber, EHL film
Fig. 6. The minimum film thickness under the motion of triangular wave (vmax=20 mm/s，L=5 mm).
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Fig. 7. The central film thickness under the motion of triangular wave (vmax=40 mm/s，L=10 mm).
Fig. 8. The minimum film thickness under the motion of triangular wave (vmax=40 mm/s，L=10 mm).
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Fig. 9. Interferograms and mid-section film thickness during the first cycle under the motion of triangular wave (vmax=200 mm/s，L=50 mm).
tion [4,5]. Fig. 10 gives the optical interferograms and mid-section film profiles in the 100th period for L=50 mm，vmax=200 mm/s. Much of the grease has left the sliding track so that a heavy starvation exists in
the whole working period. The film thickness is very low and generally horizontal. At both stroke ends, possibly by the uneven distribution of the remained thickener fiber, a curved film thickness instead of the
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Fig. 10. Interferograms and mid-section film thickness during the 100th cycle under the motion of triangular wave (vmax=200 mm/s，L=50 mm).
wedge shaped film exists. Fig. 11 shows the variations of central film thickness in a number of selected working periods for vmax=200 mm/s， L=50 mm. Grease starvation happens as quickly as at N=3 and becomes severer and
severer thereafter, shown in Figs. 11(a) and 11(b). In Fig. 11(b), it is seen that the grease starvation covers the majority of each stroke. However, in Fig. 11(c) and (d)，the severe grease starvation levels off the curves and the 5 curves overlap with one another. It seems the 382
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Fig. 11. The central film thickness under the motion of triangular wave (vmax=200 mm/s，L=50 mm).
Fig. 12. The minimum film thickness under the motion of triangular wave (vmax=200 mm/s，L=50 mm).
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Fig. 13. Variation of the starvation ratio of the triangular waves.
replenishment does not happen. In Fig. 11(d), the central film thickness drops a little again by the increase of the starvation effect. Fig. 12 shows the corresponding minimum film thickness in a number of selected working periods. It is seen that the grease starvation also starts at N=3 and gradually becomes severe. The minimum film thickness becomes constant in Fig. 12(c) and (d). As for the existence of the inlet starvation zone in each stroke, a starvation ratio Rst is defined as
Rst = 2∆ts / T
seems play an important role. In the subsequent several working periods, because there is thickener remained in the conjunction, the critical sliding speed still exists. However, the value of the speed is noticed to decrease with the increase of the working period. Therefore, the authors suppose that for time-dependent and long run mechanical elements, the critical entraining speed is not an important influential factor. The experiments under steady state sliding motion were also finished for the sliding speed ranging from 0.01 m/s to 0.4 m/s. In the experiments, the grease lumps in the all the conjunctions when the load is applied so that in the beginning of each motion, the thickened fiber is observed. The contact turns into a stable EHL one after a short time, which decreases with the increase of the sliding speed. That is to say, if the speed is very high, the existence time of the thickener fiber is very brief. Moreover, for a long-term operation, even for low speed, the existence time of such thick film is trivial compared to the service life. Thus, the authors suggests the phenomenon is a kind of "running-in" of grease lubrication.
(3)
where ∆ts is the existence time of the inlet starvation zone in each stroke. If Rst =1, it means the inlet starvation zone exists over a full stroke. Fig. 13 presents the variations of Rst in the first and the second stroke for the above 3 triangular waves. It is seen that for vmax=20 mm/ s, the starvation ratio curves for the first and the second stroke start at small values and both increase with fluctuation. From N=500, they both get stabilized to a higher value around 0.73 and 0.65, respectively. For Fig. 13(b), the tendency is the same, but the two curves approach to 1.0 and 0.9, respectively from N=500. In Fig. 13(c), the two curves reach 1.0 together at N=200. For the 3 cases, although there are discrepancy between the values of the fist and the second stroke, all the starvation ratios increase from a small value at N=1 until they reach a relatively stable state. But for oil lubrication [5], the starvation ratio is fixed for both strokes in one working period and it does not increase with the increase of the working period. Due to the existence of the thickener fiber, in the first several working periods, the variations of the film shape in the first and second stokes are different. There is thickener fiber lumped in the contact around the "startup stroke end" but not around the "end stroke end". But with the increase of the working period, the thickener fiber is gradually removed from the contact so that the variation of grease film in the first stroke approaches to the that of the second stroke. With the increase of the period, the starvation effect gradually emerges, together with the occurrence of the grease replenishment. The waxing and waning effects of starvation and replenishment fluctuate the film thickness. However, the larger the disk sliding speed vmax, the less obvious effect of the grease replenishment. Finally the central and minimum film thickness become a horizontal line during one working period, irrelevant to the variation of the disk sliding speed. There have been a number of papers discussing the "critical entraining speed" on the fully flooded grease lubrication under steady state condition, revealing the possible V-shape film thickness with the increase of the entraining speed [23,24]. However, based on the results presented in this study, it is seen that for time-dependent problem, the so-called " critical entraining speed" exists only in the first several working periods. If we compare the variations of the central film thickness for the above 3 cases, it is found the critical sliding speeds in the first working periods are different. They are 12 mm/s, 8 mm/s, 3 mm/s, respectively. The acceleration rates for the 3 cases are 80 mm/ s2，160 mm/s2 and 800 mm/s2, respectively. The acceleration rate
3.2. Rectangular wave Fig. 14 gives the variations of central film thickness in a number of selected working periods for vmax=10 mm/s，L=5 mm. Fig. 15 show the variations of the minimum film thickness. In Fig. 14(a), at the beginning of the working period, the central film thickness only decreases while at the end of the working period, the central film thickness only increases. Between the two parts, the variation of the central film thickness is the same as that in Fig. 5(a) except the drop at 0.5 T. The variation in Fig. 14(b) and (c) are similar to those in Fig. 5(b) and (c). However, when the value of N is increased to 600– 1000, the grease starvation begins to take effect during 0.1 T≤t≤0.3 T and 0.6 T≤t≤0.8 T. Around the “end stroke end”, 0.5 T, the central film thickness gains its value a little bit by the effect of the replenishment. In Fig. 15(a)–(c), the variation is similar to those of the central film thickness. In Fig. 15(d), due to the grease starvation, the minimum film thickness decreases a little bit during 0.1 T≤t≤0.35 T and 0.6 T≤t≤0.85 T. During 0.4 T≤t≤0.65 T, the minimum film thickness firstly increases before a drop at 0.5 T, followed by a hill in the second stroke. Compare Fig. 14(b) with 14(a) or Fig. 15(b) with 15(a), it is seen either the central film thickness, or the minimum film thickness fluctuates obviously for N=50 or 70. The fluctuation becomes small in Figs. 14(c) and 14(c). In Fig. 14(d) and 15(d), during 0.3 T≤t≤0.7 T, both the central and minimum film thickness have risings. Fig. 16 shows the variations of central film thickness in a number of selected working periods for vmax=20 mm/s，L=10 mm. There is a sudden drop at the “end stroke end” by the plummet of the disk velocity. And an obvious grease starvation happens earlier for N=50. But it should be pointed out that for N=70, grease starvation appears earlier in the first stroke but does not happen in the second stroke. In Fig. 16(c), the central film thickness curve for N=100 resembles that of 384
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Fig. 14. The central film thickness within each cycle under the motion of rectangular wave (vmax=10 mm/s，L=5 mm).
Fig. 15. The minimum film thickness within each cycle under the motion of rectangular wave (vmax=10 mm/s，L=5 mm).
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Fig. 16. The central film thickness under the motion of rectangular wave (vmax=20 mm/s，L=10 mm).
Fig. 17. The minimum film thickness under the motion of rectangular wave (vmax=20 mm/s，L=10 mm).
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Fig. 18. The variation of minimum film thickness with the sliding speed (a) Triangular wave, (b) Rectangular wave.
N=5, except for the parts around the “startup stroke end”. Then the whole film thickness drops again, see the results for N=200. Grease replenishment happens around the stroke ends for N=300 and 400, with the film thickness during 0 T≤t≤0.2 T and 0.8 T≤t≤1 T higher than that during 0.4 T≤t≤0.6 T. However, for N=500 the film thickness during 0 T≤t≤0.2 T and 0.8 T≤t≤1 T drops much but the film thickness around 0.4 T≤t≤0.6 T is increased greatly. Such behaviour demonstrates that the replenishment is uneven. In Fig. 16(d), for N=600, the replenishment plays a more important role. But for N=700 and 800, the replenishment effect is weak so that the film thickness is reduced on a whole. Then it increases greatly for N=900. After that it drops again at N=1000, tending to be a horizontal line during one working period. It proves that the replenishment and starvation happen alternatively. But in the long term, the central film thickness is expected to regress to a constant value during the whole working period. Fig. 17 shows the variations of minimum film thickness in a number of selected working periods for vmax=20 mm/s， L=10 mm. The variation of the minimum film thickness is generally the same as what is shown in Fig. 16. Fig. 18 shows the variation of the minimum film thickness in each working period with the sliding speed over 1–1000 working periods. It is seen that after the first 100 working periods, the minimum film thickness for the three sliding speeds fluctuates between 29 nm and 32 nm for the 3 triangle waves, as well as between 29 and 34 nm for the 2 rectangular waves. After the working periods reaches 500, the minimum film thickness decreases with the decrease of the sliding speed vmax. Take the case vmax=20 mm/s, L=5 mm for triangular wave and vmax=20 mm/s, L=10 mm for rectangular wave for a comparison, it is found that for triangular wave, it takes longer time for the wedgeshaped film formed by the reverse motion to move out of the contact. For vmax=20 mm/s, it is also seen that the replenishment is more drastically to happen for a rectangular wave so that the minimum film thickness of the rectangular wave is a little larger. Although the experiments with larger entraining velocity in the
form of a rectangular wave are not carried out, it could be concluded that for the long term, the central and minimum film thickness are expected to decrease with the grease starvation and fall to constant values over a working period. Fig. 19 shows the starvation ratios for the rectangular waves of vmax=10 mm/s and 20 mm/s. The larger the maximum sliding speed vmax, the larger the starvation ratio Rst. For vmax=20 mm/s, Rst=1.0 happens earlier at N=200.
4. Conclusions In this study, the variations of grease films in reciprocating sliding motion were explored by using optical interferometric technique. The glass disk moves in the form of a triangular wave or a rectangular wave. The conclusions are summarized as follows. (1) Due to the existence of the thickener fiber, in the first several working periods, the variations of the film shape in the first and second stokes are different. There is thickener fiber lumped in the contact around the "startup stroke end" but not around the "end stroke end". With the increase of the working period, the thickener fiber is gradually removed from the contact so that the variation of grease film in the first stroke approaches to the that of the second stroke. With the increase of the period, the starvation effect gradually emerges, together with the occurrence of the grease replenishment, resulting in fluctuations in film thickness. (2) For triangular wave, the waxing and waning effects of starvation and replenishment fluctuate the film thickness. However, the larger the disk sliding speed vmax, the less obvious effect of the grease replenishment. With larger disk sliding speed, the central and minimum film thickness become horizontal line during one working period, irrelevant to the variation of the disk sliding speed. (3) For the same sliding speed vmax, it is also seen that the replenishment is more drastic for a rectangular wave so that the
Fig. 19. Variation of the starvation ratio of the rectangular waves (a) vmax=10 mm/s, (b) vmax=20 mm/s.
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general minimum film thickness of a rectangular wave is a little thicker. Although the experiments with larger entraining velocity in the form of a rectangular wave are not carried out, it could be concluded that for the long term, the central and minimum film thickness are expected to decrease with the grease starvation and fall to constant values over a working period. (4) In the experiments, the grease lumps in the conjunction when the load is applied so that in the beginning of each motion, the thickener fiber is observed and the contact turned into an EHL one after a short time. The time decreases with the increase of the sliding speed. The existence of such thick film is brief compared with the long operation time. The authors suggests it is a kind of "running-in" of grease lubrication.
12):1013–21. [6] Izumi N, Tanaka S, Ichimaru K, Morita T. Observation and numerical simulation of oil-film formation under reciprocating rolling point contact. In: Proceedings of the 30th Leeds-Lyon symposium on tribology, transient processes in tribology. Vol. 43; 2003. p. 565–72. [7] Li G, Zhang C, Xu H, Luo J, et al. The film behaviors of grease in point contact during microoscillation. Tribol Lett 2010;38(3):259–66. [8] Li G, Zhang C, Luo J, Liu S, et al. Film-forming characteristics of grease in point contact under swaying motions. Tribol Lett 2009;35(1):57–65. [9] Sudeep U, Pandey RK, Tandon N. Effects of surface texturing on friction and vibration behaviors of sliding lubricated concentrated point contacts under linear reciprocating motion. Tribol Int 2013;62(62):198–207. [10] Cann PM, Lubrecht AA. The effect of transient loading on contact replenishment with lubricating greases. Tribol Interface Eng 2003;43(43):745–50. [11] Nagata Y, Kalogiannis K, Glovnea R. Track replenishment by lateral vibrations in grease-lubricated EHD contacts. Tribol Trans 2012;55(1):91–8. [12] Lugt PM, Velickov S, Tripp JH. On the chaotic behavior of grease lubrication in rolling bearings. Tribol Trans 2009;52(5):581–90. [13] Van Zoelen MT, Venner CH, Lugt PM. Free surface thin layer flow on bearing raceways. J Tribol 2008;130(2):319–20. [14] Van Zoelen MT, Venner CH, Lugt PM. Free surface thin layer flow in bearings induced by centrifugal effects. Tribology Trans 2010;53(3):297–307. [15] Gershuni L, Larson MG, Lugt PM. Lubricant replenishment in rolling bearing contacts. Tribol Trans 2008;51(51):643–51. [16] Ali F, Křupka I, Hartl M. Enhancing the parameters of starved EHL point conjunctions by artificially induced replenishment. Tribol Int 2013;66(7):134–42. [17] Huang L, Guo D, Wen S, et al. Effects of slide/roll ratio on the behaviours of grease reservoir and film thickness of point contact. Tribol Lett 2014;54(3):263–71. [18] Huang L, Guo D, Wen S. Film thickness decay and replenishment in point contact lubricated with different greases: a study into oil bleeding and the evolution of lubricant reservoir. Tribol Int 2016;93:620–7. [19] Cyriac F, Lugt PM, Bosman R, Venner CH. Impact of water on EHL film thickness of lubricating greases in rolling point contacts. Tribol Lett 2016;61(3):1–8. [20] Mistry A. Performance of lubricating greases in the presence of water. NLGI 2005;68(12):8–15. [21] Cyriac F, Lugt PM, Bosman R, Padberg CJ, Venner CH. Effect of thickener particle geometry and concentration on the grease EHL film thickness at medium speeds. Tribol Lett 2016;61(2):1–13. [22] Zhang YM. Studies on lubrication properties of lithium based grease [Master thesis]. Qingdao, China: Qingdao Technological University; 2015. [23] Laurentis ND, Kadiric A, Lugt P, Cann P. The influence fo bearing grease composition on friction in rolling/sliding concentrated contacts. Tribol Int 2016;94:624–32. [24] Gonçalves D, Graça B, Campos AV, Seabra J, Westbroek R. On the film thickness behaviour of polymer greases at low and high speeds. TribolInt 2015;93:435–44.
Acknowledgement This work was supported by the National Natural Science Foundation of China through grant No. 51275253. Professor J. Wang was supported by the China Scholarship Council to work as a research scholar at Oakland University, USA. Thanks also go to Dr. Weimin Li of State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences for the valuable discussion. References [1] Petrousevitch AI, Kodnir DS, Salukvadze RG, et al. The investigation of oil film thickness in lubricated ball-race rolling contact. Wear 1972;19(4):369–89. [2] Hooke CJ. The minimum film thickness in lubricated line contacts during a reversal of entrainment—general solution and the development of a design chart. Proc Inst Mech Eng Part J J Eng Tribol 1994;208(110):53–64. [3] Sugimura J, Jones WRJ, Spikes HA. EHD film thickness in non-steady state contacts. J Tribol 1998;120(3):442–52. [4] Wang J, Kaneta M, Yang P. Numerical analysis of TEHL line contact problem under reciprocating motion. Tribol Int 2005;38(2):165–78. [5] Wang J, Hashimoto T, Nishikawa H, et al. Pure rolling elastohydrodynamic lubrication of short stroke reciprocating motion. Tribol Int 2006;38(11–
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Contents lists available at ScienceDirect
Tribology International journal homepage: www.elsevier.com/locate/triboint
Grease film variation in reciprocating sliding motion a,⁎
a
a
Jing Wang , Xianghua Meng , Shanshan Wang , Qian Zou a b
MARK
b
School of Mechanical Engineering, Qingdao Technological University, Huangdao Campus, 266520 Qingdao, China School of Engineering and Computer Science, Oakland University, Rochester, MI 48309, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: Grease lubrication Reciprocating motion Grease starvation Sliding
In this study, optical interferometry experiments were carried out to investigate the grease film distribution over long working periods in sliding reciprocating motion. In the experiments, the ball was stationary while the glass disk was sliding in a triangular wave or a rectangular wave. Due to the existence of the thickener fiber, in the first several working periods, the variations of the film shape in the first and second stokes are different. With the increase of the period, the starvation effect gradually emerges, together with the occurrence of the grease replenishment. Thus the variations of the grease film in both strokes are similar. For the same sliding speed vmax, the replenishment is more drastic for a rectangular wave and the minimum film thickness is a little thicker.
1. Introduction Reciprocating motions widely exist in engineering and is an important branch of transient elastohydrodynamic lubrication (EHL). It can be found in contacts such as gear teeth, cam and its follower, rolling element bearings etc. Due to the reversal of motion, the outlet cavitation zone in one stroke becomes the inlet starvation zone in the beginning of the next stroke, making the problem more complex. In 1972, Petrousevitch et al. [1] explored the oil shape and film thickness in reciprocation motion theoretically and experimentally. Hooke et al. [2] derived the dimensionless film thickness formula for reciprocating motion numerically. Their results were validated by Sugimura et al. [3] experimentally using an ultra-thin film optical interferometric technique. Wang et al. [4] simulated the line contact reciprocating motion and revealed the mechanism of the oil film formation and its characteristics. Later Wang et al. [5] compared experimental and theoretical results under short stroke reciprocating motions in point contacts and obtained good agreement. They found that the influence of reverse oil starvation increased with the increase of the working frequency. Izumi et al. [6] pointed out the film thickness in reciprocating motion was thinner than that in unidirectional motion because of the oil starvation caused by the reversal of the surfaces. Li et al. [7,8] conducted an experimental investigation to explore the grease film behaviour of point contact lubrication during micro-oscillation in the case of pure rolling or pure sliding and spotted a critical entraining speed in their experiments. They found that when the entraining velocity was lower than the critical value, the thickener fiber played a vital role in the grease film formation while the film thickness was far
⁎
higher than the theoretical predicted value. With the increase of the entraining velocity, the thickener fiber was pushed out of the contact so that the variation of the film thickness coincided with the theoretically predicted values. Sudeep et al. [9] studied the effect of surface texture on the traction force in reciprocating motion and found around 30% off of the traction force. Grease lubrication has been studied by many researchers. Cann and Lubrecht [10] found that the loading-unloading process would contribute to lubricant replenishment. For better understanding of replenishment, some researchers found that lateral vibration [11], temperature [12], centrifugal force [13,14] and surface tension [15] would also promote grease reflowing back to the contact. Ali et al. [16] introduced an innovative mechanism by channeling the lubricant towards the centerline of the over rolled track to reduce or overcome the negative effects of starved lubrication in concentrated contacts. Huang et al. [17] showed that slide/roll ratio contributed to replenishing the contact by transferring more grease to the vicinity of the contact to form a larger lubricant reservoir. Recently, they [18] found that the higher oil bleeding ratio of grease, the larger re-formed lubricant reservoir would be. Cyriac et al. [19] and Misty et al. [20] studied the effect of a mixture of water in grease on the lubrication performance. Cyriac et al. [21] experimentally explored the influence of the thickener particle size and concentration on the grease EHL film thickness and found that the film thickness increases with the increase in the particle size and concentration at medium speed. Zhang [22] explored the lubrication characteristics of lithium grease mixed with glycerinum in point contacts on a ball-on-disk test rig by optical interferometric technique. She found that at very low speed, due to the existence of thickener fiber, the grease
Correspondence to: School of Mechanical Engineering, Qingdao Technological University, Huangdao Campus, 777 Jialingjiang Road, 266520 Qingdao, China. E-mail address: [email protected] (J. Wang).
http://dx.doi.org/10.1016/j.triboint.2017.04.049 Received 15 January 2017; Received in revised form 7 April 2017; Accepted 27 April 2017 0301-679X/ © 2017 Elsevier Ltd. All rights reserved.
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film thickness was thicker than that using the base oil as lubricant. However, at higher speed, the grease film thickness was at the same level as the base oil film thickness. Laurentis et al. [23] experimentally measured the friction coefficients and film thickness of a series of commercial bearing greases and their bled oils. They reported that for lithium greases, a quite thick film was formed at low speed, which was much higher than that of their corresponding base oil film. There existed a "critical entraining velocity", above which the film thickness became nearly the same as that of the base oil. Gonçalves et al. [24] revealed the similar behaviour on a ball-on-disc test rig with optical interferometry using polymer greases. The aim of the present study is to explore the basic behaviour of the grease lubrication film over long working periods. In the experiments, the steel ball is stationary while the glass disk is sliding in reciprocating motion in the form of a triangular wave or a rectangular wave.
the charge coupled device (CCD) used in the experiments, the working period is set as 1 s. The steel ball was loaded against the underside of the glass disk with a force of F=30 N. One working period of reciprocating motion consists of two strokes. Based on an isothermal assumption, the Reynolds equation is written as
∂(ρh ) ∂(ρh ) ∂ ⎛ ρh3 ∂p ⎞ ∂ ⎛ ρh3 ∂p ⎞ ⎜ ⎟+ ⎜ ⎟=12ue +12 ∂x ⎝ η ∂x ⎠ ∂y ⎝ η ∂y ⎠ ∂x ∂t
In oil lubricated reciprocating motion [4,5], the variation of oil film ∂(ρh ) ∂(ρh ) is controlled by wedge term (12ue ∂x ) and squeeze term (12 ∂t ). Around the stroke end, the squeeze term is dominant so that an entrapped oil film is formed with the inlet film thickness thinner than that at the outlet. Thereafter, with the increase of the entraining velocity, the wedge effect is enhanced so that the entrapped oil film is transported by the entraining velocity to the outlet, and a wedge shaped oil film is formed. Then with the further increase of the entraining velocity, the film thickness is lifted gradually, the wedge-shaped oil film is moved out of the contact, and the maximum central film thickness occurs a little later than at the stroke center. When the entraining velocity is reduced, the film thickness decreases with the decrease of the wedge effect. The squeeze effect becomes dominant again and at last an entrapped oil film is formed at the stroke end. The variation of the film thickness in the two strokes is completely same, except their different directions. The outlet cavitation zone formed in one stroke works as the inlet starvation zone in the next stroke after the moving direction is reversed. Under lower entraining velocity, the influence of oil starvation is trivial while the influence increases with the increase in working frequency [4,5]. When the starvation effect is significant, the existence time of the starvation in the two stroke should be the same if the vibration of the test rig, the measurement errors etc. are removed.
2. Experimental methods Experiments were conducted using a ball-on-disk apparatus, and the technique of relative optical interference intensity was used to study the film thickness and motion of the grease lubrication under reciprocating motion. The contacting pairs were composed of a 25.4 mm diameter steel ball and a glass disk with a diameter of 150 mm and a thickness of 15 mm. One side of the glass disk was coated with a Cr-layer approximately 20 nm thick to facilitate partial reflection. All the tests were conducted under a controlled laboratory environment with a constant room temperature of 23 °C.The properties of the steel and glass were reported in Table 1. Either the glass disk or the steel ball has its driving system. Each includes a Mitsubishi AC servo motor, a high precision speed reducer and coupling etc.. The servo motor is programmable with a nominal power output of 400 W. A red point light source with a wavelength of 630 nm was used in the experiments. Images were collected with an image capture card (OK-LV20A) and a black-white camera (OKAM1130) produced by Beijing JoinHope Image Technology Ltd. The OK camera employs LVDS(low voltage differential signaling) digital output technique. In this study, optical interferometry experiments were carried out when the ball is stationary while the glass disk was moving in the form of a triangular wave or a rectangular wave, as shown in Fig. 1. With T the working period, for triangular wave, A=0.25; while for rectangular wave, A=0.5, the stroke length L reads
L = Avmax T
3.1. Triangular wave Fig. 2 gives the optical interferograms and mid-section film profiles along the entraining direction in the first period for vmax=20 mm/s， L=5 mm. In Figs. 2(a)-(e) for the first stroke, the inlet is at the left side while in Figs. 2(g)-(l) for the second stroke, the outlet is at the right side. The same applies to Figs. 3, 4, 7, 8. At startup time instant, the steel ball is loaded against the glass disk and the grease with thickener fiber lumps in the contact, shown as in Fig. 2(a). Due to the thickener fiber, the contact grease film thickness is thick and unevenly distributed. With the increase of the entraining velocity, the glass disk leaves the first location at the stroke end, some of the thickener is pushed out of the contact during the process so that the film thickness is reduced very much, as shown in Fig. 2(b). In Fig. 2(c) there is very little thickener fiber left in the contact so that the film thickness becomes much lower. In Fig. 2(d), the entraining velocity gets its maximum and the film thickness is obviously increased. Due to the decrease of the entraining velocity, it is seen that the film thickness drops at the inlet part, as shown in Fig. 2(e). In Fig. 2(f), at the stroke end, a wedgeshaped film thickness is formed, different from the common entrapped film shape at stroke end of oil lubricated reciprocating motion [4,5]. In the beginning of the reverse stroke, like what is shown in Fig. 2(g), the outlet cavitation zone in Fig. 2(f) becomes an inlet starvation region, which does not influence the film thickness because of the low entraining speed. The very low entraining velocity results in a reduced inlet film thickness and thus a small entrapment appears in Fig. 2(g). Once the wedge-shaped oil film formed at the stroke end leaves the contact, the film thickness takes on a new wedge-shape, as shown in Fig. 2(h). The film thickness is increased in the stroke center (Fig. 2(i)) and then decreased (Fig. 2(j)). Around the end of this period, the glass disk resumes to the previous location where some of the thickened fiber remains, the thick irregular film thickness is formed in Figs. 2(k) and 2(l). Moreover, the amount of the thickener fiber in Fig. 2(l) is less than
(1)
The lithium grease of Centoplex 3 was used as the lubricant in the tests. Centoplex 3 is multi-purpose grease based on oxidation-resistant mineral oil and lithium soap. Due to the good resistance to work under normal temperatures and loads, this grease can be used for long-term lubrication, and its properties are listed in Table 2. Before all the tests, the disk, the ball and all the relevant parts of the apparatus were thoroughly cleaned with alcohol and acetone. 3. Results and discussions The experiments were performed under sliding condition where the glass disk was rotating and the ball was stationary. By the limitation of Table 1 Properties of ball and disk materials. Properties
Steel (ball)
Glass (disk)
Young's modulus (GPa) Poisson's ratio Density (kg/m3) Thermal conductivity（W/m K） Specific heat（J/kg K）
210 0.3 7850 46 470
81 0.208 2510 1.11 840
(2)
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Fig. 1. The variation of glass disc velocity.
is repelled out of the contact gradually. At the “startup stroke end”, the central film thickness is reduced gradually. At the “end stroke end”, the 5 central film profiles coincide with one another. For the 5th working period, the influence of the thickener fiber on the central film thickness around the “startup stroke end” is slight. From Fig. 5(a), it is seen that during 0.15 T≤t≤0.85 T, the central film thickness increases and then decreases with the variation of the entraining velocity in a triangular wave, similar to the central film thickness variation in oil lubrication [4,5]. In Fig. 5(b), the central film thickness for the 20th, 50th, 70th working period nearly coincide with one another and similar to the curves in Fig. 5(a) except those during 0.0 T≤t≤0.1 T and 0.9 T≤t≤0.1 T. Moreover, the central film thickness at the “startup stroke end” has fallen to the level of that at the “end stroke end”. The results during 0.0 T≤t≤0.1 T or 0.5 T≤t≤0.6 T correspond to the time period when the wedge-shaped film formed at the beginning of the stroke end passes through the contact. In Fig. 5(b), the inlet grease starvation zone by the reverse motion exerts no influence on the central film thickness. Fig. 5(c) shows the results for the working periods N=100, 200, 300, 400 and 500, respectively. The curve for the 100th working period is nearly the same as that of 70th working period. The other 4 curves fluctuate around that of the 100th working period. The authors suppose that the fluctuation is caused by the replenishment of the grease from the side reservoirs back to the sliding track. It should also be noted that for 0.15 T≤t≤0.33 T or 0.65 T≤t≤0.8 T for the curve of N=400 or for 0.15 T≤t≤0.36 T or 0.65 T≤t≤0.82 T for the curve of N=500, obvious drop is found, illustrating the significance of the grease starvation. The following film thickness rise validates the grease replenishment effect. In Fig. 5(d), the 5 curves are similar again with only smaller fluctuations, representing the decreased effect of replenishment. During 0.15 T≤t≤0.4 T or 0.65 T≤t≤0.85 T, the central film thickness is also reduced. Fig. 6 shows the variation of the minimum film thickness for vmax=20 mm/s，L=5 mm. Around the “startup stroke end” (0 T≤t≤0.1 T or 0.9 T≤t≤1 T) in Fig. 6(a), only the minimum film thickness of the 1st and 2nd is higher than the rest 3 curves due to the existence of the thickener fiber. During 0.1 T≤t≤0.9 T, the 5 curves nearly coincide with one another. Similar to the variation of the central film thickness, after the wedge-shaped oil film leaves the contact, the minimum film thickness faces an increase and then a decrease in each stroke. And the variation is in the same tendency as those for N=3, 4, 5 in Fig. 6(a). In Fig. 6(b), the 3 curves nearly coincide with each other. In Fig. 6(c), the fluctuations are drastic and there is an obvious film thickness reduction during 0.15 T≤t≤0.35 T or 0.6 T≤t≤0.85 T after N=400 by the obvious effect of grease starvation. In Fig. 6(d), the grease starvation becomes significant but the fluctuations become less significant than those in Fig. 6(c) due to the decrease effect of replenishment. The minimum film thickness for 0.5 T≤t≤0.7 T is generally higher for that during 0.0 T≤t≤0.2 T. The reason of the difference may come from the uneven grease distribution and therefore the uneven replenishment of the grease.
Table 2 Grease properties. Grease Base oil Thickener Applicable temperature range (℃) Cone penetration (25 ℃ 0.1 mm) Base oil viscosity (40 ℃ mm2/s) Base oil viscosity (100 ℃ mm2/s) Dropping point DIN ISO 2176 (℃) NLGI grade
Centoplex 3 Mineral oil Lithium soap −15 to 150 220–250 100 10 > 190 3
that in Fig. 2(a), so the film thickness in Fig. 2(l) is thinner. In oil lubricated reciprocating motion, the entrapped film shape at one stroke end is the same as that of the other, except their opposite direction. However, the film shape in Fig. 2(f) is different from Fig. 2(a) and (l), it is the feature of grease reciprocating lubrication. In order to interpret the lubrication phenomena easily in the following, 0 T is named as “startup stroke end” and 1/2 T is “end stroke end”. Fig. 3 gives the optical interferograms and mid-section film profiles in the 100th period for vmax=20 mm/s，L=5 mm. In this period, the thickener fiber has basically disappeared. In Fig. 3(a)，the “startup stroke end”，although there is slight reduction in the film thickness at the periphery of the contact area, the grease film still takes on a wedge shape with the dominance of the squeeze effect, like what is shown in Fig. 2(f). This film shape is the same as shown in that in Fig. 3(f) at the “end stoke end”, but in opposite direction. That is to say, the variation of the grease film has become similar to.that in oil lubricated contact. By comparison of Figs. 2 and 3, after 99 working periods, there is obvious film thickness reduction around the stroke end. At the beginning of each stroke, the outlet starvation region in the previous stroke becomes a much more obvious inlet starvation region. It can be seen that the existence time of the starvation area is also longer than that in Fig. 2. But compared with the mid-section film profiles in Fig. 2, the effect of grease starvation is negligibly small. Fig. 4 gives the optical interferograms and mid-section film profiles in the 1000th period for vmax=20 mm/s，L=5 mm. After long working periods, the degree of grease starvation becomes very severe. In each stroke, the grease starvation exists even longer and the starvation area is larger. By the joint effect of entraining velocity and grease starvation, the film thickness in the contact decreases and fluctuates irregularly. In Fig. 4(c), (d) and (i), (j)，the contact becomes parched by the severe grease starvation. Fig. 5 shows the variations of central film thickness over a number of selected working periods，vmax=20 mm/s，L=5 mm with N is the number of the working periods. Fig. 5(a) is for 1st, 2nd, 3rd, 4th and 5th working period. Around the “startup stroke end” in the 1st period, the central film thickness is relatively thick due to the existence of the thickener fiber. It is also thicker than that at the “end stroke end” and that at 1T. With the increase of the working period, the thickener fiber
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Fig. 2. Interferograms and mid-section film thickness during the first cycle under the motion of triangular wave (vmax=20 mm/s，L=5 mm).
is thicker and the fluctuation of the film thickness is more obvious. Especially for the 1st working period, a very shallow entrapment is found at the “end stroke end”. In Fig. 7(a), for the first 5 working periods, again, around the “startup stroke end”, i.e.,0.0 T≤t≤0.1 T and
Fig. 7 shows the variations of central film thickness in a number of selected working periods for vmax=40 mm/s，L=10 mm. The optical photos are not given because the variation of the grease film is similar as those for vmax=20 mm/s，L=5 mm. The differences are that the film 376
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Fig. 3. Interferograms and mid-section film thickness during the 100th cycle under the motion of triangular wave (vmax=20 mm/s，L=5 mm).
0.9 T≤t≤1.0 T, the grease film thickness is thick due to the existence of the thickener fiber. During 0.1 T≤t≤0.9 T,the 5 curves coincide with one another. In Fig. 7(b), the central film thickness for N=20 is nearly the same as that of N=5 except the portion around the “startup stroke
end”. Grease starvation happens earlier at N=50 during 0.25 T≤t≤0.3 T and 0.65 T≤t≤0.8 T and grows severer during 0.1 T≤t≤0.45 T and 0.55 T≤t≤0.8 T for N=70. In Fig. 7(c), the starved effect for N=100 is much severer than that of N=70. Although there are rises and falls in
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Fig. 4. Interferograms and mid-section film thickness during the 1000th cycle under the motion of triangular wave (vmax=20 mm/s，L=5 mm).
the distribution of the central film thickness in Fig. 7(c), the general tendency is to level off. In Fig. 7(d), it is seen that for N=600, 700, 800, 900 and 100, all 5 curves are identical to be a straight line. That is to say, from N=600, the variation of the entraining velocity exerts no influence on the central film thickness. Fig. 8 shows the variations of minimum film thickness for
vmax=40 mm/s，L=10 mm. Similar to the variations in Fig. 7, the grease starvation becomes obvious since N=50 and the minimum film thickness at last turns to a constant horizontal line since N=600 over one working period, irrespective of the variation of the entraining velocity. Fig. 9 demonstrates the optical interferograms and mid-section film 378
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Fig. 5. The central film thickness under the motion of triangular wave (vmax=20 mm/s，L=5 mm).
shape occurs in the rest pictures. At the “end stroke end” shown in Fig. 9(f), the grease film takes on a wedge shape with a shallow entrapped film, similar to what was found in reciprocating oil lubrica-
profiles in the 1st period for vmax=200 mm/s， L=50 mm. It is seen that except for Figs. 9(a) and 9(l), at the “startup stroke end”, where the film thickness is quite thick because of the thickener fiber, EHL film
Fig. 6. The minimum film thickness under the motion of triangular wave (vmax=20 mm/s，L=5 mm).
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Fig. 7. The central film thickness under the motion of triangular wave (vmax=40 mm/s，L=10 mm).
Fig. 8. The minimum film thickness under the motion of triangular wave (vmax=40 mm/s，L=10 mm).
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Fig. 9. Interferograms and mid-section film thickness during the first cycle under the motion of triangular wave (vmax=200 mm/s，L=50 mm).
tion [4,5]. Fig. 10 gives the optical interferograms and mid-section film profiles in the 100th period for L=50 mm，vmax=200 mm/s. Much of the grease has left the sliding track so that a heavy starvation exists in
the whole working period. The film thickness is very low and generally horizontal. At both stroke ends, possibly by the uneven distribution of the remained thickener fiber, a curved film thickness instead of the
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Fig. 10. Interferograms and mid-section film thickness during the 100th cycle under the motion of triangular wave (vmax=200 mm/s，L=50 mm).
wedge shaped film exists. Fig. 11 shows the variations of central film thickness in a number of selected working periods for vmax=200 mm/s， L=50 mm. Grease starvation happens as quickly as at N=3 and becomes severer and
severer thereafter, shown in Figs. 11(a) and 11(b). In Fig. 11(b), it is seen that the grease starvation covers the majority of each stroke. However, in Fig. 11(c) and (d)，the severe grease starvation levels off the curves and the 5 curves overlap with one another. It seems the 382
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Fig. 11. The central film thickness under the motion of triangular wave (vmax=200 mm/s，L=50 mm).
Fig. 12. The minimum film thickness under the motion of triangular wave (vmax=200 mm/s，L=50 mm).
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Fig. 13. Variation of the starvation ratio of the triangular waves.
replenishment does not happen. In Fig. 11(d), the central film thickness drops a little again by the increase of the starvation effect. Fig. 12 shows the corresponding minimum film thickness in a number of selected working periods. It is seen that the grease starvation also starts at N=3 and gradually becomes severe. The minimum film thickness becomes constant in Fig. 12(c) and (d). As for the existence of the inlet starvation zone in each stroke, a starvation ratio Rst is defined as
Rst = 2∆ts / T
seems play an important role. In the subsequent several working periods, because there is thickener remained in the conjunction, the critical sliding speed still exists. However, the value of the speed is noticed to decrease with the increase of the working period. Therefore, the authors suppose that for time-dependent and long run mechanical elements, the critical entraining speed is not an important influential factor. The experiments under steady state sliding motion were also finished for the sliding speed ranging from 0.01 m/s to 0.4 m/s. In the experiments, the grease lumps in the all the conjunctions when the load is applied so that in the beginning of each motion, the thickened fiber is observed. The contact turns into a stable EHL one after a short time, which decreases with the increase of the sliding speed. That is to say, if the speed is very high, the existence time of the thickener fiber is very brief. Moreover, for a long-term operation, even for low speed, the existence time of such thick film is trivial compared to the service life. Thus, the authors suggests the phenomenon is a kind of "running-in" of grease lubrication.
(3)
where ∆ts is the existence time of the inlet starvation zone in each stroke. If Rst =1, it means the inlet starvation zone exists over a full stroke. Fig. 13 presents the variations of Rst in the first and the second stroke for the above 3 triangular waves. It is seen that for vmax=20 mm/ s, the starvation ratio curves for the first and the second stroke start at small values and both increase with fluctuation. From N=500, they both get stabilized to a higher value around 0.73 and 0.65, respectively. For Fig. 13(b), the tendency is the same, but the two curves approach to 1.0 and 0.9, respectively from N=500. In Fig. 13(c), the two curves reach 1.0 together at N=200. For the 3 cases, although there are discrepancy between the values of the fist and the second stroke, all the starvation ratios increase from a small value at N=1 until they reach a relatively stable state. But for oil lubrication [5], the starvation ratio is fixed for both strokes in one working period and it does not increase with the increase of the working period. Due to the existence of the thickener fiber, in the first several working periods, the variations of the film shape in the first and second stokes are different. There is thickener fiber lumped in the contact around the "startup stroke end" but not around the "end stroke end". But with the increase of the working period, the thickener fiber is gradually removed from the contact so that the variation of grease film in the first stroke approaches to the that of the second stroke. With the increase of the period, the starvation effect gradually emerges, together with the occurrence of the grease replenishment. The waxing and waning effects of starvation and replenishment fluctuate the film thickness. However, the larger the disk sliding speed vmax, the less obvious effect of the grease replenishment. Finally the central and minimum film thickness become a horizontal line during one working period, irrelevant to the variation of the disk sliding speed. There have been a number of papers discussing the "critical entraining speed" on the fully flooded grease lubrication under steady state condition, revealing the possible V-shape film thickness with the increase of the entraining speed [23,24]. However, based on the results presented in this study, it is seen that for time-dependent problem, the so-called " critical entraining speed" exists only in the first several working periods. If we compare the variations of the central film thickness for the above 3 cases, it is found the critical sliding speeds in the first working periods are different. They are 12 mm/s, 8 mm/s, 3 mm/s, respectively. The acceleration rates for the 3 cases are 80 mm/ s2，160 mm/s2 and 800 mm/s2, respectively. The acceleration rate
3.2. Rectangular wave Fig. 14 gives the variations of central film thickness in a number of selected working periods for vmax=10 mm/s，L=5 mm. Fig. 15 show the variations of the minimum film thickness. In Fig. 14(a), at the beginning of the working period, the central film thickness only decreases while at the end of the working period, the central film thickness only increases. Between the two parts, the variation of the central film thickness is the same as that in Fig. 5(a) except the drop at 0.5 T. The variation in Fig. 14(b) and (c) are similar to those in Fig. 5(b) and (c). However, when the value of N is increased to 600– 1000, the grease starvation begins to take effect during 0.1 T≤t≤0.3 T and 0.6 T≤t≤0.8 T. Around the “end stroke end”, 0.5 T, the central film thickness gains its value a little bit by the effect of the replenishment. In Fig. 15(a)–(c), the variation is similar to those of the central film thickness. In Fig. 15(d), due to the grease starvation, the minimum film thickness decreases a little bit during 0.1 T≤t≤0.35 T and 0.6 T≤t≤0.85 T. During 0.4 T≤t≤0.65 T, the minimum film thickness firstly increases before a drop at 0.5 T, followed by a hill in the second stroke. Compare Fig. 14(b) with 14(a) or Fig. 15(b) with 15(a), it is seen either the central film thickness, or the minimum film thickness fluctuates obviously for N=50 or 70. The fluctuation becomes small in Figs. 14(c) and 14(c). In Fig. 14(d) and 15(d), during 0.3 T≤t≤0.7 T, both the central and minimum film thickness have risings. Fig. 16 shows the variations of central film thickness in a number of selected working periods for vmax=20 mm/s，L=10 mm. There is a sudden drop at the “end stroke end” by the plummet of the disk velocity. And an obvious grease starvation happens earlier for N=50. But it should be pointed out that for N=70, grease starvation appears earlier in the first stroke but does not happen in the second stroke. In Fig. 16(c), the central film thickness curve for N=100 resembles that of 384
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Fig. 14. The central film thickness within each cycle under the motion of rectangular wave (vmax=10 mm/s，L=5 mm).
Fig. 15. The minimum film thickness within each cycle under the motion of rectangular wave (vmax=10 mm/s，L=5 mm).
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Fig. 16. The central film thickness under the motion of rectangular wave (vmax=20 mm/s，L=10 mm).
Fig. 17. The minimum film thickness under the motion of rectangular wave (vmax=20 mm/s，L=10 mm).
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Fig. 18. The variation of minimum film thickness with the sliding speed (a) Triangular wave, (b) Rectangular wave.
N=5, except for the parts around the “startup stroke end”. Then the whole film thickness drops again, see the results for N=200. Grease replenishment happens around the stroke ends for N=300 and 400, with the film thickness during 0 T≤t≤0.2 T and 0.8 T≤t≤1 T higher than that during 0.4 T≤t≤0.6 T. However, for N=500 the film thickness during 0 T≤t≤0.2 T and 0.8 T≤t≤1 T drops much but the film thickness around 0.4 T≤t≤0.6 T is increased greatly. Such behaviour demonstrates that the replenishment is uneven. In Fig. 16(d), for N=600, the replenishment plays a more important role. But for N=700 and 800, the replenishment effect is weak so that the film thickness is reduced on a whole. Then it increases greatly for N=900. After that it drops again at N=1000, tending to be a horizontal line during one working period. It proves that the replenishment and starvation happen alternatively. But in the long term, the central film thickness is expected to regress to a constant value during the whole working period. Fig. 17 shows the variations of minimum film thickness in a number of selected working periods for vmax=20 mm/s， L=10 mm. The variation of the minimum film thickness is generally the same as what is shown in Fig. 16. Fig. 18 shows the variation of the minimum film thickness in each working period with the sliding speed over 1–1000 working periods. It is seen that after the first 100 working periods, the minimum film thickness for the three sliding speeds fluctuates between 29 nm and 32 nm for the 3 triangle waves, as well as between 29 and 34 nm for the 2 rectangular waves. After the working periods reaches 500, the minimum film thickness decreases with the decrease of the sliding speed vmax. Take the case vmax=20 mm/s, L=5 mm for triangular wave and vmax=20 mm/s, L=10 mm for rectangular wave for a comparison, it is found that for triangular wave, it takes longer time for the wedgeshaped film formed by the reverse motion to move out of the contact. For vmax=20 mm/s, it is also seen that the replenishment is more drastically to happen for a rectangular wave so that the minimum film thickness of the rectangular wave is a little larger. Although the experiments with larger entraining velocity in the
form of a rectangular wave are not carried out, it could be concluded that for the long term, the central and minimum film thickness are expected to decrease with the grease starvation and fall to constant values over a working period. Fig. 19 shows the starvation ratios for the rectangular waves of vmax=10 mm/s and 20 mm/s. The larger the maximum sliding speed vmax, the larger the starvation ratio Rst. For vmax=20 mm/s, Rst=1.0 happens earlier at N=200.
4. Conclusions In this study, the variations of grease films in reciprocating sliding motion were explored by using optical interferometric technique. The glass disk moves in the form of a triangular wave or a rectangular wave. The conclusions are summarized as follows. (1) Due to the existence of the thickener fiber, in the first several working periods, the variations of the film shape in the first and second stokes are different. There is thickener fiber lumped in the contact around the "startup stroke end" but not around the "end stroke end". With the increase of the working period, the thickener fiber is gradually removed from the contact so that the variation of grease film in the first stroke approaches to the that of the second stroke. With the increase of the period, the starvation effect gradually emerges, together with the occurrence of the grease replenishment, resulting in fluctuations in film thickness. (2) For triangular wave, the waxing and waning effects of starvation and replenishment fluctuate the film thickness. However, the larger the disk sliding speed vmax, the less obvious effect of the grease replenishment. With larger disk sliding speed, the central and minimum film thickness become horizontal line during one working period, irrelevant to the variation of the disk sliding speed. (3) For the same sliding speed vmax, it is also seen that the replenishment is more drastic for a rectangular wave so that the
Fig. 19. Variation of the starvation ratio of the rectangular waves (a) vmax=10 mm/s, (b) vmax=20 mm/s.
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general minimum film thickness of a rectangular wave is a little thicker. Although the experiments with larger entraining velocity in the form of a rectangular wave are not carried out, it could be concluded that for the long term, the central and minimum film thickness are expected to decrease with the grease starvation and fall to constant values over a working period. (4) In the experiments, the grease lumps in the conjunction when the load is applied so that in the beginning of each motion, the thickener fiber is observed and the contact turned into an EHL one after a short time. The time decreases with the increase of the sliding speed. The existence of such thick film is brief compared with the long operation time. The authors suggests it is a kind of "running-in" of grease lubrication.
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Acknowledgement This work was supported by the National Natural Science Foundation of China through grant No. 51275253. Professor J. Wang was supported by the China Scholarship Council to work as a research scholar at Oakland University, USA. Thanks also go to Dr. Weimin Li of State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences for the valuable discussion. References [1] Petrousevitch AI, Kodnir DS, Salukvadze RG, et al. The investigation of oil film thickness in lubricated ball-race rolling contact. Wear 1972;19(4):369–89. [2] Hooke CJ. The minimum film thickness in lubricated line contacts during a reversal of entrainment—general solution and the development of a design chart. Proc Inst Mech Eng Part J J Eng Tribol 1994;208(110):53–64. [3] Sugimura J, Jones WRJ, Spikes HA. EHD film thickness in non-steady state contacts. J Tribol 1998;120(3):442–52. [4] Wang J, Kaneta M, Yang P. Numerical analysis of TEHL line contact problem under reciprocating motion. Tribol Int 2005;38(2):165–78. [5] Wang J, Hashimoto T, Nishikawa H, et al. Pure rolling elastohydrodynamic lubrication of short stroke reciprocating motion. Tribol Int 2006;38(11–
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