CN103422923B - There is the double peak cam design method of diesel exhaust recirculation function - Google Patents

Abstract

A kind of double peak cam design method with diesel exhaust recirculation function, first main cam buffering ascent stage, active section, buffer falling section are set up in segmentation, major and minor cam linkage section, 6 equations of the cam tappet lifting curve h (α) such as auxiliary cam active section, buffer falling section, obtain each equational undetermined coefficient, then undetermined coefficient is updated in the mathematical equation of foundation, obtains the double peak cam molded line with diesel exhaust recirculation function.Wherein: the acceleration-constant speed formula equation designs such as major and minor breeze way employing; The active section of major and minor cam adopts high order five formula equation designs; Linkage section then adopts six seven formula equations designs.The present invention can according to the demand of artificer, control moment and waste gas inlet that engine exhaust enters cylinder again accurately, flexibly, the mixed proportion of the fresh air in cylinder and waste gas is controlled, improve the combustion condition in cylinder, reach the optimal coordination of diesel engine performance and NOx discharge.

Description

There is the double peak cam design method of diesel exhaust recirculation function

Technical field

The present invention relates to a kind of double peak cam design method with diesel exhaust recirculation function, belong to diesel emission abatement technical field.

Background technique

Diesel exhaust recirculation (Exhaust Gas Recirculation, EGR) technology is one of the most effective and reliable emission-reduction technology method in purification technics in current diesel engine.This technological method a part of waste gas is introduced cylinder or offgas discharge amount is reduced, and allows burned waste gas again participate in the burning of next work cycle.After waste gas mixes with fresh air, in cylinder, mixed gas composition there occurs change, due to inert gas (CO contained in waste gas ₂, N ₂deng) there is characteristic compared with high specific heat, in-cylinder combustion temperature gas can be made to reduce, have certain inhibitory action to the generation of noxious emission NOx, realize reducing harmful gas NOx and generate and the object of discharge.

EGR Technology is divided into waste gas to remain and waste gas heavily inhales two kinds of strategic management of technology.It is extensive that current waste gas remains strategic management of technology Application comparison in internal-combustion engine, and the core methed that waste gas remains technology realization is: minimizing offgas discharge amount, thus the burned waste gas of a part is remained in cylinder.Realize this strategy and have two kinds of approach, be that duration angle by shortening exhauxt valve opens reduces the discharge capacity of waste gas, but the height risen due to exhaust cam to reach tens millimeters, usually so the reduction of cam opening angle, the difficulty of design of cam contour line can be increased, system reliability is reduced; Simultaneously in exhaust stroke, the speed of exhaust changes along with the continuous change of cylinder inside and outside differential pressure.Reduce exhaust duration very large to the whole process influence of exhaust, the discharge capacity of waste gas cannot be controlled exactly, realize the target accurately controlling ER EGR Rate.The second approach is that application variable cam phase discriminator (VCP) adjusts valve overlap, and the phase place making exhauxt valve opens and closedown in advance, by missing effective exhaust opportunity, reaching reduction air displacement, producing the object that waste gas is residual.This method needs to increase a set of timing adjusting device in addition and goes to change former cam phase, and additional regulating device adds complexity and the cost of system.The discharge capacity adopting change valve overlap to reduce waste gas is feasible, but this gas flow and phase matching relationship complexity, still accurately cannot control residual exhaust gases amount.

The scholars such as the John Schwoerer of Jacobs vehicle system in 2004, the theory of a kind of exhaust valve secondary opening (Exhaust ValveRe-opening, EVRO) or intake valve secondary opening generation IEGR is refer to first in the literary composition being entitled as Internal EGR Systems for NOxEmission (SAE2004-01-1315); In 2006 and 2009 subsequently year, the scholars such as the Kiyoshi KAWASAKI of ShigaPrefecture university of Japan, deliver many sections respectively and improve rock gas homogeneous charge combustion ignition (HCCI) thermal efficiency and the article reducing the combustible gases in discharging about utilizing waste gas residual heat, describe in literary composition in motor work cycle, use engines distribution cam to the control action of valve, allow into or exhaust valve twice unlatching, allow the waste gas of discharging cylinder come back to thinking in cylinder.But also there is not the detailed introduction of relevant waste gas heavy suction IEGR technology concrete methods of realizing so far both at home and abroad, more have no the relevant report that this technology is implemented.

Summary of the invention

The invention discloses a kind of double peak cam design method with diesel exhaust recirculation function, object is to overcome the design of existing diesel engine cam, there is the drawback cannot carrying out accurately control to residual exhaust gases amount; Reach the method reducing offgas discharge amount according to the duration angle shortening exhauxt valve opens, design of cam contour line difficulty can be increased, system reliability is reduced; Adjust valve overlap according to variable cam phase discriminator (VCP) and reach reduction air displacement method, complexity and the cost of system can be increased, simultaneously gas flow and phase matching relationship complexity.

The key technology of the present invention's design is in motor work cycle, and make exhaust valve twice unlatching and the EGR that will be produced by the unlatching of exhaust valve second time, realization reduces the object that harmful gas NOx generates and discharges, core content sets up the cam profile mathematical model that can control secondary opening of air valve, according to the pressure condition of cylinder in intake stroke and exhaust duct, realized the characteristics of motion of adjustment secondary opening cam flexibly by adjust design parameters by artificer, the start-up time of conservative control secondary opening exhaust valve and lasting phase angle, and can be according to the actual requirements, accurately, control motor neatly at different stroke stage waste gas back amount and ER EGR Rate, the mixed proportion of live gas and waste gas in cylinder is controlled, realize the combustion condition effectively improved in cylinder, reach the object that diesel engine performance and NOx emission thing control optimal coordination.

Technical solution of the present invention is achieved in that

A kind of double peak cam design method with diesel exhaust recirculation function, first main cam buffering ascent stage, active section, buffer falling section are set up in segmentation, major and minor cam linkage section, 6 equations of the cam tappet lifting curve h (α) such as auxiliary cam active section, buffer falling section, obtain each equational undetermined coefficient, then undetermined coefficient is updated in the mathematical equation of foundation, obtains the double peak cam molded line with diesel exhaust recirculation function; Concrete implementation step is as follows:

1, cam curve equation is set up in segmentation:

In Valve Cam Design, the lift of cam states with the lift range value of plane tappet.The definition of tappet lift function is when cam turns over angle [alpha], and tappet rises displacement h from initial position, and namely tappet lift function is h=h (α).In the working procedure of a certain operating mode, the rotation of camshaft can be considered as uniform rotation, then tappet lift function be asked to the first derivative of α, what obtain is tappet geometry velocity function (abbreviation speed), namely its physical significance is the variance ratio of tappet displacement with cam angle.In like manner, tappet lift function is asked to the second dervative of α, what obtain is tappet geometry acceleration function (abbreviation acceleration), namely its physical significance is the variance ratio of tappet speed with cam angle.

This cam tappet lifting curve h (α) is made up of 6 sections of equations, and its representation is as shown in (1) ~ (6); Here, the unit of cam angle unifies usage degree (°), and lift unit is unified uses millimeter (mm), and tappet speed unit is unified uses (mm/ °), and tappet unit of acceleration is unified uses (mm/ (°) ²), and easy in order to calculate, when the molded line carrying out each section calculates, all the starting point of cam angle is set to zero, finally namely result translation can be obtained the molded line of whole piece double peak cam.

(A) first portion is main cam buffering ascent stage curve.Main cam buffering ascent stage curve h ₁(α) be made up of two sections of curvilinear equations, its representation is:

$h_1\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}{C}_B{\mathrm{\α}}^2& 0\≤\mathrm{\α}\≤{\mathrm{\β}}_1\\ E_0+E_1\mathrm{\α}& {\mathrm{\β}}_1\≤\mathrm{\α}\≤{\mathrm{\α}}_1\end{array}\right.---\left(1\right)$

In formula, α ₁for the cornerite of main cam buffering ascent stage, α is cam angle; β ₁it is the angle of two sections of equation separations; C _b﹑ E ₀﹑ E ₁be undetermined coefficient.

(B) second portion is main cam active section curve h ₂(x), its curvilinear equation mathematic(al) representation is:

h ₂(x)＝H ₁+c ₀+c _px ^p+c _qx ^q+c _rx ^r+c _sx ^s0≤α≤α ₂(2)

Wherein: $x=1-\frac{2\mathrm{\α}}{{\mathrm{\α}}_2}$

α in formula ₂for main cam active section cornerite, H ₁for main cam buffering ascent stage full lift; c ₀, c _p, c _q, c _r, c _sfor undetermined coefficient; For the value of index p, q, r, s of independent variable x in high order five formula equations, according to maximum geometry speed, the maximum positive and negative geometry acceleration of different engine cam molded line, the restriction requirement of the characteristic parameters such as radius of curvature, in equation, index p, q, r, s of independent variable x can get the different values increased progressively.

(C) Part III is main cam buffer falling section curve h ₃(α), its equation is:

$h_3\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}{E}_0-E_1(\mathrm{\α}-{\mathrm{\α}}_1)& 0\≤\mathrm{\α}\≤{\mathrm{\α}}_1-{\mathrm{\β}}_1\\ C_B{(\mathrm{\α}-{\mathrm{\α}}_1)}^2& {\mathrm{\α}}_1-{\mathrm{\β}}_1\≤\mathrm{\α}\≤{\mathrm{\α}}_1\end{array}\right.---\left(3\right)$

The starting point of main cam buffer falling section curve is the terminal of main cam active section curve.

(D) Part IV is major and minor cam linkage section curve h ₄(α), this partial trace equation is:

h ₄(α)＝A ₀-A ₁α+A ₂α ²-A ₃α ³+A ₄α ⁴-A ₅α ⁵+A ₆α ⁶0≤α≤α ₄(4)

Wherein, α ₄for the cornerite size of linkage section.The starting point of linkage section and cornerite size are set according to inner pressure of air cylinder and outlet pipe pressure wave situation by artificer.The starting point of linkage section curve is chosen a bit in the buffer falling section curve of main cam, and terminal drops on the starting point of auxiliary cam active section curve.

In formula, A ₀, A ₁, A ₂, A ₃, A ₄, A ₅, A ₆for the undetermined coefficient of linkage section, determined by the boundary conditions of the major and minor cam of the right and left and supplementary condition;

(E) Part V is auxiliary cam active section curve h ₅(x), its curve math representation is:

h ₅(x)＝H ₆+c ₀′+c _p′x ^p+c _q′x ^q+c _r′x ^r+c _s′x ^s0≤α≤α ₅(5)

Wherein: $x=1-\frac{2\mathrm{\α}}{{\mathrm{\α}}_5}$

α ₅for auxiliary cam active section cornerite, H ₆for auxiliary cam buffer falling section full lift; c ₀', c _p', c _q', c _r', c _s' be undetermined coefficient, determined by boundary conditions;

(F) Part VI curve is auxiliary cam buffer falling section curve h ₆(α), representation is:

$h_6\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}{E_0}^{\′}-{E_1}^{\′}(\mathrm{\α}-{\mathrm{\α}}_6)& 0\≤\mathrm{\α}\≤{\mathrm{\α}}_6-{\mathrm{\β}}_2\\ {C_B}^{\′}{(\mathrm{\α}-{\mathrm{\α}}_6)}^2& {\mathrm{\α}}_6-{\mathrm{\β}}_2\≤\mathrm{\α}\≤{\mathrm{\α}}_6\end{array}\right.---\left(6\right)$

In formula, α ₆for the cornerite of auxiliary cam buffer falling section, β ₂it is the angle of two sections of equation separations; C _b′ ﹑ E ₀′ ﹑ E ₁' be undetermined coefficient;

Terminal due to linkage section curve drops on the starting point of auxiliary cam active section curve, so the breeze way of auxiliary cam only has descending branch;

2, the undetermined coefficient of cam breeze way curvilinear equation, active section curvilinear equation, linkage section curvilinear equation is solved respectively;

(A) cam breeze way curvilinear equation undetermined coefficient solving method:

Main cam buffering ascent stage curvilinear equation is:

$h_1\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}{C}_B{\mathrm{\α}}^2& 0\≤\mathrm{\α}\≤{\mathrm{\β}}_1\\ E_0+E_1\mathrm{\α}& {\mathrm{\β}}_1\≤\mathrm{\α}\≤{\mathrm{\α}}_1\end{array}\right.---\left(1\right)$

Four undetermined coefficient β in formula ₁, C _b﹑ E ₀﹑ E ₁calculating determined by following formula (7) ~ (13):

As α=α ₁time, now lifting curve h ₁(α) host buffer ascent stage curve full lift H is equaled ₁, that is:

H ₁＝E ₀+E ₁α ₁(7)

At separation α=β ₁place, two sections of curve lift h ₁(α) keep continuously, that is:

$C_B\·{\mathrm{\β}}_1^2=E_0+E_1{\mathrm{\β}}_1---\left(8\right)$

Further, at this separation place, also keep continuously, that is:

2C _B·β ₁＝E ₁(9)

By being given in α=α ₁time host buffer ascent stage End of Curve speed ν ₁, obtain:

${\frac{{\mathrm{dh}}_1\left(\mathrm{\α}\right)}{d\mathrm{\α}}|}_{\mathrm{\α}={\mathrm{\α}}_1}=E_1={\mathrm{\ν}}_1---\left(10\right)$

ν ₁be the tappet speed of host buffer ascent stage End of Curve, unit is mm/ °, for Designer is according to engine speed auto-selecting parameter.

Can be released by (7) and (10):

E ₀＝H ₁-E ₁α ₁＝H ₁-ν ₁·α ₁(11)

(9) are brought into (8) to obtain:

${\mathrm{\β}}_1=-\frac{2E_0}{E_1}=\frac{2({\mathrm{\ν}}_1\·{\mathrm{\α}}_1-H_1)}{{\mathrm{\ν}}_1}---\left(12\right)$

Again according to (9), have:

$C_B=\frac{E_1}{2{\mathrm{\β}}_1}=\frac{{\mathrm{\ν}}_1^2}{4({\mathrm{\ν}}_1\·{\mathrm{\α}}_0-H_1)}---\left(13\right)$

Known by separating formula (10) ~ (13), as long as know parameter H ₁﹑ ν ₁﹑ α ₁, just can obtain its 4 undetermined coefficient β ₁, C _b﹑ E ₀﹑ E ₁, and H ₁﹑ ν ₁﹑ α ₁require to decide in advance according to the concrete condition of distribution device.

Auxiliary cam buffer falling section curvilinear equation is:

$h_6\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}{E_0}^{\′}-{E_1}^{\′}(\mathrm{\α}-{\mathrm{\α}}_6)& 0\≤\mathrm{\α}\≤{\mathrm{\α}}_6-{\mathrm{\β}}_2\\ {C_B}^{\′}{(\mathrm{\α}-{\mathrm{\α}}_6)}^2& {\mathrm{\α}}_6-{\mathrm{\β}}_2\≤\mathrm{\α}\≤{\mathrm{\α}}_6\end{array}\right.---\left(6\right)$

According to initial known conditions α ₆, H ₆, ν ₆, following solution formula can be obtained:

E ₁′＝ν ₆(14)

E ₀′＝H ₆-ν ₆·α ₆(15)

${\mathrm{\β}}_2=-\frac{2{E_0}^{\′}}{{E_1}^{\′}}=\frac{2({\mathrm{\ν}}_6\·{\mathrm{\α}}_6-H_6)}{{\mathrm{\ν}}_6}---\left(16\right)$

${C_B}^{\′}=\frac{{E_1}^{\′}}{2{\mathrm{\β}}_2}=\frac{{\mathrm{\ν}}_6^2}{4({\mathrm{\ν}}_6\·{\mathrm{\α}}_6-H_6)}---\left(17\right)$

(B) cam work section curvilinear equation undetermined coefficient solving method:

Main cam active section curvilinear equation is:

h ₂(x)＝H ₁+c ₀+c _px ^p+c _qx ^q+c _rx ^r+c _sx ^s0≤α≤α ₂(2)

Wherein, $x=1-\frac{2\mathrm{\α}}{{\mathrm{\α}}_2}$

Solve undetermined coefficient c ₀, c _p, c _q, c _r, c _s

Calculation of boundary conditions:

1., when α=0, namely during x=1, it is continuous that main cam active section beginning of curve lift and main cam cushion ascent stage End of Curve lift, then have h ₂(1)=H ₁, abbreviation obtains:

c ₀+c _p+c _q+c _r+c _s＝0 (18)

2. when α=0, namely during x=1, now main cam active section beginning of curve speed v ₂ascent stage End of Curve speed v is cushioned with main cam ₁keep continuously, namely

${\frac{{\mathrm{dh}}_2}{d\mathrm{\α}}|}_{\mathrm{\α}=0}=v_1=v_2\⇒{\frac{{\mathrm{dh}}_2}{d\mathrm{\α}}|}_{\mathrm{\α}=0}={(\frac{{\mathrm{dh}}_2}{dx}\·\frac{dx}{d\mathrm{\α}})|}_{\mathrm{\α}=0}={\frac{{\mathrm{dh}}_2\left(x\right)}{dx}|}_{x=1}.{\frac{dx}{d\mathrm{\α}}|}_{\mathrm{\α}=0}=v_2$

$({\mathrm{pc}}_p+{\mathrm{qc}}_q+{\mathrm{rc}}_r+{\mathrm{sc}}_s)\×(-\frac{2}{{\mathrm{\α}}_2})=v_2$

Abbreviation obtains:

${\mathrm{pc}}_p+{\mathrm{qc}}_q+{\mathrm{rc}}_r+{\mathrm{sc}}_s=-\frac{v_2{\mathrm{\α}}_2}{2}---\left(19\right)$

3., when α=0, namely during x=1, the acceleration that now acceleration of main cam active section beginning of curve and main cam cushion ascent stage End of Curve keeps continuously, namely thus:

p(p-1)c _p+q(q-1)c _q+r(r-1)c _r+s(s-1)c _s＝0 (20)

4., when α=0, namely during x=1, now main cam active section pulse and main cam cushion ascent stage end pulses and keep continuously, $\frac{d^3{h}_2\left(x\right)}{{\mathrm{d\α}}^3}=0,$ Namely $\frac{d^3{h}_2\left(x\right)}{{\mathrm{dx}}^3}=0,$ Thus:

p(p-1)(p-2)c _p+q(q-1)(q-2)c _q+r(r-1)(r-2)c _r+s(s-1)(s-2)c _s＝0 (21)

5. when namely during x=0, h ₂(0)=H ₂, H ₂for known main cam active section full lift, that is:

c ₀＝H ₂(22)

Simultaneous five, above-mentioned (16) ~ (20) boundary conditions can obtain following five solution formulas:

c ₀＝H ₂(23)

$c_p=\frac{-2H_{2}srq+v_2{\mathrm{\α}}_2(sr+sq+rq-s-r-q+1)}{2(s-q)(r-q)(p-q)}---\left(24\right)$

$c_q=\frac{-2H_{2}srp+v_2{\mathrm{\α}}_2(sr+sp+rq-s-r-p+1)}{2(s-q)(r-q)(q-q)}---\left(25\right)$

$c_r=\frac{-2H_{2}spq+v_2{\mathrm{\α}}_2(sq+sp+pq-s-p-q+1)}{2(s-r)(p-r)(q-r)}---\left(26\right)$

$c_s=\frac{-2H_{2}rpq+v_2{\mathrm{\α}}_2(pq+rq+rp-r-p-q+1)}{2(q-s)(r-s)(p-s)}---\left(27\right)$

Namely visible, as long as know parameter H ₂﹑ ν ₂﹑ α ₂﹑ p ﹑ q ﹑ r ﹑ s, just can obtain undetermined coefficient c ₀, c _p, c _q, c _r, c _s, and H ₂﹑ ν ₂﹑ α ₂be all require to decide in advance according to the concrete condition of distribution device, remaining index p ﹑ q ﹑ r ﹑ s is then determined when design of cam contour line.

For the value of index p, q, r, s of independent variable x in high order five formula equations, according to maximum geometry speed, the maximum positive and negative geometry acceleration of different engine cam molded line, the restriction requirement of the characteristic parameters such as radius of curvature, in equation, index p, q, r, s of independent variable x can get the different values increased progressively.

Auxiliary cam active section curvilinear equation:

h ₅(x)＝H ₆+c ₀′+c _p′x ^p+c _q′x ^q+c _r′x ^r+c _s′x ^s0≤α≤α ₅(5)

Wherein, $x=1-\frac{2\mathrm{\α}}{{\mathrm{\α}}_5}$

According to known parameters H ₅﹑ ν ₅﹑ α ₅﹑ p ﹑ q ﹑ r ﹑ s, can obtain following five solution formulas:

c ₀′＝H ₅(28)

${c_p}^{\′}=\frac{-2H_{5}srq+v_5{\mathrm{\α}}_5(sr+sq+rq-s-r-q+1)}{2(s-q)(r-q)(p-q)}---\left(29\right)$

${c_q}^{\′}=\frac{-2H_{5}srp+v_5{\mathrm{\α}}_5(sr+sp+rq-s-r-p+1)}{2(s-q)(r-q)(q-q)}---\left(30\right)$

${c_r}^{\′}=\frac{-2H_{5}spq+v_5{\mathrm{\α}}_5(sq+sp+pq-s-p-q+1)}{2(s-r)(p-r)(q-r)}---\left(31\right)$

${c_s}^{\′}=\frac{-2H_{5}rpq+v_5{\mathrm{\α}}_5(pq+rq+rp-r-p-q+1)}{2(q-s)(r-s)(p-s)}---\left(32\right)$

(C) major and minor cam linkage section curvilinear equation undetermined coefficient solving method:

Major and minor cam linkage section curvilinear equation is by equation

h ₄(α)＝A ₀-A ₁α+A ₂α ²-A ₃α ³+A ₄α ⁴-A ₅α ⁵+A ₆α ⁶0≤α≤α ₄(4)

Parameter A in formula ₀, A ₁, A ₂, A ₃, A ₄, A ₅, A ₆determined by (41) ~ (47);

1. linkage section point of curve position is determined.

The starting point of linkage section curve is chosen a bit in main cam buffer falling section curve.Selection rule carries out choosing according to the phase place of engine back pressure ripple.

2. the boundary conditions of major and minor cam is determined.

By known linkage section curve starting point cam angle and linkage section wrap angle sigma ₄, determine the cam angle at two boundary point places of linkage section curve, be respectively γ ₁, γ ₂.That the both sides of linkage section curve connect respectively is main cam buffer falling section curve h ₃(α) with auxiliary cam active section curve h ₅(x).But because when calculated curve, employing initial point is all the method for zero, so when calculating linkage section, need γ ₁be converted into h ₃(α) coordinate γ corresponding in ₁', by γ ₂be converted into h ₅x coordinate γ that () is corresponding ₂'.

γ ₁′＝γ ₁-(α ₁+α ₂) (33)

γ ₂′＝0 (34)

Due to the starting point that linkage section End of Curve is auxiliary cam active section curve, so γ ₂'=0.

Thus the boundary conditions of linkage section curve can be drawn:

Lift boundary conditions:

h ₄(0)＝h ₃(γ ₁′) (35)

h ₄(α ₄)＝h ₅(1) (36)

Velocity boundary conditions:

${\frac{{\mathrm{dh}}_4\left(\mathrm{\α}\right)}{d\mathrm{\α}}|}_{\mathrm{\α}=0}={\frac{{\mathrm{dh}}_3\left(\mathrm{\α}\right)}{d\mathrm{\α}}|}_{\mathrm{\α}={{\mathrm{\γ}}_1}^{\′}}---\left(37\right)$

${\frac{{\mathrm{dh}}_4\left(\mathrm{\α}\right)}{d\mathrm{\α}}|}_{\mathrm{\α}={\mathrm{\α}}_4}={\frac{{\mathrm{dh}}_5\left(x\right)}{d\mathrm{\α}}|}_{\mathrm{\α}=0}=-\frac{4}{{\mathrm{\α}}_5}{\frac{{\mathrm{dh}}_5\left(x\right)}{dx}|}_{x=1}---\left(38\right)$

Acceleartion boundary condition:

${\frac{{{\mathrm{dh}}_4}^2\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}=0}={\frac{{{\mathrm{dh}}_3}^2\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}={{\mathrm{\γ}}_1}^{\′}}---\left(39\right)$

${\frac{d^2{h}_4\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}={\mathrm{\α}}_4}={\frac{d^2{h}_5\left(x\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}=0}=\frac{4}{{{\mathrm{\α}}_5}^2}{\frac{d^2{h}_5\left(x\right)}{{\mathrm{dx}}^2}|}_{x=1}---\left(40\right)$

Above-mentioned condition is substituted into formula (4), obtains boundary condition equation:

A ₀＝h ₃(γ ₁′) (41)

A ₀-A ₁α ₄+A ₂α ₄ ²-A ₃α ₄ ³+A ₄α ₄ ⁴-A ₅α ₄ ⁵+A ₆α ₄ ⁶＝h ₅(1) (42)

$A_1={\frac{{\mathrm{dh}}_3\left(\mathrm{\α}\right)}{d\mathrm{\α}}|}_{\mathrm{\α}={{\mathrm{\γ}}_1}^{\′}}---\left(43\right)$

$-A_1+2A_2{\mathrm{\α}}_4-3A_3{{\mathrm{\α}}_4}^2+4A_4{{\mathrm{\α}}_4}^3-5A_5{{\mathrm{\α}}_4}^4+6A_6{{\mathrm{\α}}_4}^5=-\frac{2}{{\mathrm{\α}}_5}{\frac{{\mathrm{dh}}_5\left(x\right)}{dx}|}_{x=1}---\left(44\right)$

$2A_2={\frac{{{\mathrm{dh}}_3}^2\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}={{\mathrm{\γ}}_1}^{\′}}---\left(45\right)$

$2A_2-6A_3{\mathrm{\α}}_4+12A_4{{\mathrm{\α}}_4}^2-20A_5{{\mathrm{\α}}_4}^3+30A_6{{\mathrm{\α}}_4}^4=\frac{4}{{{\mathrm{\α}}_5}^2}{\frac{d^2{h}_5\left(x\right)}{{\mathrm{dx}}^2}|}_{x=1}---\left(46\right)$

3. supplementary condition is determined

Major and minor cam linkage section curve has 7 undetermined coefficients, but only has now these 6 constrain equations of above-mentioned (41) ~ (46), so also need increase supplementary condition; Choose any point A on major and minor cam curve, its coordinate is (α _a, h _a), directly define A point coordinates as subsidiary conditions, determine whole piece linkage section curvilinear equation, as shown in accompanying drawing (5).Selection rule: α _avalue generally approximates the half of linkage section cornerite; Lift h _avalue is at 0.05 ~ h ₄(0) between, that is:

$\left\{\begin{array}{c}{\mathrm{\α}}_A\≈\frac{{\mathrm{\α}}_4}{2}\\ h_A\∈(0.05,h_4\left(0\right))\end{array}\right.$

After selected A point, following supplementary condition equation can be listed:

A ₀-A ₁α _A+A ₂α _A ²-A ₃α _A ³+A ₄α _A ⁴-A ₅α _A ⁵+A ₆α _A ⁶＝h _A(47)

System of equations (41) ~ (47), can solve A ₀~ A ₆these 7 parameters, thus determine linkage section curvilinear equation.

3, finally all undetermined coefficients are updated in mathematical equation (1) ~ (6) of foundation, obtain the double peak cam molded line with diesel exhaust recirculation function.

When the molded line carrying out each section calculates, the starting point of cam angle is all set to zero, finally namely result translation can be obtained the molded line of whole piece double peak cam.

The present invention realizes adjustment secondary cam flexibly by adjustment cam design parameter and opens, the start-up time of conservative control secondary opening exhaust valve and lasting phase angle, according to the actual requirements, control motor accurately, flexibly in different stroke stage waste gas back amount, make the mixed proportion of live gas and waste gas in cylinder best, effective combustion condition improved in cylinder, makes diesel engine performance and NOx emission thing be effectively controlled.

Accompanying drawing explanation

The double peak cam form structure schematic diagram with diesel exhaust recirculation function that Fig. 1 designs for the present invention;

The double peak cam characteristics of motion schematic diagram with diesel exhaust recirculation function that Fig. 2 designs for the present invention;

The double peak cam each several part curve distribution schematic diagram with diesel exhaust recirculation function that Fig. 3 designs for the present invention;

Fig. 4 is major and minor cam boundary conditions schematic diagram;

Fig. 5 be lift supplementary condition choose schematic diagram.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in detail, but the present embodiment can not be used for limiting the present invention, and every employing similarity method of the present invention and similar change thereof, all should list protection scope of the present invention in.

There is the double peak cam Profile Design example of diesel exhaust recirculation function:

Curve Design initial condition parameters is as shown in table 1.

Table 1 Curve Design parameter

Easy in order to calculate, when the molded line carrying out each section calculates, the starting point of cam angle is all set to zero, finally namely result translation can be obtained the molded line of whole piece double peak cam.

1, host buffer section calculates

By initial conditions:

α ₁＝24°

H ₁＝0.438453mm

v ₁＝0.022193mm/°

And according to formula (10) ~ (13), obtain β ₁, C _b﹑ E ₀﹑ E ₁, the curvilinear equation that can solve the host buffer ascent stage is:

$h_1\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}0.0013074{\mathrm{\α}}^2& 0\≤\mathrm{\α}\≤8.48727\\ -0.094179+0.022193\mathrm{\α}& 8.48727\≤\mathrm{\α}\≤24\end{array}\right.---\left(48\right)$

According to the β obtained ₁, C _b﹑ E ₀﹑ E ₁, can obtain main cam buffer falling section curvilinear equation is:

$h_3\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}-0.094179-0.022193(\mathrm{\α}-24)& 0\≤\mathrm{\α}\≤15.51273\\ 0.0013074{(\mathrm{\α}-24)}^2& 15.51273\≤\mathrm{\α}\≤24\end{array}\right.---\left(49\right)$

Main cam buffer falling section curve starts to be substituted by linkage section curve in linkage section curve starting point.

2, main active section calculates

By initial conditions:

α ₂＝125.5°

H ₁＝0.438453mm

H ₂＝7.4mm

v ₂＝0.022193mm/°

Index is:

p＝2,q＝8,r＝20,s＝42

Use (23) ~ (27) to solve the undetermined coefficient of high power active section, obtain curvilinear equation:

h ₂(x)＝7.838453-11.1027x ²+4.56587x ⁸-0.93364x ²⁰+0.070441x ⁴²(50)

Wherein, $x=1-\frac{2\mathrm{\α}}{{\mathrm{\α}}_2}=1-\frac{2\mathrm{\α}}{125.5}$

3, subtask section calculates

By initial conditions:

α ₅＝67°

H ₅＝1.313774mm

H ₆＝0.186226mm

v ₅＝0.024502mm/°

Index is similarly:

p＝2,q＝8,r＝20,s＝42

(28) ~ (32) are used to solve each coefficient c of high power active section ₀', c _p', c _q', c _r', c _s', obtain curvilinear equation:

h ₅(x)＝1.5-1.8029x ²+0.5995x ⁸-0.11928x ²⁰+0.0089210x ⁴²(51)

Wherein, $x=1-\frac{2\mathrm{\α}}{{\mathrm{\α}}_5}=1-\frac{2\mathrm{\α}}{67}$

Afterwards according to the phase relationship (their peach point phase difference is 124 °) of submaximum and main peak, make the position of submaximum.

4, auxiliary cam buffer falling section curve calculation

By initial conditions:

α ₆＝10.5°

H ₆＝0.186226mm

v ₆＝-0.024502mm/°

And according to formula (14) ~ (17), can undetermined coefficient β be obtained ₁', C _b′ ﹑ E ₀′ ﹑ E ₁', the equation solving auxiliary cam buffer falling section is:

$h_6\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}-0.071045-0.024502(\mathrm{\α}-10.5)& 0\≤\mathrm{\α}\≤4.70088\\ 0.00211256{(\mathrm{\α}-10.5)}^2& 4.70088\≤\mathrm{\α}\≤10.5\end{array}\right.---\left(52\right)$

5, linkage section calculates

By initial conditions:

α ₄＝16.75°

γ ₁＝160.5°

α _A＝9°

h _A＝0.0675mm

Utilize formula (33), (34), obtain:

γ ₁′＝11°

γ ₂′＝0°

According to formula (35) ~ (40), obtain boundary conditions:

h ₄(0)＝h ₃(γ ₁′)＝0.19433mm

h ₄(α ₄)＝h ₅(1)＝0.186226mm

${\frac{{{\mathrm{dh}}_4}^2\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}=0}={\frac{{{\mathrm{dh}}_3}^2\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}={{\mathrm{\γ}}_1}^{\′}}=0$

${\frac{d^2{h}_4\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}={\mathrm{\α}}_4}=\frac{4}{{{\mathrm{\α}}_5}^2}{\frac{d^2{h}_5\left(x\right)}{{\mathrm{dx}}^2}|}_{x=1}=0$

According to above-mentioned condition, system of equations (41) ~ (47), can obtain undetermined coefficient A ₀, A ₁, A ₂, A ₃, A ₄, A ₅, A ₆, obtaining linkage section curvilinear equation is:

h ₄(α)＝0.19433-0.022193×α+0×α ²+(1.05364e-4)×α ³+(7.40298e-7)×α ⁴(53)

                                                                         

-(1.53485e-7)×α ⁵+(5.69e-10)×α ⁶

Finally, translation combination is carried out in above-mentioned (48) ~ (53), and use linkage section curve cam angle 160.5 ° to 177.25 °, replace curve original within the scope of this, be combined into the molded line of novel double peak cam.

The double peak cam profile that the plane tappet lift function of example calculation gained is drawn as shown in Figure 1.Learn that radius of curvature is all greater than zero by calculating, namely this cam is entirely convex, is conducive to camshaft grinding.As shown in Figure 2, lifting curve is Second Order Continuous at least for tappet lift corresponding to this double peak cam, speed, acceleration diagram, has good slickness, and its acceleration maximin is all in design limited field, shows this cam work function admirable.Five sections of constituent elements of this double peak cam and distribution situation thereof are as shown in Figure 3.The boundary conditions adopted when calculating double peak cam linkage section as shown in Figure 4.Calculate the choosing method of supplementary condition during double peak cam linkage section as shown in Figure 5.

Claims (2)

1. one kind has the double peak cam design method of diesel exhaust recirculation function, it is characterized in that: first main cam buffering ascent stage, active section, buffer falling section are set up in segmentation, major and minor cam linkage section, 6 equations of auxiliary cam active section, buffer falling section cam tappet lifting curve h (α), obtain each equational undetermined coefficient, then undetermined coefficient is updated in the equation mathematics representation of foundation, obtains the continuous double peak cam molded line with diesel exhaust recirculation function; Concrete implementation step is as follows:

(A) cam curve equation is set up in segmentation:

A () sets up main cam buffering ascent stage curve h ₁(α) equation:

$h_1\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}{C}_B{\mathrm{\α}}^2& 0\≤\mathrm{\α}\≤{\mathrm{\β}}_1\\ E_0+E_1\mathrm{\α}& {\mathrm{\β}}_1\≤\mathrm{\α}\≤{\mathrm{\α}}_1\end{array}\right.---\left(1\right)$

In formula, α ₁for the cornerite of main cam buffering ascent stage, α is cam angle; β ₁it is the angle of two sections of equation separations; C _b﹑ E ₀﹑ E ₁be undetermined coefficient;

B () sets up main cam active section curve h ₂(x) equation:

h ₂(x)＝H ₁+c ₀+c _px ^p+c _qx ^q+c _rx ^r+c _sx ^s0≤α≤α ₂(2)

Wherein: $x=1-\frac{2\mathrm{\α}}{{\mathrm{\α}}_2}$

α in formula ₂for main cam active section cornerite, H ₁for main cam buffering ascent stage full lift; c ₀, c _p, c _q, c _r, c _sfor undetermined coefficient; For the value of index p, q, r, s of independent variable x in high order five formula equations, according to the maximum geometry speed of different engine cam molded line, maximum positive and negative geometry acceleration, the restriction requirement of the characteristic parameters such as radius of curvature, in equation, index p, q, r, s of independent variable x can get the different positive integers increased progressively;

C () sets up main cam buffer falling section curve h ₃(α) equation; Because the descending branch of breeze way curve and ascent stage are point-symmetric about main cam peach point, then main cam buffer falling section curve h ₃(α) equation is:

$h_3\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}{E}_0-E_1(\mathrm{\α}-{\mathrm{\α}}_1)& 0\≤\mathrm{\α}\≤{\mathrm{\α}}_1-{\mathrm{\β}}_1\\ C_B{(\mathrm{\α}-{\mathrm{\α}}_1)}^2& {\mathrm{\α}}_1-{\mathrm{\β}}_1\≤\mathrm{\α}\≤{\mathrm{\α}}_1\end{array}\right.---\left(3\right)$

The starting point of main cam buffer falling section curve is the terminal of main cam active section curve;

(d) major and minor cam linkage section curve h ₄(α) equation is:

h ₄(α)＝A ₀-A ₁α+A ₂α ²-A ₃α ³+A ₄α ⁴-A ₅α ⁵+A ₆α ⁶0≤α≤α ₄(4)

Wherein, α ₄for the cornerite size of linkage section; The starting point of linkage section is chosen a bit in the buffer falling section curve of main cam, and terminal drops on the starting point of auxiliary cam active section curve; A ₀, A ₁, A ₂, A ₃, A ₄, A ₅, A ₆for the undetermined coefficient of linkage section;

(e) auxiliary cam active section curve h ₅x () equation is:

h ₅(x)＝H ₆+c ₀′+c _p′x ^p+c _q′x ^q+c _r′x ^r+c _s′x ^s0≤α≤α ₅(5)

Wherein: $x=1-\frac{2\mathrm{\α}}{{\mathrm{\α}}_5}$

α ₅for auxiliary cam active section cornerite, H ₆for auxiliary cam buffer falling section full lift; c ₀', c _p', c _q', c _r', c _s' be undetermined coefficient, determined by boundary conditions;

(f) auxiliary cam buffer falling section curve h ₆(α) equation is:

$h_6\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}{E_0}^{\′}-{E_1}^{\′}(\mathrm{\α}-{\mathrm{\α}}_6)& 0\≤\mathrm{\α}\≤{\mathrm{\α}}_6-{\mathrm{\β}}_2\\ {C_B}^{\′}{(\mathrm{\α}-{\mathrm{\α}}_6)}^2& {\mathrm{\α}}_6-{\mathrm{\β}}_2\≤\mathrm{\α}\≤{\mathrm{\α}}_6\end{array}\right.---\left(6\right)$

In formula, α ₆for the cornerite of auxiliary cam buffer falling section, β ₂it is the angle of two sections of curvilinear equation separations; C _b′ ﹑ E ₀′ ﹑ E ₁' be undetermined coefficient; Terminal due to linkage section curve drops on the starting point of auxiliary cam active section curve, so the breeze way curve of auxiliary cam only has descending branch curve;

(B) undetermined coefficient of cam breeze way curvilinear equation, active section curvilinear equation, linkage section curvilinear equation is solved respectively;

(a) major and minor cam breeze way curvilinear equation undetermined coefficient solving method:

Main cam buffering ascent stage curve h ₁(α) equation is:

$h_1\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}{C}_B{\mathrm{\α}}^2& 0\≤\mathrm{\α}\≤{\mathrm{\β}}_1\\ E_0+E_1\mathrm{\α}& {\mathrm{\β}}_1\≤\mathrm{\α}\≤{\mathrm{\α}}_1\end{array}\right.---\left(1\right)$

4 undetermined coefficient β in formula ₁, C _b﹑ E ₀﹑ E ₁calculating determined by following formula (7) ~ (13):

As α=α ₁time, now main cam buffering ascent stage curve h ₁(α) equal to cushion ascent stage curve full lift H ₁, that is:

H ₁＝E ₀+E ₁α ₁(7)

At separation α=β ₁place, main cam buffering ascent stage curve lift h ₁(α) keep continuously, that is:

$C_B\·{\mathrm{\β}}_1^2=E_0+E_1{\mathrm{\β}}_1---\left(8\right)$

Further, at this separation place, also keep continuously, that is:

2C _B·β ₁＝E ₁(9)

By being given in α=α ₁time buffering ascent stage End of Curve speed ν ₁, obtain:

${\frac{{\mathrm{dh}}_1\left(\mathrm{\α}\right)}{d\mathrm{\α}}|}_{\mathrm{\α}={\mathrm{\α}}_1}=E_1={\mathrm{\ν}}_1---\left(10\right)$

ν ₁be the tappet speed of buffering ascent stage End of Curve, unit is mm/ °, for Designer is according to engine speed auto-selecting parameter;

Can be released by (7) and (10):

E ₀＝H ₁-E ₁α ₁＝H ₁-ν ₁·α ₁(11)

(9) are brought into (8) to obtain:

${\mathrm{\β}}_1=-\frac{2E_0}{E_1}=\frac{2({\mathrm{\ν}}_1\·{\mathrm{\α}}_1-H_1)}{{\mathrm{\ν}}_1}---\left(12\right)$

Have according to (9) again:

$C_B=\frac{E_1}{2{\mathrm{\β}}_1}=\frac{{\mathrm{\ν}}_1^2}{4({\mathrm{\ν}}_1\·{\mathrm{\α}}_1-H_1)}---\left(13\right)$

Known by separating formula (10) ~ (13), as long as know parameter H ₁﹑ ν ₁﹑ α ₁, just can obtain its 4 undetermined coefficient β ₁, C _b﹑ E ₀﹑ E ₁, and H ₁﹑ ν ₁﹑ α ₁require to decide in advance according to the concrete condition of distribution device;

Auxiliary cam buffer falling section curve h ₆(α) equation is:

$h_6\left(\mathrm{\α}\right)=\left\{\begin{array}{cc}{E_0}^{\′}-{E_1}^{\′}(\mathrm{\α}-{\mathrm{\α}}_6)& 0\≤\mathrm{\α}\≤{\mathrm{\α}}_6-{\mathrm{\β}}_2\\ {C_B}^{\′}{(\mathrm{\α}-{\mathrm{\α}}_6)}^2& {\mathrm{\α}}_6-{\mathrm{\β}}_2\≤\mathrm{\α}\≤{\mathrm{\α}}_6\end{array}\right.---\left(6\right)$

According to initial known conditions α ₆, H ₆, ν ₆, following solution formula can be obtained:

E ₁′＝ν ₆(14)

E ₀′＝H ₆-ν ₆·α ₆(15)

${\mathrm{\β}}_2=-\frac{2{E_0}^{\′}}{{E_1}^{\′}}=\frac{2({\mathrm{\ν}}_6\·{\mathrm{\α}}_6-H_6)}{{\mathrm{\ν}}_6}---\left(16\right)$

${C_B}^{\′}=\frac{{E_1}^{\′}}{2{\mathrm{\β}}_2}=\frac{{\mathrm{\ν}}_6^2}{4({\mathrm{\ν}}_6\·{\mathrm{\α}}_6-H_6)}---\left(17\right)$

(b) major and minor cam work section curvilinear equation undetermined coefficient solving method:

By main cam active section curve h ₂(α) equation:

h ₂(x)＝H ₁+c ₀+c _px ^p+c _qx ^q+c _rx ^r+c _sx ^s0≤α≤α ₂(2)

Wherein, $x=1-\frac{2\mathrm{\α}}{{\mathrm{\α}}_2}$

Solve undetermined coefficient c ₀, c _p, c _q, c _r, c _s;

Calculation of boundary conditions:

1., when α=0, namely during x=1, it is continuous that main cam active section beginning of curve lift and main cam cushion ascent stage End of Curve lift, then have h ₂(1)=H ₁, abbreviation obtains:

c ₀+c _p+c _q+c _r+c _s＝0 (18)

2. when α=0, namely during x=1, now main cam active section beginning of curve speed v ₂ascent stage End of Curve speed v is cushioned with main cam ₁keep continuously, namely

${\frac{{\mathrm{dh}}_2}{d\mathrm{\α}}|}_{\mathrm{\α}=0}=v_1=v_2\⇒{\frac{{\mathrm{dh}}_2}{d\mathrm{\α}}|}_{\mathrm{\α}=0}={(\frac{{\mathrm{dh}}_2}{dx}\·\frac{dx}{d\mathrm{\α}})|}_{\mathrm{\α}=0}={\frac{{\mathrm{dh}}_2\left(x\right)}{dx}|}_{x=1}.{\frac{dx}{d\mathrm{\α}}|}_{\mathrm{\α}=0}=v_2$

$({\mathrm{pc}}_p+{\mathrm{qc}}_q+{\mathrm{rc}}_r+{\mathrm{sc}}_s)\×(-\frac{2}{{\mathrm{\α}}_2})=v_2$

Abbreviation obtains:

${\mathrm{pc}}_p+{\mathrm{qc}}_q+{\mathrm{rc}}_r+{\mathrm{sc}}_s=-\frac{v_2{\mathrm{\α}}_2}{2}---\left(19\right)$

3., when α=0, namely during x=1, the acceleration that now acceleration of main cam active section beginning of curve and main cam cushion ascent stage End of Curve keeps continuously, namely thus:

p(p-1)c _p+q(q-1)c _q+r(r-1)c _r+s(s-1)c _s＝0 (20)

4., when α=0, namely during x=1, now main cam active section curve pulse and main cam cushion ascent stage End of Curve pulse and keep continuously, $\frac{d^3{h}_2\left(x\right)}{{\mathrm{d\α}}^3}=0,$ Namely $\frac{d^3{h}_2\left(x\right)}{{\mathrm{dx}}^3}=0,$ Thus:

p(p-1)(p-2)c _p+q(q-1)(q-2)c _q+r(r-1)(r-2)c _r+s(s-1)(s-2)c _s＝0 (21)

5. when namely during x=0, h ₂(0)=H ₂, H ₂for known main cam active section curve full lift, that is:

c ₀＝H ₂(22)

Simultaneous five, above-mentioned (18) ~ (22) boundary conditions can obtain following five solution formulas:

c ₀＝H ₂(23)

$c_p=\frac{-2H_{2}srq+v_2{\mathrm{\α}}_2(sr+sq+rq-s-r-q+1)}{2(s-q)(r-q)(p-q)}---\left(24\right)$

$c_q=\frac{-2H_{2}srp+v_2{\mathrm{\α}}_2(sr+sp+rq-s-r-p+1)}{2(s-q)(r-q)(q-q)}---\left(25\right)$

$c_r=\frac{-2H_{2}spq+v_2{\mathrm{\α}}_2(sq+sp+pq-s-p-q+1)}{2(s-r)(p-r)(q-r)}---\left(26\right)$

$c_s=\frac{-2H_{2}rpq+v_2{\mathrm{\α}}_2(pq+rq+rp-r-p-q+1)}{2(q-s)(r-s)(p-s)}---\left(27\right)$

As long as know parameter H ₂﹑ ν ₂﹑ α ₂﹑ p ﹑ q ﹑ r ﹑ s, just can obtain undetermined coefficient c ₀, c _p, c _q, c _r, c _s, and H ₂﹑ ν ₂﹑ α ₂be require to decide in advance according to the concrete condition of distribution device, index p ﹑ q ﹑ r ﹑ s is then determined when Design of cam curves;

By auxiliary cam active section curve h ₅(x) high order five formula equations:

h ₅(x)＝H ₆+c ₀′+c _p′x ^p+c _q′x ^q+c _r′x ^r+c _s′x ^s0≤α≤α ₅(5)

Wherein, $x=1-\frac{2\mathrm{\α}}{{\mathrm{\α}}_5}$

According to known parameters H ₅﹑ ν ₅﹑ α ₅﹑ p ﹑ q ﹑ r ﹑ s, can obtain following five solution formulas:

c ₀′＝H ₅(28)

${c_p}^{\′}=\frac{-2H_{5}srq+v_5{\mathrm{\α}}_5(sr+sq+rq-s-r-q+1)}{2(s-q)(r-q)(p-q)}---\left(29\right)$

${c_q}^{\′}=\frac{-2H_{5}srp+v_5{\mathrm{\α}}_5(sr+sp+rq-s-r-p+1)}{2(s-q)(r-q)(q-q)}---\left(30\right)$

${c_r}^{\′}=\frac{-2H_{5}spq+v_5{\mathrm{\α}}_5(sq+sp+pq-s-p-q+1)}{2(s-r)(p-r)(q-r)}---\left(31\right)$

${c_s}^{\′}=\frac{-2H_{5}rpq+v_5{\mathrm{\α}}_5(pq+rq+rp-r-p-q+1)}{2(q-s)(r-s)(p-s)}---\left(32\right)$

(c) major and minor cam linkage section curvilinear equation undetermined coefficient solving method:

Major and minor cam linkage section curve h ₄(α) equation is:

h ₄(α)＝A ₀-A ₁α+A ₂α ²-A ₃α ³+A ₄α ⁴-A ₅α ⁵+A ₆α ⁶0≤α≤α ₄(4)

In formula, parameter A ₀, A ₁, A ₂, A ₃, A ₄, A ₅, A ₆determined by (41) ~ (47);

1. linkage section point of curve position is determined;

The starting point of linkage section curve is chosen a bit in main cam buffer falling section curve; Selection rule carries out choosing according to the phase place of engine back pressure ripple;

2. the boundary conditions of major and minor cam is determined;

By known linkage section curve starting point cam angle and linkage section wrap angle sigma ₄, determine the cam angle at two boundary point places of linkage section curve, be respectively γ ₁, γ ₂; That the both sides of linkage section curve connect respectively is main cam buffer falling section curve h ₃(α) with auxiliary cam active section curve h ₅(x); But because when calculated curve, employing initial point is all the method for zero, so when calculating linkage section curve, need γ ₁be converted into main cam buffer falling section curve h ₃(α) coordinate γ corresponding in ₁', by γ ₂be converted into auxiliary cam active section curve h ₅x coordinate γ that () is corresponding ₂';

γ ₁′＝γ ₁-(α ₁+α ₂) (33)

γ ₂′＝0 (34)

Terminal due to major and minor cam linkage section curve is positioned at the starting point of auxiliary cam active section curve, so γ ₂'=0;

Thus major and minor cam linkage section curve h can be drawn ₄(α) boundary conditions:

Lift boundary conditions:

h ₄(0)＝h ₃(γ ₁′) (35)

h ₄(α ₄)＝h ₅(1) (36)

Velocity boundary conditions:

${\frac{{\mathrm{dh}}_4\left(\mathrm{\α}\right)}{d\mathrm{\α}}|}_{\mathrm{\α}=0}={\frac{{\mathrm{dh}}_3\left(\mathrm{\α}\right)}{d\mathrm{\α}}|}_{\mathrm{\α}={{\mathrm{\γ}}_1}^{\′}}---\left(37\right)$

${\frac{{\mathrm{dh}}_4\left(\mathrm{\α}\right)}{d\mathrm{\α}}|}_{\mathrm{\α}={\mathrm{\α}}_4}={\frac{{\mathrm{dh}}_5\left(x\right)}{d\mathrm{\α}}|}_{\mathrm{\α}=0}=-\frac{2}{{\mathrm{\α}}_5}{\frac{{\mathrm{dh}}_5\left(x\right)}{dx}|}_{x=1}---\left(38\right)$

Acceleartion boundary condition:

${\frac{{{\mathrm{dh}}_4}^2\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}=0}={\frac{{{\mathrm{dh}}_3}^2\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}={{\mathrm{\γ}}_1}^{\′}}---\left(39\right)$

${\frac{d^2{h}_4\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}={\mathrm{\α}}_4}={\frac{d^2{h}_5\left(x\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}=0}=\frac{4}{{{\mathrm{\α}}_5}^2}{\frac{d^2{h}_5\left(x\right)}{{\mathrm{dx}}^2}|}_{x=1}---\left(40\right)$

Above-mentioned condition is substituted into formula (4), obtains boundary condition equation:

A ₀＝h ₃(γ ₁′) (41)

A ₀-A ₁α ₄+A ₂α ₄ ²-A ₃α ₄ ³+A ₄α ₄ ⁴-A ₅α ₄ ⁵+A ₆α ₄ ⁶＝h ₅(1) (42)

$A_1={\frac{{\mathrm{dh}}_3\left(\mathrm{\α}\right)}{d\mathrm{\α}}|}_{\mathrm{\α}={{\mathrm{\γ}}_1}^{\′}}---\left(43\right)$

$-A_1+2A_2{\mathrm{\α}}_4-3A_3{{\mathrm{\α}}_4}^2+4A_4{{\mathrm{\α}}_4}^3-5A_5{{\mathrm{\α}}_4}^4+6A_6{{\mathrm{\α}}_4}^5=-\frac{2}{{\mathrm{\α}}_5}{\frac{{\mathrm{dh}}_5\left(x\right)}{dx}|}_{x=1}---\left(44\right)$

$2A_2={\frac{{{\mathrm{dh}}_3}^2\left(\mathrm{\α}\right)}{{\mathrm{d\α}}^2}|}_{\mathrm{\α}={{\mathrm{\γ}}_1}^{\′}}---\left(45\right)$

$2A_2-6A_3{\mathrm{\α}}_4+12A_4{{\mathrm{\α}}_4}^2-20A_5{{\mathrm{\α}}_4}^3+30A_6{{\mathrm{\α}}_4}^4=\frac{4}{{{\mathrm{\α}}_5}^2}{\frac{d^2{h}_5\left(x\right)}{{\mathrm{dx}}^2}|}_{x=1}---\left(46\right)$

3. supplementary condition is determined

Because major and minor cam linkage section curve has 7 undetermined coefficients, but only have now these 6 equations of above-mentioned (41) ~ (46), so also need increase supplementary condition; Major and minor cam linkage section curve gets arbitrarily 1 A, and its coordinate is (α _a, h _a), directly define A point coordinates as subsidiary conditions, determine whole piece linkage section curvilinear equation, selection rule: α _avalue generally approximates the half of linkage section curve cornerite; Lift h _avalue is at 0.05 ~ h ₄(0) between, that is:

$\left\{\begin{array}{c}{\mathrm{\α}}_A\≈\frac{{\mathrm{\α}}_4}{2}\\ h_A\∈(0.05,h_4\left(0\right))\end{array}\right.$

After selected A point, following supplementary condition equation can be listed:

A ₀-A ₁α _A+A ₂α _A ²-A ₃α _A ³+A ₄α _A ⁴-A ₅α _A ⁵+A ₆α _A ⁶＝h _A(47)

System of equations (41) ~ (47), can solve A ₀~ A ₆these 7 parameters, thus determine major and minor cam linkage section curvilinear equation;

(C) finally all undetermined coefficients are updated in set up mathematical equation (1) ~ (6), obtain the double peak cam molded line with diesel exhaust recirculation function.

2. a kind of double peak cam design method with diesel exhaust recirculation function according to claim 1, it is characterized in that: when carrying out each section of cam profile and calculating, the starting point of cam angle is all set to zero, finally namely result translation can be obtained the molded line of whole piece double peak cam.