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Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate
Materials Today: Proceedings xxx (xxxx) xxx
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Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate Mitul T. Solanki, D.P. Vakharia ⇑ S. V. National Institute of Technology, Surat 395007, India
a r t i c l e
i n f o
Article history: Received 9 September 2019 Received in revised form 22 October 2019 Accepted 23 December 2019 Available online xxxx Keywords: Contact width Hollow roller Layered cylindrical hollow roller Footprint method Hertz theory
a b s t r a c t A novel roller design, a layered cylindrical hollow roller is suggested for roller type bearings, in which a small hollow cylinder is embedded into another large hollow cylinder with the same percentage of hollowness. This paper deals with a theoretical and experimental investigation for the cylinder-on-flat type contact interaction. In theoretical calculation Hertz theory is used for half contact width calculation. While experimental analysis is carried out with the help of ‘‘footprint method” for analyzing a real contact area between elastic solids. In footprint method the indentation of the roller on flat plate with regard to the applied load is measured. The theoretical data is compared for the validation of experimental technique. The test results are very close and similar with the theoretical data. With the help of this experimental technique, contact analysis between hollow roller and flat plate and between layered cylindrical hollow roller and flat plate have been carried out. Finally, in this work, experimentally evaluated contact width values are compared between hollow roller and layered cylindrical hollow roller. The experimental results suggested that the layered cylindrical hollow roller has larger contact width as compared to hollow roller with the same outside dimension and hollowness under same compressive loading conditions. Ó 2020 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Recent Advances in Materials & Manufacturing Technologies.
1. Introduction The contact interaction between two elastic solid bodies has been an interesting topic since more than one century. Hertz [1], gave the first mathematical representation of the elastic contact between two glass lenses with minimum deformation. The contact width enlarges with the applied load, and accordingly contact pressure is distributed over a broader area. In present work, the experimental investigation is carried out for the cylinder-on-flat plate type of configuration. Solid cylindrical roller bearings are typical mechanical components that find its applications in almost all machines and devices such as conveyor belt rollers, turbine engines, transmissions and gearboxes, wastewater and marine industries. In cylindrical roller bearing, multibody contact exists between rollers and inner/outer races, owing to which contact stresses occurs between them. The chief purpose is to reduce the Hertzian stresses at the contact ⇑ Corresponding author. E-mail address: [email protected] (D.P. Vakharia).
between roller and raceway surfaces, because stresses are very high in these areas of the bearing. Roller bearings are generally preferable in applications which require heavy duty load capability, which is not possible with a ball bearing [2]. In cylindrical roller bearing, the main cause of failure is due to the rolling contact fatigue (RCF) [3]. RCF is manifested as flaking off of metallic substances from the raceways and/or rolling element surfaces. The cracks which are generated below the surfaces propagate towards the surface, eventually producing a fatigue or spall failure [4]. In order to reduce this kind of failure, a hollow roller was suggested in the bearing [5]. Hollow cylindrical roller bearings are advantageous where higher speeds and loads are required in various applications [6–8]. Hollow rollers possess better lubrication, lighter weight and high rotational speeds as compared to solid rollers. Many researchers have studied that hollow rollers have extended fatigue life as compared to solid rollers [9,10]. As discussed above, different researchers attempted the numerical and experimental investigation of hollow cylindrical roller bearing. However, there are few difficulties, specifically bending
https://doi.org/10.1016/j.matpr.2019.12.224 2214-7853/Ó 2020 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Recent Advances in Materials & Manufacturing Technologies.
Please cite this article as: M. T. Solanki and D. P. Vakharia, Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.224
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M.T. Solanki, D.P. Vakharia / Materials Today: Proceedings xxx (xxxx) xxx
fatigue fracture is possible to occur in hollow roller under periodical alternative deformation stage [11]. The bending stress at the inner surface limits the life of a hollow roller [4]. Therefore, in order to reduce the hollow roller’s inner wall bending stress and improve the overall performance, a layered cylindrical hollow roller was introduced in [12]. The proposed design of the layered cylindrical hollow roller is shown in Fig. 1. The finite element analysis (FEA) results carried out for an elastic contact between a layered cylindrical hollow roller and flat plate suggested that the layered cylindrical hollow roller has better performances than both the solid and hollow roller. In case of layered cylindrical hollow roller, no standard formula is available to calculate the half contact width as it is available in case of solid roller. The contact stresses in layered cylindrical hollow roller cannot be calculated by the same procedure as in case of solid roller, because the Hertzian theory is based on several assumption, out of which one of the assumption is: two bodies profile are continuous and can be characterized with good approximations by a second degree polynomial function. However, it does not consider a situation where two bodies’ cross sections are multiply connected. Therefore, the experimental investigation of a layered cylindrical hollow roller and flat plate was carried out in [13]. The Hertz equation was extended for calculating half contact width in case of layered cylindrical hollow roller and flat plate contact. However, its contact width comparison with the hollow roller have not been done so far. Therefore, in the present work, two hollow rollers of 61% hollowness and 37% hollowness were tested with the help of footprint
method. Finally, experimentally evaluated contact width values are compared between hollow rollers and layered cylindrical hollow roller. 1.1. Footprint method Goodelle et al., [14] acquired footprints with the help of etched film on the bearing surfaces. This method’s is stated as: if a bearing race is submerged in dilute nitric acid solution, a carbon film layer is made on bearing surfaces. If a load is applied on this race, than the film in the contact area sticks tightly on races and seems like a footprint. However because of film thickness influence, the measured dimensions on the footprints are always larger as compare to the actual contact area. However, Goodelle et al., [14] solved this difficulty by the measurement of film thickness and acquired a set of calibration curves to change errors in measurement. But it is of no useful for others to use these calibration curves due to deviations in the environmental conditions and materials. In this paper the improved footprint method developed by Cheng [15], was used to calculate the contact width between roller and flat plate. This method’s principle is: before starting the test, the plate was submerged in acetone to clean its surface. Then, hot air was used to dry the surface. The plate was then placed in 10% nitric acid solution for not more than 20 s. Then, again hot air was used to dry the surface, which leave an etched film on the plate surface. A clean dry roller was gradually pressed by the applied load through UTM machine as shown in Fig. 2. A rubber eraser with water was taken for cleaning little scratch at the foot-
Fig. 1. (a) Outer hollow cylinder (b) Inner hollow cylinder (c) Layered cylindrical hollow roller (d) Its sectional view.
Please cite this article as: M. T. Solanki and D. P. Vakharia, Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.224
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M.T. Solanki, D.P. Vakharia / Materials Today: Proceedings xxx (xxxx) xxx
Fig. 2. Test set up for solid roller on flat plate test. Fig. 3. Measured contact width.
print boundaries. Then the plate was dried in hot air. The footprints were measured by a travelling microscope.
Table 2 Contact width comparison between experimental and theoretical value.
1.2. Experimental testing of solid roller and the flat test The dimensions and mechanical properties of the solid roller are shown in Table 1 which is made of AISI 52,100 steel [16]. The flat plate dimension is 200 mm 80 mm 20 mm and made from hot die steel H11 and has an Elastic Modulus and Poisson ratio of 2.1 105 N/mm2 and 0.3 respectively [17]. The solid roller of NU 2206 series standard bearing was tested for validating the method. Based on the arrangements as described above, the experimental analysis is carried out where different loads are applied on solid roller and its contact widths are measured. Fig. 3 shows the footprint obtained from a solid roller on the flat plate experiment. Table 2 shows different values of contact width with respect to different loads.
Applied Load F (N)
Theoretical half contact width b (mm)
Experimental half contact width b (mm)
% Deviation
2943 4905 5886 6867
0.111 0.147 0.161 0.173
0.112 0.15 0.165 0.178
0.892 0.02 0.024 0.028
1.3. Theoretical validation For determining the theoretical half contact width, its experimental values are compared with the solution given by Hertz [1]. The equation for calculating the half contact width value:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2F ð1 m21 Þ=E1 þ ð1 m22 Þ=E2 b¼ pl 1=d1 þ 1=d2
Fig. 4. (a) Layered cylindrical hollow roller of 61% hollowness (b) hollow roller of 37% hollowness (c) hollow roller of 61% hollowness.
ð1Þ
Now, considering solid roller and flat plate as Part 1 and Part 2, respectively; F = 2943 N E1 = 2.058 105 N/mm2 E2 = 2.1 105 N/mm2 v 1 ; v 2 = 0.3 d1 = 9 mm & d2 = 1 and l = 12 mm
Similarly, percentage deviation is carried out for all contact width values with regard to the applied load and are listed in Table 2. It can be seen from Table 2 that the percentage deviation for all cases are less than 1%, which shows good agreement between experimental value and theoretical solution given by Hertz.
2. Test of hollow roller and layered cylindrical hollow roller
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2943 ð1 0:32 Þ=205800 þ ð1 0:32 Þ=210000 b¼ 1=9 p 12
b = 0.111 mm. Now, calculating the percentage deviation between experimental and theoretical value: which is 0.892%.
There is no established method to for calculating half contact width in case of both hollow and layered cylindrical hollow roller. Here, also the footprint method is used to calculate the half contact width. All tested rollers are shown in Fig. 4. The rollers dimensions and mechanical properties are listed in Table 3. Two hollow rollers were taken for the experimentation for comparison of its results with the layered cylindrical hollow roller. Both hollow rollers of 37% hollowness and 61% hollowness as shown in Fig. 4(b, c) were manufactured using wire cut EDM process for experimentation.
Table 1 Dimensions and mechanical properties of solid roller. Cylindrical Roller
Diameter (D) mm
Length (l) mm
Elastic Modulus E (N/mm2)
Poisson ratio
Solid roller
9
12
2.058 105
0.3
v
Please cite this article as: M. T. Solanki and D. P. Vakharia, Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.224
4
M.T. Solanki, D.P. Vakharia / Materials Today: Proceedings xxx (xxxx) xxx
Table 3 Dimensions and mechanical properties of solid roller. Cylindrical Roller
Outer Diameter (Do) mm
Inner Diameter (Di) mm
Length l (mm)
Elastic Modulus E (N/mm2)
Poisson ratio
Layered cylindrical hollow roller 61%
5.4 9 9 9
3.3 5.4 5.4 3.3
12 12 12 12
2.058 105 2.058 105 2.058 105 2.058 105
0.3 0.3 0.3 0.3
Hollow roller 61% Hollow roller 37%
v
Table 5 Contact width values for 61% hollowness hollow roller. Applied Load F (N)
Experimental contact width 2b (mm)
Experimental half contact width b (mm)
1962 2943 3924 4905 5886 6867 7848 8829
0.175 0.2 0.225 0.25 0.275 0.325 0.375 0.45
0.0875 0.1 0.1125 0.125 0.1375 0.1625 0.1875 0.225
Fig. 5. Test set up for hollow roller on flat plate test.
Table 4 Contact width values for 37% hollowness hollow roller. Applied Load F (N)
Experimental contact width 2b (mm)
Experimental half contact width b (mm)
1962 2943 3924 4905 5886 6867 7848 8829 9810 10,791 11,772 12,753 13,734 14,715 15,696
0.1 0.15 0.2 0.2125 0.225 0.2375 0.25 0.2625 0.275 0.3 0.325 0.3775 0.43 0.4775 0.525
0.05 0.075 0.1 0.10625 0.1125 0.11875 0.125 0.13125 0.1375 0.15 0.1625 0.18875 0.215 0.23875 0.2625
The test set up for hollow roller is shown in Fig. 5. The loading accuracy as high as + 1% was maintained throughout the experiment. The load was applied up to the ultimate strength of the roller. 3. Results and discussions The experimentally evaluated contact width values for 37% hollowness hollow roller are listed in Table 4. Similar experimental analysis was carried out for the contact interaction between a hollow roller of 61% hollowness and flat plate and its results are listed in Table 5. Now, this experimental half contact width values of both hollow rollers are compared with the experimental half contact width of layered cylindrical hollow roller of 61% hollowness as carried out in [13].
Fig. 6. Comparison of half contact width.
The main reason to take two hollow rollers is to compare its contact width values with the layered cylindrical hollow roller. The 37% hollowness hollow roller is taken because its inner diameter is same as the inner diameter of the layered cylindrical hollow roller as shown in Table 3. The 61% hollowness hollow roller is taken because of its same percentage hollowness as the layered cylindrical hollow roller. So, comparison with two different hollowness hollow rollers were carried out and its results are shown in Fig. 6. 4. Conclusions A novel layered cylindrical hollow roller is suggested here to reduce the contact stresses occur in case of both solid and hollow rollers. The major outcome from the present work are: The footprint method was used in experimental investigation for a cylinder on plate type configuration which gave contact width values much closer to the Hertz analytical solution for solid roller. For the same applied load, the contact width values for the layered cylindrical hollow roller is significantly larger as compared to both hollow rollers as shown in Fig. 6.
Please cite this article as: M. T. Solanki and D. P. Vakharia, Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.224
M.T. Solanki, D.P. Vakharia / Materials Today: Proceedings xxx (xxxx) xxx
The larger the contact width values means lower the contact stresses. Therefore, life of the layered cylindrical hollow roller is more as compared to both solid and hollow rollers. The present footprint method can be used to calculate the contact width for other NU 22 series rollers also.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] H. Hertz, Ueber die Berührung Fester Elastischer Körper, J. Reine Angew. Math. 92 (4) (1881) 156–171. [2] A. Palmgreen, Ball and roller bearing engineering, SKF Industries Inc., Philadelphia, 1959. [3] T.A. Harris, M.N. Kotzalas, Rolling Bearing Analysis-Advanced Concepts of Bearing Technology, fifth ed., CRC Press, 2007. [4] W.L. Bowen, T.W. Murphy Jr., High speed testing of the hollow roller bearing, ASME J. Lubr. Technol. 103 (1) (1981) 1–5. [5] D. Scott, Hollow rolling elements, Tribol. Int. 9 (6) (1976) 261–264.
5
[6] W.M. Abu-Jadayil, D.R. Flugrad, Fatigue life investigation of solid and hollow rollers under pure normal loading, Tribotest 13 (4) (2007) 165–181. [7] C.P. Bhateja, R.S. Hahn, A hollow roller bearings for use in precision machine tools, Ann. CIRP 29 (1) (1980) 303–307. [8] H. Hanau, New Concepts in Bearing Design and Applications Chapter 7, Industrial Tectonics, Inc., 1975. [9] W.L. Bowen, C.P. Bhateja, The hollow roller bearing, ASME J. Lubr. Technol. 102 (2) (1980) 222–228. [10] H. Zhao, Analysis of load distributions within solid and hollow roller bearings, ASME J. Tribol. 120 (1) (1998) 134–139. [11] L. Hong, L. Jianjun, Analysis of Contact Problems on Hollow Cylindrical Rollers, Tribol. 120 (3) (1998) 253–259. [12] M.T. Solanki, D. Vakharia, A finite element analysis of an elastic contact between a layered cylindrical hollow roller and flat contact, Ind. Lubr. Tribol. 69 (1) (2017) 30–41. [13] M.T. Solanki, D. Vakharia, Extending hertz equation for an elastic contact between a layered cylindrical hollow roller and flat contact through an experimental technique, Ind. Lubr. Tribol. 69 (2) (2017) 312–324. [14] R.A. Goodelle, W.J. Derner, L.E. Root, Determination of static load distributions from elastic contacts in rolling element bearings, ASLE Trans. 14 (4) (1971) 275–291. [15] W.W. Cheng, Experimental and numerical study of multibody contact system with roller bearing-part I: an improved footprint test method, STLE Tribol. Trans. 39 (1) (1996) 75–80. [16] Y.B. Guo, C.R. Liu, Mechanical properties of hardened AISI 52100 steel in hard machining processes, Trans. ASME, J. Manf. Sci. Eng. 125 (1) (2002) 1–9. [17] D. Klobcar, J. Tusek, B. Taljat, Thermal and fatigue of materials for die casting tooling, Mater. Sci. Eng. A 472 (2008) 198–207.
Please cite this article as: M. T. Solanki and D. P. Vakharia, Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.224
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate Mitul T. Solanki, D.P. Vakharia ⇑ S. V. National Institute of Technology, Surat 395007, India
a r t i c l e
i n f o
Article history: Received 9 September 2019 Received in revised form 22 October 2019 Accepted 23 December 2019 Available online xxxx Keywords: Contact width Hollow roller Layered cylindrical hollow roller Footprint method Hertz theory
a b s t r a c t A novel roller design, a layered cylindrical hollow roller is suggested for roller type bearings, in which a small hollow cylinder is embedded into another large hollow cylinder with the same percentage of hollowness. This paper deals with a theoretical and experimental investigation for the cylinder-on-flat type contact interaction. In theoretical calculation Hertz theory is used for half contact width calculation. While experimental analysis is carried out with the help of ‘‘footprint method” for analyzing a real contact area between elastic solids. In footprint method the indentation of the roller on flat plate with regard to the applied load is measured. The theoretical data is compared for the validation of experimental technique. The test results are very close and similar with the theoretical data. With the help of this experimental technique, contact analysis between hollow roller and flat plate and between layered cylindrical hollow roller and flat plate have been carried out. Finally, in this work, experimentally evaluated contact width values are compared between hollow roller and layered cylindrical hollow roller. The experimental results suggested that the layered cylindrical hollow roller has larger contact width as compared to hollow roller with the same outside dimension and hollowness under same compressive loading conditions. Ó 2020 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Recent Advances in Materials & Manufacturing Technologies.
1. Introduction The contact interaction between two elastic solid bodies has been an interesting topic since more than one century. Hertz [1], gave the first mathematical representation of the elastic contact between two glass lenses with minimum deformation. The contact width enlarges with the applied load, and accordingly contact pressure is distributed over a broader area. In present work, the experimental investigation is carried out for the cylinder-on-flat plate type of configuration. Solid cylindrical roller bearings are typical mechanical components that find its applications in almost all machines and devices such as conveyor belt rollers, turbine engines, transmissions and gearboxes, wastewater and marine industries. In cylindrical roller bearing, multibody contact exists between rollers and inner/outer races, owing to which contact stresses occurs between them. The chief purpose is to reduce the Hertzian stresses at the contact ⇑ Corresponding author. E-mail address: [email protected] (D.P. Vakharia).
between roller and raceway surfaces, because stresses are very high in these areas of the bearing. Roller bearings are generally preferable in applications which require heavy duty load capability, which is not possible with a ball bearing [2]. In cylindrical roller bearing, the main cause of failure is due to the rolling contact fatigue (RCF) [3]. RCF is manifested as flaking off of metallic substances from the raceways and/or rolling element surfaces. The cracks which are generated below the surfaces propagate towards the surface, eventually producing a fatigue or spall failure [4]. In order to reduce this kind of failure, a hollow roller was suggested in the bearing [5]. Hollow cylindrical roller bearings are advantageous where higher speeds and loads are required in various applications [6–8]. Hollow rollers possess better lubrication, lighter weight and high rotational speeds as compared to solid rollers. Many researchers have studied that hollow rollers have extended fatigue life as compared to solid rollers [9,10]. As discussed above, different researchers attempted the numerical and experimental investigation of hollow cylindrical roller bearing. However, there are few difficulties, specifically bending
https://doi.org/10.1016/j.matpr.2019.12.224 2214-7853/Ó 2020 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Recent Advances in Materials & Manufacturing Technologies.
Please cite this article as: M. T. Solanki and D. P. Vakharia, Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.224
2
M.T. Solanki, D.P. Vakharia / Materials Today: Proceedings xxx (xxxx) xxx
fatigue fracture is possible to occur in hollow roller under periodical alternative deformation stage [11]. The bending stress at the inner surface limits the life of a hollow roller [4]. Therefore, in order to reduce the hollow roller’s inner wall bending stress and improve the overall performance, a layered cylindrical hollow roller was introduced in [12]. The proposed design of the layered cylindrical hollow roller is shown in Fig. 1. The finite element analysis (FEA) results carried out for an elastic contact between a layered cylindrical hollow roller and flat plate suggested that the layered cylindrical hollow roller has better performances than both the solid and hollow roller. In case of layered cylindrical hollow roller, no standard formula is available to calculate the half contact width as it is available in case of solid roller. The contact stresses in layered cylindrical hollow roller cannot be calculated by the same procedure as in case of solid roller, because the Hertzian theory is based on several assumption, out of which one of the assumption is: two bodies profile are continuous and can be characterized with good approximations by a second degree polynomial function. However, it does not consider a situation where two bodies’ cross sections are multiply connected. Therefore, the experimental investigation of a layered cylindrical hollow roller and flat plate was carried out in [13]. The Hertz equation was extended for calculating half contact width in case of layered cylindrical hollow roller and flat plate contact. However, its contact width comparison with the hollow roller have not been done so far. Therefore, in the present work, two hollow rollers of 61% hollowness and 37% hollowness were tested with the help of footprint
method. Finally, experimentally evaluated contact width values are compared between hollow rollers and layered cylindrical hollow roller. 1.1. Footprint method Goodelle et al., [14] acquired footprints with the help of etched film on the bearing surfaces. This method’s is stated as: if a bearing race is submerged in dilute nitric acid solution, a carbon film layer is made on bearing surfaces. If a load is applied on this race, than the film in the contact area sticks tightly on races and seems like a footprint. However because of film thickness influence, the measured dimensions on the footprints are always larger as compare to the actual contact area. However, Goodelle et al., [14] solved this difficulty by the measurement of film thickness and acquired a set of calibration curves to change errors in measurement. But it is of no useful for others to use these calibration curves due to deviations in the environmental conditions and materials. In this paper the improved footprint method developed by Cheng [15], was used to calculate the contact width between roller and flat plate. This method’s principle is: before starting the test, the plate was submerged in acetone to clean its surface. Then, hot air was used to dry the surface. The plate was then placed in 10% nitric acid solution for not more than 20 s. Then, again hot air was used to dry the surface, which leave an etched film on the plate surface. A clean dry roller was gradually pressed by the applied load through UTM machine as shown in Fig. 2. A rubber eraser with water was taken for cleaning little scratch at the foot-
Fig. 1. (a) Outer hollow cylinder (b) Inner hollow cylinder (c) Layered cylindrical hollow roller (d) Its sectional view.
Please cite this article as: M. T. Solanki and D. P. Vakharia, Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.224
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M.T. Solanki, D.P. Vakharia / Materials Today: Proceedings xxx (xxxx) xxx
Fig. 2. Test set up for solid roller on flat plate test. Fig. 3. Measured contact width.
print boundaries. Then the plate was dried in hot air. The footprints were measured by a travelling microscope.
Table 2 Contact width comparison between experimental and theoretical value.
1.2. Experimental testing of solid roller and the flat test The dimensions and mechanical properties of the solid roller are shown in Table 1 which is made of AISI 52,100 steel [16]. The flat plate dimension is 200 mm 80 mm 20 mm and made from hot die steel H11 and has an Elastic Modulus and Poisson ratio of 2.1 105 N/mm2 and 0.3 respectively [17]. The solid roller of NU 2206 series standard bearing was tested for validating the method. Based on the arrangements as described above, the experimental analysis is carried out where different loads are applied on solid roller and its contact widths are measured. Fig. 3 shows the footprint obtained from a solid roller on the flat plate experiment. Table 2 shows different values of contact width with respect to different loads.
Applied Load F (N)
Theoretical half contact width b (mm)
Experimental half contact width b (mm)
% Deviation
2943 4905 5886 6867
0.111 0.147 0.161 0.173
0.112 0.15 0.165 0.178
0.892 0.02 0.024 0.028
1.3. Theoretical validation For determining the theoretical half contact width, its experimental values are compared with the solution given by Hertz [1]. The equation for calculating the half contact width value:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2F ð1 m21 Þ=E1 þ ð1 m22 Þ=E2 b¼ pl 1=d1 þ 1=d2
Fig. 4. (a) Layered cylindrical hollow roller of 61% hollowness (b) hollow roller of 37% hollowness (c) hollow roller of 61% hollowness.
ð1Þ
Now, considering solid roller and flat plate as Part 1 and Part 2, respectively; F = 2943 N E1 = 2.058 105 N/mm2 E2 = 2.1 105 N/mm2 v 1 ; v 2 = 0.3 d1 = 9 mm & d2 = 1 and l = 12 mm
Similarly, percentage deviation is carried out for all contact width values with regard to the applied load and are listed in Table 2. It can be seen from Table 2 that the percentage deviation for all cases are less than 1%, which shows good agreement between experimental value and theoretical solution given by Hertz.
2. Test of hollow roller and layered cylindrical hollow roller
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2943 ð1 0:32 Þ=205800 þ ð1 0:32 Þ=210000 b¼ 1=9 p 12
b = 0.111 mm. Now, calculating the percentage deviation between experimental and theoretical value: which is 0.892%.
There is no established method to for calculating half contact width in case of both hollow and layered cylindrical hollow roller. Here, also the footprint method is used to calculate the half contact width. All tested rollers are shown in Fig. 4. The rollers dimensions and mechanical properties are listed in Table 3. Two hollow rollers were taken for the experimentation for comparison of its results with the layered cylindrical hollow roller. Both hollow rollers of 37% hollowness and 61% hollowness as shown in Fig. 4(b, c) were manufactured using wire cut EDM process for experimentation.
Table 1 Dimensions and mechanical properties of solid roller. Cylindrical Roller
Diameter (D) mm
Length (l) mm
Elastic Modulus E (N/mm2)
Poisson ratio
Solid roller
9
12
2.058 105
0.3
v
Please cite this article as: M. T. Solanki and D. P. Vakharia, Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.224
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M.T. Solanki, D.P. Vakharia / Materials Today: Proceedings xxx (xxxx) xxx
Table 3 Dimensions and mechanical properties of solid roller. Cylindrical Roller
Outer Diameter (Do) mm
Inner Diameter (Di) mm
Length l (mm)
Elastic Modulus E (N/mm2)
Poisson ratio
Layered cylindrical hollow roller 61%
5.4 9 9 9
3.3 5.4 5.4 3.3
12 12 12 12
2.058 105 2.058 105 2.058 105 2.058 105
0.3 0.3 0.3 0.3
Hollow roller 61% Hollow roller 37%
v
Table 5 Contact width values for 61% hollowness hollow roller. Applied Load F (N)
Experimental contact width 2b (mm)
Experimental half contact width b (mm)
1962 2943 3924 4905 5886 6867 7848 8829
0.175 0.2 0.225 0.25 0.275 0.325 0.375 0.45
0.0875 0.1 0.1125 0.125 0.1375 0.1625 0.1875 0.225
Fig. 5. Test set up for hollow roller on flat plate test.
Table 4 Contact width values for 37% hollowness hollow roller. Applied Load F (N)
Experimental contact width 2b (mm)
Experimental half contact width b (mm)
1962 2943 3924 4905 5886 6867 7848 8829 9810 10,791 11,772 12,753 13,734 14,715 15,696
0.1 0.15 0.2 0.2125 0.225 0.2375 0.25 0.2625 0.275 0.3 0.325 0.3775 0.43 0.4775 0.525
0.05 0.075 0.1 0.10625 0.1125 0.11875 0.125 0.13125 0.1375 0.15 0.1625 0.18875 0.215 0.23875 0.2625
The test set up for hollow roller is shown in Fig. 5. The loading accuracy as high as + 1% was maintained throughout the experiment. The load was applied up to the ultimate strength of the roller. 3. Results and discussions The experimentally evaluated contact width values for 37% hollowness hollow roller are listed in Table 4. Similar experimental analysis was carried out for the contact interaction between a hollow roller of 61% hollowness and flat plate and its results are listed in Table 5. Now, this experimental half contact width values of both hollow rollers are compared with the experimental half contact width of layered cylindrical hollow roller of 61% hollowness as carried out in [13].
Fig. 6. Comparison of half contact width.
The main reason to take two hollow rollers is to compare its contact width values with the layered cylindrical hollow roller. The 37% hollowness hollow roller is taken because its inner diameter is same as the inner diameter of the layered cylindrical hollow roller as shown in Table 3. The 61% hollowness hollow roller is taken because of its same percentage hollowness as the layered cylindrical hollow roller. So, comparison with two different hollowness hollow rollers were carried out and its results are shown in Fig. 6. 4. Conclusions A novel layered cylindrical hollow roller is suggested here to reduce the contact stresses occur in case of both solid and hollow rollers. The major outcome from the present work are: The footprint method was used in experimental investigation for a cylinder on plate type configuration which gave contact width values much closer to the Hertz analytical solution for solid roller. For the same applied load, the contact width values for the layered cylindrical hollow roller is significantly larger as compared to both hollow rollers as shown in Fig. 6.
Please cite this article as: M. T. Solanki and D. P. Vakharia, Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.224
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The larger the contact width values means lower the contact stresses. Therefore, life of the layered cylindrical hollow roller is more as compared to both solid and hollow rollers. The present footprint method can be used to calculate the contact width for other NU 22 series rollers also.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] H. Hertz, Ueber die Berührung Fester Elastischer Körper, J. Reine Angew. Math. 92 (4) (1881) 156–171. [2] A. Palmgreen, Ball and roller bearing engineering, SKF Industries Inc., Philadelphia, 1959. [3] T.A. Harris, M.N. Kotzalas, Rolling Bearing Analysis-Advanced Concepts of Bearing Technology, fifth ed., CRC Press, 2007. [4] W.L. Bowen, T.W. Murphy Jr., High speed testing of the hollow roller bearing, ASME J. Lubr. Technol. 103 (1) (1981) 1–5. [5] D. Scott, Hollow rolling elements, Tribol. Int. 9 (6) (1976) 261–264.
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Please cite this article as: M. T. Solanki and D. P. Vakharia, Experimental investigation of an elastic contact between a layered cylindrical hollow roller and flat plate, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.224