Method and device for determining pre-pressing amount of elastic system, elastic system and suspension assembly

Abstract

The invention provides a method and device for determining the pre-pressing amount of an elastic system, the elastic system and a suspension assembly, the elastic system comprises one or more elastic elements, and the method comprises the steps that the pre-loading force of each elastic element in the one or more elastic elements is determined; based on the preloading force of each elastic element, the prepressing amount of each elastic element is determined; wherein the preloading force and / or the prepressing amount enable an assembly connected to the one or more elastic elements to be in a static balance state, and the total prepressing amount, corresponding to the preloading force, of the one or more elastic elements is minimum. According to the method for determining the preloading amount of the elastic system, the accuracy of the preloading force is remarkably improved, meanwhile, the calculation process of the preloading force of the elastic system is simplified, and the skill threshold of operators is reduced.

Description

Technical Field

[0001] The present disclosure relates to the technical field of elastic systems, and in particular to a method and device for determining a preload amount of an elastic system, an elastic system, and a suspension assembly. Background Art

[0002] In mechanical design and engineering applications involving elastic systems (such as suspension components), the calculation of preload is an important step to ensure the normal operation and performance optimization of related systems that use the elastic system. Usually, technicians can first determine the preload force corresponding to the elastic system, and determine the preload amount based on the preload force. Common preload force calculation methods include: engineering experience method, that is, using relevant engineering experience to solve the approximate solution of the static equilibrium equation of the elastic system with respect to the preload force; and software iterative calculation method, that is, calling Computer Assisted Engineering (CAE) software to obtain the preload force through multiple iterative calculations.

[0003] However, the preload force obtained based on the engineering experience method has a large error problem. Although the preload force calculated by the software iteration method has higher accuracy than the engineering experience method, the operation process is cumbersome and time-consuming, and requires the operator to have high software operation skills and related engineering design experience. Summary of the invention

[0004] In view of this, the present disclosure is dedicated to providing a method, device, elastic system and suspension assembly for determining the preload of an elastic system.

[0005] In a first aspect, the present disclosure provides a method for determining the preload of an elastic system, wherein the elastic system comprises one or more elastic elements, and the method comprises: determining the preload force of each of the one or more elastic elements; and determining the preload of each elastic element based on the preload force of each elastic element; wherein the preload force and / or the preload cause a component connected to the one or more elastic elements to be in a static equilibrium state, and the total preload of the one or more elastic elements corresponding to the preload force is minimized.

[0006] As a possible implementation, the preload force of each elastic element is determined by a first model, which is determined based on one or more of the following variables: the preload force of the one or more elastic elements in different directions; the force arm of the one or more elastic elements in different directions; the moment of the one or more elastic elements in different directions; the gravity of the components connected to the one or more elastic elements.

[0007] As a possible implementation, the first model is represented by the following expression:

[0008]

[0009] Among them, F i represents the preload force of the i-th elastic element, M i represents the moment of the i-th elastic element, mg represents the gravity of the component connected to the one or more elastic elements, and λ represents the Lagrange multiplier.

[0010] As a possible implementation method, based on the preload force of each elastic element, the preload amount of each elastic element is determined, including: based on the preload force of each elastic element and a first curve, the preload amount of each elastic element is determined; wherein the first curve is used to indicate the stiffness of each elastic element.

[0011] As a possible implementation method, the first curve is determined based on the spline interpolation method, and the preload amount of each elastic element is determined based on the preload force of each elastic element and the first curve, including: traversing all intervals of the first curve to determine the preload force of each elastic element and the possible intervals; within the possible intervals, determining one or more candidate preload amounts corresponding to the preload force of each elastic element; and according to the actual working conditions, selecting a required preload amount from the one or more candidate preload amounts as the preload amount of each elastic element.

[0012] As a possible implementation manner, the spline interpolation method includes a cubic spline interpolation method.

[0013] As a possible implementation, the elastic system is a suspension component, which is used to connect the powertrain of the vehicle to the suspension of the vehicle, and the preload force and / or the preload amount make the powertrain in a static balance state.

[0014] In a second aspect, the present disclosure proposes a device for determining the preload of an elastic system, wherein the elastic system includes one or more elastic elements, and the device includes: a first determination module, used to determine the preload force of each of the one or more elastic elements; and a second determination module, used to determine the preload of each elastic element based on the preload force of each elastic element; wherein the preload force and / or the preload causes a component connected to the one or more elastic elements to be in a static equilibrium state, and the total preload of the one or more elastic elements corresponding to the preload force is minimized.

[0015] In a third aspect, the present disclosure proposes an elastic system, which includes one or more elastic elements, and the pre-compression of the one or more elastic elements is determined according to any method for determining the pre-compression of the elastic system in the first aspect.

[0016] In a fourth aspect, the present disclosure proposes a suspension assembly, which is used to connect a powertrain of a vehicle to a suspension of the vehicle, and the suspension assembly includes one or more elastic elements, and the pre-stress of the one or more elastic elements is determined according to any method for determining the pre-stress of the elastic system in the first aspect.

[0017] In a fifth aspect, the present disclosure proposes a device for determining the preload of an elastic system, comprising a memory and a processor, wherein the memory stores a computer program executable on the processor, and when the computer program is executed by the processor, the steps of any method for determining the preload of an elastic system as described in the first aspect are implemented.

[0018] Considering that when the component connected to the elastic system is in a static equilibrium state, there are multiple solutions for the preload force corresponding to the elastic system. Therefore, when determining the preload force corresponding to the elastic system, the embodiment of the present disclosure minimizes the total preload of one or more elastic elements corresponding to the preload force. In other words, the embodiment of the present application adds constraints to make the solutions of the preload force corresponding to the elastic system fewer or unique, so that the preload force corresponding to the elastic system can be simply solved, and the preload amount can be determined based on the preload force. The method for determining the preload amount of the elastic system provided in the embodiment of the present application is conducive to ensuring the accuracy of the preload force, and simplifies the calculation process, reducing the skill threshold of the operator. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Shown is a schematic diagram of the four-point suspension assembly of the vehicle powertrain.

[0020] Figure 2 Shown is a schematic diagram of a three-way spring.

[0021] Figure 3 The figure is a flow chart of a method for determining the preload amount of an elastic system provided by an embodiment of the present disclosure.

[0022] Figure 4 Shown is a schematic flow chart of a method for determining the preload amount of an elastic system provided by another embodiment of the present disclosure.

[0023] Figure 5 Shown is a graph of the stiffness of the vehicle suspension spring in the x-direction.

[0024] Figure 6 Shown is a schematic structural diagram of a device for determining the preload of an elastic system provided by an embodiment of the present disclosure.

[0025] Figure 7 Shown is a schematic structural diagram of a device for determining the preload amount of an elastic system provided by another embodiment of the present disclosure. DETAILED DESCRIPTION

[0026] The technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only part of the embodiments of the present disclosure, rather than all of the embodiments.

[0027] An elastic system is a system that uses elastic elements to store and release energy. Elastic elements can be various materials and structures, such as springs, rubber pads, air bags, etc. These elements absorb (i.e. store) and release energy through deformation (such as compression, stretching, etc.), thereby providing support or tension in the system.

[0028] The basic characteristic of elastic elements is the ability to return to their original state after being subjected to force. This restoring force is achieved through the elastic properties of the material. For example, a spring stores energy after being compressed or stretched, and releases the energy when unloaded, generating a corresponding reaction force.

[0029] In an elastic system, the support force or tension can be calculated using Hooke's law. Hooke's law describes the relationship between the force and the deformation, that is, the magnitude of the force is proportional to the deformation. The specific formula is:

[0030] F=k·Δx

[0031] Among them, F is the applied force (usually in Newton, i.e. N); k is the stiffness coefficient or elastic coefficient of the elastic element (usually in Newton / meter, i.e. N / m), which indicates the stiffness of the elastic element. The larger k is, the harder the elastic element is; Δx is the deformation of the elastic element (usually in meter, i.e. m).

[0032] The vehicle powertrain suspension assembly is a typical elastic system. The powertrain refers to the collection of components used in the vehicle that are responsible for generating power and transmitting it to the drive wheels, mainly including the engine, transmission, drive shaft, etc. The suspension assembly is a series of components that elastically connect the powertrain to the vehicle suspension or body, usually composed of elastic elements (such as rubber pads or metal springs), damping elements (such as hydraulic shock absorbers) and mounting brackets. The main functions of the suspension assembly include positioning and isolating vibrations, supporting the powertrain, reducing noise, absorbing shocks, etc., that is, absorbing vibrations from the engine and other power components through elastic elements, reducing structural resonance and noise caused by vibrations; ensuring that the powertrain is stably fixed in the correct position and keeping its relative movement relative to the vehicle body within a reasonable range; when encountering uneven roads, it can absorb part of the impact energy and protect the powertrain from damage.

[0033] According to the number of suspension points in common suspension components, the powertrain suspension components of the vehicle can be divided into two-point suspension, three-point suspension and four-point suspension components. Among them, the two-point suspension component refers to the powertrain fixed to the vehicle suspension or body through two suspensions (i.e. two support points), and the two suspensions are usually located at the front and rear ends of the powertrain. The design of the two-point suspension component is relatively simple, low-cost, and easy to repair; the two-point suspension component is usually suitable for small vehicles or models with low requirements for noise, vibration and sound roughness (NVH). The three-point suspension component adds a third suspension to the two-point suspension component, forming a triangular layout. This additional suspension can be set on the side of the powertrain. The three-point suspension component can provide stronger lateral rigidity and help reduce lateral vibration; compared with the two-point suspension component, the three-point suspension component can better isolate vibrations in different directions; by adding a suspension point, the three-point suspension component can more accurately control the position of the powertrain and improve the stability of the entire system.

[0034] The four-point suspension assembly refers to the use of four independent suspensions to fix the powertrain to form a more stable support structure. In order to provide the best vibration isolation effect and dynamic stability, the positions of the four suspensions are usually carefully set. Figure 1 Figure 1 shows a typical schematic diagram of a four-point suspension assembly. Figure 1 As shown, the four-point suspension assembly includes a left suspension (Left Mount) k1, a right suspension (Right Mount) k2, a left rear suspension (Left Rear Mount) k3 and a right rear suspension (Right Rear Mount) k4.

[0035] (Right Rear Mount) k4; In addition, in the four-point suspension assembly, the four mounts are symmetrically arranged around the center of mass (COM) of the powertrain, that is, the center of gravity (Gravity), to ensure that each mount is evenly stressed and reduce unnecessary torsion and bending stresses. It should be understood that in general (such as on the surface of the earth), the center of gravity of an object is the same as the center of mass.

[0036] In the four-point suspension assembly, the four mounts provide more comprehensive support for the powertrain and can effectively isolate vibrations from all directions; at the same time, the four mounts can also better control the dynamic displacement of the powertrain and reduce unnecessary noise and vibration; the four-point suspension assembly is one of the designs that can best optimize NVH performance and is suitable for high-end luxury cars and high-performance vehicles.

[0037] In addition to the vehicle powertrain suspension components, elastic systems are also involved in injection molds. Among them, injection molds are precision tools used to inject molten plastic into the mold cavity under high pressure to manufacture various plastic products. Elastic elements (such as springs, wave washers, etc.) are placed between the ejection mechanism or the movable mold plate and the fixed mold plate of the injection mold to provide the necessary elasticity and buffering capacity to ensure that the mold can run smoothly during the opening and closing process, and to apply appropriate force to the product during demolding to ensure that the product is completely removed from the mold.

[0038] In elastic systems, preload and precompression are two important parameters that directly affect the performance, stability and service life of the structural system including the elastic system. Preload refers to the force pre-applied to the elastic element in the elastic system in the absence of external load; appropriate preload can eliminate or reduce the free gap between related components (such as mechanical components), improve the motion accuracy of the system, and change the natural frequency of the system to avoid resonance. Precompression usually refers to the deformation of the elastic element after being compressed under the action of preload relative to the unstressed state. In other words, precompression is a deformation under specific circumstances; appropriate precompression can achieve better shock absorption effect, and precise control of precompression also helps to ensure the tightness of the entire system structure.

[0039] Taking the suspension assembly in a vehicle as an example, in the suspension assembly of a vehicle powertrain, the preload force refers to the force pre-applied to the suspension assembly in the absence of an external load. Under the action of the preload force, the deformation amount of the suspension in the suspension assembly is the preload amount. It should be understood that the preload amount of a suspension assembly including multiple suspensions refers to the sum of the deformation amounts of the multiple suspensions under the action of the preload force, that is, the sum of the preload amounts of the multiple suspensions, that is, the total preload amount.

[0040] Taking the elastic element in the injection mold as an example, the preload force refers to the force applied when the elastic element is compressed to a certain position when the mold is closed; the preload refers to the degree to which the elastic element is compressed when the mold is completely closed. It determines the maximum restoring force that the elastic element can provide, that is, the ability of the elastic element to return to its original shape when the mold is opened.

[0041] In order to optimize the design parameters and improve the safety and reliability of structures containing elastic systems, such as vehicle powertrains and their suspensions, injection molds, etc., it is necessary to conduct working condition analysis based on relevant parameters for structures involving elastic systems, such as powertrains, injection molds, etc., during the design stage. For example, during the design stage of the vehicle powertrain position, it is necessary to first analyze the powertrain containing the suspension components based on mass, inertia, geometric dimensions, and installation position, including geometric collision detection, natural frequency decoupling, etc., to avoid collision or resonance between the designed powertrain and other vehicle components. For another example, during the design stage of the injection mold, it is necessary to first analyze static loads, dynamic loads, etc. based on the ejection mechanism (including ejection force, ejector pin quantity and distribution), mold structure and material, etc., to prevent the inertia force during the opening and closing process of the mold, the impact force during injection, etc. from exceeding the load of the elastic element.

[0042] Since the supporting force or pulling force generated by the elastic system comes from the deformation of the elastic element, the deformation of the elastic element will correspondingly affect the position of the components connected to the elastic element. Therefore, the prerequisite for the calculation and analysis of the working conditions mentioned above is to accurately calculate the preload of the elastic system. The design based on the preload can ensure that when the component connected to the elastic element (the gravity) is loaded into the elastic system, the component connected to the elastic element will neither move horizontally nor rotate, and will remain consistent with the geometric position during design.

[0043] As we know from the previous article, the preload is the deformation amount generated by the elastic system under the action of the preload force. According to Hooke's law, the preload can be indirectly derived from the preload force. Common methods for calculating preload force are based on engineering experience and software iterative calculation methods. The engineering experience method refers to solving the approximate solution of the static equilibrium equations of the elastic system under the action of the preload force based on the principle of static equilibrium based on relevant engineering experience. Among them, the principle of static equilibrium describes the conditions that an object or system must meet when there is no acceleration (that is, it is at rest or in a state of uniform linear motion). The principle of static equilibrium includes the balance of forces (the resultant force of the object in any direction must be zero, that is, the vector sum of all external forces acting on the object is equal to zero), and the corresponding formula is:

[0044] ∑F=0

[0045] Where F represents the vector sum of all external forces acting on the object.

[0046] In addition to the balance of forces, the principle of static balance also includes the balance of moments (or torques) (for any selected reference point, the sum of the moments generated by all forces must also be zero, that is, the object will not rotate around any point), and the corresponding formula is:

[0047] ∑M=0

[0048] Where M is the vector sum of all moments acting on the object.

[0049] Based on the principle of static equilibrium, the static equilibrium equations are:

[0050]

[0051] For example, in a four-point suspension assembly of a vehicle powertrain, each suspension uses Figure 2 The three-way suspension spring shown in the figure can generate elastic forces in the x, y and z directions respectively, but will not generate bending moments. The specific expression of the suspension spring can be:

[0052]

[0053] in, denote the preload forces in the x, y and z directions generated by the i-th suspension spring, respectively. and Respectively represent the stiffness in the corresponding direction, Δx i , Δy i and Δz i are the spring preloads in the corresponding directions respectively.

[0054] According to the above, and based on the principle of static balance, the static balance equations of the four-point suspension components of the vehicle powertrain are obtained as follows:

[0055]

[0056] Among them, mg represents the gravity of the powertrain (m represents the mass of the powertrain, and g represents the acceleration due to gravity); and denote the force arms of the ith suspension spring in the x, y and z directions, respectively, which are related to the geometric position of the suspension spring; are the moments of the ith suspension spring in the x, y and z directions respectively. The other expressions are the same as above and will not be described here.

[0057] From the above formula, we can see that there are 12 unknowns in the system of 6 equations ( and Here i can be 1, 2, 3 and 4), so this system of equations is underdetermined and has countless solutions, which cannot be solved using general methods.

[0058] Based on this, the engineering experience method assumes that among the four-point suspension, only the two front main suspensions (such as Figure 1 The left mount k1 and the right mount k2) bear the weight of the powertrain, and the other two rear mounts (such as Figure 1The left rear suspension k3 and the right rear suspension k4 are only used for limiting (i.e., the latter two suspensions are rear tie rods). Therefore, the effects of the latter two suspensions can be ignored. At this time, the equations are degenerated into a generalized equations. As a method, the Gaussian elimination method can be used to directly solve the equations. After that, the preload force of each suspension in the z direction is fixed, and the tension of the rear tie rod in the x and y directions is added back to the equations. At this time, the above equation is a statically determinate equations with a unique solution. The preload force of the two rear suspensions in the x and y directions can be directly obtained, thereby solving the preload force of the four suspensions in each direction.

[0059] Similarly, when calculating the preload force of the three-point suspension assembly, the preload force of the suspension in the z direction can be obtained based on the balance of gravity, and then the preload force in the z direction is fixed, and then the force balance in the x and y directions is considered to obtain the preload forces of the three suspensions in each direction.

[0060] However, based on the above-mentioned engineering experience method, since some elastic elements in the elastic system (such as the rear suspension) are ignored, the calculated preload force may have a large error, especially for the more important but neglected elastic elements (such as the more important power suspension components of the rear suspension); in addition, the error of the preload force may affect the subsequent mechanical analysis and design optimization of the entire elastic system. It is not difficult to understand that the first thing to be affected is the calculation of the preload amount based on the preload force.

[0061] In addition to the engineering experience method, it is also a common method to calculate the preload force of the elastic system by software iteration. CAE software, as the mother of today's industry, is widely used in engineering, construction, vehicle design and manufacturing, and plays an irreplaceable key role in design, optimization, production and many other aspects. The steps of using the statics module and linear vibration module of CAE software to calculate the preload force include: first, without applying any preload force, directly perform static balance analysis on the elastic system containing the structure connected to the elastic element (such as powertrain, building and industrial equipment, etc.). In this case, the elastic element of the elastic system is deformed and generates corresponding support force due to its own gravity. Then, the force and deformation data obtained from this round of calculation are used as input and substituted into the next round of iterative calculation, and the static balance analysis is performed again to update the preload force. This process is repeated until the deformation of the elastic element in the elastic system is reduced to near zero. At this time, the input data is the preload force of the elastic system.

[0062] Although the above method of calculating the preload force by CAE software iteration has higher accuracy than the engineering experience method (because multiple iterations of simulation are performed, it can more accurately reflect the actual mechanical conditions), it also has obvious disadvantages, including complex and time-consuming operation, requiring the operator to have high CAE software operation skills and elastic system design experience. This means that although the accuracy of the preload force is improved, the implementation process is difficult and the technical requirements for the operator are high, which may not be suitable for all engineering projects, especially when time is tight or technical resources are limited.

[0063] That is to say, both of the above two methods for calculating the preload force cannot simplify the calculation process and reduce the skill threshold of the operator while ensuring the accuracy of the preload force calculation.

[0064] Based on this, the applicant, based on the principle of mechanical minimum, also known as the principle of least action, that is, the physical system always moves along a path that makes the action take an extreme value (usually a minimum value) during the evolution process, concluded that when the preload force of the elastic system takes an extreme value (usually a minimum value), the total deformation variable (total preload) of the elastic system is the smallest. Based on this, the embodiment of the present disclosure proposes a method that can be used to determine the preload of an elastic system. The method can calculate the preload force when the total preload of the elastic system is the smallest when the elastic system connected to related components (such as a powertrain) is in a static equilibrium state (that is, when the related components connected to the elastic system are in a static equilibrium state), and calculate the corresponding preload based on the preload force. That is to say, the embodiment of the present disclosure calculates the preload force when the total preload of the elastic system is the smallest by adding a static balance constraint, and calculates the corresponding preload based on the preload force.

[0065] It should be understood that based on the constraint of the static equilibrium state, the maximum value of the total preload and / or the minimum value of the total preload when the elastic system is in a static equilibrium state can be calculated, and the embodiments of the present disclosure are not limited to this. That is, the embodiments of the present disclosure can also include calculating the preload force and the corresponding preload when the elastic system connected with the relevant components is in a static equilibrium state and the total preload of the elastic system is maximum. Since the calculation of the preload force when the total preload of the elastic system is minimum is more in line with practical engineering applications, the method for determining the preload of the elastic system (when the total preload is minimum) proposed in the embodiments of the present disclosure will be described in detail below.

[0066] In the embodiment of the present disclosure, the elastic system may include one or more elastic elements. In some embodiments, the elastic system may include an elastic element. For example, in the design of a motorcycle, the engine and the frame may be connected by a central fulcrum, and this fulcrum may absorb the vibration of the engine by using elastic elements such as springs, thereby reducing the vibration transmitted to the frame and the body. In other embodiments, the elastic system may include a plurality of elastic elements, for example, the plurality of elastic elements in the elastic system may include a first elastic element and a second elastic element. It should be understood that the first and second elastic elements are merely exemplary and are not a limit to the number of the plurality of elastic elements. For example, the four-point suspension assembly of the powertrain of the vehicle includes four suspensions, that is, four elastic elements, to provide more sophisticated vibration control and stability. In addition, in an elastic system including a plurality of elastic elements, the element material of each elastic element may be the same or different, and the embodiment of the present disclosure does not limit this. For a specific introduction to the elastic element, please refer to the foregoing text, which will not be repeated here.

[0067] Figure 3 FIG. 2 is a flow chart of a method for determining the preload of an elastic system according to an embodiment of the present disclosure. Figure 3 As shown, in step S310, the preload force of each elastic element in one or more elastic elements is determined, and in step S320, the preload amount of each elastic element is determined based on the preload force of each elastic element; wherein the preload force and / or preload amount makes the component connected to the one or more elastic elements in a static equilibrium state, and the total preload amount of the one or more elastic elements corresponding to the preload force is minimized.

[0068] In which, determining the preload force of each elastic element in one or more elastic elements may refer to, when the elastic system includes one elastic element, determining the preload force of the elastic element, and when the elastic system includes multiple elastic elements, determining the preload force of each elastic element in the multiple elastic elements, for example, determining the preload force of the first elastic element and determining the preload force of the second elastic element.

[0069] The preload force of each elastic element may include the preload force of each elastic element in various different directions. In some embodiments, the preload force of each elastic element may include the preload force of each elastic element in the x, y and z directions, where x, y and z represent the dimensions in the three-dimensional space. For example, in a four-point suspension assembly of a vehicle powertrain, the preload force of each elastic element includes the preload force of the four suspensions in the x, y and z directions respectively.

[0070] In the disclosed embodiment, the calculation of the preload force and the preload amount are both based on the calculation of the component connected to the elastic system. It is not difficult to understand that the connection between the component and the elastic system is essentially the connection between the component and each elastic element in the elastic system, that is, the connection with one or more elastic elements in the elastic system. The disclosed embodiment does not limit the type of the component. For example, for a powertrain suspension component of a vehicle, the component can be a powertrain (such as an engine, etc.) connected to a suspension component (i.e., an elastic system).

[0071] The disclosed embodiments do not limit the manner of determining the preload force of each elastic element. As a manner, the first model can be used to determine the preload force of each elastic element. Wherein, the first model can be determined based on one or more mechanical parameters of each elastic element and / or the gravity of the assembly connected to each elastic element, and the relevant mechanical parameters can include preload force, lever arm, and moment. Similar to the preload force of each elastic element, the lever arm of each elastic element can include the lever arm of each elastic element in various different directions, and the moment of each elastic element can include the moment of each elastic element in various directions. In other words, the first model for determining the preload force of each elastic element can be determined based on one or more of the preload force of each elastic element in various different directions, the lever arm of each elastic element in various different directions, the moment of each elastic element in various different directions, and the gravity of the assembly connected to each elastic element.

[0072] Taking the four-point suspension assembly of the powertrain of the vehicle as an example, as a way, the first model can be determined according to the preload forces of the four suspensions in the x, y and z directions. For example, if the preload forces of the four suspensions in the x, y and z directions are known, the gravity of the powertrain and the torque of each elastic element in different directions can be obtained. As another way, the first model can be determined according to the four lever arms suspended in the x, y and z directions. For example, if the lever arms (or torques) of the four suspensions in the x, y and z directions are known, the torques (or lever arms) of each elastic element in different directions, the preload forces and the gravity of the powertrain can be obtained. As another way, the first model can be determined according to the gravity of the powertrain. For example, if the gravity of the powertrain is known, the preload forces, lever arms and torques of the four suspensions in the x, y and z directions can be obtained. It can be seen that the first model can be determined based on the gravity of the powertrain and any one of the preload forces, lever arms and torques of the four suspensions in the x, y and z directions. It is not difficult to understand that the first model can also be determined based on the gravity of the powertrain, and multiple types of preload forces, lever arms, and moments of the four suspensions in the x, y, and z directions. For the sake of simplicity, it will not be elaborated here.

[0073] In the disclosed embodiment, the preload amount of each elastic element can be determined according to the preload force of each elastic element. That is, each elastic element included in the elastic system can determine its own preload amount based on its preload force. In some embodiments, when the elastic system includes an elastic element, the preload amount of the elastic element can be determined based on the preload force of the elastic element, and the preload amount determined at this time is the total preload amount of the elastic system. In some other embodiments, the preload amount of each elastic element determined based on the preload force of each elastic element can be determined based on the preload force of the first elastic element, and the preload amount of the second elastic element can be determined based on the preload force of the second elastic element. For example, in the four-point suspension assembly of the powertrain of the vehicle, the preload amount of the left suspension can be determined based on the preload force of the left suspension, the preload amount of the right suspension can be determined based on the preload force of the right suspension, the preload amount of the left rear suspension can be determined based on the preload force of the left rear suspension, and the preload amount of the right rear suspension can be determined based on the preload force of the right rear suspension.

[0074] In the embodiment of the present disclosure, under the action of the preload force and / or preload of each elastic element, the elastic system is in a static equilibrium state, and the sum of the preloads of one or more elastic elements under the action of the preload force (i.e., the total preload) is the smallest. It should be noted that the minimum total preload corresponding to the preload force mentioned in the embodiment of the present application means that, compared with other preload forces that can make the components connected to one or more elastic elements in a static equilibrium state, the total preload corresponding to the preload force is the smallest, that is, the total preload corresponding to the preload force is not greater than (i.e., less than or equal to) the total preload corresponding to all other preload forces of the elastic system in a static equilibrium state. In other words, the preload force and preload of each elastic element in the elastic system determined by the method of the embodiment of the present disclosure make the components connected to the elastic system in a static equilibrium state, and compared with other preload forces that make the components connected to the elastic system in a static equilibrium state, the total deformation of one or more elastic elements corresponding to the preload force is the smallest.

[0075] Taking the example that the preload force that makes the component connected to the elastic system in a static equilibrium state includes a first preload force, a second preload force and a third preload force, assuming that the total preload of one or more elastic elements corresponding to the first preload force is the first preload, the total preload of one or more elastic elements corresponding to the second preload force is the second preload, the total preload of one or more elastic elements corresponding to the third preload force is the third preload, and the first preload < the second preload < the third preload, then the preload force mentioned in the embodiment of the present application is the first preload force, because the total preload of one or more elastic elements corresponding to the first preload force is the smallest.

[0076] Based on the above example, when the elastic system is a suspension component of a vehicle, the preload force and / or preload amount determined based on the method of the embodiment of the present disclosure can put the powertrain in a static balance state, and the total preload amount of the suspension component corresponding to the preload force is the smallest. That is to say, the preload force and / or preload amount of the suspension component determined based on the method of the embodiment of the present disclosure is the first preload force and / or the first preload amount. In other words, the preload force and / or preload amount determined by the embodiment of the present disclosure can put the powertrain in a static balance state, and compared with other preload forces that can put the powertrain connected to the suspension component in a static balance state, the total preload amount corresponding to the preload force is the smallest.

[0077] It should be understood that for an elastic system including multiple elastic elements, the embodiments of the present disclosure do not limit the specific content of the minimum total deformation amount or the minimum total preload amount of each elastic element mentioned above. In some embodiments, for the convenience of calculation, the minimum total deformation amount or the minimum total preload amount may refer to the minimum sum of the preload amounts of one or more elastic elements in the elastic system. For example, when a powertrain connected to a suspension assembly is in a static equilibrium state, the minimum total deformation amount of the four suspensions means that the sum of the deformation amounts of the four suspensions is the minimum.

[0078] In other embodiments, in order to improve the stability of the components connected to the elastic system and balance the wear of each elastic element, the minimum total deformation or the minimum total preload can also refer to the deformation or preload values ​​of multiple elastic elements in the elastic system being evenly distributed, that is, the fluctuation of the values ​​is not large. For example, when the powertrain connected to the suspension assembly is in a static equilibrium state, the total deformation of the four suspensions is minimized. If there are two or more different preload force distributions of the four suspensions under the premise that the sum of the deformations of the four suspensions is minimized, the deformation with a more even distribution of the deformation values ​​of the four suspensions can be selected.

[0079] It can be seen that, compared with the traditional engineering experience method, the method for determining the preload of the elastic system proposed in the embodiment of the present disclosure can obtain the preload force when the total preload is the smallest by calculating the static equilibrium equation group of the elastic system based on the preload force based on the extreme value calculation method, thereby improving the calculation accuracy; compared with the software iteration method, the calculation method proposed in the present disclosure does not need to go through the complex CAE software operation process, nor does it require rich prior knowledge of engineering personnel, and under the premise of ensuring the calculation accuracy, it does not need multiple iterative calculations, thereby simplifying the difficulty of calculation, reducing the demand for professional knowledge of technicians, and improving the design efficiency of the structural system containing the elastic system. In addition, the existing commercial CAE software does not support the calculation of the preload force when the preload of the elastic system is the minimum value under the static balance constraint in the present disclosure, and currently, the industry including automobile companies uses a semi-precision semi-engineering experience method, or manually uses commercial CAE software for iteration and calculation. Therefore, the method for determining the preload of the elastic system in the embodiment of the present disclosure not only performs well in calculation accuracy, but also shows significant advantages in calculation difficulty.

[0080] The specific form of the first model for determining the preload force of each elastic element in the elastic system in a static equilibrium state is not limited in the embodiments of the present disclosure. In some embodiments, it can be expressed by the following expression:

[0081]

[0082] Wherein, F represents the preload force of each elastic element, M represents the moment of each elastic element, i represents the number of each elastic element, mg represents the weight of the component connected to each elastic element, and λ represents the Lagrange multiplier.

[0083] In addition, Φ is the constraint condition of the first model. Specifically, equation (1) corresponds to the vector sum of all forces acting on the elastic system in a static equilibrium state, that is, the sum of the preload forces in the x, y and z directions generated by one or more elastic elements in the elastic system in a static equilibrium state. Taking the elastic system with four elastic elements as an example, the corresponding equation group is:

[0084]

[0085] The negative sign in -mg indicates the direction of the preload force of the elastic system, that is, the opposite direction of the gravity of the components connected to the elastic system.

[0086] Formula (2) in Φ corresponds to the vector sum of all moments generated by the preload force of the elastic system in static equilibrium, that is, the equation group of the sum of all moments generated by the sum of the preload force of one or more elastic elements in the elastic system in static equilibrium in the x, y and z directions. Taking the elastic system with four elastic elements as an example, the corresponding equation group is:

[0087]

[0088] It can be seen that taking Φ including equations (1) and (2) as a constraint condition means taking the elastic system in a static equilibrium state as a constraint condition.

[0089] In the above expression, It represents the square norm of the preload force of each elastic element, which can be used to represent the actual size of the preload force (only considering the value of the force, not the direction of the force). As the objective function to optimize, that is, to minimize That is, the extreme value of the preload force of each elastic element is obtained (considering the actual engineering application, the extreme value here can be understood as the minimum value), and then, in the embodiment of the present disclosure, the minimum preload amount can be determined based on the minimum value F.

[0090] In the above formula, the method used to deal with the constraint problem is the Lagrange multiplier method. The Lagrange multiplier method can incorporate the constraint conditions into the objective function by introducing the Lagrange multiplier λ, and the above formula can also be transformed into:

[0091]

[0092] The above formula is the expression of Lagrangian function, where: is the objective function, and Φλ is the Lagrange multiplier term of the constraint condition.

[0093] By solving the extreme value of the Lagrange multiplier, that is, solving and The minimum value of F that satisfies the constraints can be solved. That is, the minimum value of each elastic element that satisfies the elastic system in static equilibrium can be obtained.

[0094] The above expression essentially adds constraints to make the solutions of the preload force corresponding to the elastic system fewer or unique, so that the preload force corresponding to the elastic system can be simply solved. It not only solves the uncertainty in the original problem, but also provides a solution to obtain a better solution, that is, to minimize the total preload of the elastic system, which is also closest to the actual preload.

[0095] In the disclosed embodiment, there is no limitation on the solution method of the equation group corresponding to the above expression. As a method, Newton's iteration method can be used for solution, that is, by successively approximating the roots of the nonlinear equation group, gradually converging to the exact solution. As a further method, Newton's iteration method can be implemented through an open source mathematical library or self-coded and the equation group corresponding to the above expression can be solved. Optionally, the calculation can be completed by related functions provided by open source mathematical libraries such as Scientific Python, Symbolic Python and GNU Octave, thereby simplifying the calculation process. It can be seen that the equation group corresponding to the above expression can automatically give the value of the preload of the elastic element without human intervention.

[0096] After calculating the preload force of each elastic element in the elastic system, it is necessary to further calculate the preload amount of each elastic element. The traditional method of calculating the preload amount includes the linearization assumption method, that is, assuming that within the range corresponding to the preload force, the relationship between the deformation and force of the elastic element in the elastic system is linear, and the deformation-force curve is a straight line, that is, the stiffness of the elastic element is a fixed value.

[0097] However, the method based on linear assumption has significant limitations and large errors when dealing with certain specific application scenarios. For example, in the four-point suspension assembly of the powertrain, when the stiffness of the rear tie rod (i.e., the left rear suspension and the right rear suspension) is small, its deformation will be large after being subjected to external force, and then the rear tie rod will quickly enter the nonlinear working stage (the linear working stage means that the force and deformation follow Hooke's law in this stage and are proportional, that is, the stiffness of the suspension is a fixed value). At this time, the error of the preload calculated by the method based on the linear assumption is large. For another example, under large loads or large deformations, even a suspension with a large stiffness (in the linear working stage) will show obvious nonlinear characteristics. For example, some suspension points may show linear stiffness under low loads, but the stiffness will increase significantly under high loads, resulting in the deformation-force curve no longer being a straight line.

[0098] Based on this, the disclosed embodiment proposes a method for determining the preload amount of each elastic element based on the preload force of each elastic element in the elastic system and a first curve. Among them, the first curve can be used to indicate the stiffness of each elastic element. Specifically, the first curve can describe the stiffness of the elastic element under different deformation amounts. Compared with the linear assumption of the stiffness of traditional elastic elements, the stiffness simulation based on the first curve is more in line with the actual stiffness change of the elastic element, thereby reducing the error of the preload amount; in addition, the determination of the preload amount based on the first curve does not require further calculations such as programming, which also simplifies the difficulty of calculating the preload amount.

[0099] The embodiment of the present disclosure does not limit the method for determining the first curve. As one method, the first curve can be determined based on the spline interpolation method. The spline interpolation method is a commonly used numerical analysis technique for smooth interpolation between a given set of data points. The spline interpolation method constructs piecewise polynomial functions (i.e., spline functions) so that these functions are smoothly connected at the data points, thereby generating a smooth curve or surface in the entire interval.

[0100] In some embodiments, the deformation amount of each elastic element in the elastic system under different loads can be tested by an actual loading test, so as to simulate the first curve; the actual test method can directly obtain the preload force of the actual elastic element and the corresponding preload amount, and takes into account the nonlinear characteristics of the elastic element. In other embodiments, each elastic element in the elastic system can be modeled and simulated using Finite Element Analysis (FEA) software to obtain the preload force and preload amount curve of the elastic element; this method takes into account factors such as the nonlinearity of the elastic element material and geometric nonlinearity, and is suitable for complex elastic element structures. In some other implementations, experimental tests and numerical simulations can be combined to calibrate the numerical model using experimental data to improve the accuracy of the simulation results.

[0101] Figure 4 A possible step of obtaining the preload amount of each elastic element based on the first curve and the preload force of each elastic element is shown. It should be understood that Figure 4 This is merely exemplary and not intended to limit the process of determining the preload amount based on the preload force of each elastic element and the first curve. Figure 4 As shown, in step S410, all intervals of the first curve are traversed to determine the intervals in which the preload force of each elastic element may exist. In step S420, one or more candidate preload amounts corresponding to the preload force of each elastic element are determined within the possible intervals; in step S430, the required preload amount is selected from the one or more candidate preload amounts as the preload amount of each elastic element.

[0102] In the embodiments of the present disclosure, the type of spline interpolation method used to determine the first curve is not limited. In some embodiments, the first curve can be determined using quadratic spline interpolation (QSI), which uses a quadratic polynomial for interpolation in each interval. Using QSI can ensure that the first curve is smooth within the interval.

[0103] In some other embodiments, the first curve can be determined using cubic spline interpolation (CSI). CSI uses a cubic polynomial for interpolation in each interval and is the most common spline interpolation method for simulating nonlinearity. The first curve determined using CSI is smooth, and the derivative is continuous at the data point, which is suitable for applications with high smoothness requirements. The first curve determined based on CSI is in the interval [x i , x i+1 ], the relationship between the force F(x) and the deformation variable x is:

[0104] F(x)=ax 3 +bx 2 +cx+d,x∈(x i , x i+1 )

[0105] Among them, a, b, c, d are constant coefficients, which can be determined when the CSI curve is obtained by methods such as actual loading tests, FEA software, and a combination of experimental tests and numerical simulations.

[0106] Since the first curve determined based on CSI is monotonic in each interval and its derivative is continuous, the possible intervals and the relationship between the corresponding preload force and deformation amount can be quickly determined based on the preload force of each elastic element. Figure 5 The figure shows a typical stiffness curve of the suspension spring in the x-direction in the suspension assembly of the vehicle suspension powertrain. Based on the monotonicity of the function (curve) in each interval, when the preload force of the elastic element is known, the interval where the preload force is located and the stiffness change of the suspension spring in this interval can be quickly determined.

[0107] As a method, the Cardan formula can be used to solve one or more candidate preloads corresponding to the elastic element in the possible interval, that is, the Cardan formula is used to solve the roots of the cubic equation corresponding to the interval where the preload force is located, which are:

[0108]

[0109] in,

[0110] Among the roots of the equation obtained based on the above formula (i.e., candidate preloads, i.e., x1, x2, and x3), the preloads that meet the requirements are screened out according to the actual working conditions. It should be understood that in actual working conditions, affected by factors such as changes in system parameters, dynamic characteristics, nonlinear effects, and design variables, the preloads that meet the requirements, i.e., the roots of the equations, are usually not constants, but change with changes in these factors. Therefore, these changes need to be considered in engineering analysis to ensure the reliability and performance of the design.

[0111] For ease of understanding, the following describes in detail a method for determining the preload of an elastic system based on the proposed embodiment of the present disclosure, taking a four-point suspension assembly of a vehicle's powertrain (where four suspensions all use three-way suspension springs) as an example.

[0112] For the static balance equation of the four-point suspension assembly of the powertrain, the minimum algorithm is introduced, that is, the static balance equation is used as a constraint condition to calculate the preload force of the four suspensions when the total preload is the smallest. In other words, the preload force calculated by this method is the smallest when the total preload of the four suspensions satisfies the static balance equation. Based on this, the first model is constructed as follows:

[0113]

[0114] Among them, F i represents the preload force of the ith suspension spring, M i represents the torque of the ith suspension spring, mg represents the weight of the powertrain connected to the suspension assembly, and λ represents the Lagrange multiplier.

[0115] Among them, formula (1) is the optimization equation set based on the minimum action principle equation, and formula (2) converts the static balance equation of the suspension component into a matrix form.

[0116] Formula (1) is a nonlinear equation group, which can be solved using the Newton iteration method. More specifically, the calculation of the preload force can be automatically realized by using relevant open source databases or self-compiled codes.

[0117] After the suspension preload force is obtained based on the Newton iteration method, the cubic spline interpolation method is used to reversely solve the suspension preload. Specifically, based on the experimental test and numerical simulation, the first curves corresponding to the four suspensions in the x, y and z directions, namely the stiffness curves, are determined. First, all possible intervals under the suspension preload force are traversed to obtain the expression of the stiffness curve:

[0118] F(x)=ax 3 +bx 2 +cx+d,x∈(x i , x i+1 )

[0119] Secondly, the Kaltan formula is used to find the root according to the obtained stiffness curve expression;

[0120]

[0121] in,

[0122] After obtaining one or more of the possible preloads, ie, x1, x2, and x3, the preload that meets the requirements is screened out according to the actual working conditions. For example, the constant root may be excluded to obtain the preload of the suspension assembly that meets the working conditions.

[0123] The method embodiment of the present disclosure is described in detail above, and the device embodiment of the present disclosure is described in detail below. It should be understood that the description of the device embodiment corresponds to the description of the method embodiment, so what is not described in detail can be referred to in the previous method embodiment.

[0124] like Figure 6 , which is a schematic diagram of a device for determining the preload of an elastic system according to an embodiment of the present disclosure. The elastic system of the device 600 includes one or more elastic elements, such as Figure 6 As shown, the device 600 may include a first determination module 610, which may be used to determine the preload force of each elastic element in one or more elastic elements; the device 600 may also include a second determination module 620, which may be used to determine the preload amount of each elastic element based on the preload force of each elastic element. The preload force and / or preload amount make the components connected to the one or more elastic elements in a static equilibrium state, and the total preload amount of the one or more elastic elements corresponding to the preload force is the smallest.

[0125] The embodiment of the present disclosure further provides an elastic system, which includes one or more elastic elements, and the preload of the one or more elastic elements is determined according to any method in the method embodiments mentioned above.

[0126] The disclosed embodiments also provide a suspension assembly, which can be used to connect a powertrain of a vehicle to a suspension of the vehicle. The suspension assembly includes one or more elastic elements, and the preload of the one or more elastic elements is determined according to any of the methods in the method embodiments mentioned above.

[0127] like Figure 7 As shown, the embodiment of the present disclosure also provides a device for determining the preload amount of the elastic system, such as Figure 7 As shown, the device 700 for determining the preload of an elastic system includes a memory 710 and a processor 720, wherein the memory 710 stores a computer program that can be executed on the processor 720, and when the computer program is executed by the processor 720, the steps of the method for determining the preload of an elastic system in any of the method embodiments mentioned above are implemented.

[0128] It should be understood that in the embodiments of the present disclosure, "B corresponding to A" means that B is associated with A, and B can be determined according to A. However, it should also be understood that determining B according to A does not mean determining B only according to A, and B can also be determined according to A and / or other information.

[0129] It should be understood that the term "and / or" in this article is only a description of the association relationship of the associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0130] It should be understood that in the various embodiments of the present disclosure, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present disclosure.

[0131] In the several embodiments provided in the present disclosure, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0132] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0133] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0134] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (digital subscriber line, DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that can be read by a computer or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (eg, a floppy disk, a hard disk, a magnetic tape), an optical medium (eg, a digital video disc (DVD)), or a semiconductor medium (eg, a solid state disk (SSD)).

[0135] The above is only a specific embodiment of the present disclosure, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present disclosure, which should be included in the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be based on the protection scope of the claims.

Claims

1. A method for determining the preload of an elastic system, characterized in that: The elastic system comprises one or more elastic elements, and the method comprises: determining a preload force of each of the one or more elastic elements; and Determining a preload amount of each elastic element based on the preload force of each elastic element; The preload force and / or the preload amount make the components connected to the one or more elastic elements in a static equilibrium state, and the total preload amount of the one or more elastic elements corresponding to the preload force is minimal.

2. The method according to claim 1, characterized in that The preload force of each elastic element is determined by a first model, and the first model is determined based on one or more of the following variables: the preload force of the one or more elastic elements in different directions; The force arms of the one or more elastic elements in different directions; the moments of the one or more elastic elements in different directions; The weight of the components connected to the one or more elastic elements.

3. The method according to claim 2, characterized in that The first model is represented by the following expression: Among them, F i represents the preload force of the i-th elastic element, M i represents the moment of the i-th elastic element, mg represents the gravity of the component connected to the one or more elastic elements, and λ represents the Lagrange multiplier.

4. The method according to any one of claims 1 to 3, characterized in that Determining the preload amount of each elastic element based on the preload force of each elastic element includes: Determining a preload amount of each elastic element based on the preload force of each elastic element and the first curve; The first curve is used to indicate the stiffness of each elastic element.

5. The method according to claim 4, characterized in that The first curve is determined based on a spline interpolation method, and the preload amount of each elastic element is determined based on the preload force of each elastic element and the first curve, including: Traversing all intervals of the first curve to determine an interval in which the preload force of each elastic element may exist; Determine one or more candidate preload amounts corresponding to the preload force of each elastic element within the possible existing interval; According to actual working conditions, a required pre-compression amount is selected from the one or more candidate pre-compression amounts as the pre-compression amount of each elastic element.

6. The method according to claim 5, characterized in that The spline interpolation method includes a cubic spline interpolation method.

7. The method according to any one of claims 1 to 3, characterized in that The elastic system is a suspension component, which is used to connect the powertrain of the vehicle to the suspension of the vehicle, and the preload force and / or the preload amount make the powertrain in a static balance state.

8. A device for determining the preload of an elastic system, characterized in that The elastic system comprises one or more elastic elements, and the device comprises: A first determination module, configured to determine a preload force of each of the one or more elastic elements; and A second determination module, configured to determine a preload amount of each elastic element based on a preload force of each elastic element; The preload force and / or the preload amount make the components connected to the one or more elastic elements in a static equilibrium state, and the total preload amount of the one or more elastic elements corresponding to the preload force is minimal.

9. An elastic system, characterized in that: The elastic system comprises one or more elastic elements, and the preload of the one or more elastic elements is determined according to the method according to any one of claims 1-7.

10. A suspension assembly, characterized in that: The suspension assembly is used to connect a powertrain of a vehicle to a suspension of the vehicle, and the suspension assembly includes one or more elastic elements, and the preload of the one or more elastic elements is determined according to the method described in any one of claims 1-7.

11. A device for determining the preload of an elastic system, characterized in that The method comprises a memory and a processor, wherein the memory stores a computer program executable on the processor, and when the computer program is executed by the processor, the steps of the method for determining the preload of an elastic system as claimed in any one of claims 1 to 7 are implemented.

Images