Influence of surface microstructure parameters on wear of steel ball unfolding wheel
C. Y. Pan a,b,*, J. H. Changa,b, G. Q. Caoa,b
aKey Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education, China
bSchool of Mechanical and Power Engineering, Harbin University of Science and Technology, Harbin, China
The unfolding wheel is an important part of the steel ball tester in rolling bearing industry, and it is easy to be worn out. In this study, the pit microstructure is applied to the working surface of the unfolding wheel to reduce wear, improve its service life and reduce the testing cost of the steel ball. To analyze the influence of surface microstructure geometrical parameters on the abrasion of unfolding wheel under dry friction condition, the following research was conducted. First of all, the influence of shape, area, depth, and spacing of the microstructure pits on the abrasion of the specimen surface is studied by the orthogonal test method. Then, the subsurface stress of microstructure in contact with the steel ball is analyzed by ANSYS software. Comparing the simulated stress distribution with experimental wear mass, it is found that the more concentrated the high-stress area, the less wear. The diamond microstructure with a single pit area of 3.14×10-2 mm2 and a depth of 100 μm has the best abrasion reduction effect. Finally, the mathematical models including microstructure geometrical parameters for calculating the wear mass of microstructure surface are established. The mathematical models can be used to predict the life of steel ball unfolding wheel and assist the design.
(Received February 27, 2021; Accepted May 20, 2021)
Keywords: Steel ball unfolding wheel, Surface microstructure parameters, Wear mass, High-stress area, Mathematical model of wear mass
1. Introduction
As the rolling body of the bearing, steel ball plays an important role in its performance [1]. In the process of steel ball manufacture, some damage and defects will inevitably occur on the surface. These surface damages and defects can affect the operation of the bearing or even lead to damage of the bearing. Therefore, it is important to measure the surface quality of the steel ball [2-3]. The wear of the unfolding wheel due to friction during the test of the steel ball will affect the measuring accuracy and efficiency, which will lead to the invalidation of it [4-5].
In recent years, improving wear resistance by machining pits, bulges, or stripes on the surface of metal parts, mimicking the microstructure of the surfaces of living organisms, has proved to be very effective [6]. Many scholars have studied methods to improve the friction and wear characteristics of friction pairs based on the theory of bionic tribology [7-10]. Ma et al.
analyzed the effects of different experimental factors on the friction coefficient and wear amount of the shells of clams [11], by studying the microscopic morphology and tribological characteristics of the shells of Clam. Hu et al. used a laser to study the effect of the microstructure surface on the friction properties of GCr15 steel [12]. The scanning electron microscope (SEM) was used to observe the wear appearance of the metallographic surface. It was found that the
*Corresponding author: [email protected]
processed by laser and proved that the hardness and abrasion resistance of the workpiece surface was improved by the laser processing[14]. Tong et al. made an experimental and simulation analysis on wear resistance mechanism and properties of carbide microstructure materials [15]. Wan et al. studied the optimization of tool microstructure parameters [16].
In this paper, the pit microstructure is applied to the working surface of the unfolding wheel to reduce the wear of the wheel, improve its service life and decrease the testing cost of bearing steel balls. The effects of shape, area, depth, and spacing on wear are studied by dry friction experiments and stress simulation, and the optimum microstructure parameters for wear reduction are sought.
2. Experimental methods and analysis
As shown in Fig. 1, the working surface of the unfolding wheel consists of two offset cones with two conical axes on the same plane and at opposite angles α to the unfolding wheel axis, generally 1°. When working, the ball is subjected to force Q from the driving wheel, which spins around at angular speed ω1, drives the sphere at an angular speed ω2 around the z-axis, and steers the unfolding wheel at an angular velocity ω3. The steel ball is subjected to the normal force Fn
and the tangent friction Ff produced by the two tapered surfaces of the unfolding wheel. The tangent friction Ff drives the ball to spin around the x-axis at a slower speed of ω2. The function of the unfolding wheel is to rotate the ball around the z-axis as well as the x-axis. A point on the sphere moves in a spiral in space. During the process of detection, all points on it can pass through the inspection probe and play the role of spreading out the full surface [17].
Fig. 1. Working diagram of the unfolding wheel.
2.1. Experimental methods
During the working process, the lateral rotation of the steel ball in yoz plane produces the sliding dry friction between the ball and the cone surface, which is easy to cause the opening surface to be worn out. To reduce the wear, the pit microstructure is applied to the contact area between the two cone faces of the expanding wheel and the steel ball. To make the wear experiment more widely applicable, the surface of the unwrapping wheel is expanded and made up
into a flat ring, as shown in Fig. 2. The contact between the steel ball and the cone is replaced by the contact of the ball with the plane. The wear experiments and simulations are simplified by using a cylinder instead of the cone.
Fig. 2. Model simplification process.
The testing device is shown in Fig. 3(a). A disk-shaped specimen with a concave pit microstructure on the surface is shown in Fig. 3(b). Microstructural shapes are round, square, and diamond which are processed by laser ablation. The specimen is made of Cr1Mo2W50 with internal diameter, external diameter, and height of 28 mm, 54 mm, and 18 mm respectively, as the material of the unfolding wheel. The ball is made of GCr15 steel and has a diameter of 28 mm.
(a) (b) Fig. 3. The friction wear testing device(a) and specimen(b).
The orthogonal experimental design method was adopted, in which shape (round, square, diamond), area (7.85×10-3 mm2, 1.76×10-2 mm2, 3.14×10-2 mm2) depth (50 μm, 100 μm, 150 μm) and circumferential spacing (2.5°, 3.0°, 3.6°) were used as the experimental factors to carry out the orthogonality experiment on abrasion. The microstructures viewed under super depth of field microscope VHX-1000 were shown in Fig. 4. The experimental load was set to 2N and the wear time to 5 hours. The rotational speed of the sample was 1500 r/min. The wear mass was measured by precise electronic balance BSM 220.4.
Fig. 4. Microstructure photos of specimens under microscope.
2.2. Experimental results and analysis
The wear mass of different specimens was measured through wear experiments, and the results are listed in the Table 1.
Table 1. Experimental result.
Experiment number Shape Area/mm2 Depth/µm Spacing / ° Wear mass/mg
1 1(Round) 1(7.85×10-3) 1(50) 1（2.5°） 5.6
2 1 2(1.76×10-2) 2(100) 2（3.0°） 4.1
3 1 3(3.14×10-2) 3(150) 3（3.6°） 3.2
4 2(Square) 1 2 3 4.4
5 2 2 3 1 3.2
6 2 3 1 2 2.9
7 3(Diamond) 1 3 2 4.2
8 3 2 1 3 3.5
9 3 3 2 1 2.2
Kj1
Kj2
Kj3
Rj
12.9 10.5 9.9 1.00
14.2 10.8 8.30 1.96
12.0 10.7 10.6 0.47
11.0 11.2 11.1 0.07
- - - -
In Table 1,
. It is shown that the symbol of Rj indicates that the influence of the factor on wear mass is larger.
By analyzing the wear experimental data in Table 1, the order of significance of the influence of geometrical parameters of the microstructure is as follows: area > shape > depth > spacing.
Moreover, the value of Rj for the spacing is 0. 07, meaning the influence of spacing on wear is too small to be considered.
Because the area and shape of microstructure have an obvious influence on the wear mass of the microsurgical specimen, to intuitively reflect the effect of microstructure area and shape on the wear mass, the experimental results of table 1 are drawn as a line graph, as shown in Fig. 5.
Obviously, the wear mass decreases with the increase of pit area in the condition of the shape of the same pit. From table 1 and Fig. 5, it can be found that the least wear mass point is No. 9. That means when the microstructure is diamond, the area is 3.14×10-2 mm2, and the depth is 100 µm, it has a better anti-wear effect.
Fig. 5. Effect of area and shape on wear mass.
3. Results and analysis of stress simulation
To further study the wear mechanism of microstructure surface and considering the durability of surface contact, surface stress and subsurface stresses need to be analyzed. According to the above experiment, a three-dimensional simulation model is established, and the stress simulation is analyzed by ANSYS software. The material properties were entered and the model of contact between the steel ball and microstructure surface was established. The specimen material was Cr1Mo2W50, the elastic modulus was 5.32×105 MPa and the Poisson ratio was 0.24. The steel ball material is GCr15 with an elastic modulus of 2.07×105 MPa and a Poisson ratio of 0.30.
The stress analysis of round-shaped microstructure, square-shaped microstructure, and diamond microstructure was carried out with a depth of 100µm and an area of 3.14×10-2mm2 respectively.
The results of the stress simulation are shown in Fig. 6.
(a) (c) (e)
(b) (d) (f) Fig. 6. Stress simulation at different positions on the surface of the microstructure:
(a) (b) Round, (c) (d) Square, (e) (f) Diamond.
It can be seen that when the steel ball is in contact with the pit in the middle, it produces great stress, and the stress acts on the vicinity of one pit, other pits are unaffected. When the steel ball is in contact with the point outside the pit, the stress is small, and it has little effect on the wear. Therefore, only the stress of asingle micro-structure crater needs to be analyzed in detail.
3.1. Influence of pit area on stress distribution
To study the influence of pit area on abrasion, circular pits with the same depth of 100μm but with different size diameters of the small, medium, and large were selected. The micro-structure single pit areas were 7.85×10-3 mm2, 1.76×10-2 mm2, and 3.14×10-2 mm2.
(a) (b)
(c) (d)
Fig. 7. Stress simulation of different microstructure areas and no microstructure:
(a) 7.85×10-3 mm2 , (b) 1.76×10-2 mm2, (c) 3.14×10-2 mm2 , (b) 0 mm2 .
As can be seen from Fig. 7, the larger the area of a single crater of microstructure and the smaller the high-stress area, it is more likely that the high-stress location will be located in a hardened zone near the edge of the craters formed during laser processing. Although the larger the microstructure area, the greater the maximum stress, but the high-stress areas distributed around the microstructure crater, and very close to the surface, in the material hardening zone, so reduce the possibility of fatigue crack and micro-debris flaking. In the absence of microstructure, although the maximum stress is smaller, the high-stress zone is located in the deeper subsurface, and the high-stress area is larger, far from the specimen surface. Therefore, under the action of the deep and extensive secondary surface stress, the surface without microstructure is easy to form the peeling off of large metal particles in the working process, which is to make the abrasion aggravate.
3.2. Influence of pit shape on stress distribution
To study the influence of shape on abrasion, stress simulation was carried out on three microstructures(circular, square, diamond) with the same depth of 100μm and an area of 3.14× 10-2 mm2. The simulation results of square and diamond microstructures are shown in Fig. 8 and the stress distribution of a circular microstructure is illustrated in Fig. 7(c).
(a) (b)
Fig. 8. Stress simulation of the microstructure of square and diamond: (a) Square, (b) Diamond.
A comparison of Fig. 8 and Fig. 7(c) shows that the maximum stress of diamond microstructures is minimal (789.14 MPa). The maximum stress of the circular microstructure is 844.21 MPa. The maximum stress of the square-shaped microstructure is 816.08 MPa. The difference in the volume of the high-stress area of the three microstructure shapes is not obvious, but the value of maximum stress is different. It can be concluded that the wear of microstructures of different shapes is related to the peak stress under the same pit area. The diamond microstructure has the smallest stress peak and the best wear resistance. The peak stress of the square microstructure is slightly larger than that of the diamond, and its wear resistance is medium. The peak stress of circular microstructure is the largest and the wear resistance is relatively poor.
3.3. Influence of pit depth on stress distribution
To study the influence of depth on abrasion, micro-structures with circular pits and different depth (50 μm、100μm、150 μm) with a same area of 3.14×10-2 mm2 were selected for stress simulation. The results of stress simulation for microstructures of 50 μm and 150 μm depth are shown in Fig. 9. The results of stress simulation for microstructures of 100 μm depth are shown in Fig. 7(c).
(a) (b)
Fig. 9. Stress simulation of different depths: (a) 50μm, (b) 150μm.
A comparison of Fig. 9 and Fig. 7(c) shows that, while the maximum stress is small (711.01 MPa) at a relatively shallow depth (50 μm), a second stress concentration zone is formed at the bottom of the pit and thus leads to increased wear. When the depth of the pit is 100 μm and 150 μm, the maximum stress is 844.21 MPa and 860.08 MPa, it can be seen that when the pit reaches a certain depth (more than 100 μm), the maximum stress increases slightly and the
variation of stress distribution will not be obvious. It can be concluded that the second stress concentration area is formed at the bottom of the pit when the depth of microstructure is insufficient, and the wear resistance is not the best. With the increase of pit depth, the stress concentration at the bottom of the pit will decrease, and the performance will be improved. When the depth of the pit reaches a certain critical value, the secondary stress concentration area vanishes. At this point, if the depth of the pit continues to increase, it has no obvious effect on the reduction of abrasion.
4. Theoretical analysis
A common model of wear is the Archard wear model [15] in the form shown below.
(1) In the formula: V is wear volume; K is the wear coefficient. L is the distance of wear; P is the load; H is the materialhardness. Wear distance L can be expressed as the product of relative velocity v and time t at the point of contact.
(2)
Take the formula (2) into formula (1) and multiply the two sides of the equation by the material density
equals the expression of wear weight:(3) The material hardness H is changed and is difficult to be measured considering the hardening action of machining. The wear coefficient is recorded as K1 equaling K/H , and the expression is obtained due to deformation of above formula
(4) (5) Considering that the surface contact stress distribution of the steel ball and microstructure specimens will change K1, the microstructure area S, shape coefficient A (A is the ratio of the longest axis to the shortest axis for the geometrical center), and depth h are used to modify K1. The spacing effect is small and negligible.
Considering the hardness H of the surface material after the machining of microstructure, the probability of grinding grains K produced by the known parameters is directly proportional to K1, and K is in direct proportion to the volume V and the maximal stress σ in the high-stress region. The influence increases with depth h within a certain range, and the effect decreases with increasing depth beyond this range. At a depth of 0, K1 should be the same as K/H as measured in the microstructure free test, so the following relationship is assumed:
the microstructure free test.
According to the simulation results, the volume V of the high-stress region is mainly related to microstructure area S(mm2) and depth h(μm). Maximum stress σ is also associated with the size S and the shape coefficient A of microstructures, so that the relationship is nonlinear, as shown below.
(7) In the formula,a2、a3、a4、a5、a6、a7are unknown constants.
The formula (7) is brought into formula(6) and the constant term is combined to obtain a modified equation for K1.
(8) The K1 of different microstructures are obtained by taking the experimental data into formula (5) and are listed in Table 2. The relationship between the wear coefficient and the microstructure parameters is given by using the least square fitting method to solve the unknown constants (b0, b1, b2, b3, and b4) according to the formula (8).
Table 2. K1 calculated from the test.
Experiment number
K1 Experiment
number
K1 Experiment
number
K1
1 6.13×10-6 4 4.70×10-6 7 4.70×10-6
2 4.49×10-6 5 3.50×10-6 8 3.94×10-6
3 3.50×10-6 6 3.06×10-6 9 2.52×10-6
(9)
The fitting advantage parameter of the function in formula (9) is R2 = 0.99, which means that the formula is in good agreement with the experimental data.
The formula for calculating the wear of microstructure unfolding wheels by bringing the formula (9) into formula (5) is as follows：
(10)
The influence of the depth of microstructure is not obvious from the wear experiment.
Therefore, the following wear model is established based on the abrasion formula and considering only the effect of area and shape.
(11)
The least-square method is used to fit formula (11), and the unknown constants b0, b1, and b2 are solved, which are substituted into formula (11).
(12)
(13)
Input the data of experimental data into formula (10) and (13), calculate the wear and compare the results with experimental wear mass, as shown in Fig. 11. It shows that the wear model of equation (10) considering the influence of shape, area, and depth is similar to the experimental data. The wear model of equation (13) considering only the shape and area are not similar to experimental results in whole, the coinciding points are No.2, No.4, No.5, No.6, and No.9. The mathematical model of equation (10) performs well on the square microstructure. Using the formula (10) to calculate the surface abrasion of microstructure has higher accuracy, with a maximum error of 4.6 %. Therefore, the life of the unfolding wheel can be predicted by using equations (10) and (13). So the design of the microstructure surface unfolding wheel would be assisted.
Fig. 10. Comparison of test wear and calculation wear.
5. Conclusion
It is found that the parameters that affect the apparent degree of abrasion are area > shape >
depth > spacing. When the microstructure is diamond, the area is 3.14×10-2 mm2, and the depth is 100 µm, it has a better anti-wear effect.
Through stress simulation analysis, it is found that different geometric parameters change the stress distribution of microstructure pits and affect the volume of high-stress zones, which is the root cause of the amount of wear. The amount of wear is reduced when the area of the pit is
life of the microstructure surface unfolding wheel.
Acknowledgments
This paper was supported by the National Natural Science Foundation of China (Grant No.
51875142) and Heilongjiang Provincial Natural Science Foundation of China (Grant No.
E2017052).
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