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Strength of spline joints assembled by forming
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Strength of spline joints assembled by forming Kenji Hirota a,∗ , Kazuhiko Kitamura b , Yoshihiko Ukai c , Keiichi Matsunaga d a
Department of Materials Science and Engineering, Kyushu Institute of Technology, Kitakyushu, Fukuoka 804-8550, Japan Department of Mechanical Engineering, Nagoya Institute of Technology, Nagoya, Aichi 466-8555, Japan c Toyota Motor Corporation, Toyota, Aichi 471-8571, Japan d MEG Inc., Anjo, Aichi 446-0052, Japan b
a r t i c l e
i n f o
Article history: Received 28 June 2013 Received in revised form 20 January 2014 Accepted 2 February 2014 Available online xxx Keywords: Spline joint Torsional strength Assembly by forming
a b s t r a c t In this paper, a new assembling method of spline joints that enables tight fitting in a simple manner by allowing slight plastic deformation at the spline teeth was introduced. Experiments were carried out for the spline joints of medium carbon steel varying the overlap zone between the male and the female spline teeth. Axial joining strength was increased with increase in the overlap length due to the residual compressive stress by forming. The joint by the proposed method also showed higher torsional strength than the conventional joint. Improvement in the torsional strength was explained based on the deformation and hardness distribution around the spline teeth. With respect to the shape of overlap zone, better results were obtained when using the specimen having a uniform overlap length along the axial direction. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Spline-hub connections are reliable mechanical joints for torque transmission and widely applied to automotive parts. Since these joints are mostly subject to cyclic loading, the evaluation of fatigue strength has been a main concern. Shen et al. (2013) developed a plain-fretting fatigue unified prediction model and discussed the plain and fretting fatigue performance of involute spline shaft-hub connection teeth. It is generally said that increase in residual compressive stress at the interface of the joint is effective to improve the fatigue strength. Miyazawa et al. (2011) combined a press fit joint with a spline-joint and demonstrated that the joint proposed showed higher torsional fretting strength than conventional spline-joints. Nigrelli and Pasta (2007) evaluated the residual stress induced around the hole by split-sleeve cold expansion for the purpose of assessment of fatigue life. Joining by forming is also advantageous for improving the fatigue strength and has various excellent features of no heat influence and resulting thermal deformation, high productivity and joinability of dissimilar materials. Spot joining methods such as clinching and self-piercing riveting are the typical examples and
∗ Corresponding author at: Department of Materials Science and Engineering, Kyushu Institute of Technology, 1-1, Sensui-cho, Tobata-ku, Kitakyushu, Fukuoka 804-8550, Japan. Tel.: +81 93 884 3369; fax: +81 93 884 3369. E-mail address: [email protected] (K. Hirota).
many attempts have been made for the sheet metal parts in which spot welding can not be applied. Abe et al. (2012) reported the possibility of joining high strength steel and aluminum alloy sheets by mechanical clinching. Joining of a shaft and a disk-like part by forming has also been tried. Kanamaru et al. (1984) created a mechanical shaft-disk connection by forging the disk in such way that the material of the disk fills the grooves on the shaft. Alves and Martins (2013) developed a single stroke mechanical joining process to fix sheet panels to tubular profiles and applied it to automotive parts. Egami et al. (1997) developed a new manufacturing method for serration joints: a serration joint was obtained by pushing a serrated shaft into the hole of a mating part so that the serrations of the shaft shave the hole surface. In this method, the serrated shaft acts as a shaving tool and hence the shaft should be much harder than the hole. This process was applied to join a cam plate to a shaft and the joint obtained exhibited enough torsional fatigue strength. The authors proposed a similar method for serration joints by using cold forward extrusion: Kitamura et al. (2012) summarized the joining mechanism and optimum conditions to achieve high torsional strength and Hirota et al. (2012) investigated the effect of the shape of serrations and the rigidity of the disk on the joining strength. However, this method cannot be applied to such joints that the male and the female parts are made of the same material. In order to overcome the problem, a new method was proposed in this study. Through the experiments varying the amount of deformation, spline joints of medium carbon
http://dx.doi.org/10.1016/j.jmatprotec.2014.02.007 0924-0136/© 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: Hirota, K., et al., Strength of spline joints assembled by forming. J. Mater. Process. Tech. (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.02.007
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Fig. 1. Schematic of assembling method of serration joint by forming.
steel were successfully assembled and showed higher torsional strength than a conventional joint not accompanied by plastic deformation. 2. Mechanical joint assembled by forming 2.1. Assembling of serration joint by forming In the production of spline joints or serration joints, precise machining, which is time and cost consuming, is required to achieve a tight fit tolerance for enough fatigue strength. The authors developed a new method to obtain a tight-fit serration joint with high productivity. The procedure of the process is illustrated in Fig. 1. A shaft having serrated portion at one end and a disk with a hole at the center are prepared. The serration is given to the shaft by forward extrusion and hardened by carburizing and quenching if the disk is as hard as the shaft. The diameter of the hole is determined so that the overlap ratio of the tooth and the hole ı/h is equal to about 0.5. Next, the shaft is pushed into the hole up to the end of the serrated zone, where each tooth of the serration is indented on the surface of the hole and a mechanical engagement is created in the circumferential direction between the shaft and the disk. Thus, tight fitting is achieved in a simple operation due to the residual compressive stress by indenting. Kitamura et al. (2012) and Hirota et al. (2012) reported the optimum conditions for the lead angle ˛ and the overlap ratio ı/h to achieve high torsional strength. 2.2. Assembling of spline joint by forming The method in Fig. 1 has a limitation for the combination of materials to obtain a successful joint, i.e. the teeth of serrations should be approximately three times harder than the hole surface, otherwise the serrations collapse and no mechanical engagement is formed. In this paper, a new method was proposed to overcome the limitation. Dimensions of the spline-disk joint targeted in this study are illustrated in Fig. 2(a). A straight sided spline (designation: 6 × 18 × 22, ISO 14-1982) is provided with the shaft, while the mating teeth in the hole are designed so that a part of the tooth overlaps by ˇ per side against the tooth of the shaft. As the external spline is pushed into the internal spline, either or both of the teeth deform at the overlap zone and the spline joint tightly fitted by the residual stress on the resulting interface is obtained. This method will be applicable between the same materials since the amount of deformation is much less compared with the previous method as shown in Fig. 1. A constant gap of 0.2 mm is given at the miner diameter of the spline so that the material deformed
at the overlap zone escapes to the gap. Contrarily, no gap (with a tolerance of 0.02 mm) is given at the major diameter to assure the coaxiality and the perpendicularity of the disk to the shaft in assembling. In this method, the overlap length is considered to be the most important factor for the assembling load and the strength of the joint and hence, varied in two ways as shown in Fig. 2(b). The type I specimen has straight tooth sides and the overlap length is uniform along the axial direction, while the type II specimen has tapered tooth sides and the overlap length increases along the axial direction. The parameter sets in the experiments are summarized in Table 1, where test cases 5 and 6 are used for comparison at approximately the same overlap length (ˇ ∼ = ˇ ) between different types of disk specimens and case 7 as a reference sample of the conventional spline joint. Both the shaft and disk were made of medium carbon steel containing 0.45 wt% C (S45C (JIS)) and the spline teeth were processed by wire electro discharge machining. Since fitting is achieved by plastic deformation in this method, the manufacturing tolerance for tooth dimensions will be rather relaxed compared with that for conventional spline joints. Therefore, the teeth can be processed by forward extrusion and machine finishing of the major diameter and the type II specimens were designed based on such a processing method. The shaft and the disk were set on a die set as shown in Fig. 2(c), where the coaxiality and the position of the teeth in the circumferential direction were adjusted by the chamfers at the shaft and the hole edges, and two positioning pins, respectively. The die set was loaded by a hydraulic press at a rate of 5 mm/s and the shaft was pushed into the disk to the depth of 4 mm, where load-stroke data were measured by means of a strain gauge load cell (capacity: 200 kN) and a contact type displacement sensor (ranges: 0–10 mm). The assembled joints were subjected to strength tests. The axial strength was evaluated with the load to withdraw the shaft from the disk by using the same die set system for assembling. A torsion test was carried out as follows: both ends of the joint were fixed on the testing machine with bolts and the shaft side of the joint was rotated, where torque-torsional angle data were measured by means of a torque meter (capacity: 1kN· m) and a rotary encoder (resolution: 0.1◦ ) as shown in Fig. 2(d).
3. Results and discussions 3.1. Deformation behavior in assembling Assembling was carried out at the cases 1–4 of Table 1 and the load-stroke curves were obtained as shown in Fig. 3. The curves for type I specimens showed a logarithmic increase, meanwhile those for type II specimens an exponential increase. In order to compare the load between the type I and II specimens, the maximum overlap length is calculated for the type II specimens according to the following equation: ˇ = L tan , where L and are the engaged length and the tapered angle of the tooth side, respectively. Referring to the values of ˇ and ˇ as listed in Table 1, assembling load seems to obey the order of the overlap length. Fig. 4 shows the appearance of the spline teeth observed after disassembling the joint. The overlap zone of the teeth was deformed and the step was formed as indicated by the arrows. In all cases, neither fracturing nor adhesion was observed and the deformation of the teeth was remarkable when ˇ or was large. In the type I specimens, both teeth of the shaft and the disk deformed evenly and the step was formed on the shaft side. On the contrary in the type II specimens, deformation was only found on the disk: the overlap zone of the disk seems to be shaved by the shaft tooth and accumulate toward the assembling direction.
Please cite this article in press as: Hirota, K., et al., Strength of spline joints assembled by forming. J. Mater. Process. Tech. (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.02.007
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Fig. 2. Experimental conditions ((a) geometry and dimension of spline teeth and (b) type of disk specimen) and setup for (c) assembling and (d) static torsion test.
Table 1 Test conditions. Case
Disk type
Overlap length ˇ(see Fig. 2(b)
Tapered angle of tooth (see Fig. 2(b))
1 2 3
Type I Type I Type II
0.2 mm 0.4 mm –
4
Type II
–
5 6
Type I Type II
0.3 mm –
7
Type III
–
– – 2◦ (ˇ = 0.14 mm) 4◦ (ˇ = 0.28 mm) 6◦ (ˇ’ = 0.42 mm) –
Remarks
For comparison of torsional strength at approximately the same overlap length (between case 4 and 5) For comparison of torsional strength at approximately the same overlap length (between case 2 and 6) Conventional joint (Fitting tolerance = 0.02 mm)
Fig. 3. Assembling load – stroke curves obtained by using the setup as shown in Fig. 2(c).
Please cite this article in press as: Hirota, K., et al., Strength of spline joints assembled by forming. J. Mater. Process. Tech. (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.02.007
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Fig. 4. Appearance of teeth observed after disassembling the joint.
3.2. Strength of the joint The strength of the joints was measured in the manner as mentioned in Section 2.2. Fig. 5 shows a comparison of the axial strength of the joint, in which the right ordinate indicates the resistance required for withdrawing the shaft calculated assuming that the contact area is L × h (see Fig. 2(b)). The axial strength was higher in type I specimens than in type II specimens and the magnitude of ˇ and caused a little difference. The axial strength per unit area resulted in the order of several tens of mega-pascals in all cases, which is rather low compared with the shear strength of the medium carbon steel. Low strength is due to neither adhesion at the interface nor mechanical engagement in the axial direction. Therefore, the shaft is considered to be supported in the disk by frictional contact at the teeth. Fig. 6 shows the comparison of torque-torsional angle curves. The difference in torque is obvious at the beginning of loading but disappears as torsion proceeds. Yield torque was estimated by the limit of linearity for each curve. Fig. 7 shows the relationship between the yield torque and the overlap length, in which the overlap length in the type II specimens is plotted using the
Fig. 5. Axial strength of the joint estimated from disassembling force of the joint.
Fig. 6. Torque-torsional angle curves by torsion tests of the joint.
corresponding value ˇ (see. Fig. 2(b)). The joints by the proposed method showed over 1.2 times higher yield torque than the conventional joint (case 7) and the yield torque was increased with increase in the overlap length.
Fig. 7. Relationship between yield torque and overlap length.
Please cite this article in press as: Hirota, K., et al., Strength of spline joints assembled by forming. J. Mater. Process. Tech. (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.02.007
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Fig. 8. Vickers hardness distribution on the cross section of the shaft at L = 4 mm.
Fig. 9. Difference in deformation of the shaft after torsion tests in type II specimens.
3.3. Effect of forming on torsional strength When the joint was twisted plastically, the teeth of the shaft were sheared along the root circle of the external spline. In order to investigate the effect of plastic deformation on the torsional strength, hardness of the shaft around the contact surface was measured after disassembling the joint. Fig. 8 shows the distribution of Vickers hardness around the tooth of the shaft. The data for = 2◦ is omitted since it was almost the same as that for = 4◦ . The initial
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Fig. 11. Relationship between yield torque and overlap length (plots for ˇ = 0.3 mm and = 6◦ are added to Fig. 7).
hardness of the shaft and the disk was distributed between HV190 and HV210 and heat affection by wire cut EDM was little observed at a depth more than 0.1 mm from the surface. The plots for ˇ = 0.4 mm (case 2) resulted in higher values than the others near the root circle, which corresponds to the highest torque at case 2 in Fig. 7. Therefore, the improvement in yield torque in the type I specimens is caused by workhardening. On the other hand, the plots except ˇ = 0.4 mm showed little workhardening and hence the reason for higher torque at these conditions than the conventional joint might be enough contact pressure as well as no gap between mating teeth by plastic deformation. However, higher torque at = 4◦ than those at = 2◦ and ˇ = 0.2 mm cannot be explained by the above reasons. From the observation of deformation of the teeth after twisting, a distinctive difference was found depending on the magnitude of as shown in Fig. 9, i.e. the top face of the shaft tooth was swelled at = 2◦ by torsional loading and wasn’t swelled at = 4◦ . As shown in Fig. 4, a large step was formed on the disk teeth at = 4◦ so as to surround the top portion of the shaft tooth. Therefore, such steps probably served to prevent the top portion of the shaft teeth from swelling when the joint was twisted. In order to estimate the effect of the step on the torsional strength, three dimensional FE analysis was performed using an implicit commercial code, DEFORM-3D. Details of the analysis are
Fig. 10. FE model for evaluation of the effect of “step” on torsional strength.
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Fig. 12. Difference in deformation of the teeth depending on the tapered angle.
shown in Fig. 10. A pair of engaged teeth was modeled, where the tooth of the disk was approximated as a rigid body since it showed little plastic deformation in the torsion test. The tooth of the shaft was sheared by two kinds of mating teeth in the arrow-indicated direction. The result was that the stepped tooth (Fig. 10(a)) showed approximately 1.1 times higher yield shear force than the nonstepped tooth (Fig. 10(b)). Accordingly, the reason for higher torque for = 4◦ than those for = 2◦ and ˇ = 0.2 mm is that the step formed around the tooth increases the shear resistance of the tooth in twisting the joint. In order to compare the yield torque at approximately the same overlap length between the types I and II specimens, additional experiments were carried out at ˇ = 0.3 mm (case 5) and = 6◦ (case 6). The data obtained is superimposed on Fig. 7 and shown in Fig. 11. In the type I specimens, a linear increasing relationship was obtained between the yield torque and the overlap length and further improvement in the torsional strength will be possible with increase in ˇ. Meanwhile, the yield torque of the type II specimens took a peak at = 4◦ . Comparison of the appearance of the teeth at these conditions was shown in Fig. 12. The step observed at = 4◦ wasn’t formed at = 6◦ in spite of the increased overlap length,
which implies that the deformation would not be localized around the interface but prevail uniformly inside the teeth. Although increase in ˇ or is effective for improving the torsional strength, it also increase the assembling load and may cause distortion of the shaft and the disk, or fracture in the worst case, which gives a limitation to this method. Torsional strength is also affected by the area subjected to shear deformation. The teeth of the shaft were sheared by torsional loading in this experiment since the length of AB is much shorter than that of CD as shown in Fig. 13. If the lengths of AB and CD are designed so that shear deformation occurs at both planes simultaneously, the torsional strength will be further improved.
4. Conclusions A new method to assemble spline joints by forming was introduced in this study. A shaft with an external spline was pushed into a disk with an internal spline, in which the internal spline was designed so that a part of teeth overlapped over the external spline. Experiments using medium carbon steel were carried out, varying the overlap length and tapered angle of the tooth side. Axial strength of the joint was achieved by frictional contact at the interface of teeth and increased with increase in the overlap length. Torsional strength was also increased with increasing the overlap length and showed about more than 1.2 times higher values compared with a conventional spline joint by fitting. Two kinds of spline teeth were tested (type I with straight tooth sides and type II with tapered tooth sides) and the torsional strength was increased with the overlap length in the type I specimens, while it took a peak at a certain tapered angle in the type II specimens. Differences in torsional strength were explained based on the difference in deformation of the teeth and the distribution of hardness around the contact faces.
References
Fig. 13. Schematic illustration of shear deformation planes by torsional loading.
Abe, Y., Mori, K., Kato, T., 2012. Joining of high strength steel and aluminium alloy sheets by mechanical clinching with dies for control of metal flow. Journal of Materials Processing Technology 212, 884–889. Alves, L.M., Martins, P.A.F., 2013. Single-stroke mechanical joining of sheet panels to tubular profiles. Journal of Manufacturing Processes 15, 151–157.
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Egami, Y., Nakamura, Y., Hiraoka, T., Machida, T., 1997. Torsional strength of camshaft assembled by shave-joining method. Journal of JSTP 38 (441), 941–945 (in Japanese) 1. Hirota, K., Kitamura, K., Ukai, Y., Matsunaga, K., 2012. Plastic-flow joining of shaft and disk for providing high torsional strength. Steel Research International Special Edition: Metal Forming 2012, 603–606. Kanamaru, H., Tsuruoka, K., Oku, M., Tatsumi, H., 1984. Development of metal flow (combination with plastic flow) and application to automotive parts. JSAE Review 14, 83–89. Kitamura, K., Hirota, K., Ukai, Y., Matsunaga, K., Osakada, K., 2012. Cold joining of rotor shaft with flange by using plastic deformation. CIRP Annals – Manufacturing Technology 61, 275–278.
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Miyazawa, K., Miwa, M., Tashiro, A., Aoki, T., Kubota, M., Kondo, Y., 2011. Improvement of torsional fretting fatigue strength of splined shaft used for car air conditioning compressors by hybrid joint. Journal of Solid Mechanics and Materials Engineering 5 (12), 753–764. Nigrelli, V., Pasta, S., 2008. Finite-element simulation of residual stress induced by split-sleeve cold-expansion process of holes. Journal of Materials Processing Technology 205, 290–296. Shen, L.J., Lohrengel, A., Schäfer, G., 2012. Plain–fretting fatigue competition and prediction in spline shaft-hub connection. International Journal of Fatigue 52, 68–81.
Please cite this article in press as: Hirota, K., et al., Strength of spline joints assembled by forming. J. Mater. Process. Tech. (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.02.007
ARTICLE IN PRESS
PROTEC-13894; No. of Pages 7
Journal of Materials Processing Technology xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Strength of spline joints assembled by forming Kenji Hirota a,∗ , Kazuhiko Kitamura b , Yoshihiko Ukai c , Keiichi Matsunaga d a
Department of Materials Science and Engineering, Kyushu Institute of Technology, Kitakyushu, Fukuoka 804-8550, Japan Department of Mechanical Engineering, Nagoya Institute of Technology, Nagoya, Aichi 466-8555, Japan c Toyota Motor Corporation, Toyota, Aichi 471-8571, Japan d MEG Inc., Anjo, Aichi 446-0052, Japan b
a r t i c l e
i n f o
Article history: Received 28 June 2013 Received in revised form 20 January 2014 Accepted 2 February 2014 Available online xxx Keywords: Spline joint Torsional strength Assembly by forming
a b s t r a c t In this paper, a new assembling method of spline joints that enables tight fitting in a simple manner by allowing slight plastic deformation at the spline teeth was introduced. Experiments were carried out for the spline joints of medium carbon steel varying the overlap zone between the male and the female spline teeth. Axial joining strength was increased with increase in the overlap length due to the residual compressive stress by forming. The joint by the proposed method also showed higher torsional strength than the conventional joint. Improvement in the torsional strength was explained based on the deformation and hardness distribution around the spline teeth. With respect to the shape of overlap zone, better results were obtained when using the specimen having a uniform overlap length along the axial direction. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Spline-hub connections are reliable mechanical joints for torque transmission and widely applied to automotive parts. Since these joints are mostly subject to cyclic loading, the evaluation of fatigue strength has been a main concern. Shen et al. (2013) developed a plain-fretting fatigue unified prediction model and discussed the plain and fretting fatigue performance of involute spline shaft-hub connection teeth. It is generally said that increase in residual compressive stress at the interface of the joint is effective to improve the fatigue strength. Miyazawa et al. (2011) combined a press fit joint with a spline-joint and demonstrated that the joint proposed showed higher torsional fretting strength than conventional spline-joints. Nigrelli and Pasta (2007) evaluated the residual stress induced around the hole by split-sleeve cold expansion for the purpose of assessment of fatigue life. Joining by forming is also advantageous for improving the fatigue strength and has various excellent features of no heat influence and resulting thermal deformation, high productivity and joinability of dissimilar materials. Spot joining methods such as clinching and self-piercing riveting are the typical examples and
∗ Corresponding author at: Department of Materials Science and Engineering, Kyushu Institute of Technology, 1-1, Sensui-cho, Tobata-ku, Kitakyushu, Fukuoka 804-8550, Japan. Tel.: +81 93 884 3369; fax: +81 93 884 3369. E-mail address: [email protected] (K. Hirota).
many attempts have been made for the sheet metal parts in which spot welding can not be applied. Abe et al. (2012) reported the possibility of joining high strength steel and aluminum alloy sheets by mechanical clinching. Joining of a shaft and a disk-like part by forming has also been tried. Kanamaru et al. (1984) created a mechanical shaft-disk connection by forging the disk in such way that the material of the disk fills the grooves on the shaft. Alves and Martins (2013) developed a single stroke mechanical joining process to fix sheet panels to tubular profiles and applied it to automotive parts. Egami et al. (1997) developed a new manufacturing method for serration joints: a serration joint was obtained by pushing a serrated shaft into the hole of a mating part so that the serrations of the shaft shave the hole surface. In this method, the serrated shaft acts as a shaving tool and hence the shaft should be much harder than the hole. This process was applied to join a cam plate to a shaft and the joint obtained exhibited enough torsional fatigue strength. The authors proposed a similar method for serration joints by using cold forward extrusion: Kitamura et al. (2012) summarized the joining mechanism and optimum conditions to achieve high torsional strength and Hirota et al. (2012) investigated the effect of the shape of serrations and the rigidity of the disk on the joining strength. However, this method cannot be applied to such joints that the male and the female parts are made of the same material. In order to overcome the problem, a new method was proposed in this study. Through the experiments varying the amount of deformation, spline joints of medium carbon
http://dx.doi.org/10.1016/j.jmatprotec.2014.02.007 0924-0136/© 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: Hirota, K., et al., Strength of spline joints assembled by forming. J. Mater. Process. Tech. (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.02.007
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Fig. 1. Schematic of assembling method of serration joint by forming.
steel were successfully assembled and showed higher torsional strength than a conventional joint not accompanied by plastic deformation. 2. Mechanical joint assembled by forming 2.1. Assembling of serration joint by forming In the production of spline joints or serration joints, precise machining, which is time and cost consuming, is required to achieve a tight fit tolerance for enough fatigue strength. The authors developed a new method to obtain a tight-fit serration joint with high productivity. The procedure of the process is illustrated in Fig. 1. A shaft having serrated portion at one end and a disk with a hole at the center are prepared. The serration is given to the shaft by forward extrusion and hardened by carburizing and quenching if the disk is as hard as the shaft. The diameter of the hole is determined so that the overlap ratio of the tooth and the hole ı/h is equal to about 0.5. Next, the shaft is pushed into the hole up to the end of the serrated zone, where each tooth of the serration is indented on the surface of the hole and a mechanical engagement is created in the circumferential direction between the shaft and the disk. Thus, tight fitting is achieved in a simple operation due to the residual compressive stress by indenting. Kitamura et al. (2012) and Hirota et al. (2012) reported the optimum conditions for the lead angle ˛ and the overlap ratio ı/h to achieve high torsional strength. 2.2. Assembling of spline joint by forming The method in Fig. 1 has a limitation for the combination of materials to obtain a successful joint, i.e. the teeth of serrations should be approximately three times harder than the hole surface, otherwise the serrations collapse and no mechanical engagement is formed. In this paper, a new method was proposed to overcome the limitation. Dimensions of the spline-disk joint targeted in this study are illustrated in Fig. 2(a). A straight sided spline (designation: 6 × 18 × 22, ISO 14-1982) is provided with the shaft, while the mating teeth in the hole are designed so that a part of the tooth overlaps by ˇ per side against the tooth of the shaft. As the external spline is pushed into the internal spline, either or both of the teeth deform at the overlap zone and the spline joint tightly fitted by the residual stress on the resulting interface is obtained. This method will be applicable between the same materials since the amount of deformation is much less compared with the previous method as shown in Fig. 1. A constant gap of 0.2 mm is given at the miner diameter of the spline so that the material deformed
at the overlap zone escapes to the gap. Contrarily, no gap (with a tolerance of 0.02 mm) is given at the major diameter to assure the coaxiality and the perpendicularity of the disk to the shaft in assembling. In this method, the overlap length is considered to be the most important factor for the assembling load and the strength of the joint and hence, varied in two ways as shown in Fig. 2(b). The type I specimen has straight tooth sides and the overlap length is uniform along the axial direction, while the type II specimen has tapered tooth sides and the overlap length increases along the axial direction. The parameter sets in the experiments are summarized in Table 1, where test cases 5 and 6 are used for comparison at approximately the same overlap length (ˇ ∼ = ˇ ) between different types of disk specimens and case 7 as a reference sample of the conventional spline joint. Both the shaft and disk were made of medium carbon steel containing 0.45 wt% C (S45C (JIS)) and the spline teeth were processed by wire electro discharge machining. Since fitting is achieved by plastic deformation in this method, the manufacturing tolerance for tooth dimensions will be rather relaxed compared with that for conventional spline joints. Therefore, the teeth can be processed by forward extrusion and machine finishing of the major diameter and the type II specimens were designed based on such a processing method. The shaft and the disk were set on a die set as shown in Fig. 2(c), where the coaxiality and the position of the teeth in the circumferential direction were adjusted by the chamfers at the shaft and the hole edges, and two positioning pins, respectively. The die set was loaded by a hydraulic press at a rate of 5 mm/s and the shaft was pushed into the disk to the depth of 4 mm, where load-stroke data were measured by means of a strain gauge load cell (capacity: 200 kN) and a contact type displacement sensor (ranges: 0–10 mm). The assembled joints were subjected to strength tests. The axial strength was evaluated with the load to withdraw the shaft from the disk by using the same die set system for assembling. A torsion test was carried out as follows: both ends of the joint were fixed on the testing machine with bolts and the shaft side of the joint was rotated, where torque-torsional angle data were measured by means of a torque meter (capacity: 1kN· m) and a rotary encoder (resolution: 0.1◦ ) as shown in Fig. 2(d).
3. Results and discussions 3.1. Deformation behavior in assembling Assembling was carried out at the cases 1–4 of Table 1 and the load-stroke curves were obtained as shown in Fig. 3. The curves for type I specimens showed a logarithmic increase, meanwhile those for type II specimens an exponential increase. In order to compare the load between the type I and II specimens, the maximum overlap length is calculated for the type II specimens according to the following equation: ˇ = L tan , where L and are the engaged length and the tapered angle of the tooth side, respectively. Referring to the values of ˇ and ˇ as listed in Table 1, assembling load seems to obey the order of the overlap length. Fig. 4 shows the appearance of the spline teeth observed after disassembling the joint. The overlap zone of the teeth was deformed and the step was formed as indicated by the arrows. In all cases, neither fracturing nor adhesion was observed and the deformation of the teeth was remarkable when ˇ or was large. In the type I specimens, both teeth of the shaft and the disk deformed evenly and the step was formed on the shaft side. On the contrary in the type II specimens, deformation was only found on the disk: the overlap zone of the disk seems to be shaved by the shaft tooth and accumulate toward the assembling direction.
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Fig. 2. Experimental conditions ((a) geometry and dimension of spline teeth and (b) type of disk specimen) and setup for (c) assembling and (d) static torsion test.
Table 1 Test conditions. Case
Disk type
Overlap length ˇ(see Fig. 2(b)
Tapered angle of tooth (see Fig. 2(b))
1 2 3
Type I Type I Type II
0.2 mm 0.4 mm –
4
Type II
–
5 6
Type I Type II
0.3 mm –
7
Type III
–
– – 2◦ (ˇ = 0.14 mm) 4◦ (ˇ = 0.28 mm) 6◦ (ˇ’ = 0.42 mm) –
Remarks
For comparison of torsional strength at approximately the same overlap length (between case 4 and 5) For comparison of torsional strength at approximately the same overlap length (between case 2 and 6) Conventional joint (Fitting tolerance = 0.02 mm)
Fig. 3. Assembling load – stroke curves obtained by using the setup as shown in Fig. 2(c).
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Fig. 4. Appearance of teeth observed after disassembling the joint.
3.2. Strength of the joint The strength of the joints was measured in the manner as mentioned in Section 2.2. Fig. 5 shows a comparison of the axial strength of the joint, in which the right ordinate indicates the resistance required for withdrawing the shaft calculated assuming that the contact area is L × h (see Fig. 2(b)). The axial strength was higher in type I specimens than in type II specimens and the magnitude of ˇ and caused a little difference. The axial strength per unit area resulted in the order of several tens of mega-pascals in all cases, which is rather low compared with the shear strength of the medium carbon steel. Low strength is due to neither adhesion at the interface nor mechanical engagement in the axial direction. Therefore, the shaft is considered to be supported in the disk by frictional contact at the teeth. Fig. 6 shows the comparison of torque-torsional angle curves. The difference in torque is obvious at the beginning of loading but disappears as torsion proceeds. Yield torque was estimated by the limit of linearity for each curve. Fig. 7 shows the relationship between the yield torque and the overlap length, in which the overlap length in the type II specimens is plotted using the
Fig. 5. Axial strength of the joint estimated from disassembling force of the joint.
Fig. 6. Torque-torsional angle curves by torsion tests of the joint.
corresponding value ˇ (see. Fig. 2(b)). The joints by the proposed method showed over 1.2 times higher yield torque than the conventional joint (case 7) and the yield torque was increased with increase in the overlap length.
Fig. 7. Relationship between yield torque and overlap length.
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Fig. 8. Vickers hardness distribution on the cross section of the shaft at L = 4 mm.
Fig. 9. Difference in deformation of the shaft after torsion tests in type II specimens.
3.3. Effect of forming on torsional strength When the joint was twisted plastically, the teeth of the shaft were sheared along the root circle of the external spline. In order to investigate the effect of plastic deformation on the torsional strength, hardness of the shaft around the contact surface was measured after disassembling the joint. Fig. 8 shows the distribution of Vickers hardness around the tooth of the shaft. The data for = 2◦ is omitted since it was almost the same as that for = 4◦ . The initial
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Fig. 11. Relationship between yield torque and overlap length (plots for ˇ = 0.3 mm and = 6◦ are added to Fig. 7).
hardness of the shaft and the disk was distributed between HV190 and HV210 and heat affection by wire cut EDM was little observed at a depth more than 0.1 mm from the surface. The plots for ˇ = 0.4 mm (case 2) resulted in higher values than the others near the root circle, which corresponds to the highest torque at case 2 in Fig. 7. Therefore, the improvement in yield torque in the type I specimens is caused by workhardening. On the other hand, the plots except ˇ = 0.4 mm showed little workhardening and hence the reason for higher torque at these conditions than the conventional joint might be enough contact pressure as well as no gap between mating teeth by plastic deformation. However, higher torque at = 4◦ than those at = 2◦ and ˇ = 0.2 mm cannot be explained by the above reasons. From the observation of deformation of the teeth after twisting, a distinctive difference was found depending on the magnitude of as shown in Fig. 9, i.e. the top face of the shaft tooth was swelled at = 2◦ by torsional loading and wasn’t swelled at = 4◦ . As shown in Fig. 4, a large step was formed on the disk teeth at = 4◦ so as to surround the top portion of the shaft tooth. Therefore, such steps probably served to prevent the top portion of the shaft teeth from swelling when the joint was twisted. In order to estimate the effect of the step on the torsional strength, three dimensional FE analysis was performed using an implicit commercial code, DEFORM-3D. Details of the analysis are
Fig. 10. FE model for evaluation of the effect of “step” on torsional strength.
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Fig. 12. Difference in deformation of the teeth depending on the tapered angle.
shown in Fig. 10. A pair of engaged teeth was modeled, where the tooth of the disk was approximated as a rigid body since it showed little plastic deformation in the torsion test. The tooth of the shaft was sheared by two kinds of mating teeth in the arrow-indicated direction. The result was that the stepped tooth (Fig. 10(a)) showed approximately 1.1 times higher yield shear force than the nonstepped tooth (Fig. 10(b)). Accordingly, the reason for higher torque for = 4◦ than those for = 2◦ and ˇ = 0.2 mm is that the step formed around the tooth increases the shear resistance of the tooth in twisting the joint. In order to compare the yield torque at approximately the same overlap length between the types I and II specimens, additional experiments were carried out at ˇ = 0.3 mm (case 5) and = 6◦ (case 6). The data obtained is superimposed on Fig. 7 and shown in Fig. 11. In the type I specimens, a linear increasing relationship was obtained between the yield torque and the overlap length and further improvement in the torsional strength will be possible with increase in ˇ. Meanwhile, the yield torque of the type II specimens took a peak at = 4◦ . Comparison of the appearance of the teeth at these conditions was shown in Fig. 12. The step observed at = 4◦ wasn’t formed at = 6◦ in spite of the increased overlap length,
which implies that the deformation would not be localized around the interface but prevail uniformly inside the teeth. Although increase in ˇ or is effective for improving the torsional strength, it also increase the assembling load and may cause distortion of the shaft and the disk, or fracture in the worst case, which gives a limitation to this method. Torsional strength is also affected by the area subjected to shear deformation. The teeth of the shaft were sheared by torsional loading in this experiment since the length of AB is much shorter than that of CD as shown in Fig. 13. If the lengths of AB and CD are designed so that shear deformation occurs at both planes simultaneously, the torsional strength will be further improved.
4. Conclusions A new method to assemble spline joints by forming was introduced in this study. A shaft with an external spline was pushed into a disk with an internal spline, in which the internal spline was designed so that a part of teeth overlapped over the external spline. Experiments using medium carbon steel were carried out, varying the overlap length and tapered angle of the tooth side. Axial strength of the joint was achieved by frictional contact at the interface of teeth and increased with increase in the overlap length. Torsional strength was also increased with increasing the overlap length and showed about more than 1.2 times higher values compared with a conventional spline joint by fitting. Two kinds of spline teeth were tested (type I with straight tooth sides and type II with tapered tooth sides) and the torsional strength was increased with the overlap length in the type I specimens, while it took a peak at a certain tapered angle in the type II specimens. Differences in torsional strength were explained based on the difference in deformation of the teeth and the distribution of hardness around the contact faces.
References
Fig. 13. Schematic illustration of shear deformation planes by torsional loading.
Abe, Y., Mori, K., Kato, T., 2012. Joining of high strength steel and aluminium alloy sheets by mechanical clinching with dies for control of metal flow. Journal of Materials Processing Technology 212, 884–889. Alves, L.M., Martins, P.A.F., 2013. Single-stroke mechanical joining of sheet panels to tubular profiles. Journal of Manufacturing Processes 15, 151–157.
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Egami, Y., Nakamura, Y., Hiraoka, T., Machida, T., 1997. Torsional strength of camshaft assembled by shave-joining method. Journal of JSTP 38 (441), 941–945 (in Japanese) 1. Hirota, K., Kitamura, K., Ukai, Y., Matsunaga, K., 2012. Plastic-flow joining of shaft and disk for providing high torsional strength. Steel Research International Special Edition: Metal Forming 2012, 603–606. Kanamaru, H., Tsuruoka, K., Oku, M., Tatsumi, H., 1984. Development of metal flow (combination with plastic flow) and application to automotive parts. JSAE Review 14, 83–89. Kitamura, K., Hirota, K., Ukai, Y., Matsunaga, K., Osakada, K., 2012. Cold joining of rotor shaft with flange by using plastic deformation. CIRP Annals – Manufacturing Technology 61, 275–278.
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Miyazawa, K., Miwa, M., Tashiro, A., Aoki, T., Kubota, M., Kondo, Y., 2011. Improvement of torsional fretting fatigue strength of splined shaft used for car air conditioning compressors by hybrid joint. Journal of Solid Mechanics and Materials Engineering 5 (12), 753–764. Nigrelli, V., Pasta, S., 2008. Finite-element simulation of residual stress induced by split-sleeve cold-expansion process of holes. Journal of Materials Processing Technology 205, 290–296. Shen, L.J., Lohrengel, A., Schäfer, G., 2012. Plain–fretting fatigue competition and prediction in spline shaft-hub connection. International Journal of Fatigue 52, 68–81.
Please cite this article in press as: Hirota, K., et al., Strength of spline joints assembled by forming. J. Mater. Process. Tech. (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.02.007