Abstract
Minimizing the maximum load on rolls in ring rolling process has been the most urgent demand in producing large rings made of high-strength material. With a view to meet the essential demand, the problem was solved by a novel process design, which respectively calculated the feed-rates of mandrel and axial rolls through optimum design. Based on the finite element simulation of ring rolling process by varying the feed-rates of the mandrel and axial rolls, an improved rolling schedule was established. The design of experiments via Taguchi method and the optimum design method such as Conjugate Gradient Method were used. The FE simulation was verified by comparison with experiment results. The optimized rolling schedule was suitable and reliable in the practical manufacture for both pure and radial-axial ring rolling process.
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Abbreviations
- \(\bar \sigma\) :
-
equivalent stress
- \(\dot \bar \varepsilon\) :
-
equivalent strain rate
- Ω:
-
domain of the work-piece
- S f :
-
forced boundary surface
- τ f :
-
frictional stress
- u i :
-
vector of nodal velocity
- \(\dot \varepsilon _V\) :
-
volumetric strain rate
- α:
-
penalty constant
- σ ij :
-
stress components
- σ ij :
-
deviatoric stress components
- \(\dot \varepsilon _{ij}\) :
-
strain rate components
- β :
-
coefficient of angle
- θ A :
-
angle of SMS node A
- θ B :
-
angle of SMS node B
- θ :
-
angle of AMS node P
- Δt :
-
time increment
- V 0 :
-
initial volume of work-piece
- V 1 :
-
work-piece volume after updating AMS
- \(\overline {r_1 }\) :
-
mean ring radius after updating AMS
- \(\overline {r_2 }\) :
-
mean ring radius after corrected
- (A) θ :
-
ring cross-section area
- Δr :
-
correction value of radius
- σ f :
-
flow stress
- K 0 :
-
stiffness coefficient
- n :
-
hardening coefficient
- m :
-
strain-rate sensitivity coefficient
- F :
-
feed force
- R :
-
electric resistance strain
- A :
-
conversion coefficient
- η 1 :
-
extreme ratio of the mandrel load
- η 2 :
-
extreme ratio of the axial roll load
- i :
-
designed case number
- w i :
-
weighting factor
- s :
-
stroke of mandrel or axial roll
- t :
-
time variable.
- ν f,max :
-
maximum feed-rate of mandrel
- ν a,max :
-
maximum feed-rate of axial roll
- ν Rd :
-
linear velocity of driven roll
- ν 1,f :
-
variable of the mandrel feed speed
- ν 1,a :
-
variable of the axial roll feed speed
- MAX [L m ,i]:
-
maximum mandrel load of simulation
- MAX [L a ,i]:
-
maximum axial roll load of simulation
- MAX [L m,e ]:
-
maximum mandrel load of experiment
- MAX [L a,e ]:
-
maximum axial roll load of experiment
- \(\left( {\dot r,\dot \theta ,\dot z} \right)\) :
-
velocity vector in cylindrical coordinate
- (r, θ, z):
-
cylindrical coordinate
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Kim, N., Kim, H. & Jin, K. Optimal design to reduce the maximum load in ring rolling process. Int. J. Precis. Eng. Manuf. 13, 1821–1828 (2012). https://doi.org/10.1007/s12541-012-0239-4
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DOI: https://doi.org/10.1007/s12541-012-0239-4