CN104711412B - The step rate system simulator of a kind of billet heating furnace and analogy method thereof - Google Patents

Abstract

The present invention relates to the step rate system simulator of a kind of billet heating furnace, process simulator, trave lling girder advance process simulator and trave lling girder fallback procedures simulator is declined including trave lling girder uphill process simulator, trave lling girder, four circuit are identical, described trave lling girder rise/fall/forward/backward process simulator includes resistance R1, one termination is used for controlling trave lling girder and rises control signal, the inverting input of its other end and the first amplifier A1 is connected, and the outfan of the first amplifier A1 is connected by the inverting input of resistance R5 and the 3rd amplifier A3；The outfan output step rate rise/fall/forward/backward displacement signal of the tenth amplifier A10.The invention also discloses the analogy method of the step rate system simulator of a kind of billet heating furnace.The present invention is that the debugging before step rate control method research, control equipment development, the installation of control equipment creates condition, the step rate field adjustable time can be made to be greatly shortened, engineering construction cost can be greatly lowered.

Description

The step rate system simulator of a kind of billet heating furnace and analogy method thereof

Technical field

The present invention relates to walking beam furnace and control technical field, the step rate of a kind of billet heating furnace System simulator and analogy method thereof.

Background technology

Iron and steel is the grain of industry, and billet heating furnace is the visual plant during steel produce.Step rate is step-by-step movement steel billet The core component of heating furnace, is made up of fixing beam and trave lling girder, the action such as wherein, trave lling girder is made to rise, advance, decline, retrogressing, Transport the most forward during steel billet is heated in stove.The movement velocity of trave lling girder should ensure the rhythm produced, Ensure again the light torr of steel billet is put down gently, touch wound in order to avoid producing and damage trave lling girder and fixing beam.Therefore, it is necessary to control trave lling girder Exactly according to the rate curve motion set.

Step rate system be by fixing beam, trave lling girder, horizontal frame and lift frame, two-wheel ramp stepping mechanism, two Drive the huge of the compositions such as the hydraulic cylinder of rise and fall, a driving advance and the hydraulic cylinder retreated, control valve platform, Hydraulic Station System.Therefore, can not there is real step rate system conduct during step rate control method research, control equipment development Control object is tested, and controls effect with inspection；During engineering construction, often due to the duration is tight, task weight, it is possible to The debugging time given is extremely short, the difference such as design capacity, production technology in addition, is difficult to the step rate for each different parameters Obtain very satisfied control effect.At present, the domestic control to step rate also uses open loop approach, usually owing to ensureing Control accuracy and cause the interruption of production.

For the ease of realizing step rate in step rate control method research, control equipment development, project implementing process Control debugging, in the urgent need to developing a kind of billet heating furnace step rate simulator based on mathematical model.

Summary of the invention

The primary and foremost purpose of the present invention is that offer one can be for control method research, control equipment development, engineering construction The step rate system of the billet heating furnace of experiment condition, shortening step rate field adjustable time, reduction engineering construction cost is provided Simulator.

For achieving the above object, present invention employs techniques below scheme: the step rate system mould of a kind of billet heating furnace Intend device, decline process simulator, trave lling girder advance process simulator and movement including trave lling girder uphill process simulator, trave lling girder Beam fallback procedures simulator, four circuit are identical, and described trave lling girder rise/fall/forward/backward process simulator includes resistance R1, one termination is for controlling the control signal of trave lling girder rise/fall/forward/backward, its other end and the first amplifier A1 Inverting input be connected, the outfan of the first amplifier A1 pass through resistance R5 and the inverting input phase of the 3rd amplifier A3 Even；The inverting input of the 4th amplifier A4 connects load signal by electric capacity C4, and the outfan of the 4th amplifier is with resistance R12's One end is connected, and the other end of resistance R12 is connected with inverting input, one end of resistance R13 of the 5th amplifier A5 respectively, resistance The other end of R13 and the outfan of the 5th amplifier A5 pass through resistance R7 and the normal phase input end phase of the 3rd amplifier A3 after being connected Even；The inverting input of the second amplifier A2 connects load signal by resistance R3, and the inverting input of the second amplifier A2 is successively Connect the normal phase input end of the 3rd amplifier A3 by resistance R4, R6, the outfan of the second amplifier A2 is connected on resistance R4 and resistance Between R6；The inverting input of the 6th amplifier A6 connects hydraulic cylinder oil supply pressure signal by resistance R14, the 6th amplifier A6's Outfan is connected by the normal phase input end of resistance R8 and the 3rd amplifier A3；The outfan of the 3rd amplifier A3 passes through resistance The normal phase input end of R17 and the 7th amplifier A7 is connected, and the inverting input of the 7th amplifier A7 is put by resistance R16 and the 9th The outfan of big device A9 is connected, and the outfan of the 7th amplifier A7 passes through resistance R20 and the inverting input of the 8th amplifier A8 Being connected, the outfan of the 8th amplifier A8 is connected by the inverting input of resistance R21 and the 9th amplifier A9, the 9th amplifier The outfan of A9 is connected by the inverting input of resistance R23 and the tenth amplifier A10, and the outfan of the tenth amplifier A10 is defeated Go out trave lling girder rise/fall/forward/backward displacement signal.The inverting input of described first amplifier A1 passes sequentially through resistance The inverting input of R2, resistance R5 and the 3rd amplifier A3 is connected, the positive input end grounding of the first amplifier A1, and the 3rd amplifies The inverting input of device A3 connects its outfan by resistance R9；The positive input end grounding of the 4th amplifier A4, the 4th amplifier The inverting input of A4 is connected with its outfan by resistance R11, the positive input end grounding of the 5th amplifier A5, and the 6th amplifies The positive input end grounding of device A6, the inverting input of the 6th amplifier A6 is connected with its outfan by resistance R15；3rd puts The normal phase input end of big device A3 is exported with it by resistance R9 by resistance R10 ground connection, the inverting input of the 3rd amplifier A3 End is connected；The normal phase input end of the 7th amplifier A7 passes through resistance R18 ground connection, and the inverting input of the 7th amplifier A7 is by electricity Resistance R19 is connected with its outfan；The positive input end grounding of the 8th amplifier A8, the inverting input of the 8th amplifier A8 passes through Electric capacity C9 connects its outfan；The positive input end grounding of the 9th amplifier A9, the inverting input of the 9th amplifier A9 is by electricity Resistance R22 connects its outfan, and electric capacity C11 is connected in parallel on resistance R22；The positive input end grounding of the tenth amplifier A10, it is anti-phase defeated Enter end and connect its outfan by electric capacity C13.

Described trave lling girder uphill process simulator, trave lling girder decline process simulator, trave lling girder advance process simulator and The resistance of resistance R2, R4, R13, R15 in trave lling girder fallback procedures simulator is different, described trave lling girder uphill process simulator, The resistance of the resistance R3 in trave lling girder decline process simulator, trave lling girder fallback procedures simulator is identical and advances with trave lling girder The resistance of the resistance R3 in journey simulator is different, and described trave lling girder uphill process simulator, trave lling girder decline in process simulator The resistance of resistance R14 identical, resistance R14 in described trave lling girder advance process simulator and trave lling girder fallback procedures simulator Resistance identical, the resistance of the resistance R14 in described trave lling girder uphill process simulator and described trave lling girder advance process simulation The resistance of the resistance R14 in device is different.

Another object of the present invention is to provide the analogy method of the step rate system simulator of a kind of billet heating furnace, its It is characterised by: set up step rate system mathematic model, if U_up、U_downIt is respectively rising, declines control signal, U_forw、U_backRespectively For advancing, retreating control signal, P_sFor oil supply pressure, F_LFor load, x_pFor hydraulic cylinder piston displacement, y_up、y_downIt is respectively stepping Beam rises, declines displacement, x_forw、x_backBeing respectively step rate to advance, retreat displacement, its model expression is as follows:

Electrohydraulic proportional directional valve spool displacement X_v(s) and control signal U (s), i.e. U_up、U_down、U_forw、U_backBetween biography Delivery function is:

$W_{sv}\left(s\right)=\frac{X_v\left(s\right)}{U\left(s\right)}=\frac{K_{sv}}{T_{sv}s+1}---\left(1\right)$

Wherein, K_sv、T_svBeing respectively gain and the time constant of electrohydraulic proportional directional valve, s is dynamic factor；

Piston displacement X_Px(s) and spool displacement X_vS the transmission function between () is:

$W_o\left(s\right)=\frac{X_{px}\left(s\right)}{X_v\left(s\right)}=\frac{\frac{K_q}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(K_c+C_p)M}{A_1^2}{s}^2+s}---\left(2\right)$

Wherein, C_p=2C_i/ (1+ η), V_t1=4V₁/ (1+ η), η=A₂/A₁, V₁=A₁L/2, F_L=Mg, g are that gravity accelerates Degree, M=M in ascending and descending process_sSin θ, during forward-reverse, M is M_sFrictional force during effect, θ is two-wheel ramp formula step Enter the ramp angles of mechanism；K_qFor flow gain, A₁、A₂Being respectively hydraulic cylinder rodless cavity and the effective area of rod chamber, L is liquid Cylinder pressure haul distance, K_cFor flow pressure coefficient, β_eFor effective volume elastic modelling quantity, V₁、V₂It is respectively hydraulic cylinder rodless cavity and has The volume in bar chamber, C_iFor the hydraulic cylinder interior leakage coefficient of leakage, M is the component that load quality acts on hydraulic cylinder, M_sFor steel billet and stepping The gross mass of beam framework, s is dynamic factor；

Piston displacement X_pf(s) and load F_LS the transmission function between () is:

$W_f\left(s\right)=\frac{X_{pf}\left(s\right)}{F_L\left(s\right)}=\frac{\frac{1}{A_1^2}(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(K_c+C_p)M}{A_1^2}{s}^2+s}---\left(3\right)$

Piston displacement X_pp(s) and oil supply pressure P_sS the transmission function between () is:

$W_1\left(s\right)=\frac{X_{pp}\left(s\right)}{P_s\left(s\right)}=\frac{\frac{C_s}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(K_c+C_p)M}{A_1^2}{s}^2+s}---\left(4\right)$

Wherein, C_s=C_i(1-η)/(1+η)；

Convolution (2), (3), (4) understand, piston displacement X_p(s) be:

$\begin{array}{c}{X}_p\left(s\right)=\frac{\frac{K_q}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}U\left(s\right)\\ +\frac{-\frac{1}{A_1^2}(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+k_c)M}{A_1^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)}{A_1^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(5\right)$

Trave lling girder vertical displacement is:

Y (s)=X_p(s)sinθ (6)。

The expression formula of described trave lling girder uphill process mathematical model is:

$\begin{array}{c}{Y}_{up}\left(s\right)=\frac{\frac{K_q}{A_1}\sin \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{up}\left(s\right)\\ +\frac{-\frac{\sin \mathrm{\θ}}{A_1^2}(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_1}\sin \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(7\right)$

Described trave lling girder declines process mathematical model:

$\begin{array}{c}{Y}_{down}\left(s\right)=\frac{\frac{K_q}{A_2}\sin \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_2^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{down}\left(s\right)\\ +\frac{-\frac{\sin \mathrm{\θ}}{A_2^2}(\frac{V_{t2}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{(C_p+K_c)M}{A_2^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_2}\sin \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{(C_p+K_c)M}{A_2^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(8\right)$

Wherein, V_t2For rod chamber effective volume；

Trave lling girder horizontal displacement is:

X (s)=X_p(s)cosθ (9)；

Trave lling girder advance process mathematical model is:

$\begin{array}{c}{Y}_{forw}\left(s\right)=\frac{\frac{K_q}{A_1}\cos \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{forw}\left(s\right)\\ +\frac{-\frac{\cos \mathrm{\θ}}{A_1^2}(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_1}\cos \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(10\right);$

Trave lling girder fallback procedures mathematical model is:

$\begin{array}{c}{X}_{back}\left(s\right)=\frac{\frac{K_q}{A_2}\cos \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{(C_p+K_c)M}{A_2^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{back}\left(s\right)\\ +\frac{-\frac{\cos \mathrm{\θ}}{A_2^2}(\frac{V_{t2}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{(C_p+K_c)M}{A_2^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_2}\cos \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^2+\frac{(C_p+K_c)}{A_2^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(11\right);$

Wherein, V_t2For rod chamber effective volume.

Make flow gain K_q=1.08m²/ s, rodless cavity effective area A₁=0.0616m², rod chamber effective area A₂= 0.0301m², rodless cavity effective volume V_t1=0.076m³, rod chamber effective volume V_t2=0.0372m³, mass M=1.31 × 10⁵Kg, fluid elastic modelling quantity β_e=6.9 × 10⁸Pa, reveals coefficient C in equivalence_p=4.027 × 10^-11m⁵/ (Ngs), flow pressure K_c=2.16 × 10^-10m⁵/ (Ngs), equivalence outward leakage coefficient C_s=1.027 × 10^-11m⁵/ (Ngs), leadage coefficient C_i=3.0 × 10^-11m⁵/ (Ngs), area ratio η=0.49, θ=17 °；

Being substituted into by above-mentioned parameter in formula (7), obtain trave lling girder uphill process simulator, its expression formula is as follows:

$\begin{array}{c}{Y}_{up}\left(s\right)=5.13\frac{1}{9.5\×{10}^{-4}{s}^2+8.8\×{10}^{-3}s+1}\frac{1}{s}{U}_{up}\left(s\right)\\ -\frac{2.12\×{10}^{-9}s+1.97\×{10}^{-8}}{9.5\×{10}^{-4}{s}^2+8.8\×{10}^{-3}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -4.87\×{10}^{-11}\frac{1}{9.5\×{10}^{-4}{s}^2+8.8\×{10}^{-3}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(12\right);$

Being substituted into by above-mentioned parameter in formula (8), obtain trave lling girder and decline process simulator, its expression formula is as follows:

$\begin{array}{c}{Y}_{down}\left(s\right)=10.5\frac{1}{1.9\×{10}^{-3}{s}^2+3.71\×{10}^{-2}s+1}\frac{1}{s}{U}_{down}\left(s\right)\\ -\frac{4.35\×{10}^{-9}s+8.27\×{10}^{-8})}{1.9\×{10}^{-3}{s}^2+3.71\×{10}^{-2}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -9.98\×{10}^{-11}\frac{1}{1.9\×{10}^{-3}{s}^2+3.71\×{10}^{-2}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(13\right).$

Make flow gain K_q=2.45m²/ s, rodless cavity effective area A₁=0.038m², rod chamber effective area A₂= 0.0226m², rodless cavity effective volume V_t1=0.0157m³, rod chamber effective volume V_t2=0.0093m³, mass M=0.729 × 10⁵Kg, fluid elastic modelling quantity β_e=6.9 × 10⁸Pa, reveals coefficient C in equivalence_p=3.75 × 10^-11m⁵/ (Ngs), flow pressure K_c=2.16 × 10^-10m⁵/ (Ngs), equivalence outward leakage coefficient C_s=7.5 × 10^-11m⁵/ (Ngs), leadage coefficient C_i=3.0 × 10^-11m⁵/ (Ngs), area ratio η=0.6, θ=17 °；

Being substituted into by above-mentioned parameter in formula (10), obtain trave lling girder advance process simulator, its expression formula is as follows:

$\begin{array}{c}{X}_{forw}\left(s\right)=61.66\frac{1}{2.87\×{10}^{-4}{s}^2+1.3\×{10}^{-2}s+1}\frac{1}{s}{U}_{forw}\left(s\right)\\ -\frac{3.76\×{10}^{-9}s+1.68\×{10}^{-7}}{2.87\×{10}^{-4}{s}^2+1.3\×{10}^{-2}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -1.89\×{10}^{-10}\frac{1}{2.87\×{10}^{-4}{s}^2+1.3\×{10}^{-2}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(14\right);$

Being substituted into by above-mentioned parameter in formula (11), obtain trave lling girder fallback procedures simulator, its expression formula is as follows:

$\begin{array}{c}{X}_{back}\left(s\right)=103.67\frac{1}{8\×{10}^{-4}{s}^2+3.6\×{10}^{-2}s+1}\frac{1}{s}{U}_{back}\left(s\right)\\ -\frac{1.065\×{10}^{-8}s+4.74\×{10}^{-7}}{8\×{10}^{-4}{s}^2+3.6\×{10}^{-2}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -3.17\×{10}^{-10}\frac{1}{8\×{10}^{-4}{s}^2+3.6\×{10}^{-2}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(15\right).$

As shown from the above technical solution, the present invention is on the basis of research step rate mathematical model, based on operational amplifier Circuit, develops a simulator, for step rate control method research, control equipment development, controls the debugging before equipment is installed Providing experiment condition, the time needed for making step rate field adjustable is greatly shortened, and the enforcement that engineering can be greatly lowered becomes This；For huge step rate system, on the basis of establishing a whole set of mathematical model, use operational amplifier, it is achieved that Billet heating furnace step rate rises, declines, the simulation of the Four processes that advances, retreats.In a word, the present invention is step rate control method Debugging before research, control equipment development, the installation of control equipment creates condition, and the step rate field adjustable time can be made significantly to contract Short, engineering construction cost can be greatly lowered.

Accompanying drawing explanation

Fig. 1,2 be respectively the front view of step rate structure, side view；

Fig. 3 is the structural representation of two-wheel ramp formula stepping mechanism；

Fig. 4 is that step rate system constitutes schematic diagram；

Fig. 5 is the structural representation of step rate system mathematic model；

Fig. 6 is the structural representation of trave lling girder uphill process mathematical model；

Fig. 7 is the structural representation that trave lling girder declines process mathematical model；

Fig. 8 is the structural representation of trave lling girder advance process mathematical model；

Fig. 9 is the structural representation of trave lling girder fallback procedures mathematical model；

Figure 10 is the circuit diagram of trave lling girder uphill process simulator；

Figure 11 is the circuit diagram that trave lling girder declines process simulator；

Figure 12 is the circuit diagram of trave lling girder advance process simulator；

Figure 13 is the circuit diagram of trave lling girder fallback procedures simulator.

Detailed description of the invention

As it is shown in figure 1, step rate is constituted with trave lling girder 2 by fixing beam 3, fixing beam 3 supports steel billet 1, and trave lling girder 2 can be by steel Base 1 holds up and transports forward, and trave lling girder 2 combines with horizontal frame 4, when trave lling girder 2 rises to connect with when fixing beam 3 level Touch and hold up steel billet 1.

When trave lling girder 2 runs, have rising, decline, advance, fallback procedures.Although the structure of these process mathematical models Essentially identical, but owing to the asymmetry of hydraulic cylinder makes its parameter have certain difference.The rising of trave lling girder, decline, advance, after Move back motion to be realized by two-wheel ramp formula stepping mechanism, as shown in Figure 3.Step rate system is by some set two-wheel ramp formula steppers Structure, this mechanism is made up of lifting inclined rail chair 10, lift frame 6, double roller 7.It is positioned at the two of two-wheel ramp formula stepping mechanism both sides Individual rise and fall hydraulic cylinder 8 driving rolls moves in ramp so that lift frame 6 holds up horizontal frame 4 and rises, declines fortune Dynamic；The forward-reverse hydraulic cylinder 5 being positioned at horizontal frame 4 end drives horizontal frame 4 to advance, setback；Block 9 is to trave lling girder 2 carry out initial position fix.

In the diagram, U (U_up、U_down、U_forw、U_back) it is control signal input；F_LFor load disturbance signal input part；P_s For oil supply pressure signal input part；y(y_up、y_down)、x(x_forw、x_back) it is respectively vertical, the outfan of horizontal displacement.Oil sources pressure Power P_sThered is provided by Hydraulic Station, substantially constant；F_LFor load, the i.e. weight of steel billet.

This method includes: set up step rate system mathematic model, if U_up、U_downIt is respectively rising, declines control signal, U_forw、U_backIt is respectively advance, retreats control signal, P_sFor oil supply pressure, F_LFor load, x_pFor hydraulic cylinder piston displacement, y_up、 y_downIt is respectively step rate to rise, decline displacement, x_forw、x_backIt is respectively step rate to advance, retreat displacement, its model expression As follows:

As it is shown in figure 5, electrohydraulic proportional directional valve spool displacement X_v(s) and control signal U (s) (U_up、U_down、U_forw、U_back) Between transmission function be:

$W_{sv}\left(s\right)=\frac{X_v\left(s\right)}{U\left(s\right)}=\frac{K_{sv}}{T_{sv}s+1}---\left(1\right)$

Wherein, K_sv、T_svBeing respectively gain and the time constant of electrohydraulic proportional directional valve, s is dynamic factor；

Piston displacement X_Px(s) and spool displacement X_vS the transmission function between () is:

$W_o\left(s\right)=\frac{X_{px}\left(s\right)}{X_v\left(s\right)}=\frac{\frac{K_q}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(K_c+C_p)M}{A_1^2}{s}^2+s}---\left(2\right)$

Wherein, C_p=2C_i/ (1+ η), V_t1=4V₁/ (1+ η), η=A₂/A₁, V₁=A₁L/2, F_L=Mg, g are that gravity accelerates Degree, M=M in ascending and descending process_sSin θ, during forward-reverse, M is M_sFrictional force during effect, θ is two-wheel ramp formula step Enter the ramp angles of mechanism；K_qFor flow gain, A₁、A₂Being respectively hydraulic cylinder rodless cavity and the effective area of rod chamber, L is liquid Cylinder pressure haul distance, K_cFor flow pressure coefficient, β_eFor effective volume elastic modelling quantity, V₁、V₂It is respectively hydraulic cylinder rodless cavity and has The volume in bar chamber, C_iFor the hydraulic cylinder interior leakage coefficient of leakage, M is the component that load quality acts on hydraulic cylinder, M_sFor steel billet and stepping The gross mass of beam framework, s is dynamic factor；

Piston displacement X_pf(s) and load F_LS the transmission function between () is:

$W_f\left(s\right)=\frac{X_{pf}\left(s\right)}{F_L\left(s\right)}=\frac{\frac{1}{A_1^2}(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(K_c+C_p)M}{A_1^2}{s}^2+s}---\left(3\right)$

Piston displacement X_pp(s) and oil supply pressure P_sS the transmission function between () is:

$W_1\left(s\right)=\frac{X_{pp}\left(s\right)}{P_s\left(s\right)}=\frac{\frac{C_s}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(K_c+C_p)M}{A_1^2}{s}^2+s}---\left(4\right)$

Wherein, C_s=C_i(1-η)/(1+η)；

Convolution (2), (3), (4) understand, piston displacement X_p(s) be:

$\begin{array}{c}{X}_p\left(s\right)=\frac{\frac{K_q}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}U\left(s\right)\\ +\frac{-\frac{1}{A_1^2}(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+k_c)M}{A_1^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)}{A_1^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(5\right)$

Trave lling girder vertical displacement is:

Y (s)=X_p(s)sinθ (6)。

As shown in Figure 6, the expression formula of described trave lling girder uphill process mathematical model is:

$\begin{array}{c}{Y}_{up}\left(s\right)=\frac{\frac{K_q}{A_1}\sin \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{up}\left(s\right)\\ +\frac{-\frac{\sin \mathrm{\θ}}{A_1^2}(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_1}\sin \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(7\right);$

As it is shown in fig. 7, described trave lling girder declines process mathematical model it is:

$\begin{array}{c}{Y}_{down}\left(s\right)=\frac{\frac{K_q}{A_2}\sin \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_2^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{down}\left(s\right)\\ +\frac{-\frac{\sin \mathrm{\θ}}{A_2^2}(\frac{V_{t2}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{(C_p+K_c)M}{A_2^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_2}\sin \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{(C_p+K_c)M}{A_2^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(8\right);$

Wherein, V_t2For rod chamber effective volume；

Trave lling girder horizontal displacement is:

X (s)=X_p(s)cosθ (9)；

As shown in Figure 8, trave lling girder advance process mathematical model is:

$\begin{array}{c}{Y}_{forw}\left(s\right)=\frac{\frac{K_q}{A_1}\cos \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{forw}\left(s\right)\\ +\frac{-\frac{\cos \mathrm{\θ}}{A_1^2}(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_1}\cos \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(C_p+K_c)M}{A_1^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(10\right);$

As it is shown in figure 9, trave lling girder fallback procedures mathematical model is:

$\begin{array}{c}{X}_{back}\left(s\right)=\frac{\frac{K_q}{A_2}\cos \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{(C_p+K_c)M}{A_2^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{back}\left(s\right)\\ +\frac{-\frac{\cos \mathrm{\θ}}{A_2^2}(\frac{V_{t2}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{(C_p+K_c)M}{A_2^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_2}\cos \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^2+\frac{(C_p+K_c)}{A_2^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(11\right);$

Wherein, V_t2For rod chamber effective volume.

Visible, rise, decline, advance, fallback procedures model structure identical, only because the asymmetry of hydraulic cylinder Cause the difference of local parameter.Model is constituted by controlling passage, load and oil supply pressure disturbance passage.Make flow gain K_q= 1.08m²/ s, rodless cavity effective area A₁=0.0616m², rod chamber effective area A₂=0.0301m², rodless cavity effective volume V_t1=0.076m³, rod chamber effective volume V_t2=0.0372m³, mass M=1.31 × 10⁵Kg, fluid elastic modelling quantity β_e=6.9 ×10⁸Pa, reveals coefficient C in equivalence_p=4.027 × 10^-11m⁵/ (Ngs), flow pressure K_c=2.16 × 10^-10m⁵/ (Ngs), etc. Effect outward leakage coefficient C_s=1.027 × 10^-11m⁵/ (Ngs), leadage coefficient C_i=3.0 × 10^-11m⁵/ (Ngs), area ratio η= 0.49, θ=17 °；

Being substituted into by above-mentioned parameter in formula (7), obtain trave lling girder uphill process simulator, as shown in Figure 10, its expression formula is such as Under:

$\begin{array}{c}{Y}_{up}\left(s\right)=5.13\frac{1}{9.5\×{10}^{-4}{s}^2+8.8\×{10}^{-3}s+1}\frac{1}{s}{U}_{up}\left(s\right)\\ -\frac{2.12\×{10}^{-9}s+1.97\×{10}^{-8}}{9.5\×{10}^{-4}{s}^2+8.8\×{10}^{-3}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -4.87\×{10}^{-11}\frac{1}{9.5\×{10}^{-4}{s}^2+8.8\×{10}^{-3}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(12\right);$

Being substituted into by above-mentioned parameter in formula (8), obtain trave lling girder and decline process simulator, as shown in figure 11, its expression formula is such as Under:

$\begin{array}{c}{Y}_{down}\left(s\right)=10.5\frac{1}{1.9\×{10}^{-3}{s}^2+3.71\×{10}^{-2}s+1}\frac{1}{s}{U}_{down}\left(s\right)\\ -\frac{4.35\×{10}^{-9}s+8.27\×{10}^{-8})}{1.9\×{10}^{-3}{s}^2+3.71\×{10}^{-2}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -9.98\×{10}^{-11}\frac{1}{1.9\×{10}^{-3}{s}^2+3.71\×{10}^{-2}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(13\right).$

Make flow gain K_q=2.45m²/ s, rodless cavity effective area A₁=0.038m², rod chamber effective area A₂= 0.0226m², rodless cavity effective volume V_t1=0.0157m³, rod chamber effective volume V_t2=0.0093m³, mass M=0.729 × 10⁵Kg, fluid elastic modelling quantity β_e=6.9 × 10⁸Pa, reveals coefficient C in equivalence_p=3.75 × 10^-11m⁵/ (Ngs), flow pressure K_c=2.16 × 10^-10m⁵/ (Ngs), equivalence outward leakage coefficient C_s=7.5 × 10^-11m⁵/ (Ngs), leadage coefficient C_i=3.0 × 10^-11m⁵/ (Ngs), area ratio η=0.6, θ=17 °；

Being substituted into by above-mentioned parameter in formula (10), obtain trave lling girder advance process simulator, as shown in figure 12, its expression formula is such as Under:

$\begin{array}{c}{X}_{forw}\left(s\right)=61.66\frac{1}{2.87\×{10}^{-4}{s}^2+1.3\×{10}^{-2}s+1}\frac{1}{s}{U}_{forw}\left(s\right)\\ -\frac{3.76\×{10}^{-9}s+1.68\×{10}^{-7}}{2.87\×{10}^{-4}{s}^2+1.3\×{10}^{-2}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -1.89\×{10}^{-10}\frac{1}{2.87\×{10}^{-4}{s}^2+1.3\×{10}^{-2}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(14\right);$

Being substituted into by above-mentioned parameter in formula (11), obtain trave lling girder fallback procedures simulator, as shown in figure 13, its expression formula is such as Under:

$\begin{array}{c}{X}_{back}\left(s\right)=103.67\frac{1}{8\×{10}^{-4}{s}^2+3.6\×{10}^{-2}s+1}\frac{1}{s}{U}_{back}\left(s\right)\\ -\frac{1.065\×{10}^{-8}s+4.74\×{10}^{-7}}{8\×{10}^{-4}{s}^2+3.6\×{10}^{-2}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -3.17\×{10}^{-10}\frac{1}{8\×{10}^{-4}{s}^2+3.6\×{10}^{-2}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(15\right).$

As shown in Figure 10,11,12,13, the step rate system simulator of a kind of billet heating furnace, rose including trave lling girder Journey simulator, trave lling girder decline process simulator, trave lling girder advance process simulator and trave lling girder fallback procedures simulator, four Circuit is identical, and described trave lling girder rise/fall/forward/backward process simulator includes that resistance R1, one termination are used for controlling to move The control signal of dynamic beam rise/fall/forward/backward, the inverting input of its other end and the first amplifier A1 is connected, and first The outfan of amplifier A1 is connected by the inverting input of resistance R5 and the 3rd amplifier A3；4th amplifier A4's is anti-phase defeated Entering end and connect load signal by electric capacity C4, the outfan of the 4th amplifier is connected with one end of resistance R12, another of resistance R12 End is connected with inverting input, one end of resistance R13 of the 5th amplifier A5 respectively, and the other end of resistance R13 and the 5th amplifies The outfan of device A5 is connected by the normal phase input end of resistance R7 and the 3rd amplifier A3 after being connected；Second amplifier A2's is anti-phase Input connects load signal by resistance R3, and the inverting input of the second amplifier A2 passes sequentially through resistance R4, R6 and connects the 3rd and put The normal phase input end of big device A3, the outfan of the second amplifier A2 is connected between resistance R4 and resistance R6；6th amplifier A6's Inverting input connects hydraulic cylinder oil supply pressure signal by resistance R14, and the outfan of the 6th amplifier A6 is by resistance R8 and the The normal phase input end of three amplifier A3 is connected；The outfan of the 3rd amplifier A3 is by resistance R17 and the 7th amplifier A7 just Phase input is connected, and the inverting input of the 7th amplifier A7 is connected by the outfan of resistance R16 and the 9th amplifier A9, the The outfan of seven amplifier A7 is connected by the inverting input of resistance R20 and the 8th amplifier A8, and the 8th amplifier A8's is defeated Going out end to be connected by the inverting input of resistance R21 and the 9th amplifier A9, the outfan of the 9th amplifier A9 passes through resistance R23 It is connected with the inverting input of the tenth amplifier A10, the outfan output mobile beam rise/fall of the tenth amplifier A10/front Enter/retreat displacement signal.A1 Yu R1, R2, C1 constitute the proportional component of control signal input channel；A2 Yu R3, R4, C2 constitute negative Carry the proportional component of disturbing signal input channel；A3 Yu R5, R6, R7, R8, R9, R10, C3 constitute signal adder substracter；A4, A5 with R11, R12, R13, C5, C6 constitute the proportion differential link of load signal input channel；A6 Yu R14, R15, C7 constitute oil sources pressure Force signal input channel proportional component；A7, A8, A9 and R16, R17, R18, R19, R20, R21, R22, R23, C8, C9, C10, C12 constitutes two-step element；A10 Yu C13, C14 constitute integral element.

The inverting input of described first amplifier A1 passes sequentially through the anti-phase of resistance R2, resistance R5 and the 3rd amplifier A3 Input is connected, and the positive input end grounding of the first amplifier A1, the inverting input of the 3rd amplifier A3 is connect by resistance R9 Its outfan；The positive input end grounding of the 4th amplifier A4, the inverting input of the 4th amplifier A4 by resistance R11 and its Outfan is connected, the positive input end grounding of the 5th amplifier A5, the positive input end grounding of the 6th amplifier A6, and the 6th amplifies The inverting input of device A6 is connected with its outfan by resistance R15；The normal phase input end of the 3rd amplifier A3 passes through resistance R10 Ground connection, the inverting input of the 3rd amplifier A3 is connected with its outfan by resistance R9；The positive input of the 7th amplifier A7 Holding by resistance R18 ground connection, the inverting input of the 7th amplifier A7 is connected with its outfan by resistance R19；8th amplifies The positive input end grounding of device A8, the inverting input of the 8th amplifier A8 connects its outfan by electric capacity C9；9th amplifier The positive input end grounding of A9, the inverting input of the 9th amplifier A9 connects its outfan by resistance R22, and electric capacity C11 is in parallel On resistance R22；The positive input end grounding of the tenth amplifier A10, its inverting input connects its outfan by electric capacity C13.

Described trave lling girder uphill process simulator, trave lling girder decline process simulator, trave lling girder advance process simulator and The resistance of resistance R2, R4, R13, R15 in trave lling girder fallback procedures simulator is different, described trave lling girder uphill process simulator, The resistance of the resistance R3 in trave lling girder decline process simulator, trave lling girder fallback procedures simulator is identical and advances with trave lling girder The resistance of the resistance R3 in journey simulator is different, and described trave lling girder uphill process simulator, trave lling girder decline in process simulator The resistance of resistance R14 identical, resistance R14 in described trave lling girder advance process simulator and trave lling girder fallback procedures simulator Resistance identical, the resistance of the resistance R14 in described trave lling girder uphill process simulator and described trave lling girder advance process simulation The resistance of the resistance R14 in device is different.

In sum, the present invention, on the basis of research step rate mathematical model, based on operation amplifier circuit, develops A set of simulator, provides experiment bar for the debugging before step rate control method research, control equipment development, the installation of control equipment Part, the time needed for making step rate field adjustable is greatly shortened, and the implementation cost of engineering can be greatly lowered；For huge Step rate system, on the basis of establishing a whole set of mathematical model, uses operational amplifier, it is achieved that billet heating furnace stepping Beam rises, declines, the simulator of the Four processes that advances, retreats.

Claims (7)

1. the step rate system simulator of a billet heating furnace, it is characterised in that: include trave lling girder uphill process simulator, shifting Dynamic beam declines process simulator, trave lling girder advance process simulator and trave lling girder fallback procedures simulator, and four circuit are identical, institute State trave lling girder rise/fall/forward/backward process simulator and include resistance R1, one termination be used for controlling trave lling girder rise/under Fall/forward/backward control signal, the inverting input of its other end and the first amplifier A1 is connected, the first amplifier A1's Outfan is connected by the inverting input of resistance R5 and the 3rd amplifier A3；The inverting input of the 4th amplifier A4 is by electricity Holding C4 and connect load signal, the outfan of the 4th amplifier is connected with one end of resistance R12, and the other end of resistance R12 is respectively with the The inverting input of five amplifier A5, one end of resistance R13 are connected, the other end of resistance R13 and the output of the 5th amplifier A5 End is connected by the normal phase input end of resistance R7 and the 3rd amplifier A3 after being connected；The inverting input of the second amplifier A2 passes through Resistance R3 connects load signal, and the inverting input of the second amplifier A2 passes sequentially through resistance R4, R6 and just meeting the 3rd amplifier A3 Phase input；The outfan of the second amplifier A2 is connected between resistance R4 and resistance R6, the inverting input of the 6th amplifier A6 Connecing hydraulic cylinder oil supply pressure signal by resistance R14, the outfan of the 6th amplifier A6 passes through resistance R8 and the 3rd amplifier A3 Normal phase input end be connected；The outfan of the 3rd amplifier A3 passes through resistance R17 and the normal phase input end phase of the 7th amplifier A7 Even, the inverting input of the 7th amplifier A7 is connected by the outfan of resistance R16 and the 9th amplifier A9, the 7th amplifier A7 Outfan be connected by the inverting input of resistance R20 and the 8th amplifier A8, the outfan of the 8th amplifier A8 is by electricity The inverting input of resistance R21 and the 9th amplifier A9 is connected, and the outfan of the 9th amplifier A9 is amplified by resistance R23 and the tenth The inverting input of device A10 is connected, the outfan output mobile beam rise/fall/forward/backward displacement of the tenth amplifier A10 Signal.

The step rate system simulator of billet heating furnace the most according to claim 1, it is characterised in that: described first amplifies The inverting input of device A1 passes sequentially through the inverting input of resistance R2, resistance R5 and the 3rd amplifier A3 and is connected, and first amplifies The positive input end grounding of device A1, the inverting input of the 3rd amplifier A3 connects its outfan by resistance R9；4th amplifier The positive input end grounding of A4, the inverting input of the 4th amplifier A4 is connected with its outfan by resistance R11, and the 5th amplifies The positive input end grounding of device A5, the positive input end grounding of the 6th amplifier A6, the inverting input of the 6th amplifier A6 leads to Cross resistance R15 to be connected with its outfan；The normal phase input end of the 3rd amplifier A3 passes through resistance R10 ground connection, the 3rd amplifier A3 Inverting input be connected with its outfan by resistance R9；The normal phase input end of the 7th amplifier A7 passes through resistance R18 ground connection, The inverting input of the 7th amplifier A7 is connected with its outfan by resistance R19；The normal phase input end of the 8th amplifier A8 connects Ground, the inverting input of the 8th amplifier A8 connects its outfan by electric capacity C9；The positive input end grounding of the 9th amplifier A9, The inverting input of the 9th amplifier A9 connects its outfan by resistance R22, and electric capacity C11 is connected in parallel on resistance R22；Tenth amplifies The positive input end grounding of device A10, its inverting input connects its outfan by electric capacity C13.

The step rate system simulator of billet heating furnace the most according to claim 1, it is characterised in that: on described trave lling girder Rise process simulator, trave lling girder declines process simulator, trave lling girder advance process simulator and trave lling girder fallback procedures simulator In the resistance of resistance R2, R4, R13, R15 different, described trave lling girder uphill process simulator, trave lling girder decline process simulation The resistance of the resistance R3 in device, trave lling girder fallback procedures simulator identical and with the resistance R3 in trave lling girder advance process simulator Resistance different, described trave lling girder uphill process simulator, trave lling girder decline the resistance phase of the resistance R14 in process simulator With, described trave lling girder advance process simulator is identical with the resistance of the resistance R14 in trave lling girder fallback procedures simulator, described shifting The resistance of the resistance R14 in dynamic beam uphill process simulator and the resistance of the resistance R14 in described trave lling girder advance process simulator It is worth different.

4. the analogy method of the step rate system simulator of a billet heating furnace, it is characterised in that: set up step rate system number Learn model, if U_up、U_downIt is respectively rising, declines control signal, U_forw、U_backIt is respectively advance, retreats control signal, P_sFor Oil supply pressure, F_LFor load, x_pFor hydraulic cylinder piston displacement, y_up、y_downIt is respectively step rate to rise, decline displacement, x_forw、 x_backBeing respectively step rate to advance, retreat displacement, its model expression is as follows:

Electrohydraulic proportional directional valve spool displacement X_v(s) and control signal U (s), i.e. U_up、U_down、U_forw、U_backBetween transmission letter Number is:

$W_{sv}\left(s\right)=\frac{X_v\left(s\right)}{U\left(s\right)}=\frac{K_{sv}}{T_{sv}s+1}---\left(1\right)$

Wherein, K_sv、T_svBeing respectively gain and the time constant of electrohydraulic proportional directional valve, s is dynamic factor；

Piston displacement X_Px(s) and spool displacement X_vS the transmission function between () is:

$W_o\left(s\right)=\frac{X_{px}\left(s\right)}{X_v\left(s\right)}=\frac{\frac{K_q}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(K_c+C_p)M}{A_1^2}{s}^2+s}---\left(2\right)$

Wherein, C_p=2C_i/ (1+ η), V_t1=4V₁/ (1+ η), η=A₂/A₁, V₁=A₁L/2, F_L=Mg, g are acceleration of gravity, on Rise M=M during declining_sSin θ, during forward-reverse, M is M_sFrictional force during effect, θ is two-wheel ramp formula stepping mechanism Ramp angles；K_qFor flow gain, A₁、A₂Being respectively hydraulic cylinder rodless cavity and the effective area of rod chamber, L is hydraulic cylinder row Cheng Changdu, K_cFor flow pressure coefficient, β_eFor effective volume elastic modelling quantity, V₁、V₂It is respectively hydraulic cylinder rodless cavity and rod chamber Volume, C_iFor the hydraulic cylinder interior leakage coefficient of leakage, M is the component that load quality acts on hydraulic cylinder, M_sFor steel billet and step rate framework Gross mass, s is dynamic factor；

Piston displacement X_pf(s) and load F_LS the transmission function between () is:

$W_f\left(s\right)=\frac{X_{pf}\left(s\right)}{F_L\left(s\right)}=\frac{\frac{1}{A_1^2}(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(K_c+C_p)M}{A_1^2}{s}^2+s}---\left(3\right)$

Piston displacement X_pp(s) and oil supply pressure P_sS the transmission function between () is:

$W_1\left(s\right)=\frac{X_{pp}\left(s\right)}{P_s\left(s\right)}=\frac{\frac{C_s}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{(K_c+C_p)M}{A_1^2}{s}^2+s}---\left(4\right)$

Wherein, C_s=C_i(1-η)/(1+η)；

Convolution (2), (3), (4) understand, piston displacement X_p(s) be:

$\begin{array}{c}{X}_p\left(s\right)=\frac{\frac{K_q}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_1^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}U\left(s\right)\\ +\frac{-\frac{1}{A_1^2}\left(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p\right)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_1^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_1}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_1^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(5\right)$

Trave lling girder vertical displacement is:

Y (s)=X_p(s)sinθ (6)。

The analogy method of the step rate system simulator of billet heating furnace the most according to claim 4, it is characterised in that: institute The expression formula stating trave lling girder uphill process mathematical model is:

$\begin{array}{c}{Y}_{up}\left(s\right)=\frac{\frac{K_q}{A_1}\sin \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_1^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{up}\left(s\right)\\ +\frac{-\frac{\sin \mathrm{\θ}}{A_1^2}\left(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p\right)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_1^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_1}\sin \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_1^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(7\right)$

Described trave lling girder declines process mathematical model:

$\begin{array}{c}{Y}_{down}\left(s\right)=\frac{\frac{K_q}{A_2}\sin \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_2^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{down}\left(s\right)\\ +\frac{-\frac{\sin \mathrm{\θ}}{A_2^2}\left(\frac{V_{t2}}{4{\mathrm{\β}}_e}s+K_c+C_p\right)}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_2^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_2}\sin \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_2^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(8\right)$

Wherein, V_t2For rod chamber effective volume；

Trave lling girder horizontal displacement is:

X (s)=X_p(s)cosθ (9)；

Trave lling girder advance process mathematical model is:

$\begin{array}{c}{X}_{forw}\left(s\right)=\frac{\frac{K_q}{A_1}\cos \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_1^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{forw}\left(s\right)\\ +\frac{-\frac{\cos \mathrm{\θ}}{A_1^2}\left(\frac{V_{t1}}{4{\mathrm{\β}}_e}s+K_c+C_p\right)}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_1^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_1}\cos \mathrm{\θ}}{\frac{V_{t1}M}{4{\mathrm{\β}}_e{A}_1^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_1^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(10\right);$

Trave lling girder fallback procedures mathematical model is:

$\begin{array}{c}{X}_{back}\left(s\right)=\frac{\frac{K_q}{A_2}\cos \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_2^2}{s}^2+s}\frac{K_{sv}}{T_{sv}s+1}{U}_{back}\left(s\right)\\ +\frac{-\frac{\cos \mathrm{\θ}}{A_2^2}\left(\frac{V_{t2}}{4{\mathrm{\β}}_e}s+K_c+C_p\right)}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_2^2}{s}^2+s}{F}_L\left(s\right)\\ +\frac{\frac{C_s}{A_2}\cos \mathrm{\θ}}{\frac{V_{t2}M}{4{\mathrm{\β}}_e{A}_2^2}{s}^3+\frac{\left(C_p+K_c\right)M}{A_2^2}{s}^2+s}{P}_s\left(s\right)\end{array}---\left(11\right);$

Wherein, V_t2For rod chamber effective volume.

The analogy method of the step rate system simulator of billet heating furnace the most according to claim 5, it is characterised in that: order Flow gain K_q=1.08m²/ s, rodless cavity effective area A₁=0.0616m², rod chamber effective area A₂=0.0301m², without bar Chamber effective volume V_t1=0.076m³, rod chamber effective volume V_t2=0.0372m³, mass M=1.31 × 10⁵Kg, fluid is elastic Modulus β_e=6.9 × 10⁸Pa, reveals coefficient in equivalence

C_p=4.027 × 10^-11m⁵/ (Ngs), flow pressure K_c=2.16 × 10^-10m⁵/ (Ngs), equivalence outward leakage coefficient

C_s=1.027 × 10^-11m⁵/ (Ngs), leadage coefficient C_i=3.0 × 10^-11m⁵/ (Ngs), area ratio η=0.49, θ=17 °； Being substituted into by above-mentioned parameter in formula (7), obtain trave lling girder uphill process simulator, its expression formula is as follows:

$\begin{array}{c}{Y}_{up}\left(s\right)=5.13\frac{1}{9.5\×{10}^{-4}{s}^2+8.8\×{10}^{-3}s+1}\frac{1}{s}{U}_{up}\left(s\right)\\ -\frac{2.12\×{10}^{-9}s+1.97\×{10}^{-8}}{9.5\×{10}^{-4}{s}^2+8.8\×{10}^{-3}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -4.87\×{10}^{-11}\frac{1}{9.5\×{10}^{-4}{s}^2+8.8\×{10}^{-3}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(12\right);$

Being substituted into by above-mentioned parameter in formula (8), obtain trave lling girder and decline process simulator, its expression formula is as follows:

$\begin{array}{c}{Y}_{down}\left(s\right)=10.5\frac{1}{1.9\×{10}^{-3}{s}^2+3.71\×{10}^{-2}s+1}\frac{1}{s}{U}_{down}\left(s\right)\\ -\frac{4.35\×{10}^{-9}s+8.27\×{10}^{-8})}{1.9\×{10}^{-3}{s}^2+3.71\×{10}^{-2}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -9.98\×{10}^{-11}\frac{1}{1.9\×{10}^{-3}{s}^2+3.71\×{10}^{-2}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(13\right).$

The analogy method of the step rate system simulator of billet heating furnace the most according to claim 5, it is characterised in that: order Flow gain K_q=2.45m²/ s, rodless cavity effective area A₁=0.038m², rod chamber effective area A₂=0.0226m², without bar Chamber effective volume V_t1=0.0157m³, rod chamber effective volume V_t2=0.0093m³, mass M=0.729 × 10⁵Kg, fluid bullet Property modulus β_e=6.9 × 10⁸Pa, reveals coefficient in equivalence

C_p=3.75 × 10^-11m⁵/ (Ngs), flow pressure K_c=2.16 × 10^-10m⁵/ (Ngs), equivalence outward leakage coefficient

C_s=7.5 × 10^-11m⁵/ (Ngs), leadage coefficient C_i=3.0 × 10^-11m⁵/ (Ngs), area ratio η=0.6, θ=17 °；Will Above-mentioned parameter substitutes in formula (10), obtains trave lling girder advance process simulator, and its expression formula is as follows:

$\begin{array}{c}{X}_{forw}\left(s\right)=61.66\frac{1}{2.87\×{10}^{-4}{s}^2+1.3\×{10}^{-2}s+1}\frac{1}{s}{U}_{forw}\left(s\right)\\ -\frac{3.76\×{10}^{-9}s+1.68\×{10}^{-7}}{2.87\×{10}^{-4}{s}^2+1.3\×{10}^{-2}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -1.89\×{10}^{-10}\frac{1}{2.87\×{10}^{-4}{s}^2+1.3\×{10}^{-2}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(14\right);$

Being substituted into by above-mentioned parameter in formula (11), obtain trave lling girder fallback procedures simulator, its expression formula is as follows:

$\begin{array}{c}{X}_{back}\left(s\right)=103.67\frac{1}{8\×{10}^{-4}{s}^2+3.6\×{10}^{-2}s+1}\frac{1}{s}{U}_{back}\left(s\right)\\ -\frac{1.065\×{10}^{-8}s+4.74\×{10}^{-7}}{8\×{10}^{-4}{s}^2+3.6\×{10}^{-2}s+1}\frac{1}{s}{F}_L\left(s\right)\\ -3.17\×{10}^{-10}\frac{1}{8\×{10}^{-4}{s}^2+3.6\×{10}^{-2}s+1}\frac{1}{s}{P}_s\left(s\right)\end{array}---\left(15\right).$