1 Introduction

Hot ring rolling (HRR) is an advanced metal working technology for manufacturing seamless rings. HRR has wide application in the industrial productions of various ring-type mechanical parts, such as bearing, flange rings, gear rings, and train wheels, due to its various significant advantages such as low energy and material consumption, good forming accuracy, and high efficiency [1,2,3,4].

However, to realize the ring rolling process, a redundant manufacturing chain from material to ring blank is needed, as shown in Fig. 1a; the large consumptions of energy, materials, and time in this process obviously decrease the technical-economical effect of ring rolling production. Aimed at this problem, some experts proposed a new combined casting-hot ring rolling technology, which directly processes the ring blank by casting and can short the conventional manufacturing chain and reduce the manufacturing consumption of ring blank significantly, as shown in Fig. 1b. The invention of this new ring rolling technology gains many attentions rapidly because of its apparent technical-economical superiority in industrial production, especially in the mass production of bearing rings.

Fig. 1
figure 1

a The conventional process chain of rings manufacturing with forged ring blank; b the new process chain of rings manufacturing with casted ring blank

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With the rapid development of advanced equipments in automobile, railway, energy, aviation, and astronavigation, the property requirements of rings continuously increase to meet the complicated and changeable working conditions. Under this environment, both of academic research and industrial production of HRR have mainly focused on the microstructure evolution in order to realize the maximum property improvement of rings in recent years. For conventional ring rolling process with forged ring blank, Qin et al. [5] studied the microstructure evolution in hot ring rolling of centrifugal casting Q235B steel; Chang et al. [6] did experimental research on some the hot ring rolling of centrifugally cast bimetallic rings. Sun et al. [7] revealed the effects of forming parameters on the grain evolution and recrystallization behavior of AISI 5140 alloy steel ring during hot rolling by FE simulation. Ryttberg and Wedel [8] investigated the microstructure and texture evolution in cold rolling of 100Cr6 ring experimentally. Wang et al. [9] modeled the microstructure evolution of titanium alloy during hot ring rolling using VUMAT subroutines. Qian and Pan [10] studied the distribution laws of grain sizes, dynamic recrystallization during blank forging, and ring rolling process. Tian et al. [11] studied the microscopic and macroscopic simulation of aluminum alloy rings by finite element simulation. Qi et al. [12] analyzed the effect of blooming temperature on radial-axial rolling forming of ring.

For ring rolling process with as-cast blank which is a new technology to manufacture rings, currently, the main research work is focused on reveling and controlling of microstructure evolution behavior, which is in favor of eliminating the cast defects. Guo et al. [13] proposed a multi-scale FE model of ring rolling process based on 42CrMo ingot blank and investigated the influence rules and mechanism of the rolling ratio on the recrystallized microstructure. Li et al. [14] studied the effects of initial rolling temperature on plastic deformation and dynamic recrystallization during hot ring rolling of as-cast 42CrMo ring blank based on DEFORM-3D. Li et al. [15] proposed using casting ring blank to form 42CrMo bearing ring and studied the microstructure evolution by FE simulation and experiment. Guo et al. [16] put forward a new approach coupling with both macroscopic and microscopic based on finite element theory and cellular automata model to reveal the deformation and microstructure evolution laws during casting-rolling compound forming process of as-cast 42CrMo alloy ring.

Above researches indicate that the microstructure evolution during HRR process has close dependence on the forming conditions like feeding amount, feeding speed, and temperature, which can provide important instruction for the microstructure improving by technological optimization. Nevertheless, as a widely used material for rings, especially for bearing rings, the microstructure evolution of as-cast 100Cr6 in HRR process regrettably gets few attentions and its correlations with the forming conditions are unclear, which obviously restricts the application of combined casting-hot ring rolling technology in bearing manufacturing. Therefore, in this study, using FEA and experiment, the accurate prediction of grain evolution during HRR of as-cast 100Cr6 steel is expectedly realized; the dependence between the grain evolution and the key forming conditions are expectedly revealed, and its instruction role for the grain improvement by optimizing of forming conditions is experimentally verified.

2 FE modeling for the HRR of as-cast 100Cr6

2.1 Microstructure evolution model of 100Cr6

Through hot compression experiments and mathematical modeling, the predicting models for the flow stress, austenite grain growth, and recrystallization behaviors of as-cast GCr15 (Chinese mark of 100Cr6) were developed as follows [17,18,19]:

  1. (a)

    Flow stress

$$\dot{\varepsilon}=3.326e12{\left[\sinh \left(0.00824\sigma \right)\right]}^{-4.80311}\exp \left(-306005/ RT\right)$$
(1)

where \(\dot{\varepsilon}\) is the stain rate; R is the universal gas constant (8.31 J·mol−1·K−1); T is the absolute temperature (K); Q is the activation energy of hot deformation (KJ·mol−1); σ is the true stress (MPa).

  1. (b)

    Austenite grain growth

$${d}_g=\sqrt[4.133]{d_0^{4.133}+6.685\times {10}^{31}t\exp \left(-6.8\times {10}^5/ RT\right)}$$
(2)

where dg is the average austenite grain size at holding time of t (μm); d0 is the initial average austenite grain size; t is the holding time (s).

  1. (c)

    Dynamic recrystallization (DRX)

$${\varepsilon}_c=0.78{\varepsilon}_p$$
(3)
$${\varepsilon}_p=0.0338{d}_0^{0.0342}{\dot{\varepsilon}}^{0.1968}\exp \left(23550/ RT\right)$$
(4)
$${\varepsilon}_{0.5}=0.0087{d}_0^{0.0841}{\dot{\varepsilon}}^{0.1733}\exp \left(35484/ RT\right)$$
(5)
$${X}_{drex}=1-\exp \left[-2.67{\left(\frac{\varepsilon -{\varepsilon}_c}{\varepsilon_{0.5}}\right)}^{1.036}\right]$$
(6)
$${d}_{drex}=7.751{d}_0^{0.410}{\varepsilon}^{-0.586}{\dot{\varepsilon}}^{-0.0057}\exp \left(-8834.6/ RT\right)$$
(7)

where εc is the critical strain; εp is the peaking strain; ε0.5 is the strain of 50% dynamic recrystallization; Xdrex is the dynamic recrystallization fraction; ddrex is the grain size of DRX (μm); ε is the strain.

  1. (d)

    Static recrystallization (SRX)

$${t}_{0.5}=2.04\times {10}^{-13}{d}_0^{0.01}{\varepsilon}^{-3.29}{\dot{\varepsilon}}^{-1.07}\exp \left[225860/(RT)\right]$$
(8)
$${X}_{srex}=1-\exp \left[-0.693{\left(t/{t}_{0.5}\right)}^{0.35}\right]$$
(9)
$${d}_{srex}=6380{d}_0^{0.32}{\varepsilon}^{-0.3}{\dot{\varepsilon}}^{-0.04}\exp \left(-23763/ RT\right)$$
(10)

where Xsrex is the static recrystallization fraction; t0.5 is the time for the recrystallizing volumetric fraction of 50% (s); dsrex is the grain size of SRX (μm).

  1. (e)

    Average grain size

$${d}_a={X}_{drex}\times {d}_{drex}+{X}_{srex}\times {d}_{srex}+\left(1-{X}_{drex}-{X}_{srex}\right)\times {d}_0$$
(11)

Above-mentioned models had been proved that can accurately describe the microstructure evolution behaviors of as-cast 100Cr6 during hot deformation process, and they were employed for FE modeling process.

2.2 FE modeling

Hot ring rolling is a rolling process of hot processing. In the hot rolling process, the drive roll is active roll which is driven and rotated by the main motor of the ring rolling mill through the reducer, guide roller, and mandrel are follower rolls that can rotate freely, the initial temperature of the ring is heated to 1150 °C.

Based on material models, a subroutine of microstructure evolution model of as-cast 100Cr6 is developed using FORTRAN language under SIMUFACT environment, and it was embed into the coupled thermo-mechanical FE model of HRR (Fig. 2) to realize the microstructure evolution analysis during the simulation process according to the calculated field variables of macrodeformation. The flow chat of microstructure evolution modeling in subroutine is shown in Fig. 3.

Fig. 2
figure 2

3-D coupled thermo-mechanical FE model of HRR

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Fig. 3
figure 3

Flow chart of microstructure modeling steps during ring rolling

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The thermophysical properties of material are given by the soft. The average grain size of ring blank in FE model is 60 μm, which was set by measuring and evaluating the actual as-cast 100Cr6 ring blank. The main parameters of the FE model considering the HRR experimental verification are given in Table 1.

Table 1 Main parameters of FE model
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In Table 1, the rolling ratio K is defined as [20]:

$$K={A}_0/A$$
(12)

where A0 and A are the cross-section areas of the ring blank and the rolled ring, respectively. In this paper, the rolling ratio K can be defined as the ratio of the thickness of ring blank H0 to the thickness of rolled ring H without considering the height change of the rolled ring.

The key techniques for FE modeling can be described as follows:

  1. (1)

    The rolls are considered as isothermal analytical rigid bodies and their deformation and temperature variations are ignored to diminish computational calculation time. The workpiece is defined as a deformable body.

  2. (2)

    The hexahedron element with eight nodes is adopted to discrete the workpiece. In addition, the adaptive re-meshing technique is also employed to deal with the problem of element distortion.

  3. (3)

    The axial metal flow of the end surfaces of workpiece is constrained to symbolize the close rolling pass effects on the ring in actual HRR experiment.

  4. (4)

    Three contact pairs are defined between the driver roll and the workpiece, the mandrel and the workpiece, and the guide roll and the workpiece, respectively. Heat generation and heat transmission are set at the interface of each contact pair; heat radiation is considered between the workpiece and the ambient environment. Coulomb friction is adopted between each contact pair.

2.3 Experimental verification

To testify the reliability of the FE model, HRR experiment of as-cast 100Cr6 was carried out on D51-350 NC HRR mill, and the related experimental parameters are same with the FE model shown in Table 1. As shown in Fig. 4, three rolled rings with different deformation amount were obtained by HRR experiment. The radial feeding degree is defined as the ratio of the feeding amount ΔH to total radial thickness reduction ΔHtotal.

Fig. 4
figure 4

HRR experiment of as-cast 100Cr6: a D51-350 NC HRR mill; b HRR process; c rolled rings under different deformation amount

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The comparison of temperature of the rolled rings between experiment and simulation is shown as Fig. 5, and the maximum relative error between the actual temperature of the thermometer and the simulation temperature is within 5%, which indicates that the model is reliable.

Fig. 5
figure 5

Comparison of temperature of the rolled rings between experiment and simulation

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The comparison of average grain size of the rolled rings between experiment and simulation was performed, as shown in Fig. 6, and Fig. 7 shows the experimental results of grain size distribution in inner layer under different deformation amount. Here, considering the nonuniform grain distribution, two points located at the outer layer and inner layer of the rolled rings are selected respectively for comparison; the experimental values of grain sizes were observed by Zeiss metallographic microscope and measured using linear intercept method; the simulated grain sizes were calculated by the FE model in Section 2.2. Figure 6 indicates that the simulated values of grain size are in good agreements with the experimental ones; thus, the FE model is testified valid and reliable to predict the grain evolution during the HRR process of as-cast 100Cr6.

Fig. 6
figure 6

Comparison of average grain size of the rolled rings between experiment and simulation: a outer layer; b inner layer

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Fig. 7
figure 7

Experimental results of grain size distribution in inner layer during rolling process: a 0%; b 25%; c 63%; d 100%

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3 Results and discussions

Employing the developed FE model, the prediction of grain evolution behavior during HRR of as-cast 100Cr6 can be realized. In HRR process, rolling ratio K, feeding rate v, rotational speed n, and initial rolling temperature T are the four key process parameters directly affected the field variables of strain, stain rate, and temperature, which are regarded as the critical factors for the grain evolution. So, in this paper, the HRR processes with different values of the four process parameters are simulated so as to investigate the response behaviors of the grain evolution to the forming conditions.

3.1 Simulation conditions

Four groups of forming conditions are considered in HRR simulations.

  • Case 1: K = {1.1, 1.5, 1.7, 1.8, 2.0}, v = 4.0 mm/s, n = 70 r/min, T = 1150 °C

  • Case 2: v = {1.0, 2.0, 3.0, 4.0} mm/s, K = 1.5, n = 70 r/min, T = 1150 °C

  • Case 3: n = {50, 60, 70, 80} r/min, K = 1.5, v = 4.0 mm/s, T = 1150 °C

  • Case 4: T = {950 °C, 1050 °C, 1150 °C, 1250 °C}, K = 1.5, v = 4.0 mm/s, n = 70 r/min

3.2 Evaluated indices for discussion

It is obvious that the grain size and grain distribution have close relevance with the material property, and the fine and uniform grains usually means the good mechanical property, which are expectedly obtained by forming process. Hence, two parameters are adopted to describe the grain evolution during the HRR process. One parameter is refinement degree of grain RDG; it is defined as:

$$RDG=\frac{d_0-{d}_{avg}}{d_0}\times 100\%$$
(13)
$${d}_{avg}=\frac{1}{n}\sum_{i=1}^n{d}_i$$
(14)

where n is the node number of the rolled ring, di is the average grain size of node i, and davg is the average grain size of the rolled ring.

Another parameter is the inhomogeneity of grain IHG; it is defined as:

$$IHG=\sqrt{\sum_{i=1}^n{\left({d}_i-{d}_{avg}\right)}^2/n}$$
(15)

RDG and IHG represent the evolution of grain size and grain distribution during HRR process, the more value of RDG, the smaller the grain; the less value of IHG, the more uniform the grain distribution.

3.3 Response rules of grain evolution to forming conditions

3.3.1 Rolling ratio

In simulation case 1, the response of RDG and IHG to rolling ratio K is revealed, as shown in Figs. 8 and 9.

Fig. 8
figure 8

Relationship between radial distribution of grain size and rolling ratio K

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Fig. 9
figure 9

Responses of RDG and IHG to rolling ratio K

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Figure 8 shows that obvious grain refinement in the whole ring regions can be observed with the increase of rolling ratio, and the grain response in the outer and inner layers of ring is stronger than that in the middle layer of ring. Figure 9 illustrates that with K increases, the advantageous response of grain size generates embodied as the RDG increasing, while the advantageous and adverse responses of grain distribution generate successively, which is represented by the IHG increasing in first and decreasing at last.

As rolling ratio K increases, the plastic deformation degree also increases; thus, the larger strain level promotes the recrystallization of material and results in more recrystallized grains with small size. But the nonuniform deformation in HRR process leads to the high stain and low temperature at surface layers [14], which causes well grain refinement of the surface layers. So, with the increase of K, the integrated grain refinement of rolled ring makes grain distribute uniformly at first, then the difference of grain refinement degree between the surface layers and middle layer goes against the uniformization of grain distribution. Hence, in HRR process of as-cast 100Cr6 steel, proper increasing rolling ratio can induce the advantageous response of grain evolution and improve the grain size and distribution.

3.4 Feeding rate

In simulation case 2, the response of RDG and IHG to feeding rate v is determined, as shown in Figs. 10 and 11.

Fig. 10
figure 10

Relationship between radial distribution of grain size and feeding rate v

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Fig. 11
figure 11

Responses of RDG and IHG to feeding rate v

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In Fig. 10, we can see that when feeding rate v increases, grain refinement presents at different ring locations and the grain refinement degree of outer and inner layers is larger than middle layer. Figure 11 provides that with v increases, grain size has the advantageous response expressed by the increase of RDG, while the V-shaped curve of IHG demonstrates that grain distribution produces the advantageous and adverse responses successively.

The larger the feeding rate v, the higher the stain rate of material is, which is beneficial for the formation of small recrystallized grains. Furthermore, as v becomes larger, the feed amount per revolution increases, the plastic zone extends to the middle layer more easily, and plastic deformation becomes more homogeneous [21], which is beneficial to the uniformity of grain distribution. However, with the sustained increase of v, the difference of deformation level between the surface layers and middle layer becomes larger, and this leads to the increased difference of grain refinement level between them, as shown in Fig. 10, which advances in the increase of IHG. Therefore, in HRR process of as-cast 100Cr6 steel, reasonable feed rate should be designed to obtain the advantageous response of grain evolution.

3.4.1 Rotational speed

In simulation case 2, the response of RDG and IHG to rotational speed n is obtained, as shown in Figs. 12 and 13.

Fig. 12
figure 12

Relationship between radial distribution of grain size and rotational speed n

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Fig. 13
figure 13

Responses of RDG and IHG to rotational speed n

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From Fig. 12, it can be seen that with the increase of rotational speed n, apparent grain coarsening produces at the outer and inner layers of ring, while the grain size of middle layer has slight increase. Figure 13 indicates that with n increases, adverse responses of grain size and grain distribution both produce because of the RDG decreases and IHG increases.

From the reference [20], we know that the feed amount per revolution decreases with increased rotational speed; thus, the deformation degree reduces and the penetrability of plastic zone weakens; these restrict the grain refinement and uniform distribution, especially for the surface layers because the responses of surface layers to the forming conditions are more sensitive than the middle layer in HRR process, which can be concluded from reference [21]. So, in HRR process of as-cast 100Cr6 steel, the smaller rotational speed should be employed within the scope of stable rolling conditions [20] for the advantageous response of grain evolution.

3.4.2 Initial rolling temperature T

In simulation case 3, the response of RDG and IHG to initial rolling temperature T is presented, as shown in Figs. 14 and 15.

Fig. 14
figure 14

Relationship between radial distribution of grain size and initial rolling temperature T

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Fig. 15
figure 15

Responses of RDG and IHG to initial rolling temperature T

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Figure 14 provides that obvious grain coarsening occurs in the whole ring regions with the increase of initial rolling temperature T, particularly in the middle layer. Figure 15 shows that with T increases, the adverse response of grain refinement exists reflected by the decreased RDG, and a changed response from advantageous to adverse is created by grain distribution expressed by the V-shaped IHG curve. This is basically consistent with findings of Qi et al. [12].

Although larger T is beneficial for the recrystallization of material, it also means that the recrystallized grains have better condition to grow. When the forming conditions can sufficiently ensure the fully recrystallization to produce in HRR process, the contribution of larger T to the growing of recrystallized grains is significant, thus decrease the grain refinement degree in summary, and its influence on the middle layer is more obvious because the grains in the middle layer always gains less refinement level than the surface layers under the same forming conditions. Furthermore, the lower temperature restricts the sufficient and uniform recrystallization to generate in the different ring regions, thus harmful to the homogeneous grain distribution, and the higher temperature causes to the more obvious temperature gradient along the ring thickness during the deformation process thus also disadvantageous to the uniform grain distribution. Accordingly, the initial rolling temperature should be selected suitably to get the advantageous response of grain distribution and possibly limit the adverse response of grain size.

3.5 Response sensitivity of grain evolution to forming conditions

In the above analysis, the response rule of grain evolution to each forming condition was revealed, respectively. To compare the response behavior of grain evolution to different forming conditions, a further study was carried out in this section.

Firstly, as the measuring units of the four forming conditions are different, it is necessary to make a unity of them. The normalization method was adopted to make them uniform according to Eq. (16). Then, the refinement degree of grain RDG and inhomogeneity of grain IHG can be compared respectively in one horizontal coordinate axis to different forming conditions, as shown in Figs. 16 and 17.

$${f}_{(X)}=\frac{X-{X}_{\textrm{min}}}{X_{\textrm{max}}-{X}_{\textrm{min}}}$$
(16)

where f(X) is the value after normalization of different forming conditions and its value is from 0 to 1, X is the value of different forming conditions, Xmin is the minimum value of X, and Xmax is the maximum value of X.

Fig. 16
figure 16

Responses of RDG to different forming conditions

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Fig. 17
figure 17

Responses of IHG to different forming conditions

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Figure 16 shows that initial rolling temperature T has a more remarkable response of RDG than other three forming conditions. In the adjustment range of each forming condition, changing rolling temperature T individually can obtain the maximum refinement degree of grain RDG, changing rolling ratio K is next, and changing feeding rate v can hardly increase RDG. Figure 17 indicates that initial rolling temperature T also has a more obvious response of IHG than other three forming conditions. In the adjustment range of each forming condition, changing rolling temperature T individually can obtain the minimum inhomogeneity of grain IHG, changing feeding rate v is next, and changing rolling ratio K and rotational speed n can obtain the similar inhomogeneity of grain IHG.

To make a further study on the response behavior of grain evolution to forming conditions. The response sensitivity is proposed to measure the response size and speed of grain evolution to forming conditions. Thus, the maximum response amplitude of IHG and RDG to different forming conditions can be selected to characterize the response size of grain evolution. The response rate of IHG and RDG with f(X) may reflect the response speed of grain evolution to forming conditions.

The maximum response amplitude of RDG to different forming conditions MRARDG can be expressed as:

$$MR{A}_{RDG}= RD{G}_{\textrm{max}}- RD{G}_{\textrm{min}}$$
(17)

where RDGmax is the maximum value of RDG in the adjustment range of each forming condition, and RDGmin is the minimum value of RDG.

The maximum response amplitude of IHG to different forming conditions MRAIHG can be also defined as:

$$MR{A}_{IHG}= IH{G}_{\textrm{max}}- IH{G}_{\textrm{min}}$$
(18)

where IHGmax is the maximum value of IHG in the adjustment range of each forming condition, and IHGmin is the minimum value of IHG.

MRA RDG and MRAIHG respectively represent response size of grain size and grain inhomogeneity to forming condition. The more value of MRARDG, the larger degree the grain size can be adjusted when changing one forming condition. The more value of MRAIHG, the larger degree the grain inhomogeneity can be adjusted when changing one forming condition.

Figure 18 shows the maximum response amplitudes of RDG and IHG to different forming conditions. It indicates that the response sizes of RDG and IHG to initial rolling temperature T are both the maximum of the four forming conditions. Rolling ratio K ranks the second for the response size of RDG; feeding speed v and rotational speed n have a similar response size of RDG. For the response size of IHG, feeding speed v is the next; rolling ratio K and rotational speed n keep in a similar level. That is to say, to adjust the refinement degree of grain or inhomogeneity of grain of the rolled ring, the initial rolling temperature can make the maximum changing degree. This result is agreed with the study in reference [22].

Fig. 18
figure 18

Maximum response amplitudes of IHG and RDG to different forming conditions

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The response rate of RDG and IHG with f(X) can be calculated by the following expressions:

$$RR{X}_{RDG}=\frac{\varDelta RDG}{\varDelta {f}_{(X)}}$$
(19)
$$RR{X}_{IHG}=\frac{\varDelta IHG}{\varDelta {f}_{(X)}}$$
(20)

where RRXRDG is the response rate of RDG, RRXIHG is the response rate of IHG, and ∆RDG is the variation of RDG when f(X) changes with ∆f(X). ∆IHG is the variation of IHG when f(X) changes with ∆f(X).

RRX RDG and RRXIHG respectively represent response speed of grain size and grain inhomogeneity to forming condition. The more value of RRXRDG, the faster variation the grain size can be realized when adjusting one forming condition. The more value of RRXIHG, the faster variation the grain inhomogeneity can be realized when adjusting one forming condition.

Figure 19 provides that the response rate of RDG to the initial rolling temperature T is negative and its absolute value is the largest. That is to say, to decrease T is the most obvious way to increase RDG. The response rate of RDG to rolling ratio K is positive and the value is in the second level. Besides when f(X) increases to a certain value, the response rate will decrease quickly closing to 0. It means that to increase K is the second preferred way to increase RDG, but when K increases to a certain value, the RDG increases hardly. The response rates of RDG to feeding speed v and rotational speed n are in similar level, but the former one is negative and the latter one is positive. Thus, to decrease v will reduce RDG and to decrease n may increase RDG.

Fig. 19
figure 19

Response rates of RDG to different forming conditions

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Figure 20 indicates that the response rate of IHG to the initial rolling temperature T is changing from negative value to positive value and its absolute value is the largest. That is to say, to decrease T is the fastest way to decrease IHG. And when T is selected between 950 and 1050 °C, IHG is in a lower level. Feeding speed v is the second factor to affect the response rate of IHG. When v is close to 2 mm/s, IHG locates in a valley value. Rolling ratio K ranks the third. When K is selected between 1.5 and 1.7, a small value of IHG will occur. Rotational speed n has a weak effect on the response rate of IHG. When n is selected in a small level, a well IHG can be obtained.

Fig. 20
figure 20

Response rates of IHG to different forming conditions

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4 Results verification

It is obvious that the response of grain evolution to forming conditions has important relation with the forming condition optimization to improve microstructure of the rolled ring. According to the grain evolution response investigated above, the optimization for the initial forming conditions in Table 1 can be performed, as shown following:

  1. (a)

    Initial forming conditions: k = 1.5, T = 1150 °C, v = 4 mm/s, n = 70 r/min

  2. (b)

    Optimized forming conditions: k = 1.8, T = 950 °C, v = 4 mm/s, n = 50 r/min

Then, simulation and experiment of HRR with as-cast 100Cr6 steel were carried out with above two groups of forming conditions to evaluate the effect of forming condition optimization on grain improvement and verify the reliability of obtained results.

From the simulation results as shown in Fig. 21, it can be seen that under the optimized forming conditions, the grain size of whole ring decreases, and the difference of grain sizes between the surface layers and middle layer reduces. The comparisons in Fig. 22 indicate that the grain size and grain distribution of the rolled ring improve significantly with the optimized forming conditions.

Fig. 21
figure 21

Grain chats of the rolled rings under the initial and optimized forming conditions: a initial forming conditions; b optimized forming conditions

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Fig. 22
figure 22

Simulative comparisons of grain size and grain distribution between the rolled rings with initial forming conditions and optimized forming conditions

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Figures 23 and 24 show the experimental grain comparisons under the initial and optimized forming conditions. The average grain sizes of the middle layer and inner layer under the initial forming conditions were respectively 41 μm and 25 μm. Under optimized forming conditions, the average grain sizes of the middle layer and inner layer under the initial forming conditions were respectively improved to 23 μm and 15 μm. As it can be seen that the grain size was decreased significantly and the difference of grain sizes between the inner layers and middle layer was reduced with the optimized forming conditions. It has a good agreement with the simulative result.

Fig. 23
figure 23

Experimental grain sizes of the rolled rings under the initial forming conditions: a middle layer; b inner layer

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Fig. 24
figure 24

Experimental grain sizes of the rolled rings under the optimized forming conditions: a middle layer; b inner layer

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5 Conclusions

In our work, the response behavior of grain evolution to forming conditions during hot ring rolling of as-cast 100Cr6 steel has been studied, including rolling ratio, feeding rate, rotational speed, and initial rolling temperature. Based on the analysis, an optimization for forming conditions is performed by simulation and experiment successfully. The research can provide a scientific guidance for optimizing parameters of the forming condition, which is beneficial to the development and application of the new combined casting-ring rolling technology. The main conclusions can be drawn as follows:

  1. (1)

    When rolling ratio or feeding rate increases, the refinement degree of grain increases, and the inhomogeneity of grain firstly decreases then increases. When rotational speed increases, the refinement degree of grain decreases, and the inhomogeneity of grain increases. When initial rolling temperature increases, the refinement degree of grain decreases, and the inhomogeneity of grain firstly decreases then increases. The advantageous response of grain evolution will generate to improve the grain refinement and grain uniformization with the proper increases of rolling ratio and feeding rate and the appropriate decreases of rotational speed and initial rolling temperature.

  2. (2)

    For the refinement degree of grain, initial rolling temperature has the most remarkable response sensitivity, rolling ratio is the next, and then rotational speed and feeding rate have similar response sensitivity. For the inhomogeneity of grain, initial rolling temperature also shows the most remarkable response sensitivity, feeding rate ranks the second, and then rolling ratio and rotational speed lie in similar level. The remarkable response sensitivity of grain evolution will be beneficial to effectively adjust the grain refinement and grain uniformization with the preferred forming condition of lower initial rolling temperature.