CN110069855A - Engine timing transmission system Design Optimization for Vibration method containing non-circular crankshaft pulley - Google Patents

Engine timing transmission system Design Optimization for Vibration method containing non-circular crankshaft pulley Download PDF

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CN110069855A
CN110069855A CN201910323182.9A CN201910323182A CN110069855A CN 110069855 A CN110069855 A CN 110069855A CN 201910323182 A CN201910323182 A CN 201910323182A CN 110069855 A CN110069855 A CN 110069855A
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timing
crankshaft pulley
belt
optimization
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CN110069855B (en
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朱浩
樊伟
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Sichuan University
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Sichuan University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation

Abstract

The engine timing transmission system Design Optimization for Vibration method containing non-circular crankshaft pulley that the invention discloses a kind of, timing driving system includes Timing Belt, crankshaft pulley and several attachment belt wheels, crankshaft pulley drives each accessory tapes wheel to rotate by Timing Belt, crankshaft pulley is elliptic gear, and method is the following steps are included: Step 1: establish its initial driving force model according to the initial configuration of timing driving system；Step 2: defining design variable and establishing optimization object function；Step 3: optimizing using optimization algorithm to timing driving system, optimum results are obtained；Step 4: being verified to optimum results.The present invention can reduce the twisting vibration of timing driving system, improve the service life of Timing Belt, and without increasing additional damping device, save the installation space of damping device.

Description

Engine timing transmission system Design Optimization for Vibration method containing non-circular crankshaft pulley
Technical field
The invention belongs to car engine timing transmission system fields, and in particular to a kind of to start containing non-circular crankshaft pulley The vibration control optimum design method of machine timing driving system.
Background technique
Timing driving system is the essential component part of automobile engine air distributing device, plays and is accurately realized timing Open and close the effect of corresponding inlet and outlet valve.Since Timing Belt has, noise is small, high transmission accuracy, maintainability Well, the advantages that not needing lubrication and light weight, is widely used in engine timing transmission system.
The dynamic performance of timing driving system largely will affect the working performance of each driving attachment.Car engine Machine crankshaft cyclic irregularity and the cyclic fluctuation of camshaft loading moment can cause Timing Belt to vibrate.Timing transmission system Common oscillatory type of uniting has the laterally and axially vibration of Timing Belt and the twisting vibration of each attachment belt wheel, Timing Belt Axial vibration and the parametric excitations such as belt tension cyclic fluctuation can cause belt oscillation crosswise wild effect.These vibrations Dynamic one side can generate noise, and still further aspect will cause the service life that belt tension fluctuates and then substantially reduces belt.
It is mounted on automatic tensioner in existing timing driving system, on the one hand initial tensioning is provided for Timing Belt Power, the vibration of system can be reduced, have damping machine inside still further aspect stretcher to avoid resonance by improving belt initial tension Structure can be absorbed part system damping, and then reduce vibration, but increase belt initial tension can greatly shorten the use of belt Service life.In addition to this it is possible to reduce system vibration, but cam axle damper pair by way of installing cam axle damper Installation space has higher requirements, and will increase more cost.
Summary of the invention
In view of the above technical problems, the present invention is intended to provide a kind of vibration that can reduce timing driving system, same to time delay The car engine timing transmission system optimum design method of the service life of long Timing Belt.
For this purpose, the technical scheme adopted by the invention is as follows: a kind of engine timing transmission system containing non-circular crankshaft pulley Design Optimization for Vibration method, the timing driving system include Timing Belt, crankshaft pulley, automatic tensioner and several accessory tapes Wheel, the automatic tensioner include that tensioning wheel, embedded torsional spring and stretcher swing arm, the crankshaft pulley are driven by Timing Belt Each accessory tapes wheel rotation, the automatic tensioner maintain the tensile force of Timing Belt by tensioning wheel, and the crankshaft pulley is ellipse Knucle-gear the described method comprises the following steps:
Step 1: establishing its initial driving force model according to the initial configuration of the timing driving system；
The timing driving system includes n belt wheel, and n belt wheel includes 1 crankshaft pulley, 1 tensioning wheel and n-2 attached Part belt wheel, to all belt wheel number consecutivelies, wherein crankshaft pulley number is 1, the tensioning wheel is i-th of belt wheel, described Tensioning wheel is between any two belt wheel, therefore i is 2,3 ..., and Timing Belt is divided into n by the arbitrary value in n, n belt wheel A band section derives the timing driving system twisting vibration kinetics equation by Newton's third law:
J in above formulaj、θj、cjAnd DjThe rotary inertia of respectively j-th belt wheel, corner, bearing viscous damping and pitch circle are straight Diameter；θtIt is the corner of the stretcher swing arm, initial value θt0, β1And β2Be two adjacent thereto of the stretcher swing arm just When belt band section angle, m1It is the quality of the tensioning wheel, JarmIt is the rotary inertia of the stretcher swing arm, ltIt is described The brachium of tight device swing arm, meIt is the quality of the automatic tensioner, ctIt is the automatic tensioner equivalent viscous damping ratio, le It is the distance of the automatic tensioner centroid distance swing arm center of rotation, MjIt is the load torque of j-th of attachment belt wheel, ktAnd Qt It is the torsion stiffness and initial torque of the embedded torsional spring respectively, ρ and v are the density and axial movement of the Timing Belt respectively Speed, TjFor j-th of dynamic tension with section of the Timing Belt, calculated by following formula:
Tj=-kj(Dj+1θj+1-Djθj)/2+Tj0, j=2,3 ..., n, j ≠ i-1, i (5)
T in above formulaj0, j=1,2 ..., n are j-th of initial tension with section of the Timing Belt, kjFor j-th with section Tensible rigidity, above-mentioned formula meet n+1=1 always, define the effective diameter D of any t moment of the crankshaft pulley1It (t) is it Center OcsThe point of contact P tangent with Timing Belt band section to itcsDistance, the crankshaft pulley long and short shaft length difference Labeled as daAnd db, define elliptic contour parameter ε=(d of the crankshaft pulleya-db)/d1, define the initial of the crankshaft pulley Setting angle θc0For transverseAnd position vectorAngle, whereinFor PcsInitial position, when any The diameter for carving crankshaft pulley described in t is calculate by the following formula to obtain:
Wherein θc=θ1+θc0For the crankshaft pulley at any time t when position angle；
Step 2: defining design variable and establishing optimization object function；
Firstly, choosing the relevant parameter ε and its initial settling angle degree θ of the elliptic contour of the crankshaft pulleyc0It is set for optimization Variable is counted, and defines the design space of design variable permission:
In formula, { θc0}min{ θc0}maxRespectively variable θc0Allowing maximum value and minimum value desirable in design space, εminAnd εmaxRespectively variable ε is in the maximum value and minimum value for allowing to can use in design space；
Then, the kinetic model of the timing driving system based on foundation calculates different turn by runge kutta method The twisting vibration of each belt wheel under fast operating condition chooses each belt wheel in the biggish multiple speed conditions of twisting vibration amplitude as typical work Condition establishes the timing driving system optimization design using the weighted average of the twisting vibration amplitude of each belt wheel as optimization aim Objective function:
A in formulamFor each belt wheel twisting vibration amplitude,For corresponding weight coefficient,Value should be reversed according to each belt wheel Vibration amplitude determines the influence degree of system body vibration level, according to dynamics calculation as a result, the vibration width of each belt wheel Value is in the same order of magnitude substantially, that is, thinks that it is suitable to the twisting vibration influence degree of system, thereforeValue be
Simultaneously using the Timing Belt n tension fluctuation ranges with section as constraint condition:
gj=| Tj-Tj0| -1000≤0, j=1,2 ..., n (11)
By formula (10) and formula (11), the objective function of belt restraining is obtained by penalty factor method:
λ is penalty factor in formula (12), and λ is positive number, and is greater than the twisting vibration amplitude of any belt wheel, ξjFor corresponding inequality Weight coefficient every in (11) is constrained, if gj≤ 0 sets up, value 0, conversely, its value is 1；
Step 3: optimizing using optimization algorithm to the timing driving system, optimum results, i.e. crankshaft pulley are obtained 1 optimal elliptic contour relevant parameter ε and its initial settling angle degree θc0, excellent according to the optimization aim and constraint condition setting The condition of convergence of change, judges whether optimum results meet the condition of convergence, if the optimum results meet the condition of convergence, Then determine that the optimum results can be as the optimal design of the timing driving system；
Step 4: verifying to optimum results, the initial driving force model based on the timing driving system, use is excellent Change the relevant parameter ε and its initial settling angle degree θ of the elliptic contour for the crankshaft pulley that result providesc0As initial parameter, calculate The twisting vibration of the timing driving system after optimization, and then verify the reasonability of optimum results.
Preferably, the optimization algorithm is genetic algorithm.
Preferably, the condition of convergence is the absolute value of the difference of two iteration step target function value of front and back less than 10-3Or Maximum number of iterations is no more than 800.
Beneficial effects of the present invention: it is carried out by the relevant parameter and initial settling angle degree of the elliptic contour to crankshaft pulley Reasonable optimization design keeps Timing Belt periodically flexible according to certain rule during operation, can offset crankshaft and The part periodic twisting vibration of cam shafting, to reduce the twisting vibration of timing driving system；The tensile wave of Timing Belt It is dynamic to be greatly improved, improve the service life of Timing Belt；Without increasing additional damping device, damping device has been saved Installation space.
Detailed description of the invention
Fig. 1 is the general structural schematic diagram of the present invention；
Fig. 2 is the structural schematic diagram that timing driving system includes five belt wheels；
Fig. 3 is the sign picture of each parameter in crankshaft pulley initial makeup location in the present invention；
Fig. 4 is remaining each belt wheel when the speed of crankshaft of crankshaft pulley rotation being driven to be 2000 revs/min in the embodiment of the present invention With the twisting vibration time history curve before stretcher swing arm optimization；
Fig. 5 is remaining each belt wheel when the speed of crankshaft of crankshaft pulley rotation being driven to be 2000 revs/min in the embodiment of the present invention With the twisting vibration time history curve after stretcher swing arm optimization.
Specific embodiment
By way of example and in conjunction with the accompanying drawings, the invention will be further described:
As shown in Figures 1 to 5, timing driving system is by crankshaft pulley 1, automatic tensioner 5, Timing Belt 6 and several attached Part belt wheel composition, crankshaft pulley 1 drive each accessory tapes wheel to rotate by Timing Belt 6, and Timing Belt 6 passes through automatic tensioner 5 Tensile force is maintained, which is reduced to the assembly being made of tensioning wheel 5a, embedded torsional spring 5b and stretcher swing arm 5c Body.
In the present embodiment, using typical engine timing transmission system, attachment belt wheel include idle pulley 2, connection exhaust it is convex First cam shaft pulley 3 of wheel shaft and the second cam shaft pulley 4 of connection admission cam shaft, crankshaft pulley 1 is elliptic gear.One Engine timing transmission system Design Optimization for Vibration method of the kind containing non-circular crankshaft pulley, comprising the following steps:
Step 1: establishing its initial driving force model according to the initial configuration of timing driving system；
Specifically, passing through Newton's third law derivation system twisting vibration kinetics equation:
J in above formulaj、θj、cjAnd DjThe rotary inertia of respectively j-th belt wheel, corner, bearing viscous damping and pitch circle are straight Diameter；θtIt is the corner of stretcher swing arm 5c, initial value θt0。β1And β2It is stretcher swing arm 5c two adjacent thereto with section Angle, m1It is the quality of tensioning wheel 5a, JarmIt is the rotary inertia of stretcher swing arm 5c, ltIt is the brachium of stretcher swing arm 5c, me It is the quality of automatic tensioner 5, leIt is the distance of the centroid distance swing arm 5c center of rotation of automatic tensioner 5, ctIt is auto-tensioning The equivalent viscous damping ratio of device 5, MjIt is the load torque of j-th of attachment belt wheel.ktAnd QtIt is the torsion of embedded torsional spring 5b respectively Rigidity and initial torque.ρ and v is the density and axial movement speed of Timing Belt 6, T respectivelyjFor j-th of dynamic tension with section, It can be calculated by following formula:
Tj=-kj(Dj+1θj+1-Djθj)/2+Tj0, j=2,3 (5)
T4=-k4(D5θ5-D4θ4)/2+k4lt(θt-θt0)sinβ1+T40 (6)
T in formulaj0, j=1,2 ..., 5 be j-th of initial tension with section, kjFor j-th of tensible rigidity with section, this reality The initial makeup location of the crankshaft pulley 1 in example is applied as shown in figure 3, defining crankshaft pulley 1 in the effective diameter D of any t moment1 It (t) is its center OcsTo the point of contact P tangent with section of itself and Timing Belt 6csDistance, the long and short axis of crankshaft pulley 1 Length is respectively labeled as daAnd db, the elliptic contour parameter for defining crankshaft pulley 1 is ε=(da-db)/d1.Crankshaft pulley 1 it is initial Setting angle θc0It is defined as transverseAnd position vectorAngle, whereinFor PcsInitial position.
According to Fig. 3, the diameter of any time t crankshaft pulley 1 can be calculate by the following formula to obtain:
Wherein θc=θ1+θc0For crankshaft pulley 1 at any time t when position angle.
Step 2: defining design variable and establishing optimization object function
Firstly, choosing the relevant parameter ε and its initial settling angle degree θ of the elliptic contour of crankshaft pulley 1c0For optimization design change Amount, and define the design space of design variable permission:
Then, the kinetic model of the timing driving system based on foundation calculates different rotating speeds work by runge kutta method The twisting vibration of each belt wheel under condition.Each belt wheel is chosen in the biggish speed conditions of twisting vibration amplitude as typical condition, with each The weighted average of the twisting vibration amplitude of belt wheel is optimization aim, establishes the objective function of Optimized System Design:
A in formulamFor each belt wheel twisting vibration amplitude,For corresponding weight coefficient,Value should be reversed according to each belt wheel Vibration amplitude determines the influence degree of system body vibration level, according to dynamics calculation as a result, the vibration width of each belt wheel Value is substantially in the same order of magnitude, it can thinks that it is suitable to the twisting vibration influence degree of system, therefore in the present embodiment Value be 1/5.
The tension fluctuation range using 5 of Timing Belt 1 with section is constraint condition simultaneously:
gj=| Tj-Tj0| -1000≤0, j=1,2 ..., 5 (11)
By formula (10) and formula (11), the objective function of belt restraining is obtained by penalty factor method:
λ is penalty factor in formula (12), and λ is positive number, and is greater than the twisting vibration amplitude of any belt wheel.As λ can take one Biggish positive number such as 105, ξjTo correspond to weight coefficient every in inequality constraints (11), if gj≤ 0 sets up, value 0, instead It, value 1.
Step 3: optimizing using optimization algorithm is optimized to timing driving system, optimum results, i.e. crankshaft band are obtained Take turns 1 optimal elliptic contour relevant parameter ε and its initial settling angle degree θc0.In the present embodiment, optimization algorithm is using heredity Algorithm judges whether optimum results meet the condition of convergence according to the condition of convergence of optimization aim and constraint condition setting optimization, if Optimum results meet the condition of convergence, it is determined that the optimum results can be as the optimal design of timing driving system.The present embodiment In, the condition of convergence is the absolute value of the difference of two iteration step target function value of front and back less than 10-3Or maximum number of iterations is no more than 800。
Step 4: being verified to optimum results；
Specifically: the initial driving force model based on timing driving system, the crankshaft pulley 1 provided using optimum results The relevant parameter and its initial settling angle degree of elliptic contour are as initial parameter, the torsion vibration of timing driving system after calculation optimization It is dynamic, and then verify the reasonability of optimum results.It is shown in Fig. 3 and Fig. 4 when the speed of crankshaft for driving crankshaft pulley 1 to rotate is At 2000 revs/min, idle pulley 2, the first cam shaft pulley 3, the second cam shaft pulley 4, tensioning wheel 5 and the torsion with stretcher swing arm 5c Rotational oscillation moves time history curve, and Fig. 3 and Fig. 4 are compared, it can be seen that idle pulley 2, first in timing driving system after optimization It cam shaft pulley 3, the second cam shaft pulley 4, tensioning wheel 5 and is substantially reduced, imitates with the twisting vibration amplitude of stretcher swing arm 5c Fruit is significant, it is seen that uses design method proposed by the present invention, the twisting vibration of timing driving system has obtained very big improvement.We The Thoughts on Optimized Design of method can also promote the use of the case where crankshaft pulley 1 is other non-circular profiles, and this method uses most Optimization algorithm is genetic algorithm, can also be the overall situations such as other optimization algorithms such as particle algorithm, simulated annealing, ant group algorithm Optimization algorithm.

Claims (3)

1. a kind of engine timing transmission system Design Optimization for Vibration method containing non-circular crankshaft pulley, the timing driving system Including Timing Belt, crankshaft pulley, automatic tensioner and several attachment belt wheels, the automatic tensioner includes tensioning wheel, embeds Torsional spring and stretcher swing arm, the crankshaft pulley drive each accessory tapes wheel to rotate by Timing Belt, and the automatic tensioner is logical Cross tensioning wheel maintain Timing Belt tensile force, which is characterized in that the crankshaft pulley be elliptic gear, the method includes with Lower step:
Step 1: establishing its initial driving force model according to the initial configuration of the timing driving system；
The timing driving system includes n belt wheel, and n belt wheel includes 1 crankshaft pulley, 1 tensioning wheel and n-2 accessory tapes Wheel, to all belt wheel number consecutivelies, wherein crankshaft pulley number is 1, the tensioning wheel is i-th of belt wheel, the tensioning Wheel is between any two belt wheel, therefore i is 2,3 ..., and Timing Belt is divided into n band by the arbitrary value in n, n belt wheel Section, derives the timing driving system twisting vibration kinetics equation by Newton's third law:
J in above formulaj、θj、cjAnd DjRotary inertia, corner, bearing viscous damping and the pitch diameter of respectively j-th belt wheel；θt It is the corner of the stretcher swing arm, initial value θt0, β1And β2It is the stretcher swing arm two timing skins adjacent thereto Angle of the band with section, m1It is the quality of the tensioning wheel, JarmIt is the rotary inertia of the stretcher swing arm, ltIt is the stretcher The brachium of swing arm, meIt is the quality of the automatic tensioner, ctIt is the automatic tensioner equivalent viscous damping ratio, leIt is institute State the distance of automatic tensioner centroid distance swing arm center of rotation, MjIt is the load torque of j-th of attachment belt wheel, ktAnd QtRespectively It is the torsion stiffness and initial torque of the embedded torsional spring, ρ and v are the density of the Timing Belt respectively and are axially moved fast Degree, TjFor j-th of dynamic tension with section of the Timing Belt, calculated by following formula:
Tj=-kj(Dj+1θj+1-Djθj)/2+Tj0, j=2,3 ..., n, j ≠ i-1, i (5)
T in above formulaj0, j=1,2 ..., n are j-th of initial tension with section of the Timing Belt, kjFor j-th of stretching with section Rigidity, above-mentioned formula meet n+1=1 always, define the effective diameter D of any t moment of the crankshaft pulley1It (t) is its center Position OcsThe point of contact P tangent with Timing Belt band section to itcsDistance, the long and short shaft length of the crankshaft pulley marks respectively For daAnd db, define elliptic contour parameter ε=(d of the crankshaft pulleya-db)/d1, define the initial installation of the crankshaft pulley Angle, θc0For transverseAnd position vectorAngle, whereinFor PcsInitial position, any time t institute The diameter for stating crankshaft pulley is calculate by the following formula to obtain:
Wherein θc=θ1+θc0For the crankshaft pulley at any time t when position angle；
Step 2: defining design variable and establishing optimization object function；
Firstly, choosing the relevant parameter ε and its initial settling angle degree θ of the elliptic contour of the crankshaft pulleyc0For optimization design change Amount, and define the design space of design variable permission:
In formula, { θc0}min{ θc0}maxRespectively variable θc0In the maximum value and minimum value for allowing to can use in design space, εmin And εmaxRespectively variable ε is in the maximum value and minimum value for allowing to can use in design space；
Then, the kinetic model of the timing driving system based on foundation calculates different rotating speeds work by runge kutta method The twisting vibration of each belt wheel under condition, chooses each belt wheel in the biggish multiple speed conditions of twisting vibration amplitude as typical condition, Using the weighted average of the twisting vibration amplitude of each belt wheel as optimization aim, the mesh of the timing driving system optimization design is established Scalar functions:
A in formulamFor each belt wheel twisting vibration amplitude,For corresponding weight coefficient,Value should be according to each belt wheel twisting vibration Amplitude determines the influence degree of system body vibration level, according to dynamics calculation as a result, the vibration amplitude base of each belt wheel Originally it is in the same order of magnitude, that is, thinks that it is suitable to the twisting vibration influence degree of system, thereforeValue be
Simultaneously using the Timing Belt n tension fluctuation ranges with section as constraint condition:
gj=| Tj-Tj0| -1000≤0, j=1,2 ..., n (11)
By formula (10) and formula (11), the objective function of belt restraining is obtained by penalty factor method:
λ is penalty factor in formula (12), and λ is positive number, and is greater than the twisting vibration amplitude of any belt wheel, ξjFor corresponding inequality constraints (11) every weight coefficient in, if gj≤ 0 sets up, value 0, conversely, its value is 1；
Step 3: optimize using optimization algorithm to the timing driving system, obtain optimum results, i.e. crankshaft pulley 1 Optimal elliptic contour relevant parameter ε and its initial settling angle degree θc0, according to the optimization aim and constraint condition setting optimization The condition of convergence, judge whether optimum results meet the condition of convergence, if the optimum results meet the condition of convergence, Determine that the optimum results can be as the optimal design of the timing driving system；
Step 4: being verified to optimum results, the initial driving force model based on the timing driving system, tied using optimization The relevant parameter ε and its initial settling angle degree θ of the elliptic contour for the crankshaft pulley that fruit providesc0As initial parameter, calculation optimization The twisting vibration of the timing driving system afterwards, and then verify the reasonability of optimum results.
2. the engine timing transmission system Design Optimization for Vibration method according to claim 1 containing non-circular crankshaft pulley, It is characterized by: the optimization algorithm is genetic algorithm.
3. the engine timing transmission system Design Optimization for Vibration side according to claim 1 or 2 containing non-circular crankshaft pulley Method, it is characterised in that: the condition of convergence is the absolute value of the difference of two iteration step target function value of front and back less than 10-3Or it is maximum The number of iterations is no more than 800.
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