CN106641055A - Role playing load designing method for secondary spring of end-contacting type parabola type plate spring - Google Patents

Abstract

The invention relates to a role playing designing method for a secondary spring of an end-contacting type parabola type plate spring, which belongs to the technical field of a suspension steel plate spring. A load that the secondary spring of the end-contacting type parabola type plate spring begins to play a role can be designed according to vehicle mass parameters, structural parameters of each leaf spring, an elasticity modulus and a maximal allowable security stress. By testing of a model machine loading deformation trial, it can be known that the role playing designing method for the secondary spring of an end-contacting type parabola type plate spring is correct, an accurate and reliable load design value that the secondary spring begins to play a role can be obtained, and a reliable technical foundation is laid for the design of the end-contacting type parabola type main and secondary springs and the development of CAD software. By using this method, the product design level, quality and performance and vehicle driving smoothness can be improved, meanwhile, product design and trial testing expenses are reduced, and a product development rate is improved.

Description

Ends contact formula parabolic type leaf spring auxiliary spring works load design method

Technical field

The load the present invention relates to vehicle suspension leaf spring, particularly ends contact formula parabolic type leaf spring auxiliary spring work Method for designing.

Background technology

With vehicle energy saving, comfortableization, lightweight, the fast development of safe, few piece variable-section steel sheet spring is because of tool Have lightweight, stock utilization is high, and little without rubbing or rubbing between piece, vibration noise is low, the advantages of long service life, be increasingly subject to The highest attention of vehicle suspension expert, manufacturing enterprise and vehicle manufacture enterprise, and obtained in vehicle suspension system extensively Using.Generally for the design requirement for meeting processing technology, stress intensity, rigidity and hanger thickness, can be by few piece Variable Section Steel Flat spring is processed as the different structure forms such as reinforced parabolic type, bias type, root, reinforcement end, two ends are reinforced, and Because the stress of few flat spring of piece variable-section steel sheet spring the 1st is complex, vertical load is subjected to, while also subject to torsion Load and longitudinal loading, therefore, the thickness and length of the end flat segments of the 1st flat spring designed by reality are each more than other The thickness and length of flat spring end flat segments, i.e., mostly using few piece variable-section steel sheet spring of the non-grade structure in end, to meet The complicated requirement of 1st flat spring stress, few piece additionally, the rigidity Design under in order to meet different loads is required, generally become and cut Face leaf spring is designed as the few piece parabolic type variable cross-section major-minor spring form of ends contact formula.However, due to ends contact formula it is few The structure of piece parabolic type variable cross-section major-minor spring and contact type are complicated, and it is extremely difficult to be analyzed calculating to it, according to looking into money Material understands, had not provided reliable ends contact formula parabolic type leaf spring auxiliary spring always at present both at home and abroad and has worked load design side Method.The continuous improvement required with Vehicle Speed and its to ride comfort, to the few piece parabolic type major-minor spring of end contact Put forward higher requirement, therefore, it is necessary to set up a kind of accurate, reliable ends contact formula parabolic type leaf spring auxiliary spring work Load design method, is that the auxiliary spring of the few piece parabolic type leaf spring of ends contact formula functions to load design and establishes reliability Technical foundation, meet the few piece parabolic type major-minor spring of Vehicle Industry fast-developing, vehicle ride performance and ends contact formula Design requirement, improve product design level, quality and performance, meet the design requirement of vehicle ride performance；Meanwhile, reduce Design and testing expenses, accelerate product development speed.

The content of the invention

For defect present in above-mentioned prior art, the technical problem to be solved be to provide it is a kind of easy, Reliable ends contact formula parabolic type leaf spring auxiliary spring works load design method, its design flow diagram, as shown in Figure 1.End Contact few piece parabolic type variable cross-section major-minor spring in portion's is symmetrical structure, and the half symmetrical structure of major-minor spring can see cantilever as Beam, i.e. symmetrical center line are root fixing end, and the end stress point of main spring and the contact of auxiliary spring are respectively as main spring end points and pair Spring end points, the structural representation of the major-minor spring of half symmetrical structure, as shown in Fig. 2 including main spring 1, root shim 2 is secondary Spring 3, end pad 4.Half length of the main spring 1 per piece is L_M, it is by three sections of root flat segments, parabolic segment and end flat segments Constituted, per piece, the thickness of the root flat segments of main spring is h_2M, per piece, the half of main spring installing space is l₃, the main spring per piece Width is b；The thickness and length of the end flat segments of the non-grade main spring of structure, i.e., the 1st of end flat segments of each of main spring 1, is more than Other each thickness and length, the thickness and length of the end flat segments of each main spring are respectively h_1MiAnd l_1Mi, i=1, Reed number based on 2 ..., m, m；Per piece the middle variable cross-section of main spring be parabolic segment, the thickness ratio of the parabolic segment of each main spring For β_i=h_1Mi/h_2M, per piece the root of the parabolic segment of main spring to main spring end points distance be l_2M=L_M-l₃, the throwing of each main spring The end of thing line segment is to main spring end points apart from l_1Mi=l_2Mβ_i ²；Each root flat segments of main spring 1 and put down with the root of auxiliary spring 3 Root shim 2 is provided between straight section, the end flat segments of each of main spring 1 are provided with end pad 4, and the material of end pad 4 is carbon Fibrous composite, for reducing the frictional noise produced during spring works；Half length of the auxiliary spring 3 per piece is L_A, it is by root Three sections of portion's flat segments, parabolic segment and end flat segments are constituted, and the thickness of the root flat segments of every auxiliary spring is h_2A, per piece pair The half of spring installing space is l₃, the width of every auxiliary spring is b；The thickness and length of the end flat segments of each auxiliary spring is respectively h_1AjAnd l_1Aj, j=1,2 ..., n, n are auxiliary spring piece number；The middle variable cross-section of every auxiliary spring be parabolic segment, the throwing of each auxiliary spring The thickness ratio of thing line segment is β_Aj=h_1Aj/h_2A, the distance of the root of the parabolic segment of every auxiliary spring to auxiliary spring end points is l_2A=L_A- l₃, the end of the parabolic segment of each auxiliary spring is to auxiliary spring end points apart from l_1Aj=l_2Aβ_Aj ²；The m pieces end flat segments of main spring 1 Major and minor spring gap delta is provided with and the ends points of auxiliary spring 3 between；When load works load more than auxiliary spring, auxiliary spring and main spring end Certain point contacts in portion's flat segments, and auxiliary spring is l with the distance of main spring contact point to main spring end points₀；When major-minor spring ends contact it Afterwards, each end stress of major-minor spring is differed, and the main spring contacted with auxiliary spring is in addition to by end points power, also at contact point Bear the support force of auxiliary spring.Safely should in vehicle mass parameter, the structural parameters of each flat spring, elastic modelling quantity and maximum allowable In the case of power is given, load is functioned to the auxiliary spring that end contact lacks piece parabolic type variable-section steel sheet spring and is set Meter.

To solve above-mentioned technical problem, ends contact formula parabolic type leaf spring auxiliary spring provided by the present invention works load Method for designing, it is characterised in that using following design procedure：

(1) calculating of the major and minor spring end points deformation coefficient of the few piece parabolic type leaf spring of ends contact formula：

I steps：The calculating of each main spring end points deformation coefficient under end points stressing conditions：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, Parabola root is to spring end points apart from l_2M, elastic modulus E, the thickness of the parabolic segment of i-th main spring compares β_i, wherein, i= Reed number based on 1,2 ..., m, m, to end points stressing conditions under deformation coefficient G of each main spring at end points_x-DiCounted Calculate, i.e.,

II steps：The calculating of the m pieces main spring deformation coefficient at auxiliary spring contact point under end points stressing conditions：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, Parabola root is to spring end points apart from l_2M, elastic modulus E, the thickness of the parabolic segment of the main spring of m pieces compares β_m, auxiliary spring and master Spring contact point is to main spring end points apart from l₀, the main spring of m pieces under end points stressing conditions is contacted in end flat segments with auxiliary spring Deformation coefficient G at point_x-CDCalculated, i.e.,

III steps：The calculating of the main spring end points deformation coefficient of m pieces at major-minor spring contact point under stressing conditions：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, Parabola root is to spring end points apart from l_2M, elastic modulus E, the thickness of the parabolic segment of the main spring of m pieces compares β_m, auxiliary spring and master Spring contact point is to main spring end points apart from l₀, to the main spring of m pieces under stressing conditions at major-minor spring contact point at endpoint location Deformation coefficient G_x-DzmCalculated, i.e.,

IV steps：The meter of the m pieces main spring deformation coefficient at auxiliary spring contact point at major-minor spring contact point under stressing conditions Calculate：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, Parabola root is to spring end points apart from l_2M, elastic modulus E, the thickness of the parabolic segment of the main spring of m pieces compares β_m, auxiliary spring and master Spring contact point is to main spring end points apart from l₀, to the main spring of m pieces under stressing conditions at major-minor spring contact point in end flat segments With the deformation coefficient G at auxiliary spring contact point_x-CDzCalculated, i.e.,

V steps：The calculating of each auxiliary spring end points deformation coefficient under end points stressing conditions：

According to half length L of few piece parabolic type variable-section steel sheet spring auxiliary spring_A, width b, half l of installing space₃, Parabola root is to spring end points apart from l_2A, elastic modulus E, the thickness of the parabolic segment of jth piece auxiliary spring compares β_Aj, wherein, j =1,2 ..., n, n are auxiliary spring piece number, to end points stressing conditions under deformation coefficient G of each auxiliary spring at endpoint location_x-DAjEnter Row is calculated, i.e.,

Wherein, the deformation coefficient G after the superposition of n pieces auxiliary spring_x-DATFor

(2) calculating of the major and minor each clamping rigidity of spring of the few piece parabolic type leaf spring of ends contact formula：

Step A：Each main spring before auxiliary spring contact clamps stiffness K_MiCalculating：

According to main spring root thickness h_2M, and calculated G in the I steps of step (1)_x-Di, before determining auxiliary spring contact Each main spring half stiffness K in the clamp state_Mi, i.e.,

Wherein, reed number based on m；

Step B：Each main spring after auxiliary spring contact clamps stiffness K_MAiCalculating：

According to main spring root thickness h_2M, auxiliary spring root thickness h_2A, calculated G in the I steps of step (1)_x-Di, II step Calculated G in rapid_x-CD, calculated G in III steps_x-Dzm, calculated G in IV steps_x-CDzAnd V steps are fallen into a trap The G for obtaining_x-DAT, determine each main spring half stiffness K in the clamp state after the contact of major-minor spring_MAi, i.e.,

Wherein, reed number based on m；

Step C：Each auxiliary spring clamps stiffness K_AjCalculating：

According to auxiliary spring root thickness h_2A, and calculated G in the V steps of step (1)_x-DAj, determine each auxiliary spring in folder Half stiffness K under tight state_Aj, i.e.,

Wherein, n is auxiliary spring piece number；

(3) auxiliary spring functions to the calculating of minimum load：

According to single-wheel zero load sprung mass m_e, gravity acceleration g determines the half minimum load that auxiliary spring is functioned to F_min, i.e.,

(4) calculating of maximum load is functioned to based on the auxiliary spring of maximum allowable safe stress：

I steps：Worked maximum load F based on the auxiliary spring of first main spring maximum allowable safe stress_M1Calculating：

According to the fully loaded sprung mass m of single-wheel_f, gravity acceleration g, the one of the main spring of few piece parabolic type variable-section steel sheet spring Half length L_M, width b, half l of installing space₃, root thickness h_2M, main reed number m, maximum allowable safe stress [σ], and step Suddenly the K for determining in the step A of (2)_Mi, the K that determines in step B_MAi, it is determined that the pair based on first main spring maximum allowable safe stress Spring functions to maximum load F_M1, i.e.,

Ii steps：Worked maximum load F based on the auxiliary spring of the main spring maximum allowable safe stress of tailpiece_MmCalculating：

According to the fully loaded sprung mass m of single-wheel_f, gravity acceleration g, the width b of few piece parabolic type variable-section steel sheet spring, Main spring parabola root is to spring end points apart from l_2M, main spring root thickness h_2M, auxiliary spring root thickness h_2A, the throwing of the main spring of m pieces The thickness of thing line segment compares β_m, main reed number m, auxiliary spring piece number n, auxiliary spring is with main spring contact point to main spring end points apart from l₀, maximum permitted With safe stress [σ], calculated G in the II steps of step (1)_x-CD, calculated G in IV steps_x-CDz, in V steps Calculated G_x-DAT, and the K determined in the step A of step (2)_Mi, the K that determines in step B_MAi, the K that determines in step C_Aj, It is determined that functioning to maximum load F based on the auxiliary spring of the main spring maximum allowable safe stress of tailpiece_Mm, i.e.,

Iii steps：Worked maximum load F based on the auxiliary spring of first auxiliary spring maximum allowable safe stress_A1Calculating：

According to the fully loaded sprung mass m of single-wheel_f, gravity acceleration g, the one of few piece parabolic type variable-section steel sheet spring auxiliary spring Half length L_A, width b, half l of installing space₃, main spring root thickness h_2M, auxiliary spring root thickness h_2A, main reed number m, auxiliary spring Piece number n, maximum allowable safe stress [σ], calculated G in the II steps of step (1)_x-CD, it is calculated in IV steps G_x-CDz, calculated G in V steps_x-DAT, and the K determined in the step B of step (2)_MAi, the K that determines in step C_Aj, it is determined that Maximum load F is functioned to based on the auxiliary spring of first auxiliary spring maximum allowable safe stress_A1, i.e.,

Iv steps：Half maximum load F worked based on the auxiliary spring of maximum allowable safe stress_maxCalculating：

According to the F determined in i steps_M1, the F determined in ii steps_Mm, and the F determined in iii steps_A1, it is determined that based on most Half maximum load F that the auxiliary spring of big safe stress allowable is functioned to_max, i.e.,

F_max=min (F_M1,F_Mm,F_A1)；

Wherein, min (F_M1,F_Mm,F_A1) represent take F_M1、F_MmAnd F_A1In minimum numerical value；

(5) the few piece parabolic type variable-section steel sheet spring auxiliary spring of ends contact formula functions to the design of load：

According to the F determined in step (3)_min, and the F determined in the iv steps of step (4)_max, to the few piece of end contact The auxiliary spring of parabolic type variable-section steel sheet spring functions to load and is designed, i.e.,

F_k=0.618F_min+0.382F_max。

The present invention has the advantage that than prior art

Because the structure and contact type of the few piece parabolic type variable cross-section major-minor spring of ends contact formula are complicated, it is carried out point Analysis calculates extremely difficult, understands according to consulting reference materials, and has not provided reliable ends contact formula parabolic type always both at home and abroad at present Leaf spring auxiliary spring works load design method.The present invention can be according to vehicle mass parameter, the structural parameters of each flat spring, springform Amount and maximum allowable safe stress, function to the auxiliary spring of the few piece parabolic type variable-section steel sheet spring of end contact Load is designed.Tested by model machine deformation under load test, ends contact formula parabola template provided by the present invention The spring auxiliary spring load design method that works is correct, and available accurately and reliably auxiliary spring functions to load design value, is Reliable technical foundation has been established in the design and CAD software exploitation of the few piece parabolic type variable cross-section major-minor spring of ends contact formula；Together When, using the method, product design level, product quality and vehicle ride performance can be improved；Meanwhile, can also reduce design and Experimental test expense, accelerates product development speed.

Description of the drawings

For a better understanding of the present invention, it is described further below in conjunction with the accompanying drawings.

Fig. 1 is that ends contact formula parabolic type leaf spring auxiliary spring works the design flow diagram of load；

Fig. 2 is the structural representation of the half of the few piece parabolic type variable cross-section major-minor spring of ends contact formula.

Specific embodiment

The present invention is described in further detail below by embodiment.

Embodiment：The single-wheel zero load sprung mass m of certain vehicle_e=163.26kg, the fully loaded sprung mass m of single-wheel_f= 620.40kg, the few piece parabolic type variable cross-section major-minor spring of its ends contact formula is made up of 2 main springs and 1 auxiliary spring, i.e., main reed Number m=2, auxiliary spring piece number n=1, wherein, each main spring parameter is：Half length L_M=575mm, width b=60mm, root is put down The thickness h of straight section_2M=11mm, half l of installing space₃=55mm, the root of parabolic segment is to main spring end points apart from l_2M= L_M-l₃=520mm, elastic modulus E=200GPa, the thickness h of the end flat segments of the 1st main spring_1M1=7mm, parabolic segment Thickness compares β₁=h_1M1/h_2MThe thickness h of the end flat segments of the=0.64, the 2nd main spring_1M2=6mm, the thickness of parabolic segment compares β₂ =h_1M2/h_2M=0.55；Auxiliary spring parameter is：Half length L_A=525mm, width b=60mm, the thickness h of root flat segments_2A= 14mm, half l of installing space₃=55mm, the root of parabolic segment is to auxiliary spring end points apart from l_2A=L_A-l₃=470mm, the 1st The thickness h of the end flat segments of piece auxiliary spring_1A1=8mm, the thickness of parabolic segment compares β_A1=h_1A1/h_2A=0.57；Auxiliary spring and main spring Contact point be located at main spring end flat segments in, and contact point to main spring end points apart from l₀=50mm；Gravity acceleration g= 9.8m/s².Maximum allowable safe stress [the σ]=900MPa of the spring, to the few piece parabolic type variable cross-section of the ends contact formula The auxiliary spring of leaf spring functions to load and is designed.

The ends contact formula parabolic type leaf spring auxiliary spring that present example is provided works load design method, its design Flow process is as shown in figure 1, comprise the following steps that：

(1) calculating of the major and minor spring end points deformation coefficient of the few piece parabolic type leaf spring of ends contact formula：

I steps：The calculating of each main spring end points deformation coefficient under end points stressing conditions：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to spring end points apart from l_2M=520mm, elastic modulus E=200GPa, the The thickness of the parabolic segment of 1 main spring compares β₁The thickness of the parabolic segment of the=0.64, the 2nd main spring compares β₂=0.55, end points is received The 1st in the case of power, the deformation coefficient G of the 2nd main spring at end points_x-D1、G_x-D2Calculated, i.e.,

II steps：The calculating of the 2nd main spring deformation coefficient at auxiliary spring contact point under end points stressing conditions：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to spring end points apart from l_2M=520mm, elastic modulus E=200GPa, the The thickness of the parabolic segment of 2 main springs compares β₂=0.55, auxiliary spring is with main spring contact point to main spring end points apart from l₀=50mm is right Deformation coefficient G of the 2nd main spring under end points stressing conditions at end flat segments and auxiliary spring contact point_x-CDCalculated, i.e.,

III steps：The calculating of the 2nd main spring end points deformation coefficient at major-minor spring contact point under stressing conditions：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to spring end points apart from l_2M=520mm, elastic modulus E=200GPa, the The thickness of the parabolic segment of 2 main springs compares β₂=0.55, auxiliary spring is with main spring contact point to main spring end points apart from l₀=50mm is right Deformation coefficient G of the 2nd main spring at major-minor spring contact point under stressing conditions at endpoint location_x-Dz2Calculated, i.e.,

IV steps：The meter of the 2nd main spring deformation coefficient at auxiliary spring contact point at major-minor spring contact point under stressing conditions Calculate：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to spring end points apart from l_2M=520mm, elastic modulus E=200GPa, the The thickness of the parabolic segment of 2 main springs compares β₂=0.55, auxiliary spring is with main spring contact point to main spring end points apart from l₀=50mm is right Deformation coefficient G of the 2nd main spring at major-minor spring contact point under stressing conditions at end flat segments and auxiliary spring contact point_x-CDzEnter Row is calculated, i.e.,

V steps：The calculating of each auxiliary spring end points deformation coefficient under end points stressing conditions：

According to half length L of few piece parabolic type variable-section steel sheet spring auxiliary spring_A=525mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to spring end points apart from l_2A=470mm, elastic modulus E=200GPa, the The thickness of the parabolic segment of 1 auxiliary spring compares β_A1=0.57, to end points stressing conditions under the 1st change of the auxiliary spring at endpoint location Shape coefficient G_x-DA1Calculated, i.e.,

Wherein, the deformation coefficient G after 1 auxiliary spring superposition_x-DATFor

(2) calculating of the major and minor each clamping rigidity of spring of the few piece parabolic type leaf spring of ends contact formula：

Step A：Each main spring before auxiliary spring contact clamps stiffness K_MiCalculating：

According to main spring root thickness h_2MCalculated G in=11mm, and the I steps of step (1)_x-D1=89.29mm⁴/ N、G_x-D2=93.78mm⁴/ N, determines the 1st, the 2nd main spring half stiffness K in the clamp state before auxiliary spring contact_M1、 K_M2, i.e.,

Step B：Each main spring after auxiliary spring contact clamps stiffness K_MAiCalculating：

According to main spring root thickness h_2M=11mm, auxiliary spring root thickness h_2A=14mm, calculates in the I steps of step (1) The G for arriving_x-D1=89.29mm⁴/N、G_x-D2=93.78mm⁴Calculated G in/N, II steps_x-CD=77.28mm⁴/ N, III are walked Calculated G in rapid_x-Dz2=77.28mm⁴Calculated G in/N, IV steps_x-CDz=64.85mm⁴/ N and V steps are fallen into a trap The G for obtaining_x-DAT=69.24mm⁴/ N, determine the 1st after the contact of major-minor spring, the 2nd main spring in the clamp state one Half stiffness K_MA1、K_MA2, i.e.,

Step C：Each auxiliary spring clamps stiffness K_AjCalculating：

According to auxiliary spring root thickness h_2ACalculated G in=14mm, and the V steps of step (1)_x-DA1=69.24mm⁴/ N, determines the 1st auxiliary spring half stiffness K in the clamp state_A1, i.e.,

(3) auxiliary spring functions to the calculating of minimum load：

According to single-wheel zero load sprung mass m_e=163.26kg, gravity acceleration g=9.8m/s², determine that auxiliary spring starts to act as Half minimum load F_min, i.e.,

(4) calculating of maximum load is functioned to based on the auxiliary spring of maximum allowable safe stress：

I steps：Worked maximum load F based on the auxiliary spring of first main spring maximum allowable safe stress_M1Calculating：

According to the fully loaded sprung mass m of single-wheel_f=620.40kg, gravity acceleration g=9.8m/s², few piece parabolic type change section Half length L of the main spring of face leaf spring_M=575mm, width b=60mm, half l of installing space₃=55mm, root thickness h_2M=11mm, main reed number m=2, the K determined in maximum allowable safe stress [σ]=900MPa, and the step A of step (2)_M1 =14.91N/mm, K_M2The K determined in=14.19N/mm, step B_MA1=14.91N/mm, K_MA2=40.20N/mm, it is determined that being based on The auxiliary spring of first main spring maximum allowable safe stress functions to maximum load F_M1, i.e.,

Ii steps：Worked maximum load F based on the auxiliary spring of the main spring maximum allowable safe stress of tailpiece_M2Calculating：

According to the fully loaded sprung mass m of single-wheel_f=620.40kg, gravity acceleration g=9.8m/s², few piece parabolic type change section The width b=60mm of face leaf spring, main spring parabola root is to spring end points apart from l_2M=520mm, main spring root thickness h_2M=11mm, auxiliary spring root thickness h_2A=14mm, the thickness of the parabolic segment of the 2nd main spring compares β₂=0.55, main reed number m= 2, auxiliary spring piece number n=1, auxiliary spring is with main spring contact point to main spring end points apart from l₀=50mm, maximum allowable safe stress [σ]= 900MPa, calculated G in the II steps of step (1)_x-CD=77.28mm⁴Calculated G in/N, IV steps_x-CDz= 64.85mm⁴Calculated G in/N, V steps_x-DAT=69.24mm⁴The K determined in/N, and the step A of step (2)_M1= 14.91N/mm、K_M2The K determined in=14.19N/mm, step B_MA1=14.91N/mm, K_MA2In=40.20N/mm, step C really Fixed K_A1=39.63N/mm, it is determined that functioning to maximum load based on the auxiliary spring of the main spring maximum allowable safe stress of tailpiece F_M2, i.e.,

Iii steps：Worked maximum load F based on the auxiliary spring of first auxiliary spring maximum allowable safe stress_A1Calculating：

According to the fully loaded sprung mass m of single-wheel_f=620.40kg, gravity acceleration g=9.8m/s², few piece parabolic type change section Half length L of face leaf spring auxiliary spring_A=525mm, width b=60mm, half l of installing space₃=55mm, main spring root Thickness h_2M=11mm, auxiliary spring root thickness h_2A=14mm, main reed number m=2, auxiliary spring piece number n=1, maximum allowable safe stress [σ]=900MPa, calculated G in the II steps of step (1)_x-CD=77.28mm⁴It is calculated in/N, IV steps G_x-CDz=64.85mm⁴Calculated G in/N, V steps_x-DAT=69.24mm⁴Determine in/N, and the step B of step (2) K_MA1=14.91N/mm, K_MA2The K determined in=40.20N/mm, step C_A1=39.63N/mm, it is determined that being based on first auxiliary spring maximum The auxiliary spring of safe stress allowable functions to maximum load F_A1, i.e.,

Iv steps：Half maximum load F worked based on the auxiliary spring of maximum allowable safe stress_maxCalculating：

According to the F determined in i steps_M1The F determined in=3123.50N, ii step_M2In=3690.80N, and iii steps It is determined that F_A1=-1631.50N, it is determined that the half maximum load functioned to based on the auxiliary spring of maximum allowable safe stress F_max, i.e.,

F_max=min (F_M1,F_Mm,F_A1)=3123.50N；

(5) the few piece parabolic type variable-section steel sheet spring auxiliary spring of ends contact formula functions to the design of load：

According to the F determined in step (3)_minThe F determined in=800N, and the iv steps of step (4)_max=3123.50N, Load is functioned to the auxiliary spring that end contact lacks piece parabolic type variable-section steel sheet spring to be designed, i.e.,

F_k=0.618F_min+0.382F_max=1687.60N.

Tested by prototype test, it is reliable that the auxiliary spring of spring functions to load design value, can meet end Contact few piece parabolic type variable-section steel sheet spring auxiliary spring in portion's functions to the design requirement of load, as a result shows the invention The ends contact formula parabolic type leaf spring auxiliary spring for the being provided load design method that works is correct, and parameter design value is accurate Reliably.

Claims (1)

1. ends contact formula parabolic type leaf spring auxiliary spring works load design method, wherein, the few piece parabola of ends contact formula The half symmetrical structure of type variable-section steel sheet spring is made up of 3 sections of root flat segments, parabolic segment and end flat segments, each master The end flat segments of spring are non-isomorphic, the i.e. thickness and length of the end flat segments of the 1st main spring, more than other thickness of each Degree and length, to meet the requirement of the 1st main spring complicated applied force；It is provided with certain between main spring end flat segments and auxiliary spring contact Major-minor spring gap, is worked the design requirement of load with meeting auxiliary spring；Vehicle mass parameter, the structural parameters of each flat spring, In the case of elastic modelling quantity and maximum allowable safe stress are given, to the few piece parabolic type variable-section steel sheet spring of end contact Auxiliary spring function to load and be designed, specific design step is as follows：

(1) calculating of the major and minor spring end points deformation coefficient of the few piece parabolic type leaf spring of ends contact formula：

I steps：The calculating of each main spring end points deformation coefficient under end points stressing conditions：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, parabolic Line root is to spring end points apart from l_2M, elastic modulus E, the thickness of the parabolic segment of i-th main spring compares β_i, wherein, i=1, Reed number based on 2 ..., m, m, to end points stressing conditions under deformation coefficient G of each main spring at end points_x-DiCalculated, I.e.

$G_{x-Di}=\frac{4\[l_{2M}^3(1-{\mathrm{\β}}_i^3)+{(L_M-l_3/2)}^3\]}{Eb};$

II steps：The calculating of the m pieces main spring deformation coefficient at auxiliary spring contact point under end points stressing conditions：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, parabolic Line root is to spring end points apart from l_2M, elastic modulus E, the thickness of the parabolic segment of the main spring of m pieces compares β_m, auxiliary spring connects with main spring Contact is to main spring end points apart from l₀, to the main spring of m pieces under end points stressing conditions at end flat segments and auxiliary spring contact point Deformation coefficient G_x-CDCalculated, i.e.,

$\begin{array}{c}{G}_{x-CD}=\frac{4{(L_M-l_3/2)}^3-6l_0{(L_M-l_3/2)}^2-4l_{2M}^3+6l_0{l}_{2M}^2}{Eb}+\frac{2{(l_0-l_{2M}{\mathrm{\β}}_m^2)}^2(2l_{2M}{\mathrm{\β}}_m^2+l_0)}{{\mathrm{Eb\β}}_m^3}-\\ \frac{8l_{2M}^2({\mathrm{\β}}_m-1)(l_{2M}-3l_0+l_{2M}{\mathrm{\β}}_m^2+l_{2M}{\mathrm{\β}}_m)}{Eb}\end{array};$

III steps：The calculating of the main spring end points deformation coefficient of m pieces at major-minor spring contact point under stressing conditions：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, parabolic Line root is to spring end points apart from l_2M, elastic modulus E, the thickness of the parabolic segment of the main spring of m pieces compares β_m, auxiliary spring connects with main spring Contact is to main spring end points apart from l₀, to change of the main spring of m pieces under stressing conditions at major-minor spring contact point at endpoint location Shape coefficient G_x-DzmCalculated, i.e.,

$\begin{array}{c}{G}_{x-D_{z}m}=\frac{4{(L_M-l_3/2)}^3-6l_0{(L_M-l_3/2)}^2-4l_{2M}^3+6l_0{l}_{2M}^2}{Eb}+\frac{2{(l_0-l_{2M}{\mathrm{\β}}_m^2)}^2(2l_{2M}{\mathrm{\β}}_m^2+l_0)}{{\mathrm{Eb\β}}_m^3}-\\ \frac{8l_{2M}^2({\mathrm{\β}}_m-1)(l_{2M}-3l_0+l_{2M}{\mathrm{\β}}_m^2+l_{2M}{\mathrm{\β}}_m)}{Eb}\end{array};$

IV steps：The calculating of the m pieces main spring deformation coefficient at auxiliary spring contact point at major-minor spring contact point under stressing conditions：

According to half length L of the main spring of few piece parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, parabolic Line root is to spring end points apart from l_2M, elastic modulus E, the thickness of the parabolic segment of the main spring of m pieces compares β_m, auxiliary spring connects with main spring Contact is to main spring end points apart from l₀, to the main spring of m pieces under stressing conditions at major-minor spring contact point in end flat segments and pair Deformation coefficient G at spring contact point_x-CDzCalculated, i.e.,

$\begin{array}{c}{G}_{x-{\mathrm{CD}}_z}=\frac{4(L_M-l_3/2-l_{2M})\[{(L_M-l_3/2)}^2-3(L_M-l_3/2)l_0+(L_M-l_3/2)l_{2M}+3l_0^2-3l_0{l}_{2M}+l_{2M}^2\]}{Eb}-\\ \frac{4{(l_0-l_{2M}{\mathrm{\β}}_m^2)}^3}{{\mathrm{Eb\β}}_m^3}-\frac{12l_{2M}}{Eb}\[4l_0{l}_{2M}(1-{\mathrm{\β}}_m)+2l_0^2(1-\frac{1}{{\mathrm{\β}}_m})+\frac{2l_{2M}^2({\mathrm{\β}}_m^3-1)}{3}\]\end{array};$

V steps：The calculating of each auxiliary spring end points deformation coefficient under end points stressing conditions：

According to half length L of few piece parabolic type variable-section steel sheet spring auxiliary spring_A, width b, half l of installing space₃, parabolic Line root is to spring end points apart from l_2A, elastic modulus E, the thickness of the parabolic segment of jth piece auxiliary spring compares β_Aj, wherein, j=1, 2 ..., n, n are auxiliary spring piece number, to end points stressing conditions under deformation coefficient G of each auxiliary spring at endpoint location_x-DAjCounted Calculate, i.e.,

$G_{x-DAj}=\frac{4\[l_{2A}^3(1-{\mathrm{\β}}_{Aj}^3)+{(L_A-l_3/2)}^3\]}{Eb};$

Wherein, the deformation coefficient G after the superposition of n pieces auxiliary spring_x-DATFor

$G_{x-DAT}=\frac{1}{\underset{j=1}{\overset{n}{\Σ}}\frac{1}{G_{x-DAj}}};$

(2) calculating of the major and minor each clamping rigidity of spring of the few piece parabolic type leaf spring of ends contact formula：

Step A：Each main spring before auxiliary spring contact clamps stiffness K_MiCalculating：

According to main spring root thickness h_2M, and calculated G in the I steps of step (1)_x-Di, determine each before auxiliary spring contact The main spring of piece half stiffness K in the clamp state_Mi, i.e.,

$K_{Mi}=\frac{h_{2M}^3}{G_{x-Di}},i=1,2,...,m;$

Wherein, reed number based on m；

Step B：Each main spring after auxiliary spring contact clamps stiffness K_MAiCalculating：

According to main spring root thickness h_2M, auxiliary spring root thickness h_2A, calculated G in the I steps of step (1)_x-Di, in II steps Calculated G_x-CD, calculated G in III steps_x-Dzm, calculated G in IV steps_x-CDzAnd calculate in V steps The G for arriving_x-DAT, determine each main spring half stiffness K in the clamp state after the contact of major-minor spring_MAi, i.e.,

$K_{MAi}=\left\{\begin{array}{cc}\frac{h_{2M}^3}{G_{x-Di}},& i=1,2,...,m-1\\ \frac{h_{2M}^3(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)}{G_{x-Dm}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)-G_{x-D_{z}m}{G}_{x-CD}{h}_{2A}^3},& i=m\end{array}\right.;$

Wherein, reed number based on m；

Step C：Each auxiliary spring clamps stiffness K_AjCalculating：

According to auxiliary spring root thickness h_2A, and calculated G in the V steps of step (1)_x-DAj, determine that each auxiliary spring is clamping shape Half stiffness K under state_Aj, i.e.,

$K_{Aj}=\frac{h_{2A}^3}{G_{x-DAj}},j=1,2,...,n;$

Wherein, n is auxiliary spring piece number；

(3) auxiliary spring functions to the calculating of minimum load：

According to single-wheel zero load sprung mass m_e, gravity acceleration g determines the half minimum load F that auxiliary spring is functioned to_min, i.e.,

$F_{min}=\frac{m_{e}g}{2};$

(4) calculating of maximum load is functioned to based on the auxiliary spring of maximum allowable safe stress：

I steps：Worked maximum load F based on the auxiliary spring of first main spring maximum allowable safe stress_M1Calculating：

According to the fully loaded sprung mass m of single-wheel_f, gravity acceleration g, less the half of the main spring of piece parabolic type variable-section steel sheet spring is long Degree L_M, width b, half l of installing space₃, root thickness h_2M, main reed number m, maximum allowable safe stress [σ], and step (2) K determined in step A_Mi, the K that determines in step B_MAi, it is determined that the auxiliary spring based on first main spring maximum allowable safe stress Function to maximum load F_M1, i.e.,

$F_{M1}=\frac{{\mathrm{bh}}_{2M}^2\[\mathrm{\σ}\]\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}{6(L_M-l_3/2)(K_{Mi}\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}-K_{MAi}\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi})}-\frac{0.75m_f{\mathrm{gK}}_{MAi}\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}{(K_{Mi}\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}-K_{MAi}\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi})};$

Ii steps：Worked maximum load F based on the auxiliary spring of the main spring maximum allowable safe stress of tailpiece_MmCalculating：

According to the fully loaded sprung mass m of single-wheel_f, gravity acceleration g, the width b of few piece parabolic type variable-section steel sheet spring, main spring Parabola root is to spring end points apart from l_2M, main spring root thickness h_2M, auxiliary spring root thickness h_2A, the parabola of the main spring of m pieces The thickness of section compares β_m, main reed number m, auxiliary spring piece number n, auxiliary spring is with main spring contact point to main spring end points apart from l₀, maximum allowable peace Resultant stress [σ], calculated G in the II steps of step (1)_x-CD, calculated G in IV steps_x-CDz, calculate in V steps The G for obtaining_x-DAT, and the K determined in the step A of step (2)_Mi, the K that determines in step B_MAi, the K that determines in step C_Aj, it is determined that Maximum load F is functioned to based on the auxiliary spring of the main spring maximum allowable safe stress of tailpiece_Mm, i.e.,

$F_{Mm}=\frac{\frac{b{\left({\mathrm{\β}}_m{h}_{2M}\right)}^2\[\mathrm{\σ}\]}{6}+\underset{j=1}{\overset{n}{\Σ}}\left(\frac{0.75m_f{\mathrm{gK}}_{Aj}{K}_{MAm}{G}_{x-CD}{h}_{2A}^3({\mathrm{\β}}_m^2{l}_{2M}-l_0)}{\underset{j=1}{\overset{n}{\Σ}}{K}_{Aj}\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}-(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)}\right)-\frac{0.75m_f{\mathrm{gK}}_{MAm}{\mathrm{\β}}_m^2{l}_{2M}}{\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}}}{\[\frac{K_{Mm}}{\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}-\frac{K_{MAm}{\mathrm{\β}}_m^2{l}_{2M}}{\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}}+\underset{j=1}{\overset{n}{\Σ}}\left(\frac{K_{Aj}{K}_{MAm}{G}_{x-CD}{h}_{2A}^3({\mathrm{\β}}_m^2{l}_{2M}-l_0)}{\underset{j=1}{\overset{n}{\Σ}}{K}_{Aj}\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)}\right)\]};$

Iii steps：Worked maximum load F based on the auxiliary spring of first auxiliary spring maximum allowable safe stress_A1Calculating：

According to the fully loaded sprung mass m of single-wheel_f, gravity acceleration g, less the half of piece parabolic type variable-section steel sheet spring auxiliary spring is long Degree L_A, width b, half l of installing space₃, main spring root thickness h_2M, auxiliary spring root thickness h_2A, main reed number m, auxiliary spring piece number N, maximum allowable safe stress [σ], calculated G in the II steps of step (1)_x-CD, calculated G in IV steps_x-CDz、 Calculated G in V steps_x-DAT, and the K determined in the step B of step (2)_MAi, the K that determines in step C_Aj, it is determined that based on head The auxiliary spring of piece auxiliary spring maximum allowable safe stress functions to maximum load F_A1, i.e.,

$F_{A1}=0.75m_{f}g-\frac{{\mathrm{bh}}_{2A}^2\[\mathrm{\σ}\]\underset{j=1}{\overset{n}{\Σ}}{K}_{Aj}\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)}{6K_{Aj}{K}_{MAm}{G}_{x-CD}{h}_{2A}^3(L_A-l_3/2)};$

Iv steps：Half maximum load F worked based on the auxiliary spring of maximum allowable safe stress_maxCalculating：

According to the F determined in i steps_M1, the F determined in ii steps_Mm, and the F determined in iii steps_A1, it is determined that being permitted based on maximum Half maximum load F functioned to the auxiliary spring of safe stress_max, i.e.,

F_max=min (F_M1,F_Mm,F_A1)；

Wherein, min (F_M1,F_Mm,F_A1) represent take F_M1、F_MmAnd F_A1In minimum numerical value；

(5) the few piece parabolic type variable-section steel sheet spring auxiliary spring of ends contact formula functions to the design of load：

According to the F determined in step (3)_min, and the F determined in the iv steps of step (4)_max, to the few piece parabolic of end contact The auxiliary spring of line style variable-section steel sheet spring functions to load and is designed, i.e.,

F_k=0.618F_min+0.382F_max。