CN113158530B - Method for evaluating fatigue damage of random ratchet wheel of liquid-containing tank truck - Google Patents
Method for evaluating fatigue damage of random ratchet wheel of liquid-containing tank truck Download PDFInfo
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Abstract
The invention relates to a method for evaluating fatigue and multiple damages of a random ratchet wheel of a tank truck, which comprises the following steps: and carrying out fluid-solid coupling random vibration analysis on the tank truck containing the liquid under the action of road spectrum load to obtain a random fatigue damage coefficient of a concerned position, and simplifying a tank body calculation model and load of the tank truck containing the liquid by taking the random fatigue damage coefficient as a reference. Applying 0-1 time of equivalent acceleration, 0-2 times of equivalent acceleration and 0-3 times of equivalent acceleration to the simplified model, performing cyclic plasticity analysis on the simplified model under the premise of applying internal pressure to the tank body in a load range to obtain a ratchet wheel strain rule of the tank body supporting area, further obtaining a random ratchet wheel effect damage coefficient of the structure, and superposing the random ratchet wheel effect damage coefficient and the random fatigue damage coefficient to obtain the random ratchet wheel fatigue multi-damage coefficient of the tank car supporting area under the action of the road spectrum load. And the fatigue multi-damage coefficient of the random ratchet wheel is used for evaluating the integrity of the structure in the region, and when the fatigue multi-damage coefficient of the random ratchet wheel is not less than 1, the fatigue damage is considered to be generated.
Description
Technical Field
The invention relates to the field of random fatigue damage of a tank truck, in particular to a random ratchet wheel fatigue multi-damage evaluation method of the tank truck.
Background
With the rapid development of the energy industry, low-temperature liquid transportation has become an indispensable transportation means at present in view of the superiority of efficient transportation of Liquefied Natural Gas (LNG), liquid hydrogen, liquid oxygen, and the like. The semitrailer is mostly adopted for highway transportation of low-temperature liquid, a container in the semitrailer is used for containing low-temperature medium, aiming at the safety problem in the transportation process, the main design basis given by JB/T4780-2002 liquefied natural gas tank container and JB/T4781-2005 liquefied gas tank container is still the static strength design based on GB150 fixed pressure container and JB4732-1995 steel pressure container-analysis design standard, and the static strength is far insufficient for the inertia force caused by road bumping, acceleration, braking, turning and the like in transportation by taking the static strength as the check basis.
For the inner container supporting part, large average stress caused by internal pressure exists, alternating stress caused by inertia force is superposed on the stress, and damage caused by cyclic plasticity accumulation, namely ratchet effect and interaction of the ratchet effect and low-cycle fatigue are easy to occur. In addition, the tank body can bear the effect of a road load spectrum in the transportation process, but the research on the fatigue damage caused by the road load spectrum at the connecting part of the tank body and the walking mechanism and the mutual supporting part of the inner container and the shell is blank, and a multi-damage failure evaluation method caused by the ratchet effect of a high stress area of the supporting part and the fatigue interaction is not established.
In order to ensure the safety and reliability of the liquefied gas tank truck in the process of lightweight design, the invention provides a method for evaluating the fatigue and the multiple damages of a random ratchet wheel of the tank truck.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to solve the technical problem of providing a method for evaluating fatigue and multiple damages of the random ratchet wheel of the tank truck. The method considers the fatigue damage under the condition of liquid existence and under the action of a road surface load spectrum, and the checking is more accurate.
The technical scheme adopted by the invention for solving the technical problems is as follows: the method for evaluating the fatigue and the multiple damages of the random ratchet wheel of the tank truck comprises the following steps:
establishing a finite element model for the tank truck containing liquid and carrying out fluid-solid coupling modal analysis;
converting the spatial frequency power spectrum density into a time frequency displacement power spectrum density under the determined running speed and road surface grade conditions;
the time frequency displacement power spectrum density is used as excitation, random vibration response analysis is carried out on the basis of fluid-solid coupling modal analysis, random fatigue analysis is carried out on a supporting area of an inner container of the LNG tank car according to a three-interval method based on Gauss distribution and Miner linear cumulative damage law, a random fatigue damage coefficient of the structure is obtained and is used as a comparison reference for model simplification and load simplification;
carrying out first-step simplification on a finite element model established by the tank truck containing liquid, and carrying out equivalent simplification on liquid, namely, equivalently adding the mass of the liquid to the wall of the inner container tank in a density form, so that the random vibration response characteristic of the inner container tank is equivalent to the response of the tank truck containing liquid, namely, the inner container tank has similar 1 sigma maximum stress solution and characteristic frequency, and further determining the proportion of the liquid equivalent of the current tank truck containing liquid;
after the liquid equivalent proportion with the same random vibration response characteristic as the liquid-containing tank truck is determined, simplifying a finite element model and a road spectrum load in a second step, namely omitting a spring support, simplifying the road spectrum load into n times of gravity acceleration g, applying equivalent acceleration during static calculation to enable the stress response of an inner container support area to be equivalent to a 1 sigma (sigma index standard deviation) stress solution of the liquid-containing tank truck, and determining the equivalent acceleration of the current liquid-containing tank truck;
after the proportion of liquid equivalent and the equivalent acceleration are determined, and the final simplified model of the liquid-containing tank body is obtained after the spring support is omitted, the simplified model is subjected to static analysis to obtain a 1 sigma stress solution equivalent to that of the current liquid-containing tank car, the fatigue damage evaluation is directly carried out according to a three-interval method based on Gauss distribution and Miner linear accumulative damage law, and a random fatigue damage coefficient is obtained;
performing cyclic plasticity analysis on the tank body in a final simplified model of the liquid-containing tank body, wherein the load range of the cyclic plasticity analysis is 0-1 time equivalent acceleration, 0-2 times equivalent acceleration and 0-3 times equivalent acceleration, performing the cyclic plasticity analysis on the tank body under the premise of applying internal pressure in the load range to obtain a ratchet wheel strain rule of a supporting area of the tank body, and obtaining a random ratchet wheel effect damage coefficient of the structure based on a three-interval method of Gauss distribution and Miner linear accumulative damage law,
and superposing the random ratchet wheel effect damage coefficient and the random fatigue damage coefficient to give a random ratchet wheel fatigue multi-damage coefficient under the action of road spectrum load in a tank car supporting area, wherein the random ratchet wheel fatigue multi-damage coefficient is used for evaluating the integrity of the structure in the area, and when the random ratchet wheel fatigue multi-damage coefficient is not less than 1, the fatigue damage is considered to be generated.
In the invention, when fluid-solid coupling modal analysis and calculation, attention needs to be paid to the setting of a fluid-solid coupling interface, the setting of a free liquid level and the selection of a modal calculation method, and an asymmetric matrix method is selected for modal solution due to the fluid-solid coupling effect; in addition, a large number of liquid vibration modes often exist in low-order modes, and the modes are ensured to contain enough coupled vibration modes with solid participation, namely a selective beam mode.
Establishing a relation between the liquid equivalent proportion and the equivalent acceleration value of each low-temperature liquid and different types of tank cars under different road surfaces and different driving speeds, and directly determining the liquid equivalent proportion and the equivalent acceleration value after determining the road surface, the driving speed, the liquid type and the tank car type; and (3) directly performing static analysis and cyclic plasticity analysis in a final simplified model of the liquid-containing tank body at the later stage, namely determining a random fatigue damage coefficient and a random ratchet effect damage coefficient respectively without performing random vibration response analysis on the liquid-containing tank truck.
The invention also provides a simplifying method of the tank truck model, which is used for carrying out flow-solid coupling random vibration analysis on the tank truck under the action of road spectrum load to obtain the random fatigue damage coefficient of the concerned position, and simplifying the tank body calculation model and the load of the tank truck by taking the random fatigue damage coefficient as a reference, and specifically comprises the following steps:
firstly, determining the proportion of the liquid mass equivalent to the wall of an inner container to ensure that the random vibration characteristic of the tank-free truck is consistent with that of the tank-containing truck, namely the tank-free truck has the same 1 sigma solution and vibration dominant frequency; and then removing the spring support, determining the equivalent acceleration, and enabling the static calculation result to be consistent with the 1 sigma solution, thereby completing the calculation of the random fatigue damage coefficient and completing the simplification of the tank truck model.
Compared with the prior art, the invention has the beneficial effects that:
the model simplification method of the invention carries out fluid-solid coupling random vibration analysis on the tank truck under the action of road spectrum load, obtains the random fatigue damage coefficient of the concerned position (such as the inner container supporting part), and simplifies the tank body calculation model and the load of the tank truck by taking the random fatigue damage coefficient as a reference; firstly, determining the proportion of the liquid mass equivalent to the wall of the inner container to ensure that the random vibration characteristic of the tank-free truck is consistent with that of the tank truck containing liquid, namely the tank truck has the same 1 sigma solution and vibration dominant frequency; and then removing the spring support, determining the equivalent acceleration, and enabling the static calculation result to be consistent with the 1 sigma solution, thereby completing the calculation of the random fatigue damage coefficient.
After the proportion of the liquid equivalent and the equivalent acceleration are determined, and the spring support is saved, the final simplified model of the liquid-containing tank body is obtained, 0-1 times of equivalent acceleration, 0-2 times of equivalent acceleration and 0-3 times of equivalent acceleration are applied to the simplified model, performing cyclic plasticity analysis on the tank body under the premise of applying internal pressure to the tank body in a load range to obtain a ratchet wheel strain rule of a supporting area of the tank body, obtaining a random ratchet wheel effect damage coefficient of the structure on the basis of a three-interval method of Gauss distribution and Miner linear accumulated damage law, superposing the random ratchet wheel effect damage coefficient and the random fatigue damage coefficient to give a random ratchet wheel fatigue multi-damage coefficient of the supporting area of the tank car under the action of road spectrum load, wherein the random ratchet wheel fatigue multi-damage coefficient is used for evaluating the integrity of the structure in the area, and when the random ratchet wheel fatigue multi-damage coefficient is not less than 1, considering that fatigue damage can be generated.
The evaluation method of the invention aims at the liquid-containing tank truck to carry out fluid-solid coupling modal analysis and random vibration response analysis, combines the two analysis modes together, determines the proportion of liquid equivalent and the applied equivalent acceleration, simplifies a finite element model on the premise of fully considering vibration main frequency and keeping original vibration characteristics, and then obtains a random fatigue damage coefficient and a random ratchet effect damage coefficient directly through static analysis and cyclic plasticity analysis based on the simplified finite element model, and the sum of the two coefficients is used for final damage evaluation. The invention firstly provides random fatigue analysis and calculation for the tank truck, is convenient for engineering application, and reduces the inconvenience caused by the need of carrying out a large amount of vibration response analysis on the tank truck in the prior art.
The method obtains a simplified model of the tank body of the low-temperature liquid-containing tank truck, can determine two damage coefficients of random ratchet wheel fatigue and random fatigue, determines the main causes of damage, and realizes multi-damage evaluation.
The method can evaluate the ratchet wheel damage of the part which is most easy to generate the ratchet wheel fatigue damage under the action of road spectrum load, can evaluate other tank body areas, and fills the blank of fatigue damage research caused by road load spectrum at the connecting part of the tank body and the walking mechanism and the mutual supporting part of the inner container and the shell.
Drawings
To more clearly illustrate the objects of the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. The drawings in the following description are merely exemplary and exemplary of the present invention, and it will be apparent to those skilled in the art that other drawings can be obtained from the methods and drawings provided without inventive effort. In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and all other embodiments obtained by a person of ordinary skill in the art without any creative work belong to the scope of protection of the present invention.
The invention will now be described by way of example and with reference to the accompanying drawings.
FIG. 1 is a schematic view of the overall structure of a tank truck in the embodiment of the present application;
FIG. 2 is a simplified diagram of a geometric model of an LNG tank truck according to an embodiment of the present application;
FIG. 3 is a constraint in an embodiment of the present application;
FIG. 4 is a fluid-solid coupled FSI marker in an embodiment of the present application;
FIG. 5 is a first third order beam mode diagram of the present embodiment, wherein (a) is a first order beam mode diagram, (b) is a second order beam mode diagram, and (c) is a third order beam mode diagram;
FIG. 6 is a cloud chart of the equivalent stress of the level A road surface due to random vibration in the embodiment of the application;
FIG. 7 is a displacement response spectrum curve of the node 73468 in the embodiment of the present application;
FIG. 8 is a cloud chart of the equivalent stress of the level B road surface due to random vibration in the embodiment of the application;
FIG. 9 is a low temperature S30408S-N curve in the embodiment of the present application;
FIG. 10 is an equivalent stress cloud for the saddle to shell attachment area in an embodiment of the present application;
FIG. 11 is an equivalent stress cloud chart of a connecting area of a saddle and a shell after the thickness of a saddle rib plate is increased by 3mm in the embodiment of the application;
FIG. 12 is a cloud of equivalent stress for random vibration in an embodiment of the present application;
FIG. 13 is a graph of displacement response spectra of the node 30106 in the embodiment of the present application;
FIG. 14 is a simplified model constraint in an embodiment of the present application;
FIG. 15 is a cloud graph of static force analysis equivalent stress in an embodiment of the present application; wherein, (a) is a static analysis equivalent stress cloud picture under the condition of 1g load, (b) is a static analysis equivalent stress cloud picture under the condition of 0.9g load, and (c) is a static analysis equivalent stress cloud picture under the condition of 0.95g load; (d) a static analysis equivalent stress cloud chart under the condition of 0.94g of load;
FIG. 16 is a uniaxial tension curve in an example of the present application;
FIG. 17 shows the calculation results of cyclic plasticity in the examples of the present application; wherein (a) is a calculation result of cyclic plasticity under the condition of 1 sigma stress; (b) the calculation result of the cyclic plasticity under the condition of 2 sigma stress is obtained; (c) calculating the result of the cyclic plasticity under the condition of 3 sigma stress;
FIG. 18 is a stress-strain curve in the example of the present application; wherein (a) is a stress-strain curve under a 1 sigma stress condition; (b) is a stress-strain curve under the condition of 2 sigma stress; (c) is a stress-strain curve under the condition of 3 sigma stress;
FIG. 19 shows simulation results and a fitting curve in the present embodiment, wherein (a) is the simulation results under 1 σ stress condition; (b) simulating a calculation result for the 2 sigma stress condition; (c) the calculation results were simulated for the 3 σ stress condition.
Detailed description and examples
To facilitate understanding of the technical contents of the present invention, the embodiment of the present invention is given by taking model DC18 as an example.
According to the fatigue multi-damage evaluation method for the random ratchet wheel of the tank truck, the spatial frequency power spectrum density is converted into the time frequency displacement power spectrum density under the conditions of certain running speed and road surface grade according to a road surface power spectrum density fitting formula specified in GB/T7031-2005.
Establishing a finite element model for the liquid-containing LNG tank truck, carrying out fluid-solid coupling modal analysis and random vibration response analysis, carrying out random vibration response analysis on a container supporting area in the LNG tank truck by using time frequency displacement power spectral density as excitation on the basis of the fluid-solid coupling modal analysis and carrying out random fatigue analysis according to a three-interval method based on Gauss distribution and Miner linear cumulative damage law to obtain a random fatigue damage coefficient of the structure, wherein the random fatigue damage coefficient is used as a comparison reference for model simplification and load simplification;
carrying out first-step simplification on a finite element model established by the tank truck containing liquid, and carrying out equivalent simplification on liquid, namely, equivalently adding the mass of the liquid to the wall of the inner container tank in a density form, so that the random vibration response characteristic of the inner container tank is equivalent to the response of the tank truck containing liquid, namely, the inner container tank has similar 1 sigma maximum stress solution and characteristic frequency, and further determining the proportion of the liquid equivalent of the current tank truck containing liquid;
after the liquid equivalent proportion with the same random vibration response characteristic as that of the tank truck is determined, carrying out second-step simplification on a finite element model and a road spectrum load, namely omitting a spring support, simplifying the road spectrum load into n times of gravity acceleration g, applying equivalent acceleration during static calculation, enabling the stress response of an inner container support area to be equivalent to a 1 sigma (sigma index standard deviation) stress solution of the tank truck, and determining the equivalent acceleration of the current tank truck;
after the proportion of liquid equivalent and the equivalent acceleration are determined, and the final simplified model of the liquid-containing tank body is obtained after the spring support is omitted, static analysis is carried out on the simplified model to obtain a 1 sigma stress solution equivalent to that of the current liquid-containing tank truck, and the fatigue damage is directly evaluated according to a three-interval method based on Gauss distribution and Miner linear accumulative damage law to obtain a random fatigue damage coefficient;
and carrying out cyclic plasticity analysis on the tank body in a final simplified model of the liquid-containing tank body, wherein the load range of the cyclic plasticity analysis is 0-1 time equivalent acceleration, 0-2 times equivalent acceleration and 0-3 times equivalent acceleration, the cyclic plasticity analysis is carried out on the premise of applying internal pressure to the tank body in the load range to obtain a ratchet wheel strain rule of a supporting area of the tank body, and a random ratchet wheel effect damage coefficient of the structure is obtained based on a three-interval method of Gauss distribution and Miner linear cumulative damage law.
And superposing the random ratchet effect damage coefficient and the random fatigue damage coefficient to give a random ratchet fatigue multi-damage coefficient under the road spectrum load action of a tank car supporting area, wherein the random ratchet fatigue multi-damage coefficient is used for evaluating the integrity of the structure in the area, and when the random ratchet fatigue multi-damage coefficient is not less than 1, the fatigue damage is considered to be generated.
In the embodiment, the liquid equivalent proportion is 40%, the equivalent acceleration is 0.95g, cyclic plasticity analysis is carried out under the internal pressure of the tank body and the equivalent accelerations of 0-0.95 g, 0-1.9 g and 0-2.85 g, the ratchet wheel strain rule of the supporting area of the tank body is obtained, namely the ratchet wheel strain rate in each stress range is obtained, and the actual cycle number multiplied by the ratchet wheel strain rate of the ratchet wheel strain damage is divided by the strain limit epsilon f And (4) obtaining. The stress range of 0-0.95 g corresponds to the 1 sigma interval, the stress range of 0-1.9 g corresponds to the 1 sigma-2 sigma interval, and the stress range of 0-2.85 g corresponds to the 2 sigma-3 sigma interval. Then carrying out cyclic plasticity analysis on the tank body under the conditions of internal pressure and 0-0.95 g, 0-1.9 g and 0-2.85 g equivalent acceleration based on the final simplified model of the liquid-containing tank body to obtain the ratchet wheel strain rule of the supporting area of the tank bodyThe method comprises the steps of obtaining a structural random ratchet effect damage coefficient based on Gauss distribution and a Miner linear accumulated damage law, superposing the structural random ratchet effect damage coefficient with the random fatigue damage coefficient, giving out a random ratchet fatigue multi-damage coefficient under the road spectrum load action of a support area of the tank car, using the random ratchet fatigue multi-damage coefficient for integrity evaluation of the structure (the tank car) in the area (the area concerned in the embodiment, the support area in the embodiment) and considering that no fatigue damage occurs, wherein the random ratchet fatigue multi-damage coefficient is smaller than 1 and considering that no fatigue damage occurs, otherwise, considering that the fatigue damage occurs, and taking corresponding improvement measures.
In the invention, the probability of small load is high and the probability of large load is low during the road surface advancing, and the damage is calculated according to the occurrence probability. According to the method, fluid-solid coupling modal analysis and random vibration response analysis are carried out on different road surfaces, different running speeds, different liquids and different tank bodies, and then the proportion and the equivalent acceleration of the corresponding proper liquid equivalent under the conditions of different road surfaces, different running speeds, different liquids and different tank bodies can be determined, so that a large database for evaluating the fatigue and the damage of the random ratchet wheel of the liquid-containing tank truck is formed, when the fatigue and the damage of the random ratchet wheel of the liquid-containing tank truck are evaluated in the later period, the proportion and the equivalent acceleration of the liquid equivalent of the current scene object can be determined directly according to the information in the large database, and then the corresponding damage coefficient is determined according to static calculation and cyclic plasticity analysis, so that the damage evaluation is realized.
Example 1
As shown in fig. 1, the liquefied natural gas tanker comprises a tank body 1, a control box 2 and a travelling mechanism 3, wherein a tank body saddle is fixed on the travelling mechanism through bolts; the tank body consists of an inner container and an outer container, and is supported in a heat insulation way through an epoxy resin glass steel pipe, the inner container is used for containing liquefied natural gas, and a plurality of layers of aluminum foil paper are arranged between the inner container and the outer container to carry out vacuum cold insulation on the inner container. In fig. 1, a tank car is shown as an integral example, a low-temperature liquid tank body 1 is additionally arranged behind a tractor 11, a control box 2 is arranged behind the low-temperature liquid tank 1, the low-temperature liquid tank 1 is arranged on a running mechanism 3 (a semi-trailer does not contain a power source part and needs to be dragged by the tractor, after a front support of the running mechanism is put down, the tractor is driven away, the running mechanism can be automatically supported, after the running mechanism is connected with the tractor, the front support is folded, and the front support can be dragged by the tractor), an electrostatic conducting adhesive tape C type 4 is arranged behind the running mechanism, and a dry powder fire extinguisher 5, an emergency cut-off valve control device 6, a protective guard assembly 7, a spare tire frame 8, a nameplate 9 and a supporting leg frame 10 are further arranged on the tank car.
The diameter of the shell is 2484mm, the length is 11795mm, the effective thickness of the shell is 3.7mm, and the material is Q345R; the end sockets on two sides are disc-shaped end sockets, and the straight edge height of the end sockets is 40 mm. The diameter of the inner container is 2410mm, the length of the inner container is 11395mm, the thickness of the shell is 6mm, and the material is S30408; the end sockets on two sides are elliptical end sockets, and the straight edge height of the end sockets is 40 mm. The cross sections of the shell reinforcing ring and the inner container supporting ring are rectangular with the length of 6.7mm and the width of 30mm, the material of the reinforcing ring of the shell is Q235B, the material of the inner container supporting ring is S30408, and 11 supporting rings are distributed on the inner wall of the inner container to support the swash plate; 4 points of the front and the back of the epoxy resin glass steel pipe support the outer shell and the inner container; the tank saddle material is Q345R. The transverse beams and the longitudinal beams of the traction mechanism and the travelling mechanism are I-shaped beams made of Q345R and are respectively provided with two longitudinal beams; four cross beams are uniformly distributed between two longitudinal beams in the traction mechanism, and six cross beams are uniformly distributed between two longitudinal beams of the walking mechanism. The liquid level in the liquid tank is 2025mm, and the filling coefficient is 90%. The physical properties of the materials used are shown in Table 1.
TABLE 1 physical Properties of the materials
Establishing finite element model
Neglecting structures which have little influence on the rigidity of the whole structure, such as vacuum heat insulation materials between an inner container and an outer container with light weight, an inner container inner wave-proof plate which can be equivalent to the wall of the tank in an equivalent density mode, and the like, only establishing the inner container and the outer shell of the tank body, liquid in the inner container, a reinforcing ring of the outer shell, a supporting ring of the inner container, a supporting tube of the inner container and the outer shell, a saddle, longitudinal beams and cross beams of a walking mechanism and a traction mechanism to form an original model. A simplified diagram of the original model is shown in fig. 2.
The outer Shell, the inner container, the epoxy glass fiber reinforced plastic support tube, the saddle, the travelling mechanism and the longitudinal Beam of the traction mechanism are all subjected to mesh division by adopting a Shell63 unit of ANSYS software, liquid is subjected to mesh division by adopting a Fluid30 unit, a reinforcing ring of the outer Shell, a supporting ring of the inner container, a Beam of the travelling mechanism and a Beam of the traction mechanism are subjected to mesh division by adopting a Beam188 unit, and the tire and the plate spring are replaced by a combination 14 unit.
In order to determine the proper grid size, a larger size is selected for trial calculation, and then the grid is encrypted continuously until the difference between the last two results is within 5%.
Constraints in the Y direction (axial direction) and the X direction (transverse direction) are applied to the transverse and longitudinal beams (only the action of vertical road spectrum load is considered), full constraint is applied to the lower node of the spring unit, and the constraint situation is shown in fig. 3. The lower node of the spring unit refers to the position of the tire, and the rigidity of the spring is obtained by comprehensively considering the rigidity of the plate spring and the rigidity of the tire. A pressure of 0 is applied to the free surface of the liquid in the tank and a fluid-solid coupled FSI marker is applied at the interface of the liquid and the structure, as shown in fig. 4.
Fluid-solid coupling modal analysis
The fluid-solid coupling modal analysis method adopts an asymmetric matrix method to solve. The first ten orders of vibration frequencies are shown in table 2, and the beam mode begins to appear when the frequency reaches 4.1764Hz, and the beam mode diagram of the first three orders is shown in fig. 5.
TABLE 2 first 10 natural frequencies of tank cars
(III) random vibration and fatigue analysis of tank truck
1. Power spectral density
The pavement frequency domain model is a pavement model which is commonly applied at the present stage. The displacement power spectral density obtained by the method is determined in a meaningful frequency band range and is given according to the road surface unevenness condition in the range. ISO/8068 and GB/T7031-2005 specify the road surface power spectral density fitting formula for road surfaces (non-track):
in which n is the spatial frequency (m) -1 ) The value is the reciprocal of the wavelength λ, which represents the number of wavelengths contained in a unit length, and the value range of n: 0.011m -1 <n<2.83m -1 ；n 0 ＝0.1m -1 Is a reference spatial frequency;
G d (n 0 ) Coefficient of road surface irregularity, being reference spatial frequency n 0 Power spectral density value of lower pavement in m 2 /m -1 ＝m 3 ；
w determines the frequency structure of the power spectral density of the road surface, wherein w is a frequency index and is generally equal to 2; g d (n) is a spatial frequency power spectral density function.
When a transport vehicle runs through the road surface unevenness with the space frequency n and the speed v, the space frequency power spectrum density G needs to be adjusted d (n) conversion to time-frequency power spectral density G d (f) In that respect The spatial and temporal frequency relationship is as follows:
f＝vn (2)
thus, can derive G d (n) and G d (f) The relation of (A) is as follows:
standard GB/T7031-2005 according to road surface roughness coefficient G d (n 0 ) The road surface was classified into 8 grades from A to H (Table 3).
TABLE 3 road surface grades
2. Random vibration analysis
When random vibration analysis is carried out, the power spectral density of the road surface is used as excitation, and is approximately applied to the constraint positions of 10 spring units (namely the lower node of the spring unit, 6 walking mechanisms on 10 walking mechanisms and 4 traction mechanisms) according to the actual transportation condition, wherein the direction is the vertical direction (Z-axis direction). The simulation analysis is mainly carried out on the condition that the vehicle runs on a class A road surface at the speed of 80 km/h. Since the natural frequency needs to be within a certain frequency band, for the convenience of calculation, the time frequency power spectral density input after converting the unit is shown in table 4.
TABLE 4 time frequency Power spectral Density
Taking the calculated pavement displacement power spectral density under the condition of 80km/h of the A-level pavement as input excitation, continuously carrying out random vibration analysis on the basis of the modal analysis obtained in the previous STEP, exiting the calculation after the calculation, entering a POST processor POST1 in ANSYS software to find a node calculation result, and reading the VON MISES stress distribution of the structure when the LOAD STEP 3( LOAD STEP 3, 1 sigma displacement solution, which represents the root mean square response value under normal distribution in probability statistics) is carried out, as shown in FIG. 6, the maximum stress is 132.548MPa, and the maximum stress is located at the contact position of the inner cylinder and the supporting tube.
The PSD response is the responsive power spectral density to stress or displacement at a node. The displacement response power spectral density in the Z direction of the amplitude maximum node 73468 was obtained by entering a time history POST processor POST26 in ANSYS software, as shown in fig. 7 where the resonant peak frequency of the structure is 4.17Hz within the random excitation band.
And taking the pavement displacement power spectrum density calculated under the condition of the B-level pavement with the speed of 60km/h as input excitation, and continuously carrying out random vibration analysis on the basis of the modal analysis obtained in the previous step. After the calculation is finished, the calculation is quitted, the node calculation result is found in a POST processor POST1, the VON MISES stress distribution of the structure in which the LOAD STEP 3( LOAD STEP 3, 1 sigma displacement solution, which represents the root mean square response value under normal distribution in probability statistics) is read is shown in FIG. 8, and the maximum stress is 229.548MPa and is located at the contact position of the inner cylinder body and the support pipe.
3. Stochastic fatigue analysis
Since the random load is input into the structure as an excitation for analysis and calculation, the response result of the obtained system is also a random process, which makes the fatigue calculation more difficult. But it can be known from a large amount of actual measurement data: the distribution rule of the input random excitation caused by the road unevenness and the output vibration response of the vehicle to the excitation conforms to the Gauss distribution. Therefore, the random fatigue damage of the tank car was calculated using a three-interval method (stress interval shown in table 5) based on Gauss distribution and Miner's linear cumulative damage law as a theoretical basis.
TABLE 5 stress interval of three intervals method
In the embodiment, the load range corresponding to the 1 sigma interval is-0.95 g, the stress range is calculated, the stress amplitude is obtained by calculating 0-0.95 g, and the stress amplitude is half of the stress range; in the same way, the load range corresponding to the 2 sigma interval is-1.9 g, and the stress amplitude is obtained by calculating 0-1.9 g; the load range corresponding to the 3 sigma interval is-2.85 g, and the stress amplitude is obtained by calculating 0-2.85 g.
The probability that stress occurs in the interval greater than 3 σ is only 0.27%, a small probability event, and is ignored here. The overall damage calculation formula can be written as:
in the formula, n 1σ Is equal to or lowerActual number of cycles at 1 σ level (0.683N), N 2σ Actual number of cycles (0.271N), N, at or below 2 σ level 3σ The actual number of cycles at or below the 3 σ level (0.0433N), N being the actual number of cycles; n is a radical of 1σ ，N 2σ ，N 3σ The corresponding allowable cycle numbers at the stress levels of 1 sigma, 2 sigma and 3 sigma are respectively expressed, and the values can be found from corresponding fatigue curves according to the tank car material.
(1) Fatigue analysis under single road condition
a) Fatigue analysis at maximum stress values
According to the random vibration analysis result of the storage tank, the maximum 1 sigma stress value is 132.548MPa when the storage tank is driven on the A-grade road surface. The actual maximum transport distance is about 1500000km, and when the transport vehicle travels at a speed of 80km/h, the vibration time (transport time) T is 6.75 × 10 7 And s. To find its characteristic frequency N 0 At 4.17Hz, the actual cycle number is N ═ N 0 ×T＝2.8×10 8 . Calculated n 1σ ，n 2σ ，n 3σ Respectively as follows: n is a radical of an alkyl radical 1σ ＝0.683N＝1.9×10 8 ，n 2σ ＝0.271N＝7.6×10 7 ，n 3σ ＝0.0433N＝1.2×10 7 . According to the S-N curve of S30408 at low temperature, as shown in fig. 9, the allowable cycle life of S30408 at each stress level at low temperature can be found as follows: stress 1 σ 132.548 MPa: n is a radical of 1σ Infinity, +,; stress 2 σ 265.096 MPa: n is a radical of 2σ ＝4.15×10 10 (ii) a Stress 3 σ 397.644 MPa: n is a radical of 3σ ＝2.47×10 7 . Substituting the calculation result into an equation (5) to obtain:
in the same manner, assuming that the maximum transport distance is 1500000km and the speed is 60km/h when the vehicle travels on a B-grade road surface, the overall damage factor is 2.91X 10 3 。
According to the research method, the random fatigue damage evaluation of the liquid-containing LNG semitrailer tank based on fluid-solid coupling calculation is realized.
b) Fatigue analysis of saddle and shell joint
FIG. 10 is a calculated 1 σ displacement solution equivalent stress cloud plot for a saddle and shell junction under class A road conditions.
As can be seen from the figure, the maximum 1 sigma stress value is 47.07MPa, and the actual cycle number is 2.8 multiplied by 10 8 . Calculated n 1σ ，n 2σ ，n 3σ Respectively as follows: n is a radical of an alkyl radical 1σ ＝0.683N＝1.9×10 8 ，n 2σ ＝0.271N＝7.6×10 7 ，n 3σ ＝0.0433N＝1.2×10 7 . The allowable cycle life can be determined from the stress level according to the S-N curve found in the analysis design criteria for steel pressure vessels in JB4732-1995(2005 validation edition): stress 1 σ 47.07 MPa: n is a radical of hydrogen 1σ Infinity, +,; stress 2 σ 94.14 MPa: n is a radical of 2σ ＝2.73×10 10 (ii) a Stress 3 σ of 141.21 MPa: n is a radical of 3σ ＝5.75×10 6 . Substituting the calculation result into an equation (5) to obtain:
according to the result of the fatigue calculation, the LNG tank truck is shown to generate fatigue failure at the joint of the saddle and the shell after a certain time when the LNG tank truck runs on the grade A road surface at the speed of 80 km/h. Therefore, the thickness of the saddle rib plate causing fatigue failure is increased by 3mm, and the calculation result is shown in fig. 11.
And fatigue evaluation is carried out again according to the stress result obtained by calculation after the thickness of the saddle rib plate is increased, so that the damage coefficient is 0.609, and the fatigue damage caused by road load can not be generated in transportation. Therefore, it is an effective method to increase the thickness of the sheet material at the saddle portion where fatigue failure is likely to occur.
In the same manner, assuming that the maximum transport distance is 1500000km and the speed is 60km/h when the vehicle travels on a class B road surface, the overall damage factor is 17.51.
(2) Fatigue analysis under combined road conditions
The total damage coefficient under a single road condition of each level is divided by the transport distance to obtain the corresponding damage coefficient per km transport distance, and the two different road conditions are combined and evaluated. Assuming that the driving range under the condition of the class a road surface accounts for 99.99% of the total mileage, the class B accounts for 0.01%, and the class C road surface is a country road and is not basically considered, the damage coefficient under the combined evaluation can be obtained as shown in table 6.
TABLE 6 Combined fatigue evaluation
(IV) simplifying the calculation model and carrying out random ratchet wheel fatigue evaluation
1. Simplified model and load
(1) Simplified model
And simplifying the established finite element model of the LNG tank truck containing liquid based on the analysis result of the grade A road condition. In actual engineering calculations, the liquid mass equivalent is calculated on the tank wall for modeling and computational simplification. And the maximum stress value of the simplified model after the equivalent is matched with the maximum stress value of the model containing the actual liquid by adjusting the proportion of the mass of the equivalent liquid.
The method comprises the STEPs of taking the pavement displacement power spectral density as input excitation, continuously carrying out random vibration analysis on the basis of fluid-solid coupling modal analysis on a finite element model which is initially simplified (parts which do not influence stress analysis on a tank car, such as heat insulation materials, lines and the like are omitted), withdrawing from calculation after calculation, entering a POST-processor POST1 to find a node calculation result, and reading VON MISES stress distribution of a structure when a LOAD STEP 3( LOAD STEP 3, 1 sigma displacement solution, which represents a root mean square response value under normal distribution in probability statistics) is carried out. Von Mises is a yield criterion, the value of which is commonly referred to as the equivalent stress.
And calculating the random fatigue damage according to a three-interval method of Gauss distribution and Miner linear accumulative damage law. Calculating the actual circulation number n of the model of the equivalent liquid with different proportions according to different characteristic frequencies and maximum 1 sigma stress values 1σ ，n 2σ ，n 3σ And allow the cycleNumber of cycles N 1σ ，N 2σ ，N 3σ And overall damage coefficient D, the specific data are shown in table 7.
TABLE 7 fatigue analysis results
From the above table analysis, it can be seen that when the equivalent liquid ratio is 40%, the first-step simplified model has a maximum stress value of 1 σ close to that of the original model and a close overall damage coefficient D. Therefore, the first-step simplified model can be used for equivalently replacing the original model to perform random vibration response analysis and random fatigue analysis, so that the calculation difficulty and cost are greatly reduced.
As shown in fig. 12, the maximum stress is 132.432MPa, and is located at the contact position between the inner cylinder and the support tube. The displacement response power spectral density of the amplitude maximum node 30106 in the Z direction is calculated by a POST processor of the POST26 time history, and the frequency of the resonance peak of the structure in the random excitation frequency band is 5.02Hz as shown in fig. 13.
(2) Load simplification
In order to further simplify the calculation method, the road spectrum load is further subjected to equivalent simplification to n times of gravity acceleration g on the basis of a first simplified model of equivalent liquid mass on the wall of the tank. The stress result and the overall damage coefficient matched with the original model containing the actual liquid can be obtained by only carrying out static calculation, and the constraint condition of the model is shown in figure 14. The stress results for different gravitational acceleration loading are shown in fig. 15.
And calculating the random fatigue damage according to a three-interval method of Gauss distribution and Miner linear cumulative damage law. Calculating the actual cycle number n of each model applying inertial loads with different proportions by using the characteristic frequency of 4.17Hz and the maximum stress value of 1 sigma 1σ ，n 2σ ，n 3σ And the allowable number of cycles N 1σ ，N 2σ ，N 3σ And overall damage coefficient D, the specific data are shown in table 8.
TABLE 8 fatigue analysis results
And when n is 0.95 obtained through multiple times of simulation calculation, the obtained stress result is matched with the original model.
2. Ratchet fatigue analysis
The supporting area of the inner container of the LNG semitrailer tank body is likely to generate a ratchet effect under the action of internal pressure and alternating road spectrum load, particularly in the process of structural lightweight, the strain strengthening inner container is still designed in a full stress mode, a local high-stress area of the strain strengthening inner container is likely to enter plasticity, if the stress has alternating components, high average stress exists, and cyclic plasticity accumulation, namely the ratchet effect, is likely to be caused. It is therefore necessary to investigate the cyclic plastic damage caused by the ratcheting effect that is additive to fatigue damage.
The follow-up enhanced constitutive model for cyclic plasticity analysis is a Chaboche model, which is proposed by Chaboche in 1986. Ratchet strain of the material was predicted by stacking several a-F models. The formula of the model is as follows:
in which α is the back stress, ε p And C and gamma are plastic strain, C and gamma are model parameters, p is accumulated plastic strain, i is subscript (value is 1-M), and M is the quantity of back stress components.
FIG. 16 is a uniaxial tensile curve of a material. At low temperatures, transformation martensite induces plasticity leading to the development of a yield plateau, after which the material undergoes secondary hardening due to the presence of a large amount of deformed martensite and the strong interaction of the austenite dislocations with the hardening phase martensite. Although the nominal yield strength is 330MPa, the initial yield stress corresponding to the yield face size is only 120MPa and will be used in later plastic analysis. As can be seen from fig. 16, the strain corresponding to the yield plateau is 8.3%. In a practical engineering structure, the cyclic load would not exceed 8.3%, so the plastic segment including the yield plateau but no second hardened segment was considered in the subsequent analysis.
The Chaboche model divides the uniaxial tensile curve into three sections, namely a yield initial section, a nonlinear section and a stable section with a higher strain range. In the formula C i Evolution of modulus, gamma, for back stress i As a material parameter, C 1 Should be a very large value to match the plastic modulus at yield, and corresponding gamma 1 Should also be large enough to stabilize alpha immediately 1 And (4) hardening. C 3 Determined by the slope of the linear segment of the hysteresis curve in the high strain range. Pass test pair C 2 And gamma 2 Evaluation was performed to show well the experimentally stable hysteresis curve, γ 3 Best fit was determined by single axis ratchet experiments. Finally determining model parameters: c 1-3 :5998900，117000，500，γ 1-3 :90500，320，3。
Because only the inner cylinder supporting part which is subjected to internal pressure can generate the ratchet effect under the action of average stress and road load, only the inner cylinder, the inner supporting ring and the supporting tube part need to be subjected to cyclic plasticity analysis. And (3) respectively applying the loading inertial acceleration required by the conditions of 1 sigma stress, 2 sigma stress and 3 sigma stress and applying the internal pressure of 0.9MPa to the inner tank by adopting the finally simplified model, performing cyclic plasticity analysis by using a Chaboche constitutive model, wherein the number of cycles is 10, and the calculation result is shown in figure 17. Stress strain data were extracted and plotted as shown in fig. 18.
To quantitatively investigate the rule of plastic strain accumulation, ratchet strain was defined:
the results of the simulation analysis calculations gave a scatter plot of the corresponding number of cycles versus ratchet strain as shown in fig. 19. The ratchet strain obtained under the 3 σ stress condition does not reach stability within 10 circles, so the obtained simulation result needs to be fitted to obtain the ratchet strain corresponding to the actual cycle number, and the fitting curve is shown in fig. 19. And substituting the actual number of cycles to obtain the corresponding ratchet strain according to a curve formula obtained by fitting.
Due to the ratchet strain, it is necessary to superimpose the damage caused by the ratchet strain during the fatigue evaluation. Ratchet strain damage can be determined by multiplying the actual cycle number by the ratchet strain rate and dividing by the strain limit ε f And (4) obtaining. Epsilon is known from low-temperature uniaxial tensile test f The ratchet strain rate is divided by the total ratchet strain epsilon for the last cycle, divided by the number of cycles, 0.65. As can be seen from fig. 19, the ratchet strain is stabilized within 10 cycles under the stress condition of 1 σ and 2 σ, and the ratchet strain under the stress condition of 3 σ can be obtained by:
ε＝4.96×10 -4 +3.04×10 -5 ×n 0.42546 (8)
total actual number of cycles N-N 0 ×T＝2.8×10 8 . Calculating the number of cycles n per interval 1σ ，n 2σ ，n 3σ Respectively as follows: n is 1σ ＝0.683N＝1.9×10 8 ，n 2σ ＝0.271N＝7.6×10 7 ，n 3σ ＝0.0433N＝1.2×10 7 . From the ratchet strain curve, epsilon 1σ ＝9.16×10 -5 ，ε 2σ ＝2.25×10 -4 N is to be 3σ Substituting into equation (8) to obtain ε 3σ ＝3.18×10 -2 And then:
after obtaining the damage coefficient D epsilon of the ratchet effect, the damage coefficient D epsilon and the fatigue damage are linearly superposed to obtain the overall damage coefficient D:
it can be seen that the damage caused by the ratcheting effect is approximately 9.19% of the total damage.
Nothing in this specification is said to apply to the prior art.
Claims (8)
1. A method for evaluating fatigue and multiple damages of a random ratchet wheel of a tank truck comprises the following steps:
establishing a finite element model for the tank truck containing liquid and carrying out fluid-solid coupling modal analysis;
converting the spatial frequency power spectrum density into a time frequency displacement power spectrum density under the determined running speed and road surface grade conditions;
the time frequency displacement power spectrum density is used as excitation, random vibration response analysis is carried out on the basis of fluid-solid coupling modal analysis, random fatigue analysis is carried out on a supporting area of an inner container of the LNG tank car according to a three-interval method based on Gauss distribution and Miner linear cumulative damage law, a random fatigue damage coefficient of the structure is obtained and is used as a comparison reference for model simplification and load simplification;
carrying out first-step simplification on a finite element model established by the liquid-containing tank truck, and carrying out equivalent simplification on liquid, namely, equivalently loading the mass of the liquid on the wall of an inner container tank in a density form, so that the random vibration response characteristic of the inner container tank is equivalent to that of the liquid-containing tank truck, namely, the random vibration response characteristic has similar 1 sigma maximum stress solution and characteristic frequency, and further the proportion of the liquid equivalent of the current liquid-containing tank truck is determined;
after the liquid equivalent proportion with the same random vibration response characteristic as that of the tank truck is determined, carrying out second-step simplification on a finite element model and a road spectrum load, namely omitting a spring support, simplifying the road spectrum load into n times of gravity acceleration g, applying equivalent acceleration during static calculation, enabling the stress response of an inner container support area to be equivalent to a 1 sigma stress solution of the tank truck, and determining the equivalent acceleration of the current tank truck; σ is the standard deviation;
after the proportion of liquid equivalent and the equivalent acceleration are determined, and the final simplified model of the liquid-containing tank body is obtained after the spring support is omitted, static analysis is carried out on the simplified model to obtain a 1 sigma stress solution equivalent to that of the current liquid-containing tank truck, and the fatigue damage is directly evaluated according to a three-interval method based on Gauss distribution and Miner linear accumulative damage law to obtain a random fatigue damage coefficient;
performing cyclic plasticity analysis on the tank body in a final simplified model of the liquid-containing tank body, wherein the load range of the cyclic plasticity analysis is 0-1 time equivalent acceleration, 0-2 times equivalent acceleration and 0-3 times equivalent acceleration, performing the cyclic plasticity analysis on the tank body under the premise of applying internal pressure in the load range to obtain the ratchet wheel strain rule of the supporting area of the tank body, and obtaining the random ratchet wheel effect damage coefficient of the structure based on a three-interval method of Gauss distribution and Miner linear cumulative damage law,
and superposing the random ratchet effect damage coefficient and the random fatigue damage coefficient to give a random ratchet fatigue multi-damage coefficient under the road spectrum load action of a tank car supporting area, wherein the random ratchet fatigue multi-damage coefficient is used for evaluating the integrity of the structure in the area.
2. The evaluation method according to claim 1, wherein fatigue failure is considered to occur when the random ratchet fatigue multiple damage factor is not less than 1.
3. The evaluation method according to claim 1, wherein the fluid-solid coupling interface setting, the free liquid level setting and the mode calculation method selection need attention during fluid-solid coupling mode analysis calculation, and an asymmetric matrix method is selected for mode solution due to the fluid-solid coupling effect; and selecting a beam mode according to the coupling vibration mode.
4. The evaluation method according to claim 1, wherein a relationship between the proportion of the liquid equivalent and the value of the equivalent acceleration corresponding to each cryogenic liquid and different types of tank cars at different road surfaces and different traveling speeds is established, and after the road surfaces, the traveling speeds, the types of the liquid and the types of the tank cars are determined, the proportion of the liquid equivalent and the value of the equivalent acceleration can be directly determined; and (3) directly performing static analysis and cyclic plasticity analysis in a final simplified model of the liquid-containing tank body at the later stage, namely determining a random fatigue damage coefficient and a random ratchet effect damage coefficient respectively without performing random vibration response analysis on the liquid-containing tank truck.
5. Evaluation according to claim 1The method is characterized in that the liquid equivalent proportion is 40%, the equivalent acceleration is 0.95g, cyclic plasticity analysis is carried out under the internal pressure of the tank body and the equivalent accelerations of 0-0.95 g, 0-1.9 g and 0-2.85 g, the ratchet wheel strain rule of the supporting area of the tank body is obtained, the ratchet wheel strain rate in each stress range is obtained, and the actual cycle number of ratchet wheel strain damage is multiplied by the ratchet wheel strain rate and then divided by the strain limit epsilon f And (4) obtaining.
6. The evaluation method according to claim 1, wherein the method is used for carrying out fluid-solid coupling modal analysis and random vibration response analysis on different road surfaces, different running speeds, different liquids and different tank bodies, so that the proportion and the equivalent acceleration of the corresponding liquid equivalent under the conditions of different road surfaces, different running speeds, different liquids and different tank bodies can be determined, and a large database for evaluating the fatigue and the damage of the random ratchet wheel of the tank truck is formed.
7. The evaluation method according to claim 1, wherein a finite element model is established before the fluid-solid coupling modal analysis, a structure which has little influence on the rigidity of the whole structure is ignored in the establishment of the finite element model, the finite element model comprises a vacuum heat insulation material between an inner container and an outer container, an inner container inner wave guard plate which can be equivalent to the wall of the tank in an equivalent density mode, and only the inner container and the outer shell of the tank body, the liquid in the inner container, a reinforcing ring of the outer shell, a supporting ring of the inner container, a supporting pipe of the inner container and the outer shell, a saddle, longitudinal beams and cross beams of a travelling mechanism and a traction mechanism are established to form an original model;
the outer Shell, the inner container, the epoxy glass fiber reinforced plastic support tube, the saddle, the travelling mechanism and the longitudinal Beam of the traction mechanism are all subjected to mesh division by adopting a Shell63 unit of ANSYS software, liquid is subjected to mesh division by adopting a Fluid30 unit, a reinforcing ring of the outer Shell, a supporting ring of the inner container, a Beam of the travelling mechanism and a Beam of the traction mechanism are subjected to mesh division by adopting a Beam188 unit, and tires and plate springs are replaced by a combination 14 unit;
a pressure of 0 is applied to the free surface of the liquid in the tank, and a fluid-solid coupling FSI mark is applied to the interface of the liquid and the structure.
8. A method for simplifying a tank truck model is characterized in that the method carries out flow-solid coupling random vibration analysis on the tank truck under the action of road spectrum load to obtain a random fatigue damage coefficient of a concerned position, and simplifies a tank body calculation model and load of the tank truck by taking the random fatigue damage coefficient as a reference, and specifically comprises the following steps:
firstly, determining the proportion of the liquid mass equivalent to the wall of the inner container to ensure that the random vibration characteristic of the tank-free truck is consistent with that of the tank truck containing liquid, namely the tank truck has the same 1 sigma solution and vibration dominant frequency; and then removing the spring support, determining the equivalent acceleration, and enabling the static calculation result to be consistent with the 1 sigma solution, thereby completing the calculation of the random fatigue damage coefficient and completing the simplification of the tank truck model.
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