CN104156547A - Method for designing optimal damping characteristics of shock absorber of vehicle steel plate spring suspension system - Google Patents

Abstract

The invention relates to a method for designing optimal damping characteristics of a shock absorber of a vehicle steel plate spring suspension system, and belongs to the technical field of vehicle steel plate spring suspensions. The method is characterized by including the steps of conducting optimization design on the optimal damping ratio required by the suspension system according to parameters of the vehicle suspension system, calculating and analyzing the damping ratio of the steel plate spring suspension system according to displacement and loads measured through steel plate spring loading and unloading deformation tests, and designing the optimal damping characteristics of the shock absorber of the vehicle steel plate spring suspension system on this basis. It can be known from Matlab/simulink simulation verification that the optimal damping characteristic design value of the shock absorber of the steel plate spring suspension system can be designed according to the method, the optimal damping matching can be achieved for the vehicle steel plate spring suspension system, and vehicle driving smoothness is improved; meanwhile, repeated tests and verification can be avoided, the development speed of products can be increased, and design and test expenses can be reduced.

Description

The method for designing of vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic

Technical field

The present invention relates to vehicle Leaf Spring Suspension System, particularly the method for designing of vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic.

Background technology

Mostly adopt Leaf Spring Suspension System for a lot of goods carrying vehicles, although leaf spring has certain effectiveness in vibration suppression, but rely on separately leaf spring to be difficult to make vehicle suspension to reach optimum damping coupling, can not meet the requirement of Vehicle Driving Cycle ride comfort and security.Along with the fast development of Vehicle Industry and improving constantly of Vehicle Speed, the design of goods carrying vehicle Leaf Spring Suspension System has been proposed to higher designing requirement, therefore, need to increase hydraulic buffer to vehicle Leaf Spring Suspension System, but never provide reliable method for designing but increase hydraulic buffer for Leaf Spring Suspension System at present, conventionally according to type of vehicle, select by rule of thumb certain vibration damper, then entrucking, through Vehicle Driving Cycle Ride Comfort, finally obtains the vibration damper matching with this vehicle Leaf Spring Suspension System.The traditional design method of vehicle Leaf Spring Suspension System vibration damper at present, can not meet the designing requirement of vehicle development and Vehicle Driving Cycle ride comfort, and the design cycle is long, and test and design cost are high.Therefore, must set up a kind of method for designing of accurate, reliable vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic, the damping ratio having according to Leaf Spring Suspension System self, by to the needed optimal damper ratio of vehicle suspension system, optimum damping to the required vibration damper of vehicle Leaf Spring Suspension System designs, thereby improve Vehicle Driving Cycle ride comfort, reduce design and testing expenses simultaneously.

Summary of the invention

For the defect existing in above-mentioned prior art, technical matters to be solved by this invention is to provide a kind of method for designing of accurate, reliable vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic, and its design cycle as shown in Figure 1.

In order to solve the problems of the technologies described above, the method for designing of vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic provided by the present invention, its technical scheme implementation step is as follows:

(1) determine that the needed optimal damper of vehicle suspension system compares ξ _o:

According to vehicle parameter, determine that the needed optimal damper of vehicle Leaf Spring Suspension System compares ξ _o, concrete steps are as follows:

A step: determine the vehicle suspension system optimum damping ratio ξ based on comfortableness _oc:

According to the sprung mass m of vehicle single-wheel suspension ₂, suspension rate k ₂, unsprung mass m ₁, and tire stiffness k _t, determine the vehicle suspension system optimum damping ratio ξ based on comfortableness _oc, that is:

${\mathrm{\ξ}}_{\mathrm{oc}}=\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}};$

In formula, r _m=m ₂/ m ₁, r _k=k _t/ k ₂;

B step: determine the vehicle suspension system optimum damping ratio ξ based on security _os:

According to the sprung mass m of vehicle single-wheel suspension ₂, suspension rate k ₂, unsprung mass m ₁, and tire stiffness k _t, determine the vehicle suspension system optimum damping ratio ξ based on security _os, that is:

${\mathrm{\ξ}}_{\mathrm{os}}=\frac{1}{(1+r_m)}\sqrt{\frac{R}{{4r}_m{r}_k}};$

In formula, r _m=m ₂/ m ₁, r _k=k _t/ k ₂, R=r _mr _k(r _mr _k-2-2r _m)+(1+r _m) ³;

C step: determine that the vehicle suspension system optimal damper based on comfortableness and security compares ξ _o:

According to determined ξ in A step _ocwith determined ξ in B step _os, determine that the vehicle suspension system optimal damper based on comfortableness and security compares ξ _o, that is:

ξ _o＝ξ _oc+0.618(ξ _os-ξ _oc)；

(2) determine the damping ratio ξ that Leaf Spring Suspension System self has _g:

Load and unloading deformation test according to suspension leaf spring, by analysis and the processing of the test figure to measured, obtain the damping ratio that Leaf Spring Suspension System self has, concrete steps are as follows:

I step: utilize leaf spring testing machine, according to the sprung mass m of single-wheel Leaf Spring Suspension under rated load ₂and the maximum load F bearing _max=m ₂g, carries out progressively loading and unloading test to suspension leaf spring, the deflection of respective loads is tested simultaneously, and the load array F that test applies and measured distortion array X, be respectively:

F={F (i) }, X={x (i) }, wherein i=1,2,3 ..., n;

Wherein, the number of displacement data or the number of institute imposed load of n for gathering in one-period cyclic test.

II step: according to the sprung mass m of vehicle single-wheel suspension ₂, suspension rate k ₂, determine the natural frequency f of Leaf Spring Suspension System ₀, that is:

$f_0=\frac{1}{2\mathrm{\π}}\sqrt{\frac{k_2}{m_2}};$

III step: according to the maximum velocity V under suspension leaf spring normal operating conditions, the natural frequency f of definite Leaf Spring Suspension System in II step ₀, and in I step, test applied load array F={F (i) } and measured distortion array X={x (i), wherein i=1,2,3 ..., n, to the Equivalent damping coefficient C of leaf spring _decalculate, that is:

$C_{\mathrm{de}}=\frac{{2f}_0\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}\left|F\left(j\right)\right|.|x(j+1)-x\left(j\right)|}{V^2};$

IV step: according to the sprung mass m of vehicle single-wheel suspension ₂, suspension rate k ₂, and determined C in III step _de, determine the damping ratio ξ that Leaf Spring Suspension System self has _g, that is:

${\mathrm{\ξ}}_g=\frac{C_{\mathrm{de}}}{2\sqrt{k_2{m}_2}};$

(3) determine that vehicle suspension system reaches the damping ratio ξ that optimum should increase _c:

According to the determined ξ of C step in step (1) _o, and the determined ξ of IV step in step (2) _g, determine that vehicle suspension system reaches the damping ratio ξ that optimum should increase _c, that is:

ξ _c＝ξ _o-ξ _g；

(4) Leaf Spring Suspension System vibration damper optimal damping constant C _ddesign:

According to the sprung mass m of vehicle single-wheel suspension ₂, the setting angle α of vibration damper, lever ratio i, the natural frequency f of the determined Leaf Spring Suspension System of II step in step (2) ₀, and in step (3), determined vehicle suspension system reaches the damping ratio ξ that optimum should increase _c, to the optimal damping constant C of Leaf Spring Suspension System vibration damper _ddesign, that is:

$C_d=\frac{4\mathrm{\π}{\mathrm{\ξ}}_c{f}_0{m}_2}{i^2{\cos }^2\mathrm{\α}}.$

The present invention has advantages of than prior art:

The previous design for vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic, never provide accurate, reliable method for designing, it is mostly the method that adopts " experience+repetition test ", according to type of vehicle, select by rule of thumb certain vibration damper, then Vehicle Driving Cycle Ride Comfort is carried out in entrucking, finally obtains the vibration damper that matches with this vehicle Leaf Spring Suspension System, is difficult to obtain reliably.The method for designing of the vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic that the present invention sets up, according to the needed optimal damper ratio of vehicle suspension system, the damping ratio that Leaf Spring Suspension System self has, analytical calculation Leaf Spring Suspension System reaches the damping ratio that optimum should increase, obtain the optimum damping of the required vibration damper of vehicle Leaf Spring Suspension System, improve the ride comfort of Vehicle Driving Cycle, simultaneously, also can avoid repetition test, checking and amendment, reduce the testing expenses of leaf spring vibration damper.

Be further described below in conjunction with accompanying drawing in order to understand better the present invention.

The design flow diagram of the method for designing of Fig. 1 vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic;

Fig. 2 is that embodiment suspension leaf spring loads and the measured regression curve of unloading deformation test;

Fig. 3 is that embodiment mates the vibration damper time dependent simulation curve of bouncing of automobile body acceleration before;

Fig. 4 is that embodiment mates the vibration damper time dependent simulation curve of bouncing of automobile body acceleration afterwards.

Specific embodiments

Below by embodiment, the method for designing of vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic provided by the present invention is described in further detail, design cycle as shown in Figure 1.

Embodiment: certain truck adopts Leaf Spring Suspension System, the sprung mass m of front axle single-wheel suspension ₂=35000kg, unsprung mass m ₁=3500kg, suspension k ₂=3618700N/m, tire stiffness k _t=32568300N/m, the maximum velocity V=0.5084m/s under suspension leaf spring normal operating conditions, setting angle α=10 ° of vibration damper, lever ratio i=0.9.

The method for designing of the vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic that example of the present invention provides, its concrete steps are as follows:

(1) determine that the needed optimal damper of vehicle suspension system compares ξ _o:

According to vehicle parameter, determine that the needed optimal damper of vehicle Leaf Spring Suspension System compares ξ _o, concrete steps are as follows:

A step: determine the vehicle suspension system optimum damping ratio ξ based on comfortableness _oc:

According to the sprung mass m of vehicle single-wheel suspension ₂=35000kg, unsprung mass m ₁=3500kg, suspension rate k ₂=3618700N/m, and tire stiffness k _t=32568300N/m, determines the vehicle suspension system optimum damping ratio ξ based on comfortableness _oc, that is:

${\mathrm{\ξ}}_{\mathrm{oc}}=\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}}=0.1748;$

In formula, r _m=m ₂/ m ₁, r _k=k _t/ k ₂;

B step: determine the vehicle suspension system optimum damping ratio ξ based on security _os:

According to the sprung mass m of vehicle single-wheel suspension ₂=35000kg, suspension rate k ₂=3618700N/m, unsprung mass m ₁=3500kg, and tire stiffness k _t=32568300N/m, determines the vehicle suspension system optimum damping ratio ξ based on security _os, that is:

${\mathrm{\ξ}}_{\mathrm{os}}=\frac{1}{(1+r_m)}\sqrt{\frac{R}{{4r}_m{r}_k}}=0.4136;$

In formula, r _m=m ₂/ m ₁, r _k=k _t/ k ₂, R=r _mr _k(r _mr _k-2-2r _m)+(1+r _m) ³;

C step: determine that the vehicle suspension system optimal damper based on comfortableness and security compares ξ _o:

According to determined ξ in A step _oc=0.1748 and B step in definite ξ _os=0.4136, determine that the vehicle suspension system optimal damper based on comfortableness and security compares ξ _o, that is:

ξ _o＝ξ _oc+0.618(ξ _os-ξ _oc)＝0.3224；

(2) determine the damping ratio ξ that Leaf Spring Suspension System self has _g:

Load and unloading deformation test according to suspension leaf spring, by the analysis to measured test figure and processing, obtain the damping ratio that Leaf Spring Suspension System self has, concrete steps are as follows:

I step: utilize leaf spring testing machine, according to the sprung mass m of single-wheel Leaf Spring Suspension under rated load ₂and the maximum load F bearing _max=m ₂g, carries out progressively loading and unloading test to suspension leaf spring, the deflection of respective loads is tested the load array F={F (i) that test applies simultaneously } and measured displacement array X={x (i), be respectively:

F＝{F(i)}＝[0.640.172.634.035.286.787.98.9210.211.2512.313.5714.615.5916.8417.8518.8620.0921.0822.1123.3824.3925.426.6427.7228.7930.0231.0332.1133.4634.4735.5536.837.8538.9940.0941.4542.4443.7944.9145.9947.2848.3849.4850.8851.9353.0554.3455.4256.5457.9458.9560.0761.5462.6663.7865.1266.1967.468.5169.8370.9772.1373.5474.5575.7677.1278.2879.480.7881.9683.0884.5785.5886.7288.2489.3890.691.8693.0894.3195.7296.997.9799.47100.67101.79103.29104.4105.54107.03108.22109.4110.83111.99113.22114.71115.9117.08118.53119.71120.92122.46123.62124.8126.32127.54128.71130.27131.34132.63134.19135.4136.56138.07139.32140.55142.07143.21144.76146147.25148.72149.94151.24152.51154.09155.34156.43158.06159.29160.58162.1163.32164.49166.13167.38168.65170.12171.37172.69174.27175.52176.68178.26179.56180.79182.37183.59184.82186.44187.7189.19190.48191.82193.47194.74195.83197.61198.84200.11201.61202.9204.25205.89207.12208.33209.93211.23212.51214.13215.29216.68218.33219.67221.01222.43223.8225.2226.8228.04229.31231232.23233.57235.15236.4237.83239.48240.88242.01243.74245.06246.42248.04249.28250.66252.35253.6255.03256.7257.87259.25260.98262.39263.71265.24266.65268.01269.7270.94272.28274.03275.31276.69278.34279.57281.02282.75284.16285.34287.1288.49289.89291.58292.81294.24296297.34298.68299.89279.17264.63255.32250.26247.08244.44241.78239.66237.85236.23234.85232.62231.26230.23228.47228.3227.07224.76223.23221.91220.66219.29218.15217.07215.65215.19213.12211.85210.64209.47208.13207.17205.47204.36203.26202.14200.69199.52198.27197.22196.45194.36193.55192.67191.01190.33189.51188.37186.14184.82183.53182.45180.83180.59178.5177.19176.51175.1174.16172.17170.94170.06168.35166.94165.63164.55163.08161.94161.13160.03158.39156.92155.93154.9153.54152.55151.46150.03148.74147.57146.57145.2144.06143.12141.91140.6139.22138.19137.22136.69134.98134.06132.44131.34130.26128.93128.09126.87125.59124.69123.62122.63121.34120.4119.43117.85117.39115.99114.62113.44112.13111.31110.15108.9107.96107.08106.09104.65103.79102.67101.42100.799.6798.596.8895.9395.6993.9892.7391.7490.7489.6688.6187.486.6385.5484.2483.4782.5681.6880.3279.4878.1777.0976.4675.1674.0473.1471.8571.170.1468.8568.1267.3365.9765.0964.2263.0161.9661.3660.0559.0258.1256.9356.1755.254.0453.1152.3951.2550.3549.4848.3547.3346.4745.4844.543.6642.4841.7140.8639.6938.9338.0336.8836.0135.3134.1433.2732.4631.4530.5729.7828.7727.9427.0626.3125.2924.4523.4622.721.8820.920.0919.318.3817.5916.8615.8815.1814.513.5312.8312.0211.1410.49.749.038.137.436.735.885.224.543.662.982.171.510.85]；

X＝{x(i)}＝[0.01-0.030.370.71.051.511.862.192.62.953.293.714.054.384.85.135.445.846.176.496.897.27.517.98.238.568.949.249.569.9710.2810.610.9711.2811.611.9212.312.612.9813.313.6113.9814.2914.61515.3115.6215.9916.316.621717.2917.6118.0118.3218.6319.0119.3219.6419.9520.3220.6320.9521.3321.6221.9422.3222.6322.9423.3123.6323.9324.3424.6124.9225.3325.6525.9626.3226.6326.9527.3327.6427.9328.3228.6428.9429.3429.6329.9330.3330.6430.9431.3331.6231.9432.3332.6432.9433.3233.6333.9434.3434.6334.9335.3335.6435.9536.3436.6236.9437.3337.6437.9438.3138.6338.9439.3239.6140.0140.3340.644141.3141.6341.9542.3342.6542.9343.3243.6443.9544.3444.6444.9345.3345.6445.9546.3346.6246.9447.3347.6447.9348.3148.6348.9449.3449.6349.9350.3350.645151.3151.6352.0252.3352.6153.0153.3253.625454.354.6155.0155.3255.65656.3156.6257.0157.2957.615858.3258.645959.3159.6360.0260.3260.6161.0161.3161.6362.0162.362.626363.3363.626464.3164.6265.0165.365.6166.0166.366.6367.0167.3167.626868.3268.636969.3169.6270.0170.3170.671.0171.3171.6272.0172.2972.617373.3273.6173.9874.374.6275.0275.3175.6176.0176.3276.6376.5976.3876.0575.775.3675.0874.7674.474.173.7373.4473.1572.7672.4772.1671.7871.5271.2370.8370.570.1969.8369.4869.268.8168.5168.2567.8267.5167.1866.8366.5266.2265.8265.5165.2264.8764.5264.2363.8363.5463.2862.8462.5662.2461.8761.5761.2960.960.5860.2459.959.5859.2158.9258.5858.2257.8757.5657.2756.8656.5656.2655.8955.5455.2254.8954.5254.2253.8653.5653.2552.8452.5552.2451.8751.5651.2550.8950.5550.2349.949.5549.2148.8548.5948.2547.8547.5447.2646.9146.5746.2845.8745.5645.2544.8844.5944.2643.8943.5943.2842.8942.6142.341.9141.5541.2440.940.5840.2439.8639.5839.2538.8838.5838.2837.9137.5937.2936.8936.5536.2335.9135.5835.1734.8734.6234.2333.8733.5733.2332.8932.5832.1831.9331.5931.1930.930.5830.2229.929.629.2228.8828.6228.2327.8927.5927.1826.8926.626.1925.9125.5925.2124.924.624.2223.8723.6123.2322.8922.5922.1821.9121.5921.220.8820.5920.2219.9119.5919.2218.8818.5818.2217.8917.5917.1916.8916.616.215.915.5815.1814.8714.614.213.8913.5913.2212.912.6112.2211.911.5811.310.9110.5910.229.929.69.228.98.598.217.97.67.26.96.636.225.925.595.24.94.614.33.923.623.32.942.642.331.941.621.260.960.65]；

Wherein, the suspension leaf spring that test obtains loads and the measured regression curve of unloading deformation test, as shown in Figure 2;

II step: according to the sprung mass m of vehicle single-wheel suspension ₂=35000kg, suspension rate k ₂=3618700N/m, determines the natural frequency f of Leaf Spring Suspension System ₀, that is:

$f_0=\frac{1}{2\mathrm{\π}}\sqrt{\frac{k_2}{m_2}}=1.6183\mathrm{Hz};$

III step: according to the maximum velocity V=0.5084m/s under suspension leaf spring normal operating conditions, the natural frequency f of definite Leaf Spring Suspension System in II step ₀=1.6183Hz, and in I step, test the load array F={F (i) that gained arrives } and distortion array X={x (i), wherein i=1,2,3 ..., n, wherein n=460, to the Equivalent damping coefficient C of leaf spring _decalculate, that is:

$C_{\mathrm{de}}=\frac{{2f}_0\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}\left|F\left(j\right)\right|.|x(j+1)-x\left(j\right)|}{V^2}=26530N.s/m;$

Wherein, the time dependent simulation curve of bouncing of automobile body acceleration, as shown in Figure 3;

IV step: according to the sprung mass m of vehicle single-wheel suspension ₂=35000kg, suspension rate k ₂=3618700N/m, and determined C in III step _de=26530N.s/m, determines the damping ratio ξ that Leaf Spring Suspension System self has _g, that is:

${\mathrm{\ξ}}_g=\frac{C_{\mathrm{de}}}{2\sqrt{k_2{m}_2}}=0.0373;$

(3) determine that vehicle suspension system reaches the damping ratio ξ that optimum should increase _c: IV step

According to the determined ξ of C step in step (1) _o=0.3224, and the determined ξ of IV step in step (2) _g=0.0373, determine that vehicle suspension system reaches the damping ratio ξ that optimum should increase _c, that is:

ξ _c＝ξ _o-ξ _g＝0.2851；

(4) Leaf Spring Suspension System vibration damper optimal damping constant C _ddesign:

According to the sprung mass m of vehicle single-wheel suspension ₂=35000kg, setting angle α=10 ° of vehicle Leaf Spring Suspension System vibration damper, lever ratio i=0.9, the determined f of II step in step (2) ₀=1.6183Hz, and determined damping ratio ξ in step (3) _c=0.2851, to the optimal damping constant C of Leaf Spring Suspension System vibration damper _ddesign, that is:

$C_d=\frac{4\mathrm{\π}{\mathrm{\ξ}}_c{f}_0{m}_2}{i^2{\cos }^2\mathrm{\α}}=258310N.s/m.$

By matlab/simulink, this vehicle Leaf Spring Suspension is joined to the forward and backward bouncing of automobile body acceleration of vibration damper in a design and carry out simulation analysis, wherein, the time dependent simulation curve of bouncing of automobile body acceleration before coupling design vibration damper, as shown in Figure 3; The time dependent simulation curve of bouncing of automobile body acceleration after coupling design vibration damper, as shown in Figure 4; The bouncing of automobile body acceleration of known Leaf Spring Suspension after coupling vibration damper significantly reduces, and shows that the method for designing of this vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic is accurately, can significantly improve the ride performance of vehicle.

Claims (1)

1. the method for designing of vehicle Leaf Spring Suspension System vibration damper optimum damping characteristic, its specific design step is as follows:

(1) determine that the needed optimal damper of vehicle suspension system compares ξ _o:

According to vehicle parameter, determine that the needed optimal damper of vehicle Leaf Spring Suspension System compares ξ _o, concrete steps are as follows:

A step: determine the vehicle suspension system optimum damping ratio ξ based on comfortableness _oc:

According to the sprung mass m of vehicle single-wheel suspension ₂, suspension rate k ₂, unsprung mass m ₁, and tire stiffness k _t, determine the vehicle suspension system optimum damping ratio ξ based on comfortableness _oc, that is:

${\mathrm{\ξ}}_{\mathrm{oc}}=\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}};$

In formula, r _m=m ₂/ m ₁, r _k=k _t/ k ₂;

B step: determine the vehicle suspension system optimum damping ratio ξ based on security _os:

According to the sprung mass m of vehicle single-wheel suspension ₂, suspension rate k ₂, unsprung mass m ₁, and tire stiffness k _t, determine the vehicle suspension system optimum damping ratio ξ based on security _os, that is:

${\mathrm{\ξ}}_{\mathrm{os}}=\frac{1}{(1+r_m)}\sqrt{\frac{R}{{4r}_m{r}_k}};$

In formula, r _m=m ₂/ m ₁, r _k=k _t/ k ₂, R=r _mr _k(r _mr _k-2-2r _m)+(1+r _m) ³;

C step: determine that the vehicle suspension system optimal damper based on comfortableness and security compares ξ _o:

According to determined ξ in A step _ocwith determined ξ in B step _os, determine that the vehicle suspension system optimal damper based on comfortableness and security compares ξ _o, that is:

ξ _o＝ξ _oc+0.618(ξ _os-ξ _oc)；

(2) determine the damping ratio ξ that Leaf Spring Suspension System self has _g:

Load and unloading deformation test according to suspension leaf spring, by analysis and the processing of the test figure to measured, obtain the damping ratio that Leaf Spring Suspension System self has, concrete steps are as follows:

I step: utilize leaf spring testing machine, according to the sprung mass m of single-wheel Leaf Spring Suspension under rated load ₂and the maximum load F bearing _max=m ₂g, carries out progressively loading and unloading test to suspension leaf spring, the deflection of respective loads is tested simultaneously, and the load array F that test applies and measured distortion array X, be respectively:

F={F (i) }, X={x (i) }, wherein i=1,2,3 ..., n;

Wherein, the number of displacement data or the number of institute imposed load of n for gathering in one-period cyclic test.

II step: according to the sprung mass m of vehicle single-wheel suspension ₂, suspension rate k ₂, determine the natural frequency f of Leaf Spring Suspension System ₀, that is:

$f_0=\frac{1}{2\mathrm{\π}}\sqrt{\frac{k_2}{m_2}};$

III step: according to the maximum velocity V under suspension leaf spring normal operating conditions, the natural frequency f of definite Leaf Spring Suspension System in II step ₀, and in I step, test applied load array F={F (i) } and measured distortion array X={x (i), wherein i=1,2,3 ..., n, to the Equivalent damping coefficient C of leaf spring _decalculate, that is:

$C_{\mathrm{de}}=\frac{{2f}_0\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}\left|F\left(j\right)\right|.|x(j+1)-x\left(j\right)|}{V^2};$

IV step: according to the sprung mass m of vehicle single-wheel suspension ₂, suspension rate k ₂, and determined C in III step _de, determine the damping ratio ξ that Leaf Spring Suspension System self has _g, that is:

${\mathrm{\ξ}}_g=\frac{C_{\mathrm{de}}}{2\sqrt{k_2{m}_2}};$

(3) determine that vehicle suspension system reaches the damping ratio ξ that optimum should increase _c:

According to the determined ξ of C step in step (1) _o, and the determined ξ of IV step in step (2) _g, determine that vehicle suspension system reaches the damping ratio ξ that optimum should increase _c, that is:

ξ _c＝ξ _o-ξ _g；

(4) Leaf Spring Suspension System vibration damper optimal damping constant C _ddesign:

According to the sprung mass m of vehicle single-wheel suspension ₂, the setting angle α of vibration damper, lever ratio i, the natural frequency f of the determined Leaf Spring Suspension System of II step in step (2) ₀, and in step (3), determined vehicle suspension system reaches the damping ratio ξ that optimum should increase _c, to the optimal damping constant C of Leaf Spring Suspension System vibration damper _ddesign, that is:

$C_d=\frac{4\mathrm{\π}{\mathrm{\ξ}}_c{f}_0{m}_2}{i^2{\cos }^2\mathrm{\α}}.$