Producing Hollow Shafts in a New Horizontal Mill by Novel Flat-Kning Cross-Wedge Rolling With Single Guide

To meet the requirement of lightweight, there are increasing solid shafts being 30 designed to be hollow in transportation industry. In this study, a novel method of flat- 31 knifing cross-wedge rolling (FCWR) with single guide is proposed including a 32 modified roller, a horizontal mill and a single-guide structure, and its key problems are 33 studied by numerical simulations and experimental tests. A mathematical model of 34 FCWR roller is established, which reveals the wedge length of rollers is effectively 35 reduced by modifying knifing wedge from normalized roller. Further, a horizontal 36 multifunctional mill is invented and constructed to carry out the FCWR experiment 37 with single guide. According to the results from the numerical simulations and 38 corresponding experiments, it is observed that the typical defects of hole expansion and 39 knifing groove are absolutely avoided because the improved flat-knifing wedge 40 produces a radial force to shrink the inner hole and avoid the deformation concentration 41 of the outer surface during knifing stage. Moreover, the single guide rolling performed 42 in the horizontal mill efficiently improve rolling stability because the workpiece is 43 restricted into a smaller workspace. To the authors’ knowledge, a ll these integrated 44 improvements of FCWR roller, single guide rolling and horizontal mill are innovative, 45 which are of great engineering significance to manufacture hollow shafts on account of 46 the advantages of avoiding forming defect, reducing roller diameter, improving rolling 47 stability and simplifying mill structure.


Producing hollow shafts in a new horizontal mill by novel flat-
Mandrel diameter 63

D0, d0
Outer and inner diameter of workpiece before rolling 64

D1, d1
Outer and inner diameter of workpiece after rolling 65

LR
Wedge length reduction from NCWR to FCWR 69

Introduction 71
Since hollow shafts have advantages of lightweight structure, low rotating inertia 72 and convenient flaw detection, more and more solid parts are designed to be hollow 73 such as railway axles [1], engine valves [2], and truck shafts [3]. Up to now, these 74 hollow shafts are mainly formed by forging, extrusion and drilling, which result in the 75 waste of material and low production efficiency. 76 Cross wedge rolling (CWR), a near-net shape metal manufacturing process with 77 high production efficiency and low material consumption, has an extensive application 78 in solid shafts including large-elongated parts (e.g., automobile camshafts, stepped 79 shafts) and die-forging preforms (e.g., engine valves, connecting rods, double-ended 80 spanners) as reviewed by Hu  To establish a reliable technique for rolling hollow shaft, CWR without mandrel 100 was early proposed and investigated. Bartnicki and Pater [9,10] analyzed the numerical 101 simulation results and found the thinner wall thickness may cause the slipping and 102 flattening of billet, and concluded the three-roller CWR can improve rotation conditions. 103 Urankar et al. [11] proposed a dimensionless crushing parameter to predict forming 104 limit of the hollow products, and the defect of hole expansion was shown in their study. 105 However, CWR without a mandrel has a common shortcoming that its inner hole is 106 unable to be regularly formed because the hole is formed randomly. 107 A process of CWR with mandrel was proposed to control the dimensions of inner 108 hole, and researches have been done to improve its forming performance. groove occur in the knifing position of rolled shafts. Therefore, modifying the shape of 125 roller on knifing zone is of great significance. flat-knifing CWR 128 In this study, a novel flat-knifing cross-wedge rolling (FCWR) with single guide 129 for hollow shafts (Fig.1b) is proposed whereby modifying roller and mill from the base 130 of normalized cross-wedge rolling (NCWR), which takes advantages of avoiding the 131 defects of hole expansion and knifing groove, reducing the diameter of rollers, 132 improving rolling stability and simplifying mill structure. 133 In order to study the new process systematically, its key points are investigated by 134 numerical simulation and experimental research. Firstly, the new process of FCWR 135 with single guide is described in detail. Secondly, the mathematical model of FCWR 136 roller is established and the length reduction is calculated and visually presented. 137 Thirdly, numerical simulations are conducted to compare the NCWR and FCWR 138 process from the aspects of defect formation mechanisms, workpiece deformation 139 characteristics and influences of new parameter. At last, corresponding physical FCWR 140 experiments are performed to verify the FE results, and the advantages and 141 disadvantages of these improvements are discussed.
2 Flat-knifing cross-wedge rolling with single guide 143

Novel process principle 144
The process principles of normalized cross-wedge rolling (NCWR) with two 145 guides and flat-knifing cross-wedge rolling (FCWR) with single guide are shown in Fig.  146 2. They have same deform mechanism that a cylindrical hollow billet is deformed into 147 a stepped hollow shaft under the action of roller whereby wedged rollers moving 148 tangentially relative to each other. 149 There are some improvements: 1) the knifing wedge of FCWR roller is flatted, 151 while that of NCWR is sharped; 2) differing from NCWR has a vertical structure, 152 FCWR process changes into a horizontal arrangement that can achieve single guide 153 rolling under gravity; 3) by single guide rolling, FCWR workpiece is steadily restricted 154 into a smaller workspace. As a result, the novel process is estimated has advantages of: 155 · the defects of hole expansion and knifing groove can be absolutely avoided; 156 · the diameter of two rollers can be evidently shortened; 157 · the mill can be simplified into single guide structure; 158

New type of horizontal multifunctional mill 160
In order to achieve the technical objective of single guide rolling, a laboratory mill 161 with a horizontal structure is indispensable. Up to now, the traditional CWR mills 162 commonly have a vertical structure [4,5,22], which apparently cannot meet the 163 requirement of this study. 164 Therefore, a new type of rolling mill is invented and constructed by the authors 165 [23]. The freedoms of this mill has been increased by two angle adjusting systems, one 166 radial feeding system, and a synchronous unit (worked by two matched gears). Its 3D 167 model is shown in Fig. 3, the mill is presented in Fig. 4, and the technical specifications 168 are given in Table. 1. 169  This mill is characteristic of multiple freedom degree because has several 175 movements of circumferential rotating, radial feeding and angle adjusting, and thus it 176 can be used for different types of laboratory rolling tests such as longitudinal rolling, 177 cross rolling, and skew rolling. 178 All the motions of this mill are directly driven by servo motors that mill structure 179 is compact. As signed in Fig.3, two C-type frames are used to enchence mill strength, 180 the automation system is controlled by a accurate servo drive which programed in PLC 181 language. All these features may take this type of mill advantages of compact structure, 182 high strength and high precision, so that it can be expected to be industrially applied as 183 thread rolling mill, ball rolling mill and CWR mill. 184

New type of flat-knifing roller 185
Roller modification is a main innovation of this paper. In the hope of 186 mathematically describing the FCWR roller in detail, both the geometrical models of 187 FCWR and NCWR roller are designed and shown in Fig. 5 with a plane layout way. 188 In order to mathematically compare FCWR and NCWR roller, the calculation of 204 wedge length is a basic work, which need to be undertaken primarily. 205 At the knifing zone, notwithstanding the different geometries, the wedge lengths 206 of FCWR and NCWR roller are equally formulated as Eq. 1, where h is the height of 207 wedge, α is forming angle, and β is the stretching angle. 208 1 1 cot cot At the stretching zone, because the initial position of FCWR wedge have a straight 210 section, LN2 is obviously longer than LF2, and they are respectively calculated by Eq. 2 211 and Eq. 3, where L represents the sizing width (signed in Fig. 5)  (3) 215 Owing to the geometries at sizing zone of NCWR and FCWR are exactly same, 216 they have same sizing length which can be formulated by Eq. 4, where D0 and D1 are 217 the outer diameter of the workpiece before and after rolling. 218 Because the length of each zone is determined through the above equations, the 220 length reduction LR can be calculated by Eq. 5. 221 For a purpose of a more intuitive comparison of the wedge length of roller, their 223 formulas are summarized in Table 2. It can be concluded that the lengths of knifing 224 wedge and sizing wedge of NCWR and FCWR roller are equal in value, while FCWR 225 stretching length is shorter than that of NCWR. 226 cot cot In order to visually reveal the relationship between wedge-length reduction and 228 process parameters, a three-dimensional graphic have been drawn as expressed in (2) The forming angle α. Forming angle is an important roller parameter, which 249 directly determines the contact surface of of forming area and then affects the metal 250 flow. In the reason that hollow billet is more prone to elliptical and then the axial flow 251 of the metal may become worse, the forming angle of the hollow shafts rolling is 252 generally greater than that of solid shafts, whose value is usually derived as follows： 253 30 °<α<50 ° (7) 254 (3) The stretching angle β. Stretching angle is another important tool parameter.

255
Increasing its value is beneficial to decrease the length of roller but enlarges the 256 tangential deformation of the workpiece, as a result, it is easy to cause oval deformation. 257 Therefore, the stretching angle for hollow shafts is generally smaller than solid shafts, 258 its range is： 259 1.5 °<β< 4.5 ° (8) 260 (4) The mandrel diameter dm. The mandrel is used to control the shapes and 261 dimensions of inner hole. When its diameter is too small, mandrel will unable to contact 262 inner hole and out of service. And when its value gets too large, it makes the rolling 263 wall thin seriously and wall deformation become severe, thus billet cannot rotate 264 normally. Its value is usually designed as Eq. 9, in which d0 is the initial diameter of 265 inner hole.  The FE projects of NCWR and FCWR with single guide were modeled as Fig. 8 shows. 292 Both the geometric models of NCWR and FCWR were consisted of two rollers, one 293 guide, one mandrel and one workpiece. The positional relationships between each part 294 were set up as marked in Fig. 2. The workpiece axis was downwardly offset from roller 295 centre with a 3 mm distance. The billet is C45 steel rod with an outer diameter of 50 mm, an inner diameter of 298 30 mm and a length of 100 mm. Its material data were taken from Simufact.Material. 299 The properties (i.e., density, Young's modulus and Poisson's ratio) were set as default. 300 The flow stress of C45 steel was defined by Eq. 11, in which σF is the flow stress (MPa), 301 φ is the eff ective strain (-) and T is the temperature (°C): The friction coefficients between tools and workpiece were modeled by Shear 304 model (two rollers were 0.8, guide and mandrel were 0.2. [28] The temperature of tools 305 (rollers, guide and mandrel) was constantly maintained at 300 °C [28]. The initial 306 temperature of workpiece was 1050 °C and the coefficient of heat transfer between tools 307 and workpiece was 10 kW/m 2 K [28]. Besides, the mesh of billet was created by 308 ringmesh mesher, whose element size equals to 1.4 mm, and will be automatically 309 reconstruected if the eff ective strain increases by 0.4 [28]. Both the NCWR and FCWR 310 rollers rotated at a same speed of 6 rpm. 311

Comparison of forming defects 312
Four FE results with the parameters of D0=50 mm, d0=30 mm, α=45 °, β=2 °, 313 dm=22 mm and B=18 mm was extracted from the software postprocessor and shown in 314 Fig. 9. With the help of the numerical simulation, the shape of rolling workpiece can be 315 acquired at every moment. But at the end of knifing stage, there is a difference that FCWR workpiece contacts with 320 mandrel while NCWR does not. Considering the values of mandrel diameters are the 321 same, it can be concluded that, the radial deformation of inner hole in FCWR process 322 is more serious than that in NCWR during the whole knifing stage. 323 The defects of hole expansion and knifing groove primitively appear on the 324 NCWR shafts at the middle of stretching stage regardless of whether it has mandrel or 325 not (Fig.9c). But in the case of FCWR shafts at this stage, these defects are completely 326 absent. Inversely, there is a hole shrinkage on the FCWR shaft without mandrel. As a 327 result, we can get the FE conclusion that: 1) no matter with or without mandrel, NCWR 328 rolled shafts universally have the defects of hole expansion and knifing groove; 2) 329 FCWR process without mandrel have a defect of hole shrinkage; 3) the FCWR process 330 with mandrel has a good geometric accuracy on outer and inner surface. The conclusion 331 optimistically verifies the technological assumptions, as a result, the FCWR with 332 mandrel was adopted on hollow shafts forming in later studies. 333

Hole expansion 334
Since hole expansion is a major defect in this study, it is necessary to reveal its 335 formation mechanism from aspects of contact surface, loading states and the shape of 336 inner hole (Fig. 10). 337 The contact surface of workpiece was drawn by Boolean subtraction operation in 340 CAD software, which has indicated the different of deformation morphology between 341 NCWR and FCWR. As shown the Fig. 10a, under the same forming angle α and 342 stretching angle β, the main difference between NCWR and FCWR contact surface is 343 that there is a rectangle contacting zone on the middle of FCWR workpiece. 344 Based on the drawn contact surface, the loading states can be acquired as Fig. 10b  345 shows. At the NCWR knifing stage, because AB and BA segments individually produce 346 a axial component on the side of knifing position, the inner hole is tensioned in axial 347 direction and then expanded radially. But in FCWR process, the added BB segment 348 provides a radial force during the knifing stage that promotes the radial flow of the 349 metal, and thus the inner hole is shrunk. Eventually, FCWR hole contacts with the 350 mandrel while NCWR does not (Fig. 10c). 351 In short, FCWR process has an added radial force during knifing stage, which is 352 helpful to the radial flow of the metal and then shrink the inner hole, so that the defect 353 of hole expansion can be avoided in principle. 354

Knifing groove 355
Another defect concerned about in this study is the knifing groove, which typically 356 appears on the CWR shafts regardless of whether they are hollow or solid [18,19]. 357 According to engineering practice, this defect can be avoided via chamfering the 358 knifing-wedge. Obviously, this method cannot solve this defect at design stage. The 359 geometric appearances of NCWR and FCWR workpiece are compared in Fig. 11. 360 The knifing groove initially appears on the NCWR shaft at the end of knifing stage 363 and then remains until the end. It can be explained that deformation concentration exists 364 on NCWR knifing area which makes the metal of surface undergo a severe local deformation. As a result, a groove appears on the knifing position. When it comes to 366 stretching and sizing stage, this defect is hard to be resolved because the height of 367 wedge is constant. In the FCWR process, there is a flat segment BB existing on the 368 middle as Fig. 10b shows, which can avoid the concentrated deformation that the defect 369 of knifing groove does not appeared fundamentally. 370

Hole ovality 372
The novel process introduces a new process parameter named knifing width B. 373 Since it has an influence on the ovality of inner hole, an observation section selected 374 from the axial centre of the workpiece are contrastively compared in Fig 12, which 375 demonstrates that, as the knifing width B increases, the ovalization of inner hole 376 becomes serious. 377 The ovality of inner hole has negative effect on rolling stability. When the ovality 379 of inner hole is too large, the radial deformation of workpiece will be unstable. Under 380 this situation, even if rollers are rotating normally, the slipped billet cannot rotate 381 regularly. Hence, considering elliptical hole is bad for rolling stability, the value of 382 knifing width should not be too large. 383

Rolling force and rotating torque 384
Rolling force in the radial direction and rotating torque are the basic data of rolling 385 equipment, which directly determine the capacity of mill and can be predicted by FE results as shown in Fig. 13. 387

Formation of the inner hole 397
The formation of inner hole is a critical problem of hollow shafts rolling, which 398 directly influences the forming accuracy and the rolled-wall performance. A cross-399 section is selected from the axial center of workpiece and observed at different rolling 400 stages as Fig. 14 shows. 401  Table 3, the mandrel is away from the inner hole and out of work at the 407 initial stage. However, as rolling process goes on, the inner hole becomes elliptical and 408 then workpiece is beginning to contact the mandrel. Latterly, under the double action 409 of mandrel and rollers, the ovality of inner hole becomes small and small and finally 410 growth into round. 411 The strain distribution of the workpiece is also obtained in Fig. 14

Rolling experiments 419
The experiments of FCWR hollow shafts with single guide were performed at 420 University of Science and Technology Beijing in the new type of horizontal mill. 421 Experimental tools consisted of two FCWR rollers, several mandrels and one guide as 422 shown in Fig. 15. 423 The process parameters of physical experiments corresponded to those of 425 numerical simulations as shown in Tab.3. The guide was mounted between two rollers 426 and downwardly offset from roller centre line with a 28 mm distance. 427 The rolling experiments was conducted as Fig. 16 shows. Prior to the rolling, the 428 billet was preheated to 1050 ℃ in an electric tube furnace and then immediately 429 transferred to the mill. During the rolling stage, the billet was rotated and deformed 430 under the action of rotating wedges of rollers. After the rolling, the rolled product laid 431 on the top of the guide and then hollow shaft was gained.  The grain size of rolled part is one of the most significant indicators, which decides 479 the mechanical properties of the hollow products. The microstructure morphology of 480 the rolled shaft is obtained in a microscope with 200 times magnification. As Fig. 20  481 shows, the grain sizes of the rolled regions (P1, P2) are significantly smaller than that 482 of unrolled region (P3), which can be explained that the grains are refined under FCWR 483 deformation. Besides, the grain size at the knifing position (P1) is smaller than that at 484 the stretching position (P2), which is consistent with the distribution of strain shown in 485 Fig.18d, and can be considered that the knifing zone has a larger deformation than the 486 stretching zone. 487 Although this new process has the above advantages, there are some disadvantages 489 as well. As arisen in the numerical simulations and physical experiments, the rolled 490 shaft cannot be automatically ejected from the mill so a new discharging device is 491 needed. Besides, FCWR process deteriorates the ellipse of hole and increases rolling 492 force and rotating torque. 493

Application to the solid shafts 494
For solid shafts, the FCWR advantage of avoiding hole expansion is no longer 495 necessary. However, it also takes advantages of avoiding knifing groove and reducing 496 the perimeter of rollers. 497 The major considerations for solid shafts rolling are whether billet can rotate 498 normally and whether central cracks can be avoided. On the one hand, because an BB 499 section (shown in Fig. 10b) is added at the knifing zone, the friction conditions at 500 knifing stage are improved theoretically owing to the contacting area increases. On the 501 other hand, the trend of central cracking is relieved because the added radial 502 compression-force is beneficial to metal bonding. And when it comes to stretching and 503 sizing stage, the deformation of NCWR and FCWR is the same. Therefore, it can be 504 estimated that this novel FCWR process can be used for solid shafts under the condition 505 of reasonable knifing width. 506

Summary and conclusions 507
In this paper, a novel process of flat-knifing cross-wedge rolling (FCWR) with 508 single guide was proposed to manufacture hollow shafts, including a CWR roller, single 509 guide rolling and a horizontal multifunctional mill. The following conclusions are 510 obtained: 511 (1) The defects of hole expansion and knifing groove are absolutely avoided 512 because FCWR roller produces a radial force to shrink the hole and avoids the 513 deformation concentration of outer surface during knifing stage; 514 (2) The new type of horizontal multifunctional mill can be used to perform 515 laboratory tests such as longitudinal rolling, cross rolling and helical rolling and expected to have industrial application as thread rolling mill, ball rolling mill and cross-517 wedge rolling mill; 518 (3) The single guide rolling can be realized by workpiece axis offset from the 519 center line of two rollers, and can improves the rolling stability and simplifies the mill 520 structure; 521 (4) The flat-knifing roller reduce the wedge length in the range of 200~800 mm; 522 (5) The process of flat-knifing cross-wedge rolling with single guide brings the 523 shortcomings of non-automatic ejecting, hole ellipse and increasement of rolling force 524 and rotating torque; 525 (6) The process of FCWR with single guide is estimated to form the solid shafts 526 under the condition that knifing width is designed reasonably. 527

Availability of data and materials 549
The datasets generated and/or analysed during the current study are available from 550 the corresponding author on reasonable request. 551

Consent to participate 552
Applicable. 553

Consent to publish 554
Applicable. 555  The constructed horizontal multifunctional mill           The FCWR produced hollow shafts: (a) initial status; (b) after shot peening  Hollow shafts formed by FCWR with single guide in the horizontal multifunctional mill Figure 20 Grain size of the FCWR rolled shaft at different locations