CN104156550A - Method for analyzing and calculating damping ratio of vehicle steel plate spring suspension system - Google Patents

Abstract

The invention relates to a method for analyzing and calculating the damping ratio 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 step of analyzing and calculating the equivalent damping coefficient and the damping ratio of a suspension steel plate spring according to vehicle parameters and suspension system parameters through the loading array and the deformation array which are measured through suspension steel plate spring loading and unloading deformation tests and through analysis and processing of test data. When the damping ratio of the vehicle steel plate spring suspension system is calculated according to the method, the reliable damping ratio can be obtained, and the reliable technical basis is provided for the matching design of the shock absorber of the vehicle steel plate spring suspension system; meanwhile, the design level of the steel plate spring suspension system can be increased, the design speed of the vehicle steel plate spring suspension system can be increased, and design and test expenses can be reduced.

Description

Analysis and Calculation Method of Damping Ratio of Vehicle Leaf Spring Suspension System

technical field

The invention relates to a vehicle leaf spring suspension system, in particular to an analysis and calculation method for the damping ratio of the vehicle leaf spring suspension system.

Background technique

Leaf spring suspension systems are used on many non-load-bearing hard-core off-road vehicles, trucks and medium and large trucks. The damping ratio of the suspension system has an important impact on the ride comfort, safety and ride comfort of the vehicle. Although many experts have done a lot of research on the damping ratio of the leaf spring suspension system, there is no simple, accurate and reliable calculation method for the calculation of the damping ratio of the leaf spring suspension system, and most of them use finite element analysis. The simulation method calculates the damping ratio of the leaf spring suspension system, and then uses the method of trial and error and modification to finally obtain the damping ratio of the leaf spring suspension system of a certain vehicle. With the rapid development of the automobile industry, the current calculation method of the damping ratio of the vehicle leaf spring suspension system cannot meet the design requirements of the development of the leaf spring suspension and the ride comfort and safety. Therefore, it is necessary to establish a simple, accurate and reliable analysis and calculation method for the damping ratio of the vehicle leaf spring suspension system, that is, according to the deformation test data of the suspension leaf spring under loading and unloading, through the analysis and processing of the test data, the obtained The damping ratio of the vehicle leaf spring suspension system, while reducing design and test costs, and speeding up the calculation of the damping ratio of the vehicle leaf spring suspension system.

Contents of the invention

Aiming at the above-mentioned defects in the prior art, the technical problem to be solved by the present invention is to provide a simple, accurate and reliable method for analyzing and calculating the damping ratio of the vehicle leaf spring suspension system, the design process of which is shown in Figure 1.

In order to solve the above-mentioned technical problems, the method for analyzing and calculating the damping ratio of the vehicle leaf spring suspension system provided by the present invention, the implementation steps of the technical solution are as follows:

(1) Loading and unloading deformation test of suspension leaf spring:

Using the leaf spring testing machine, according to the sprung mass m ₂ of the single-wheel leaf spring suspension under the rated load and the maximum load F _max = m ₂ g, the suspension leaf spring is gradually loaded and unloaded. The deformation of the corresponding load is tested, and the load array and deformation array measured by the test are:

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

Among them, n is the number of load data or displacement data collected in a cycle test;

(2) Analysis and calculation of suspension leaf spring stiffness K:

According to the load array F={F(i)} and deformation array X={x(i)} obtained in the step (1), the data obtained in the loading test process and the unloading test process are respectively subjected to curve fitting analysis, To obtain the stiffness of the suspension leaf spring, the specific steps are as follows:

A step: according to the load data and displacement data obtained in the loading test process in step (1), the straight line slope K ₁ of the leaf spring loading process is obtained by fitting;

Step B: According to the load data and the displacement data obtained in the unloading test process in the step (1), the straight line slope K ₂ obtained by fitting the unloading process of the leaf spring;

Step C: According to K ₁ obtained in step A and K ₂ obtained in step B, analyze and calculate the stiffness K of the suspension leaf spring, namely:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>$

(3) Calculation of the work W consumed during a cycle of loading and unloading of the leaf spring:

According to the load array F={F(i)} and the deformation array X={x(i)} obtained by the test in step (1), wherein i=1, 2, 3,..., n, the leaf spring is loaded and The work W consumed in unloading a cycle test is calculated, that is:

$\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; ;</span>$

(4) Calculation of leaf spring equivalent damping coefficient C _d :

According to the vehicle parameters, the K obtained in step (2), and the W obtained by analysis and calculation in step (3), the equivalent damping coefficient C _d of the leaf spring is calculated, and the specific steps are as follows:

Step I: According to the sprung mass m ₂ of the single-wheel suspension of the vehicle and K obtained in step (2), determine the natural frequency f ₀ of the leaf spring suspension system, namely:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\sqrt{\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ;</span>$

Step II: Determine the vibration displacement amplitude A of the leaf spring according to the maximum dynamic deflection f _d of the leaf spring of the vehicle suspension under normal working conditions, namely:

A = f _d ;

Step III: According to the vibration displacement amplitude A in step II and the natural frequency f ₀ of the leaf spring suspension system determined in step I, determine the maximum vibration velocity V of the leaf spring, namely:

V = 2πf ₀ A;

Step IV: According to the V determined in Step III, the natural frequency f ₀ of the leaf spring suspension system determined in Step I, and the W calculated in Step (3), determine the equivalent damping coefficient C _d of the leaf spring, Right now:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; W</span>}}{{\mathrm{<span\; class="notranslate">\; V</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ;</span>$

(5) Calculation of the damping ratio _ξ0 of the vehicle leaf spring suspension system:

According to the sprung mass m ₂ of the single-wheel suspension of the vehicle, K obtained in step (2), and the equivalent damping coefficient C _d of the leaf spring determined in step (4), the damping of the leaf spring suspension system of the vehicle than ξ ₀ for calculation, namely:

${\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; K</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; .</span>$

The present invention has the advantage over prior art:

Previously, no simple, accurate and reliable calculation method has been given for the calculation of the damping ratio of the vehicle leaf spring suspension system. Most of them use finite element analysis and simulation methods to calculate the damping ratio of the vehicle leaf spring suspension system, and then use The damping ratio of the leaf spring suspension system of a certain vehicle is finally obtained through trial and error and modification. The analysis and calculation method of the damping ratio of the vehicle leaf spring suspension system established by the present invention, according to the load array and deformation array measured by the suspension leaf spring loading and unloading deformation test, through the analysis and processing of the test data, the leaf spring The equivalent damping coefficient is analyzed and calculated to obtain the damping ratio of the vehicle leaf spring suspension system, which can reduce design and test costs, speed up the calculation of the damping ratio of the vehicle leaf spring suspension system, and reduce vibration for the vehicle leaf spring suspension system The design of the optimal damping matching of the damper provides a reliable technical basis.

In order to better understand the present invention, the following will be further described in conjunction with the accompanying drawings.

Fig. 1 is a design flow chart of the analysis and calculation method for the damping ratio of the vehicle leaf spring suspension system;

Fig. 2 is the regression line of embodiment one suspension leaf spring loading and unloading deformation test;

Fig. 3 is the regression line of the loading and unloading deformation tests of the suspension leaf spring of the second embodiment.

specific implementation plan

The method for analyzing and calculating the damping ratio of the vehicle leaf spring suspension system provided by the present invention will be further described in detail through examples below, and the design process is shown in FIG. 1 .

Embodiment 1: A truck leaf spring suspension system, the sprung mass m ₂ of the front axle single wheel suspension is 35000kg, and the maximum dynamic deflection f _d of the suspension leaf spring under normal working condition is 0.05m.

The analytical calculation method of the damping ratio of the vehicle leaf spring suspension system provided by the example of the present invention, its concrete steps are as follows:

(1) Loading and unloading deformation test of suspension leaf spring:

Using the leaf spring testing machine, according to the sprung mass m ₂ of the single-wheel leaf spring suspension under the rated load and the maximum load F _max = m ₂ g, the suspension leaf spring is gradually loaded and unloaded. The deformation of the corresponding load is tested, and the load array F={F(i)} and displacement array X={x(i)} measured by the test are respectively:

F＝{F(i)}＝[0.64 0.17 2.63 4.03 5.28 6.78 7.9 8.92 10.2 11.25 12.3 13.57 14.6 15.59 16.84 17.8518.86 20.09 21.08 22.11 23.38 24.39 25.4 26.64 27.72 28.79 30.02 31.03 32.11 33.46 34.47 35.5536.8 37.85 38.99 40.09 41.45 42.44 43.79 44.91 45.99 47.28 48.38 49.48 50.88 51.93 53.05 54.3455.42 56.54 57.94 58.95 60.07 61.54 62.66 63.78 65.12 66.19 67.4 68.51 69.83 70.97 72.13 73.5474.55 75.76 77.12 78.28 79.4 80.78 81.96 83.08 84.57 85.58 86.72 88.24 89.38 90.6 91.86 93.0894.31 95.72 96.9 97.97 99.47 100.67 101.79 103.29 104.4 105.54 107.03 108.22 109.4 110.83111.99 113.22 114.71 115.9 117.08 118.53 119.71 120.92 122.46 123.62 124.8 126.32 127.54128.71 130.27 131.34 132.63 134.19 135.4 136.56 138.07 139.32 140.55 142.07 143.21 144.76 146147.25 148.72 149.94 151.24 152.51 154.09 155.34 156.43 158.06 159.29 160.58 162.1 163.32164 .49 166.13 167.38 168.65 170.12 171.37 172.69 174.27 175.52 176.68 178.26 179.56 180.79182.37 183.59 184.82 186.44 187.7 189.19 190.48 191.82 193.47 194.74 195.83 197.61 198.84200.11 201.61 202.9 204.25 205.89 207.12 208.33 209.93 211.23 212.51 214.13 215.29 216.68218.33 219.67 221.01 222.43 223.8 225.2 226.8 228.04 229.31 231 232.23 233.57 235.15 236.4237.83 239.48 240.88 242.01 243.74 245.06 246.42 248.04 249.28 250.66 252.35 253.6 255.03256.7 257.87 259.25 260.98 262.39 263.71 265.24 266.65 268.01 269.7 270.94 272.28 274.03275.31 276.69 278.34 279.57 281.02 282.75 284.16 285.34 287.1 288.49 289.89 291.58 292.81294.24 296 297.34 298.68 299.89 279.17 264.63 255.32 250.26 247.08 244.44 241.78 239.66237.85 236.23 234.85 232.62 231.26 230.23 228.47 228.3 227.07 224.76 223.23 221.91 220.66219 .29 218.15 217.07 215.65 215.19 213.12 211.85 210.64 209.47 208.13 207.17 205.47 204.36203.26 202.14 200.69 199.52 198.27 197.22 196.45 194.36 193.55 192.67 191.01 190.33 189.51188.37 186.14 184.82 183.53 182.45 180.83 180.59 178.5 177.19 176.51 175.1 174.16 172.17170.94 170.06 168.35 166.94 165.63 164.55 163.08 161.94 161.13 160.03 158.39 156.92 155.93 154.9 153.54 15 2.55 151.46 150.03 148.74 147.57 146.57 145.2 144.06 143.12 141.91 140.6139.22 138.19 137.22 136.69 134.98 134.06 132.44 131.34 130.26 128.93 128.09 126.87 125.59124.69 123.62 122.63 121.34 120.4 119.43 117.85 117.39 115.99 114.62 113.44 112.13 111.31110.15 108.9 107.96 107.08 106.09 104.65 103.79 102.67 101.42 100.7 99.67 98.5 96.88 95.9395.69 93.98 92.73 91.74 90.74 89.66 88.61 87.4 86.63 85.54 84.24 83.47 82.56 81.68 80.32 79.4878.17 77.09 76.46 75.16 74.04 73.14 71.85 71.1 70.14 68.85 68.12 67.33 65.97 65.09 64.22 63.0161.96 61.36 60.05 59.02 58.12 56.93 56.17 55.2 54.04 53.11 52.39 51.25 50.35 49.48 48.35 47.3346.47 45.48 44.5 43.66 42.48 41.71 40.86 39.69 38.93 38.03 36.88 36.01 35.31 34.14 33.27 32.4631.45 30.57 29.78 28.77 27.94 27.06 26.31 25.29 24.45 23.46 22.7 21.88 20.9 20.09 19.3 18.3817.59 16.86 15.88 15.18 14.5 13.53 12.83 12.02 11.14 10.4 9.74 9.03 8.13 7.43 6.73 5.88 5.22 4.54 3.66 2.98 2.17 1.51 0.85];

X＝{x(i)}＝[0.01 -0.03 0.37 0.7 1.05 1.51 1.86 2.19 2.6 2.95 3.29 3.71 4.05 4.38 4.8 5.13 5.445.84 6.17 6.49 6.89 7.2 7.51 7.9 8.23 8.56 8.94 9.24 9.56 9.97 10.28 10.6 10.97 11.28 11.6 11.9212.3 12.6 12.98 13.3 13.61 13.98 14.29 14.6 15 15.31 15.62 15.99 16.3 16.62 17 17.29 17.61 18.0118.32 18.63 19.01 19.32 19.64 19.95 20.32 20.63 20.95 21.33 21.62 21.94 22.32 22.63 22.94 23.3123.63 23.93 24.34 24.61 24.92 25.33 25.65 25.96 26.32 26.63 26.95 27.33 27.64 27.93 28.32 28.6428.94 29.34 29.63 29.93 30.33 30.64 30.94 31.33 31.62 31.94 32.33 32.64 32.94 33.32 33.63 33.9434.34 34.63 34.93 35.33 35.64 35.95 36.34 36.62 36.94 37.33 37.64 37.94 38.31 38.63 38.94 39.3239.61 40.01 40.33 40.64 41 41.31 41.63 41.95 42.33 42.65 42.93 43.32 43.64 43.95 44.34 44.6444.93 45.33 45.64 45.95 46.33 46.62 46.94 47.33 47.64 47.93 48.31 48.63 48.94 49.34 49.63 49.9350.33 50.64 51 51.31 51.63 52.02 52.33 52.61 53.01 53.32 53.62 54 54.3 54.61 55.01 55.32 55.6 5656.31 56.62 57.01 57.29 57.61 58 58.32 58.64 59 59.31 59.63 60.02 60.32 60.61 61.01 61.31 61.6362.01 62.3 62.62 63 63.33 63.62 64 64.31 64.62 65.01 65.3 65.61 66.01 66.3 66.63 67.01 67.3167.62 68 68.32 68.63 69 69.31 69.62 70.01 70.31 70.6 71.01 71.31 71.62 72.01 72.29 72.61 7373.32 73.61 73.98 74.3 74.62 75.02 75.31 75.61 76.01 76.32 76.63 76.59 76.38 76.05 75.7 75.3675.08 74.76 74.4 74.1 73.73 73.44 73.15 72.76 72.47 72.16 71.78 71.52 71.23 70.83 70.5 70.1969.83 69.48 69.2 68.81 68.51 68.25 67.82 67.51 67.18 66.83 66.52 66.22 65.82 65.51 65.22 64.8764.52 64.23 63.83 63.54 63.28 62.84 62.56 62.24 61.87 61.57 61.29 60.9 60.58 60.24 59.9 59.5859.21 58.92 58.58 58.22 57.87 57.56 57.27 56.86 56.56 56.26 55.89 55.54 55.22 54.89 54.52 54.2253.86 53.56 53.25 52.84 52.55 52.24 51.87 51.56 51.25 50.89 50.55 50.23 49.9 49.55 49.21 48.8548.59 48.25 47.85 47.54 47.26 46.91 46.57 46.28 45.87 45.56 45.25 44.88 44.59 44.26 43.89 43.5943.28 42.89 42.61 42.3 41.91 41.55 41.24 40.9 40.58 40.24 39.86 39.58 39.25 38.88 38.58 38.2837.91 37.59 37.29 36.89 36 .55 36.23 35.91 35.58 35.17 34.87 34.62 34.23 33.87 33.57 33.23 32.8932.58 32.18 31.93 31.59 31.19 30.9 30.58 30.22 29.9 29.6 29.22 28.88 28.62 28.23 27.89 27.5927.18 26.89 26.6 26.19 25.91 25.59 25.21 24.9 24.6 24.22 23.87 23.61 23.23 22.89 22.59 22.1821.91 21.59 21.2 20.88 20.59 20.22 19.91 19.59 19.22 18.88 18.58 18.22 17.89 17.59 17.19 16.8916.6 16.2 15.9 15.58 15.18 14.87 14.6 14.2 13.89 13.59 13.22 12.9 12.61 12.22 11.9 11.58 11.310.91 10.59 10.22 9.92 9.6 9.22 8.9 8.59 8.21 7.9 7.6 7.2 6.9 6.63 6.22 5.92 5.59 5.2 4.9 4.61 4.33.92 3.62 3.3 2.94 2.64 2.33 1.94 1.62 1.26 0.96 0.65];

Among them, the regression line of the suspension leaf spring loading and unloading deformation test obtained from the test is shown in Figure 2;

(2) Analysis and calculation of suspension leaf spring stiffness K:

According to the load array F={F(i)} and deformation array X={x(i)} obtained in the step (1), the data obtained in the loading test process and the unloading test process are respectively subjected to curve fitting analysis, To obtain the stiffness of the suspension leaf spring, the specific steps are as follows:

Step A: According to the load data and displacement data obtained in the loading test process in step (1), the linear slope K ₁ =3909800N/m of the leaf spring loading process is obtained by fitting;

Step B: According to the load data and displacement data obtained in the unloading test process in step (1), the straight line slope K ₂ =3327600N/m in the unloading process of the leaf spring is obtained by fitting;

Step C: According to K ₁ = 3909800N/m obtained in step A and K ₂ = 3327600N/m obtained in step B, analyze and calculate the stiffness K of the suspension leaf spring, namely:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3618700</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ;</span>$

(3) Calculation of the work W consumed during a cycle of loading and unloading of the leaf spring:

Obtained load array F={F(i)} and deformation array X={x(i)} according to the test in step (1), wherein i=1, 2, 3,..., n, wherein n=460, Calculate the work W consumed in the leaf spring loading and unloading cycle test, namely:

$\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2118.7</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ;</span>$

(4) Calculation of leaf spring equivalent damping coefficient C _d :

According to the vehicle parameters, K=3618700N/m obtained in step (2), and W=2118.7Nm obtained by analysis and calculation in step (3), the equivalent damping coefficient C _d of the leaf spring is calculated, and the specific steps are as follows:

Step I: According to the sprung mass m ₂ =35000kg of the single-wheel suspension of the vehicle, and K=3618700N/m obtained in step (2), determine the natural frequency f ₀ of the leaf spring suspension system, namely:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\sqrt{\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1.6183</span>}\mathrm{<span\; class="notranslate">\; Hz</span>}<span\; class="notranslate">\; ;</span>$

Step II: According to the maximum dynamic deflection f _d =0.05m of the vehicle suspension leaf spring under normal working conditions, determine the vibration displacement amplitude A of the leaf spring, namely:

A = f _d = 0.05m;

Step III: According to the vibration displacement amplitude A=0.05m in step II, and the natural frequency f ₀ =1.6183Hz of the leaf spring suspension system determined in step I, determine the maximum vibration velocity V of the leaf spring, namely:

V=2πf ₀ A=0.5084m/s;

Step IV: According to V=0.5084m/s determined in step III, the natural frequency f ₀ of the leaf spring suspension system determined in step I=1.6183Hz, and W=2118.7Nm calculated in step (3), Determine the equivalent damping coefficient C _d of the leaf spring, namely:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; W</span>}}{{\mathrm{<span\; class="notranslate">\; V</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 26530</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ;</span>$

(5) Calculation of the damping ratio _ξ0 of the vehicle leaf spring suspension system:

According to the sprung mass m ₂ of the single-wheel suspension of the vehicle = 35000kg, K = 3618700N/m obtained in step (2), and the equivalent damping coefficient C _d of the leaf spring determined in step (4) = 26530N.s /m, calculate the damping ratio ξ ₀ of the vehicle leaf spring suspension system, namely:

${\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; K</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.0373</span>}<span\; class="notranslate">\; .</span>$

Embodiment 2: For a leaf spring suspension system of a truck, the sprung mass of the single wheel suspension of the front axle is m ₂ =7800kg, and the maximum dynamic deflection f _d of the suspension leaf spring under normal working conditions is 0.05m.

The analytical calculation method of the damping ratio of the vehicle leaf spring suspension system provided by the example of the present invention, its concrete steps are as follows:

(1) Loading and unloading deformation test of suspension leaf spring:

Using the leaf spring testing machine, according to the sprung mass m ₂ of the single-wheel leaf spring suspension under the rated load and the maximum load F _max = m ₂ g, the suspension leaf spring is gradually loaded and unloaded. The deformation of the corresponding load is tested, and the load array F={F(i)} and displacement array X={x(i)} measured by the test are respectively:

F＝{F(i)}＝[0.487 0.104 0.826 1.179 1.535 1.771 2.061 2.303 2.576 2.808 3.081 3.299 3.5723.78 4.045 4.263 4.52 4.72 4.987 5.185 5.427 5.627 5.861 6.044 6.283 6.468 6.697 6.874 7.1097.29 7.516 7.699 7.932 8.113 8.291 8.514 8.7 8.917 9.11 9.331 9.516 9.738 9.925 10.143 10.32210.544 10.727 10.942 11.134 11.355 11.54 11.766 11.94 12.154 12.343 12.561 12.755 12.97713.149 13.378 13.552 13.779 13.966 14.182 14.369 14.587 14.764 14.99 15.18 15.402 15.57615.788 15.977 16.198 16.38 16.603 16.781 17.001 17.182 17.362 17.581 17.766 17.986 18.16818. 397 18.574 18.799 18.979 19.159 19.383 19.569 19.786 19.969 20.196 20.368 20.603 20.77921.007 21.191 21.416 21.6 21.817 21.986 22.218 22.391 22.611 22.795 23.012 23.196 23.4123.586 23.77 23.987 24.175 24.395 24.576 24.789 24.977 25.186 25.37 25.598 25.768 25.98826.165 26.382 26.562 26.79 26.963 27.169 27.349 27.577 27.747 27.967 28.148 28.361 28.55228.762 28.931 29.159 29.325 29.546 29.73 29.95 30.127 30.34 30.52 30.737 30.914 31.1361 31.51.3 904 32.121 32.297 32.522 32.691 32.923 33.096 33.32 33.5 33.714 33.883 34.11534.295 34.512 34.696 34.905 35.093 35.262 35.483 35.66 35.877 36.094 36.27 36.495 36.66836.844 37.069 37.245 37.469 37.646 37.874 38.04 38.276 38.452 38.673 38.856 39.017 39.24539.421 39.641 39.817 40.038 40.206 40.426 40.61 40.823 41.014 41.226 41.403 41.63 41.79942.004 42.188 42.415 42.599 42.812 42.98 43.2 43.377 43.597 43.78 43.993 44.162 44.382 44.55844.778 44.962 45.131 45.343 45.527 45.74 45.916 46.136 46.312 46.525 46.701 46.929 47.09747.318 47.494 47.714 47.897 48.11 48.279 48.514 48.683 48.896 49.072 49.292 49.476 49.69649.872 50.085 50.276 50.481 50.665 50.885 51.054 51.274 51.45 51.67 51.854 52.023 52.2552.419 52.639 52.815 53.043 53.212 53.425 53.608 53.828 53.997 54.217 54.394 54.621 54.79755.01 55.179 55.414 55.583 55.796 55.972 56.199 56.368 56.588 56.765 56.985 57.168 57.37457.55 57.778 57.954 58.167 58.35 58.526 58.739 58.923 59.135 59.319 59.525 59.708 59.93660.104 60.325 60.501 60.721 60.89 7 61.11 61.286 61.499 61.683 61.903 62.072 62.306 62.46162.688 62.864 63.077 63.261 63.481 63.657 63.877 64.046 64.266 64.435 64.67 64.846 65.05965.235 65.455 65.646 65.852 66.021 66.219 66.439 66.608 66.835 67.019 67.224 67.401 67.62867.812 68.032 68.201 68.428 68.612 68.825 69.008 69.221 69.39 69.595 69.786 70.014 70.1970.41 70.586 70.814 70.983 71.21 71.379 71.607 71.775 72.003 72.187 72.407 72.59 72.76672.987 73.177 73.39 73.567 73.794 73.963 74.19 74.367 74.601 74.77 74.998 75.174 75.39475.563 75.798 75.974 76.3 76.54 76.73 76.96 77.14 77.35 77.53 77.75 77.93 78.17 78.34 78.2376.93 75.844 74.954 74.249 73.603 73.133 72.539 72.187 71.834 71.497 71.137 70.895 70.56470.263 69.97 69.676 69.434 69.302 69.008 68.854 68.56 68.384 68.105 67.966 67.738 67.51167.291 67.1 66.879 66.762 66.505 66.351 66.153 65.947 65.683 65.529 65.353 65.155 64.97864.773 64.641 64.354 64.2 63.958 63.819 63.576 63.43 63.209 63.048 62.798 62.666 62.41762.277 62.13 61.91 61.697 61.58 61.294 61.11 60.956 60.743 6 0.589 60.383 60.222 60.009 59.90659.62 59.436 59.231 59.077 58.857 58.71 58.497 58.335 58.13 57.917 57.704 57.609 57.33 57.19857.036 56.831 56.632 56.464 56.251 56.045 55.862 55.664 55.473 55.304 55.098 54.944 54.7954.562 54.335 54.173 54.012 53.814 53.652 53.439 53.263 53.043 52.904 52.654 52.507 52.34652.148 51.942 51.78 51.56 51.391 51.186 51.002 50.819 50.665 50.445 50.276 50.122 49.87949.725 49.512 49.358 49.16 48.991 48.786 48.595 48.382 48.22 48.03 47.853 47.619 47.49447.259 47.119 46.892 46.723 46.525 46.363 46.151 45.982 45.769 45.637 45.402 45.248 45.04244.844 44.646 44.47 44.287 44.14 43.912 43.751 43.553 43.362 43.149 43.01 42.782 42.62142.423 42.254 42.048 41.872 41.703 41.498 41.278 41.153 40.926 40.757 40.573 40.39 40.18440.06 39.861 39.627 39.465 39.26 39.106 38.907 38.731 38.533 38.364 38.144 37.968 37.74537.591 37.374 37.205 37.01 36.829 36.612 36.465 36.292 36.086 35.913 35.704 35.56 35.31735.156 34.957 34.791 34.571 34.416 34.214 34.037 33.828 33.666 33.452 33.29 33 .055 32.92632.72 32.536 32.323 32.168 31.955 31.797 31.587 31.414 31.212 31.039 30.866 30.697 30.47630.281 30.116 29.902 29.752 29.546 29.369 29.159 29.001 28.784 28.611 28.416 28.247 28.02627.886 27.647 27.519 27.302 27.118 26.912 26.735 26.547 26.386 26.172 26.003 25.815 25.60625.455 25.227 25.087 24.881 24.712 24.498 24.348 24.123 23.95 23.748 23.575 23.362 23.21523.005 22.847 22.626 22.457 22.251 22.078 21.872 21.699 21.511 21.331 21.121 20.956 20.73520.584 20.372 20.203 20.002 19.826 19.65 19.463 19.232 19.064 18.897 18.691 18.539 18.30718.162 17.942 17.766 17.569 17.42 17.189 17.039 16.81 16.644 16.442 16.283 16.056 15.91115.695 15.53 15.328 15.164 14.94 14.775 14.577 14.396 14.195 14.033 13.876 13.665 13.48413.288 13.108 12.896 12.735 12.52 12.352 12.143 11.982 11.762 11.603 11.377 11.218 11.01810.833 10.637 10.456 10.247 10.09 9.872 9.692 9.489 9.335 9.115 8.95 8.745 8.575 8.364 8.1928.016 7.814 7.646 7.437 7.274 7.069 6.898 6.673 6.51 6.301 6.134 5.912 5.749 5.529 5.374 5.1564 .989 4.771 4.61 4.384 4.212 3.999 3.827 3.602 3.212 3.032 2.862 2.638 2.473 2.262 2.0861.874 1.7 1.04 0.927 0.719 0.347 0.181];

X＝{x(i)}＝[0.14 0 0.43 0.76 1.18 1.5 1.9 2.23 2.64 2.96 3.36 3.68 4.08 4.39 4.78 5.1 5.49 5.786.18 6.48 6.86 7.17 7.55 7.85 8.24 8.55 8.92 9.22 9.6 9.9 10.27 10.57 10.95 11.26 11.56 11.93 12.2412.6 12.91 13.28 13.58 13.95 14.25 14.62 14.92 15.29 15.59 15.96 16.27 16.64 16.94 17.32 17.617.97 18.27 18.64 18.95 19.32 19.61 19.99 20.28 20.65 20.96 21.33 21.62 21.99 22.29 22.65 22.9623.33 23.62 23.98 24.29 24.66 24.96 25.34 25.63 25.99 26.3 26.59 26.96 27.27 27.63 27.93 28.3128. 6 28.98 29.28 29.6 29.97 30.27 30.64 30.94 31.31 31.6 31.98 32.27 32.65 32.95 33.32 33.6333.98 34.28 34.66 34.95 35.32 35.63 35.99 36.3 36.66 36.95 37.26 37.63 37.93 38.3 38.6 38.9639.27 39.64 39.93 40.31 40.6 40.97 41.27 41.64 41.95 42.32 42.61 42.98 43.27 43.65 43.94 44.3244 .62 44.99 45.3 45.65 45.95 46.33 46.62 46.99 47.3 47.65 47.96 48.32 48.62 48.99 49.29 49.6749.96 50.28 50.64 50.94 51.31 51.6 51.98 52.27 52.65 52.94 53.31 53.63 53.99 54.28 54.66 54.9555.32 55.63 55.99 56.29 56.58 56.95 57.25 57.63 57.99 58.3 58 .67 58.97 59.27 59.64 59.93 60.3160.61 60.98 61.28 61.66 61.95 62.33 62.63 62.92 63.3 63.6 63.96 64.26 64.64 64.92 65.3 65.665.97 66.27 66.64 66.94 67.32 67.61 67.97 68.28 68.65 68.96 69.32 69.61 69.99 70.28 70.65 70.9671.33 71.62 71.99 72.29 72.66 72.96 73.25 73.62 73.93 74.29 74.59 74.96 75.27 75.63 75.93 76.3176.6 76.97 77.27 77.64 77.95 78.31 78.6 78.99 79.29 79.65 79.94 80.32 80.62 80.99 81.29 81.6581.96 82.32 82.62 82.99 83.29 83.65 83.96 84.33 84.63 84.92 85.29 85.6 85.96 86.26 86.64 86.9387.3 87.61 87.97 88.27 88.63 88.93 89.32 89.61 89.97 90.27 90.65 90.94 91.3 91.6 91.99 92.2892.65 92.95 93.32 93.62 93.99 94.28 94.66 94.95 95.33 95.63 95.93 96.29 96.59 96.96 97.27 97.6397.93 98.3 98.6 98.97 99.28 99.64 99.94 100.3 100.6 100.97 101.27 101.64 101.94 102.32 102.6102.98 103.27 103.64 103.95 104.33 104.61 104.99 105.28 105.65 105.95 106.32 106.62 106.99107.28 107.66 107.96 108.32 108.94 109.6 109.98 110.28 110.94 111.3111.61 112.65 112.95 113.322.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32. 113 113 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 113 112 112 113 112 112 113 112 113 112s. 113.62 113.99 114.28 114.64 114.94 115.32 115.62115.99 116.28 116.66 116.95 117.31 117.61 117.99 118.29 118.66 118.96 119.33 119.62 119.92120.29 120.6 120.96 121.27 121.64 121.92 122.29 122.59 122.97 123.26 123.63 123.92 124.29124.59 124.96 125.27 125.59 125.98 126.28 126.65 126.96 127.32 127.62 127.98 128.29 128.65128. 87 128.86 128.49 128.08 127.78 127.44 127.06 126.75 126.35 126.01 125.65 125.32 124.92124.68 124.29 123.97 123.57 123.21 122.86 122.63 122.21 121.92 121.51 121.19 120.82 120.57120.18 119.84 119.48 119.16 118.81 118.55 118.15 117.86 117.49 117.19 116.79 116.51 116.21115.85 115.54 115.18 114.89 114.5 114.2 113.81 113.53 113.13 112.85 112.48 112.19 111.79111.52 111.11 110.85 110.55 110.18 109.86 109.53 109.13 108.81 108.53 108.16 107.87 107.5107.2 106.83 106.56 106.16 105.84 105.48 105.17 104.79 104.54 104.12 103.87 103.5 103.15102.79 102.56 102.11 101.85 101.5 101.18 100.82 100.53 100.14 99.81 99.48 99.14 98.8 98.4998.13 97.84 97.51 97.16 96.78 96.5 96.21 95.85 95.53 95.18 94.86 94.46 94.18 93.79 93.52 93.1792.86 92.48 92.21 91.8 91.5 91.14 90.82 90.47 90.18 89.8 89.5 89.15 88.81 88.53 88.14 87.8787.52 87.2 86.84 86.51 86.16 85.84 85.48 85.17 84.8 84.55 84.13 83.87 83.49 83.18 82.83 82.5282.14 81.84 81.48 81.21 80.79 80.53 80.17 79.82 79.47 79.15 78.81 78.52 78.14 77.85 77.48 77.1676.79 76.53 76.14 75.84 75.48 75.17 74.8 74.49 74.15 73.82 73.44 73.18 72.8 72.49 72.15 71.8471.47 71.19 70.82 70.48 70.2 69.81 69.54 69.18 68.87 68.51 68.2 67.83 67.52 67.14 66.84 66.4666.17 65.8 65.49 65.12 64.84 64.53 64.17 63.87 63.5 63.21 62.82 62.52 62.16 61.85 61.48 61.260.84 60.53 60.15 59.86 59.47 59.19 58.79 58.53 58.15 57.84 57.47 57.18 56.79 56.51 56.13 55.8355.47 55.16 54.86 54.51 54.17 53.82 53.53 53.14 52.87 52.51 52.19 51.83 51.52 51.15 50.85 50.4850.18 49.81 49.54 49.13 48.87 48.49 48.16 47.8 47.49 47.14 46.85 46.46 46.16 45.81 45.49 45.244.8 44.54 44.17 43.87 43.5 43.2 42.83 42.52 42.16 41.85 41.47 41.21 40.83 40.53 40.17 39.8639.48 39.18 38.82 38.5 38.16 37. 85 37.4 837.18 36.79 36.52 36.14 35.84 35.48 35.17 34.87 34.5134.12 33.83 33.52 33.14 32.87 32.46 32.2 31.82 31.5 31.14 30.88 30.47 30.19 29.8 29.51 29.1428.85 28.47 28.19 27.81 27.51 27.15 26.86 26.47 26.18 25.82 25.5 25.14 24.83 24.54 24.18 23.8623.5 23.2 22.82 22.53 22.15 21.85 21.49 21.2 20.81 20.52 20.14 19.84 19.49 19.17 18.82 18.5218.13 17.85 17.48 17.17 16.81 16.52 16.14 15.85 15.48 15.18 14.8 14.52 14.21 13.84 13.55 13.1712.88 12.51 12.21 11.83 11.53 11.16 10.88 10.49 10.2 9.83 9.53 9.16 8.86 8.49 8.19 7.81 7.51 7.156.85 6.47 6.18 5.81 5.52 5.21 4.84 4.54 4.19 3.88 3.52 3.22 2.84 2.56 2.18 1.88 1.52 1.22 0.860.57];

Among them, the regression line of the suspension leaf spring loading and unloading deformation test obtained from the test is shown in Figure 3;

(2) Analysis and calculation of suspension leaf spring stiffness K:

According to the load array F={F(i)} and deformation array X={x(i)} obtained in the step (1), the data obtained in the loading test process and the unloading test process are respectively subjected to curve fitting analysis, To obtain the stiffness of the suspension leaf spring, the specific steps are as follows:

Step A: according to the load data and displacement data obtained in the loading test process in step (1), the linear slope K ₁ =595580N/m of the leaf spring loading process is obtained by fitting;

Step B: according to the load data and displacement data obtained in the unloading test process in step (1), the straight line slope K ₂ =565990N/m in the unloading process of the leaf spring is obtained by fitting;

Step C: According to K ₁ = 595580N/m obtained in step A and K ₂ = 565990N/m obtained in step B, analyze and calculate the stiffness K of the suspension leaf spring, namely:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 580785</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ;</span>$

(3) Calculation of the work W consumed during a cycle of loading and unloading of the leaf spring:

Obtained load array F={F(i)} and deformation array X={x(i)} according to the test in step (1), wherein i=1, 2, 3,..., n, wherein n=772, Calculate the work W consumed in the leaf spring loading and unloading cycle test, namely:

$\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 424</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; 6296</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ;</span>$

(4) Calculation of leaf spring equivalent damping coefficient C _d :

According to the vehicle parameters, K=580785N/m obtained in step (2), and W=424.6296Nm obtained through analysis and calculation in step (3), the equivalent damping coefficient C _d of the leaf spring is calculated, and the specific steps are as follows:

Step I: According to the sprung mass m ₂ =7800kg of the single-wheel suspension of the vehicle, and K=580785N/m obtained in step (2), determine the natural frequency f ₀ of the leaf spring suspension system, namely:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\sqrt{\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; 3733</span>}\mathrm{<span\; class="notranslate">\; Hz</span>}<span\; class="notranslate">\; ;</span>$

Step II: According to the maximum dynamic deflection f _d =0.05m of the vehicle suspension leaf spring under normal working conditions, determine the vibration displacement amplitude A of the leaf spring, namely:

A = f _d = 0.05m;

Step III: According to the vibration displacement amplitude A=0.05m in the step II, and the natural frequency f ₀ =1.3733Hz of the leaf spring suspension system determined in the step I, determine the maximum vibration velocity V of the leaf spring, namely:

V=2πf ₀ A=0.4314m/s;

Step IV: According to V=0.4314m/s determined in step III, the natural frequency f ₀ of the leaf spring suspension system determined in step I=1.3733Hz, and W=424.6296Nm calculated in step (3), Determine the equivalent damping coefficient C _d of the leaf spring, namely:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; W</span>}}{{\mathrm{<span\; class="notranslate">\; V</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 6265.6</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ;</span>$

(5) Calculation of the damping ratio _ξ0 of the vehicle leaf spring suspension system:

According to the sprung mass m ₂ of the single-wheel suspension of the vehicle = 7800kg, K = 580785N/m obtained in step (2), and the equivalent damping coefficient C _d of the leaf spring determined in step (4) = 6265.6Ns/ m, calculate the damping ratio _ξ0 of the vehicle leaf spring suspension system, namely:

${\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; K</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.0465</span>}<span\; class="notranslate">\; .</span>$

Claims (1)

1. the analysis calculation method of vehicle Leaf Spring Suspension System damping ratio, its specific design step is as follows:

(1) suspension leaf spring loads and unloading deformation test:

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, tests measured load array and distortion array, is respectively:

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

Wherein, n is the load data that gathers in one-period cyclic test or the number of displacement data;

(2) analytical calculation of suspension leaf spring stiffness K:

According to resulting load array F={F (i) in step (1) } and distortion array X={x (i), respectively to the data that obtain in load test process and the unloading test process analysis that carries out curve fitting, the rigidity that obtains suspension leaf spring, concrete steps are as follows:

A step: according to the resulting load data of load test process in step (1) and displacement data, matching obtains the straight slope K of leaf spring loading procedure ₁;

B step: according to the resulting load data of unloading test process in step (1) and displacement data, matching obtains the straight slope K of leaf spring uninstall process ₂;

C step: the K obtaining according to A step ₁and the K that obtains of B step ₂, suspension leaf spring stiffness K is carried out to analytical calculation, that is:

$K=\frac{K_1+K_2}{2};$

(3) leaf spring loads and unloads the calculating of the consumed work W of institute in a cyclic process:

According to test resulting load array F={F (i) in step (1) } and be out of shape array X={x (i) }, i=1 wherein, 2,3 ..., n, loads and unloads to leaf spring the merit W consuming in one-period cyclic test and calculate, that is:

$W=\underset{j=1}{\overset{n-1}{\mathrm{\&Sigma;}}}\left|F\left(j\right)\right|.|x(j+1)-x\left(j\right)|;$

(4) leaf spring Equivalent damping coefficient C _dcalculating:

According to vehicle parameter, the K obtaining in step (2), and the W that in step (3), analytical calculation obtains, the Equivalent damping coefficient C to leaf spring _dcalculate, concrete steps are as follows:

I step: according to the sprung mass m of vehicle single-wheel suspension ₂, and the K obtaining in step (2), determines the natural frequency f of Leaf Spring Suspension System ₀, that is:

$f_0=\frac{1}{2\mathrm{\&pi;}}\sqrt{\frac{K}{m_2}};$

II step: according to the maximum dynamic deflection f under vehicle suspension leaf spring normal operating conditions _d, determine the vibration displacement amplitude A of leaf spring, that is:

A＝f _d；

III step: according to the vibration displacement amplitude A in II step, and the natural frequency f of determined Leaf Spring Suspension System in I step ₀, determine the maximum velocity V of leaf spring, that is:

V＝2πf ₀A；

IV step: according to determined V in III step, the natural frequency f of definite Leaf Spring Suspension System in I step ₀, and the W calculating in step (3), determines the Equivalent damping coefficient C of leaf spring _d, that is:

$C_d=\frac{2f_{0}W}{V^2};$

(5) vehicle Leaf Spring Suspension System damping ratio ξ ₀calculating:

According to the sprung mass m of vehicle single-wheel suspension ₂, the K obtaining in step (2), and the Equivalent damping coefficient C of determined leaf spring in step (4) _d, the damping ratio ξ to vehicle Leaf Spring Suspension System ₀calculate, that is:

${\mathrm{\&xi;}}_0=\frac{C_d}{2\sqrt{K{m}_2}}.$