CN107013616B - High-intensitive first-order gradient rigidity leaf spring clamps the emulated computation method of stiffness characteristics - Google Patents
High-intensitive first-order gradient rigidity leaf spring clamps the emulated computation method of stiffness characteristics Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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Abstract
本发明涉及高强度一级渐变刚度板簧加紧刚度特性的仿真计算方法，属于悬架钢板弹簧技术领域。本发明可根据主簧和副簧的结构设计参数，及主簧和副簧初始切线弧高设计值，在接触载荷仿真计算的基础上，对高强度一级渐变刚度板簧在不同载荷下的加紧刚度特性进行仿真计算。通过样机试验结果对比可知，本发明所提供的高强度一级渐变刚度板簧加紧刚度特性的仿真计算方法是正确的，可得到准确可靠在不同载荷下的加紧刚度仿真计算值，为高强度一级渐变刚度板簧特性仿真奠定了可靠的技术基础；利用该方法确保所设计板簧满足渐变加紧刚度特性要求，提高产品设计水平、质量和性能及车辆行驶平顺性；同时，还可降低设计和试验测试费用，加快产品开发速度。
The invention relates to a simulation calculation method for the tightening stiffness characteristics of a high-strength one-stage gradually changing stiffness leaf spring, and belongs to the technical field of suspension leaf springs. According to the structural design parameters of the main spring and the auxiliary spring, and the design value of the initial tangent arc height of the main spring and the auxiliary spring, on the basis of the contact load simulation calculation, the high-strength one-stage gradient stiffness leaf spring under different loads Tighten the stiffness characteristics for simulation calculations. Through the comparison of the prototype test results, it can be seen that the simulation calculation method of the tightening stiffness characteristics of the high-strength one-stage gradient stiffness leaf spring provided by the present invention is correct, and accurate and reliable tightening stiffness simulation calculation values under different loads can be obtained, which is a high-strength one-stage The characteristic simulation of step gradient stiffness leaf spring has laid a reliable technical foundation; using this method to ensure that the designed leaf spring meets the requirements of gradient tightening stiffness characteristics can improve product design level, quality and performance and vehicle ride comfort; at the same time, it can also reduce design and Trial testing costs to speed up product development.
Description
技术领域technical field
本发明涉及车辆悬架板簧，特别是高强度一级渐变刚度板簧夹紧刚度特性的仿真计算方法。The invention relates to a vehicle suspension leaf spring, in particular to a method for simulating and calculating the clamping stiffness characteristics of a high-strength, first-order gradient-stiffness leaf spring.
背景技术Background technique
随着高强度钢板材料的出现，可采用高强度一级渐变刚度板簧，以满足在不同载荷下的车辆行驶平顺性及悬架渐变偏频保持不变的设计要求，其中，渐变刚度板簧的夹紧刚度影响悬架系统偏频和车辆行驶平顺性，而且其渐变夹紧刚度特性，不仅与渐变刚度板簧的各片主簧和副簧的结构参数有关，而且还与主副簧开始接触载荷和完全接触载荷有关。因此，对于给定设计结构参数的高强度一级渐变刚度板簧，是否满足刚度特性的设计要求，应通过仿真计算给出所设计板簧的夹紧刚度随载荷变化特性曲线。然而，由于在渐变过程中的板簧挠度计算非常复杂，且受重叠部分等效厚度计算及接触载荷反求关键问题的制约，据所查资料可知，先前国内外一直未给出高强度一级渐变刚度板簧夹紧刚度特性的仿真计算方法。随着车辆行驶速度及其对平顺性要求的不断提高，对高强度一级渐变刚度设计板簧提出了更高要求，因此，必须建立一种精确、可靠的高强度一级渐变刚度板簧夹紧刚度特性的仿真计算方法，为高强度一级渐变刚度板簧特性仿真计算及仿真软件开发奠定可靠的技术基础，满足车辆行业快速发展、车辆行驶平顺性对高强度一级渐变刚度板簧的设计要求，通过刚度特性仿真计算可及时发现产品设计所存在问题，确保满足刚度特性设计要，从而提高产品设计水平、质量和性能；同时，还可降低设计及试验费用，加快产品开发速度。With the emergence of high-strength steel plate materials, high-strength one-level gradient stiffness leaf springs can be used to meet the design requirements of vehicle ride comfort and suspension gradient bias frequency under different loads. Among them, gradient stiffness leaf springs The clamping stiffness affects the bias frequency of the suspension system and the ride comfort of the vehicle, and its gradual clamping stiffness characteristics are not only related to the structural parameters of the main springs and auxiliary springs of the leaf springs with gradual stiffness, but also related to the starting point of the main and auxiliary springs. Contact loads are related to full contact loads. Therefore, for a high-strength one-stage gradual stiffness leaf spring with given design structural parameters, whether it meets the design requirements of stiffness characteristics, the characteristic curve of the clamping stiffness of the designed leaf spring as a function of load should be given through simulation calculations. However, since the calculation of leaf spring deflection in the gradual change process is very complicated, and is restricted by the calculation of the equivalent thickness of the overlapping part and the key issues of contact load inverse calculation, according to the information obtained, no high-strength level has been given at home and abroad. A simulation calculation method for the clamping stiffness characteristics of a gradient stiffness leaf spring. With the continuous improvement of vehicle speed and its requirements for ride comfort, higher requirements are put forward for high-strength one-stage gradual stiffness design leaf springs. Therefore, it is necessary to establish an accurate and reliable high-strength one-stage gradual stiffness leaf spring clamp The simulation calculation method of tight stiffness characteristics lays a reliable technical foundation for the simulation calculation and simulation software development of high-strength one-level gradient stiffness leaf spring characteristics, and meets the needs of high-strength one-level gradient stiffness leaf springs for the rapid development of the vehicle industry and vehicle ride comfort. According to the design requirements, the problems existing in the product design can be found in time through the simulation calculation of the stiffness characteristics to ensure that the design requirements of the stiffness characteristics are met, thereby improving the product design level, quality and performance; at the same time, it can also reduce design and test costs and speed up product development.
发明内容Contents of the invention
针对上述现有技术中存在的缺陷，本发明所要解决的技术问题是提供一种简便、可靠的高强度一级渐变刚度板簧夹紧刚度特性的仿真计算方法，仿真计算流程图，如图1所示。板簧采用高强度钢板，宽度为b，弹性模量为E，各片板簧为以中心穿装孔对称的结构，其安装夹紧距的一半L0为骑马螺栓夹紧距的一半L0；高强度一级渐变刚度板簧的一半对称结构如图2所示，由主簧1和副簧2构成，其中，主簧1的片数为n，各片主簧的厚度为hi，一半作用长度为Lit，一半夹紧长度为Li＝Lit-L0/2，i＝1,2,…,n；副簧2的片数为m，各片副簧的厚度为hAj，一半作用长度为LAjt，一半夹紧长度为LAj＝Ln+j＝LAjt-L0/2，j＝1,2,…,m。末片主簧的下表面与首片副簧的上表面之间的主副簧渐变间隙δMA，其大小是由主簧初始切线弧高与副簧初始切线弧高所决定的。当载荷达到开始起作用载荷Pk时，在骑马螺栓夹紧距外侧，末片主簧下表面与首片副簧上表面开始接触；当载荷达到完全接触载荷Pw时，末片主簧下表面与首片副簧上表面完全接触。当载荷在[Pk,Pw]范围内变化时，主簧末片下表面与副簧首片上表面的接触位置及主副簧渐变复合夹紧刚度KkwP随载荷而变化，从而满足悬架偏频保持不变的设计要求。在高强度一级渐变刚度板簧的结构设计参数给定情况下，对其在不同载荷下的夹紧刚度特性进行仿真计算。In view of the above-mentioned defects in the prior art, the technical problem to be solved by the present invention is to provide a simple and reliable simulation calculation method for the clamping stiffness characteristics of a high-strength one-level gradient stiffness leaf spring. The simulation calculation flow chart is shown in Figure 1 shown. The leaf spring is made of high-strength steel plate, the width is b, and the elastic modulus is E. Each leaf spring is a symmetrical structure with a central piercing hole, and half of the installation clamping distance L 0 is half of the saddle bolt clamping distance L 0 ; The semi-symmetrical structure of a high-strength one-stage gradually changing stiffness leaf spring is shown in Figure 2, consisting of a main spring 1 and an auxiliary spring 2, wherein the number of pieces of the main spring 1 is n, and the thickness of each main spring is h i , Half of the working length is L it , half of the clamping length is L i ＝L it -L 0 /2, i=1,2,...,n; the number of pieces of secondary spring 2 is m, and the thickness of each piece of secondary spring is h Aj , half of the working length is L Ajt , half of the clamping length is L Aj =L n+j =L Ajt -L 0 /2, j=1,2,...,m. The gradual gap δ MA between the lower surface of the last main spring and the upper surface of the first auxiliary spring is determined by the initial tangent arc height of the main spring and the initial tangent arc height of the auxiliary spring. When the load reaches the starting load P k , the lower surface of the main spring of the last leaf is in contact with the upper surface of the auxiliary spring of the first leaf at the outside of the saddle bolt clamping distance; when the load reaches the full contact load P w , the main spring of the last leaf is released The surface is in full contact with the upper surface of the first secondary spring. When the load changes within the range of [P k , P w ], the contact position between the lower surface of the main spring end and the upper surface of the first auxiliary spring and the gradual compound clamping stiffness K kwP of the main and auxiliary springs change with the load, so as to satisfy the suspension The design requirement that the bias frequency remains unchanged. Under the condition that the structural design parameters of high-strength graded stiffness leaf spring are given, the clamping stiffness characteristics under different loads are simulated and calculated.
为解决上述技术问题，本发明所提供的高强度一级渐变刚度板簧夹紧刚度特性的仿真计算方法，其特征在于采用以下仿真计算步骤：In order to solve the above-mentioned technical problems, the simulation calculation method of the clamping stiffness characteristics of the high-strength one-level gradual stiffness leaf spring provided by the present invention is characterized in that the following simulation calculation steps are adopted:
(1)高强度一级渐变刚度板簧的各不同片数重叠段的等效厚度计算：(1) Calculation of the equivalent thickness of the overlapping sections of the high-strength one-stage gradient stiffness leaf springs with different numbers of pieces:
根据主簧片数n,各片主簧的厚度hi，i＝1,2,...,n；副簧片数m,各片副簧的厚度hAj，j＝1,2,...,m；主副簧总片数N＝n+m，对高强度一级渐变刚度板簧的各不同片数k重叠段的等效厚度hke进行计算，k＝1,2,...,N，即According to the number of main reeds n, the thickness h i of each main spring, i=1,2,...,n; the number of secondary reeds m, the thickness h Aj of each secondary spring, j=1,2,. .., m; the total number of primary and secondary springs N=n+m, calculate the equivalent thickness h ke of the overlapping sections with different numbers k of high-strength one-stage gradient stiffness leaf springs, k=1,2,. .., N, namely
其中，主簧根部重叠部分的等效厚度 Among them, the equivalent thickness of the overlapping part of the root of the main spring
(2)高强度一级渐变刚度板簧的主簧夹紧刚度和主副簧复合夹紧刚度的仿真计算：(2) The simulation calculation of the clamping stiffness of the main spring and the composite clamping stiffness of the main and auxiliary springs of the high-strength one-level gradient stiffness leaf spring:
I步骤：主簧夹紧刚度KM的仿真计算Step I: Simulation calculation of main spring clamping stiffness K M
根据高强度一级渐变刚度板簧的宽度b，弹性模量E；主簧片数n,各片主簧的一半夹紧长度Li，及步骤(1)中计算得到的hke，k＝i＝1,2,...,n，对主簧夹紧刚度KM进行仿真计算，即According to the width b and elastic modulus E of the leaf spring with high-strength grade one gradient stiffness; the number of main reeds n, half the clamping length L i of each main spring, and h ke calculated in step (1), k= i=1,2,...,n, the simulation calculation of the clamping stiffness K M of the main spring, that is
II步骤：主副簧复合夹紧刚度KMA的仿真计算Step II: Simulation Calculation of the Composite Clamping Stiffness K MA of the Primary and Secondary Springs
根据高强度一级渐变刚度板簧的宽度b，弹性模量E；主簧片数n,各片主簧的一半夹紧长度Li，i＝1,2,...,n；副簧片数m，各片副簧的一半夹紧长度LAj＝Ln+j，j＝1,2,...,m，主副簧总片数N，及步骤(1)中计算得到的hke，k＝1,2,...,N；对主副簧复合夹紧刚度KMA进行仿真计算，即According to the width b and elastic modulus E of the high-strength one-stage gradual stiffness leaf spring; the number of main reeds n, half the clamping length L i of each main spring, i=1,2,...,n; the auxiliary spring The number of pieces m, half the clamping length L Aj =L n+j of each piece and secondary spring, j=1,2,...,m, the total number of primary and secondary springs N, and the calculated value in step (1) h ke , k=1,2,...,N; simulate the composite clamping stiffness K MA of the primary and secondary springs, namely
(3)高强度一级渐变刚度板簧的开始接触载荷Pk的仿真计算：(3) Simulation calculation of the initial contact load Pk of the high-strength one-stage gradient stiffness leaf spring:
A步骤：末片主簧下表面初始曲率半径RM0b的仿真计算Step A: Simulation calculation of the initial radius of curvature R M0b of the lower surface of the last main spring
根据主簧片数n，各片主簧的厚度hi，i＝1,2,...,n，首片主簧的一半夹紧长度L1，主簧初始切线弧高HgM0，对末片主簧下表面的初始曲率半径RM0b进行分钟计算，即According to the number n of main reeds, the thickness h i of each main spring, i=1,2,...,n, half the clamping length L 1 of the first main spring, and the initial tangent arc height H gM0 of the main spring, for The initial radius of curvature R M0b of the lower surface of the last main spring is calculated in minutes, namely
B步骤：首片副簧上表面初始曲率半径RA0a的仿真计算Step B: Simulation calculation of the initial radius of curvature R A0a on the upper surface of the first auxiliary spring
根据首片副簧的一半夹紧长度LA1，副簧初始切线弧高HgA0，对首片副簧上表面的初始曲率半径RA0a，即According to half the clamping length L A1 of the first auxiliary spring, the initial tangent arc height H gA0 of the auxiliary spring, and the initial curvature radius R A0a of the upper surface of the first auxiliary spring, that is
C步骤：高强度一级渐变刚度板簧开始接触载荷Pk的仿真计算：Step C: Simulation calculation of initial contact load P k of high-strength grade-1 gradient stiffness leaf spring:
根据高强度一级渐变刚度板簧的宽度b，弹性模量E；首片主簧的一半夹紧跨长度L1，步骤(1)中计算得到的hMe；A步骤中计算得到的RM0b，B步骤中计算得到的RA0a，对高强度一级渐变刚度板簧的开始接触载荷Pk进行仿真计算，即According to the width b and elastic modulus E of the high-strength first-level gradual stiffness leaf spring; half the clamping span length L 1 of the first main spring, h Me calculated in step (1); R M0b calculated in step A , R A0a calculated in step B, the initial contact load P k of the high-strength one-stage gradient stiffness leaf spring is simulated and calculated, namely
(4)高强度一级渐变刚度板簧的完全接触载荷Pw的仿真计算：(4) Simulation calculation of the full contact load P w of the high-strength one-stage gradient stiffness leaf spring:
根据步骤(2)中仿真计算得到的KM和KMA，步骤(3)中仿真计算得到的Pk，对高强度一级渐变刚度板簧的完全接触载荷Pw进行仿真计算，即According to the K M and K MA obtained from the simulation calculation in step (2), and the P k obtained from the simulation calculation in step (3), the full contact load P w of the high-strength one-stage gradient stiffness leaf spring is simulated and calculated, namely
(5)高强度一级渐变刚度板簧在不同载荷下的夹紧刚度特性的仿真计算：(5) Simulation calculation of clamping stiffness characteristics of high-strength one-stage gradient stiffness leaf spring under different loads:
根据额定载荷PN，步骤(2)中计算得到的KM和KMA；步骤(3)中仿真计算得到的Pk，步骤(4)中仿真计算得的Pw，对高强度一级渐变刚度板簧在不同载荷P下的夹紧刚度KP特性进行仿真计算，即According to the rated load P N , the K M and K MA calculated in step (2); the P k calculated in step (3) and the P w calculated in step (4), for high-strength first-order gradient The clamping stiffness K P characteristics of the stiffness leaf spring under different loads P are simulated and calculated, namely
本发明比现有技术具有的优点Advantages of the present invention over prior art
由于主副簧渐变接触过程中的挠度计算非常复杂，同时受板簧重叠部分等效厚度计算和接触载荷反求等关键问题的制约，据所查资料可知，先前国内外一直未给出高强度一级渐变刚度板簧夹紧刚度特性的仿真计算方法。本发明可根据主簧和副簧的结构设计参数，及主簧和副簧初始切线弧高设计值，在接触载荷仿真计算的基础上，对高强度一级渐变刚度板簧在不同载荷下的夹紧刚度特性进行仿真计算，给出夹紧刚度随载荷的变化特性曲线。通过样机试验结果对比可知，本发明所提供的高强度一级渐变刚度板簧夹紧刚度特性的仿真计算方法是正确的，可得到准确可靠在不同载荷下的夹紧刚度仿真计算值，为高强度一级渐变刚度板簧特性仿真奠定了可靠的技术基础；利用该方法确保所设计板簧满足渐变夹紧刚度特性的设计要求，提高产品设计水平、质量和性能及车辆行驶平顺性；同时，还可降低设计和试验测试费用，加快产品开发速度。Since the calculation of the deflection in the gradual contact process of the main and auxiliary springs is very complicated, and at the same time, it is restricted by key issues such as the calculation of the equivalent thickness of the overlapping part of the leaf spring and the reverse calculation of the contact load. A simulation calculation method for the clamping stiffness characteristics of a first-order gradient stiffness leaf spring. According to the structural design parameters of the main spring and the auxiliary spring, and the design value of the initial tangent arc height of the main spring and the auxiliary spring, on the basis of the contact load simulation calculation, the high-strength one-stage gradient stiffness leaf spring under different loads The clamping stiffness characteristic is simulated and calculated, and the characteristic curve of the clamping stiffness changing with the load is given. Through the comparison of the prototype test results, it can be seen that the simulation calculation method of the clamping stiffness characteristics of the high-strength one-level gradual stiffness leaf spring provided by the present invention is correct, and accurate and reliable clamping stiffness simulation calculation values under different loads can be obtained, which is high. The characteristic simulation of strength-level gradient stiffness leaf spring has laid a reliable technical foundation; using this method to ensure that the designed leaf spring meets the design requirements of gradient clamping stiffness characteristics, improve product design level, quality and performance, and vehicle ride comfort; at the same time, It can also reduce design and experimental testing costs and speed up product development.
附图说明Description of drawings
为了更好地理解本发明，下面结合附图做进一步的说明。In order to better understand the present invention, further description will be made below in conjunction with the accompanying drawings.
图1是高强度一级渐变刚度板簧夹紧刚度特性的仿真计算流程图；Fig. 1 is a simulation calculation flow chart of the clamping stiffness characteristics of a high-strength one-stage gradient stiffness leaf spring;
图2是高强度一级渐变刚度板簧的一半对称结构示意图；Fig. 2 is a schematic diagram of a semi-symmetrical structure of a high-strength one-stage gradient stiffness leaf spring;
图3是实施例的仿真计算所得到的高强度一级渐变刚度板簧的夹紧刚度KP随载荷P的变化特性曲线。Fig. 3 is the variation characteristic curve of the clamping stiffness K P of the high-strength one-stage gradually changing stiffness leaf spring with the load P obtained by the simulation calculation of the embodiment.
具体实施方案specific implementation plan
下面通过实施例对本发明作进一步详细说明。The present invention will be described in further detail below by way of examples.
实施例：某高强度一级渐变刚度板簧的宽度b＝63mm，骑马螺栓夹紧距的一半L0＝50mm，弹性模量E＝200Gpa。主簧片数n＝3片，各片主簧的厚度h1＝h2＝h3＝7mm，各片主簧的一半作用长度分别为L1t＝525mm，L2t＝461mm，L3t＝399mm；各片主簧的一半夹紧长度分别为L1＝L1t-L0/2＝500mm，L2＝L2t-L0/2＝436mm，L3＝L3t-L0/2＝374mm。副簧片数m＝2片，各片副簧的厚度hA1＝hA2＝12mm，各片副簧的一半作用长度分别为LA1t＝350mmLA2t＝250mm，各片副簧的一半夹紧长度分别为LA1＝L4＝LA1t-L0/2＝325mm，LA2＝L5＝LA2t-L0/2＝200mm。主簧初始切线弧高设计值HgM0＝112.5mm，首片副簧的初始切线弧高设计值HgA0＝21.5mm。额定载荷PN＝7227N。根据各片主簧和副簧的结构参数，主簧初始切线弧高HgM0和副簧初始切线弧高HgA0，对该高强度一级渐变刚度板簧夹紧刚度特性进行仿真计算。Example: The width b of a high-strength one-stage gradually changing stiffness leaf spring is 63 mm, half of the saddle bolt clamping distance L 0 is 50 mm, and the elastic modulus E is 200 Gpa. The number of main reeds is n=3, the thickness of each main spring is h 1 =h 2 =h 3 =7mm, and half the working length of each main spring is L 1t =525mm, L 2t =461mm, L 3t =399mm ;Half the clamping length of each main spring is L 1 ＝L 1t -L 0 /2＝500mm, L 2 ＝L 2t -L 0 /2＝436mm, L 3 ＝L 3t -L 0 /2＝374mm . The number of secondary reeds m=2 pieces, the thickness of each secondary spring h A1 =h A2 =12mm, half the working length of each secondary spring is L A1t =350mmL A2t =250mm, half the clamping length of each secondary spring L A1 = L 4 = L A1t - L 0 /2 = 325 mm, L A2 = L 5 = L A2t - L 0 /2 = 200 mm, respectively. The design value of the initial tangent arc height of the main spring H gM0 = 112.5mm, and the design value of the initial tangent arc height of the first auxiliary spring H gA0 = 21.5mm. Rated load P N =7227N. According to the structural parameters of the main spring and auxiliary spring of each leaf, the initial tangent arc height H gM0 of the main spring and the initial tangent arc height H gA0 of the auxiliary spring, the clamping stiffness characteristics of the high-strength one-stage gradual stiffness leaf spring were simulated and calculated.
本发明实例所提供的高强度一级渐变刚度板簧夹紧刚度特性的仿真计算方法，其仿真计算流程如图1所示，具体仿真计算步骤如下：The simulation calculation method of the clamping stiffness characteristics of the high-strength one-level gradual stiffness leaf spring provided by the example of the present invention, its simulation calculation process is as shown in Figure 1, and the specific simulation calculation steps are as follows:
(1)高强度一级渐变刚度板簧的各不同片数重叠段的等效厚度计算：(1) Calculation of the equivalent thickness of the overlapping sections of the high-strength one-stage gradient stiffness leaf springs with different numbers of pieces:
根据主簧片数n＝3,各片主簧的厚度h1＝h2＝h3＝7mm；副簧片数m＝2,各片副簧的厚度hA1＝hA2＝12mm，主副簧总片数N＝n+m＝5，对该高强度一级渐变刚度板簧的各不同片数k重叠段的等效厚度hke进行计算，k＝1,2,...,N，即According to the number of main reeds n=3, the thickness of each main spring h 1 =h 2 =h 3 =7mm; the number of auxiliary reeds m=2, the thickness of each auxiliary spring h A1 =h A2 =12mm, the main and auxiliary The total number of reeds N=n+m=5, calculate the equivalent thickness h ke of the overlapping sections with different numbers k of the high-strength one-stage gradient stiffness leaf spring, k=1,2,...,N ,Right now
h1e＝h1＝7.0mm，h 1e =h 1 =7.0mm,
其中，主簧根部重叠部分的等效厚度hMe＝h3e＝10.1mm。Wherein, the equivalent thickness h Me =h 3e =10.1mm of the overlapping portion of the root of the main spring.
(2)高强度一级渐变刚度板簧的主簧夹紧刚度和主副簧复合夹紧刚度的仿真计算：(2) The simulation calculation of the clamping stiffness of the main spring and the composite clamping stiffness of the main and auxiliary springs of the high-strength one-level gradient stiffness leaf spring:
I步骤：主簧夹紧刚度KM的仿真计算Step I: Simulation calculation of main spring clamping stiffness K M
根据高强度一级渐变刚度板簧的宽度b＝63mm，弹性模量E＝200GPa；主簧片数n＝3,各片主簧的一半夹紧长度L1＝500mm，L2＝436mm，L3＝374mm，及步骤(1)中计算得到h1e＝7.0mm，h2e＝8.8mm，h3e＝10.1mm，k＝i＝1,2,...,n，对主簧夹紧刚度KM进行仿真计算，即According to the width b=63mm of the high-strength one-stage gradual stiffness leaf spring, the elastic modulus E=200GPa; the number of main reeds n=3, half the clamping length of each main spring L 1 =500mm, L 2 =436mm, L 3 ＝374mm, and h 1e ＝7.0mm, h 2e ＝8.8mm, h 3e ＝10.1mm, k＝i＝1,2,...,n calculated in step (1), for the clamping stiffness of the main spring K M is simulated and calculated, that is
II步骤：主副簧复合夹紧刚度KMA的仿真计算Step II: Simulation Calculation of the Composite Clamping Stiffness K MA of the Primary and Secondary Springs
根据渐变刚度板簧的宽度b＝63mm，弹性模量E＝200GPa；主簧片数n＝3,各片主簧的一半夹紧长度L1＝500mm，L2＝436mm，L3＝374mm；副簧片数m＝2，各片副簧的一半夹紧长度LA1＝L4＝325mm，LA2＝L5＝200mm；主副簧总片数N＝5；及步骤(1)中计算得到的h1e＝7.0mm，h2e＝8.8mm，h3e＝10.1mm，h4e＝14mm，h5e＝16.5mm；k＝1,2,...,N，对主副簧复合夹紧刚度KMA进行仿真计算，即According to the width b=63mm of the leaf spring with gradual stiffness, the modulus of elasticity E=200GPa; the number of main reeds n=3, half the clamping length of each main spring L 1 =500mm, L 2 =436mm, L 3 =374mm; The number of auxiliary reeds m=2, the half clamping length of each auxiliary spring L A1 =L 4 =325mm, L A2 =L 5 =200mm; the total number of main and auxiliary reeds N=5; and calculation in step (1) The obtained h 1e = 7.0mm, h 2e = 8.8mm, h 3e = 10.1mm, h 4e = 14mm, h 5e = 16.5mm; k = 1, 2,..., N, combined clamping of the main and secondary springs Stiffness K MA for simulation calculation, that is
(3)高强度一级渐变刚度板簧的开始接触载荷Pk的仿真计算：(3) Simulation calculation of the initial contact load Pk of the high-strength one-stage gradient stiffness leaf spring:
A步骤：末片主簧下表面初始曲率半径RM0b的仿真计算Step A: Simulation calculation of the initial radius of curvature R M0b of the lower surface of the last main spring
根据主簧片数n＝3，各片主簧的厚度hi＝7mm，i＝1,2,3，首片主簧的一半夹紧长度L1＝500mm，主簧初始切线弧高HgM0＝112.5mm，对末片主簧下表面初始曲率半径RM0b进行分钟计算，即According to the number of main reeds n=3, the thickness of each main spring h i =7mm, i=1,2,3, half the clamping length of the first main spring L 1 =500mm, the initial tangent arc height of the main spring H gM0 =112.5mm, the initial radius of curvature R M0b of the lower surface of the last main spring is calculated in minutes, that is
B步骤：首片副簧上表面初始曲率半径RA0a的仿真计算Step B: Simulation calculation of the initial radius of curvature R A0a on the upper surface of the first auxiliary spring
根据首片副簧的一半夹紧长度LA1＝325mm，副簧初始切线弧高HgA0＝21.5mm，对首片副簧上表面初始曲率半径RA0a，即According to half the clamping length L A1 of the first auxiliary spring = 325mm and the initial tangent arc height H gA0 of the auxiliary spring = 21.5mm, the initial radius of curvature R A0a on the upper surface of the first auxiliary spring is:
C步骤：高强度一级渐变刚度板簧的开始接触载荷Pk的仿真计算Step C: Simulation calculation of the initial contact load P k of the high-strength one-stage gradient stiffness leaf spring
根据高强度一级渐变刚度板簧的宽度b＝63mm，弹性模量E＝200GPa；首片主簧的一半夹紧跨长度L1＝500mm，步骤(1)中计算得到的hMe＝10.1mm；A步骤中计算得到的RM0b＝1188.4mm，B步骤中计算得到的RA0a＝2467.1mm，对该高强度一级渐变刚度板簧的开始接触载荷Pk进行仿真计算，即According to the width b=63mm of the high-strength first-level gradient stiffness leaf spring, the modulus of elasticity E=200GPa; half the clamping span length L 1 of the first main spring=500mm, hMe =10.1mm calculated in step (1) R M0b calculated in the A step = 1188.4mm, and R A0a calculated in the B step = 2467.1mm, and the initial contact load P k of the high-strength one-level gradient stiffness leaf spring is simulated, namely
(4)高强度一级渐变刚度板簧的完全接触载荷Pw的仿真计算：(4) Simulation calculation of the full contact load P w of the high-strength one-stage gradient stiffness leaf spring:
根据步骤(2)中仿真计算得到的KM＝51.3N/mm和KMA＝173.7N/mm，及步骤(3)中仿真计算得到的Pk＝1885N，对该高强度一级渐变刚度板簧的完全接触载荷Pw进行仿真计算，即According to the K M =51.3N/mm and K MA =173.7N/mm calculated by the simulation in step (2), and the P k =1885N obtained by the simulation calculation in the step (3), the high-strength primary gradient stiffness plate The full contact load P w of the spring is simulated and calculated, that is
(5)高强度一级渐变刚度板簧在不同载荷下的夹紧刚度特性的仿真计算：(5) Simulation calculation of clamping stiffness characteristics of high-strength one-stage gradient stiffness leaf spring under different loads:
根据额定载荷PN＝7227N，步骤(2)中仿真计算得到的KM＝51.3N/mm和KMA＝173.7N/mm；步骤(3)中仿真计算得到的Pk＝1885N，步骤(4)中仿真计算得到的Pw＝6383N，对该高强度一级渐变刚度板簧在不同载荷P下的夹紧刚度KP特性进行仿真计算，即According to the rated load P N =7227N, K M =51.3N/mm and K MA =173.7N/mm obtained by simulation calculation in step (2); P k =1885N obtained by simulation calculation in step (3), step (4 ) obtained by the simulation calculation in P w =6383N, the clamping stiffness K P characteristic of the high-strength one-stage gradient stiffness leaf spring under different loads P is simulated and calculated, namely
利用Matlab计算程序，仿真计算所得到的该高强度一级渐变刚度板簧的夹紧刚度KP随载荷P的变化特性曲线，如图3所示，其中，当载荷P＝Pk＝1885N时，KP＝KM＝51.3N/mm，当载荷P＝Pw＝6383N时，KP＝KMA＝173.7N/mm；当载荷P在[Pk,Pw]范围内变化时，渐变夹紧刚度KP随载荷P的增大而增大，即渐变夹紧刚度KP从KM＝51.3N/mm逐渐增大到KMA＝173.7N/mm。Using the Matlab calculation program, the characteristic curve of the clamping stiffness K P of the high-strength one-stage gradient stiffness leaf spring obtained by simulation calculation with the load P is shown in Figure 3, wherein, when the load P=P k =1885N , K P ＝K M ＝51.3N/mm, when the load P＝P w ＝6383N, K P ＝K MA ＝173.7N/mm; when the load P changes within the range of [P k , P w ], the gradual change The clamping stiffness K P increases with the increase of the load P, that is The gradual clamping stiffness K P increases gradually from K M =51.3 N/mm to K MA =173.7 N/mm.
通过样机加载挠度试验可知，该高强度一级渐变刚度板簧的主簧夹紧刚度、主副簧复合夹紧刚度、及渐变复合夹紧刚度的仿真计算值，与测试结果接近，表明本发明所提供的高强度一级渐变刚度板簧夹紧刚度特性的仿真计算方法是正确的，为高强度一级渐变刚度板簧的夹紧刚度仿真验证及特性仿真软件开发奠定了可靠的技术基础。利用该方法可得到准确可靠的高强度一级渐变刚度板簧在不同载荷情况下的夹紧刚度仿真计算值，确保夹紧刚度特性满足板簧设计要求，提高产品的设计水平、质量和性能及车辆行驶平顺性；同时，降低设计及试验费用，加快产品开发速度。Through the loading deflection test of the prototype, it can be seen that the simulation calculation values of the main spring clamping stiffness, the composite clamping stiffness of the primary and secondary springs, and the gradient composite clamping stiffness of the high-strength one-stage gradient stiffness leaf spring are close to the test results, indicating that the present invention The simulation calculation method of the clamping stiffness characteristics of the high-strength one-stage gradient stiffness leaf spring is correct, and it has laid a reliable technical foundation for the clamping stiffness simulation verification and characteristic simulation software development of the high-strength one-stage gradient stiffness leaf spring. This method can be used to obtain accurate and reliable clamping stiffness simulation calculation values of high-strength one-stage gradient stiffness leaf springs under different load conditions, ensuring that the clamping stiffness characteristics meet the design requirements of leaf springs, and improving the design level, quality and performance of products. Improve vehicle ride comfort; at the same time, reduce design and test costs and speed up product development.
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