Limited slip differential

By installing planetary gears inside the housing in the differential and using the friction circle theory to set the self-locking threshold, the problem of uneven torque distribution when one wheel slips in the differential is solved, achieving higher traction performance and structural stability, and reducing costs.

CN122447469APending Publication Date: 2026-07-24朱红臣
View PDF 2 Cites 0 Cited by

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
朱红臣
Filing Date
2026-06-15
Publication Date
2026-07-24

AI Technical Summary

Technical Problem

Existing differentials suffer from uneven torque distribution when one wheel slips, resulting in insufficient driving force for the wheel on the side with high traction. They also have problems such as complex structure, high cost, or reduced limited-slip performance.

Method used

Design a limited-slip differential that uses planetary gears installed inside a housing. By setting a limiting part and a support part, the axial movement of the planetary gears is restricted. The self-locking threshold is set using the friction circle theory to achieve uniform torque distribution and self-locking function.

Benefits of technology

It improves the vehicle's traction performance under different road conditions, reduces the overall size and manufacturing cost of the differential, and enhances structural stability and limited-slip performance.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN122447469A_ABST
    Figure CN122447469A_ABST
Patent Text Reader

Abstract

The application discloses a limited slip differential. The limited slip differential comprises a housing capable of rotating around a main axis, a first half axle gear and a second half axle gear both rotatably installed on the housing and both having an axis coinciding with the main axis, and a planetary gear arranged between the first half axle gear and the second half axle gear and engaging with both. The housing is provided with a mounting cavity for mounting the planetary gear, and the mounting cavity has a support part. The planetary gear has a planetary gear shaft, a side surface of the planetary gear shaft being rotatably supported on the support part, and an axis of the planetary gear being perpendicular to the main axis. The planetary gear is configured so that a ratio of a force arm l of an acting force F of any one of the first half axle gear and the second half axle gear on the planetary gear to a fitting radius r between the side surface and the support part is less than or equal to a self-locking threshold. The limited slip differential realizes limited slip by using a self-locking principle of a rotating pair.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] This invention relates to a differential, and more particularly to a limited-slip differential. Background Technology

[0002] An open differential allows the left and right wheels to rotate at different speeds to meet the speed difference requirements when the vehicle is turning. However, its inherent drawback is that when one wheel slips, the differential will distribute most of the torque to the slipping side, resulting in insufficient driving force on the wheel with high traction and limiting the vehicle's ability to get out of trouble.

[0003] The Torsen differential employs a worm gear drive structure, utilizing the unidirectional self-locking characteristic of the worm gear to achieve limited slip function. This means the worm can drive the worm wheel to rotate, but the worm wheel cannot drive the worm in the opposite direction. While allowing for normal driving speed differences, this differential, based on its self-locking characteristic, can transfer torque to the side with high traction when the traction of one wheel decreases, thereby improving traction performance. However, the Torsen differential has a precise and complex structure, resulting in high manufacturing costs.

[0004] Patent application No. 201610339694.0 discloses a variable-pitch limited-slip differential and its design method. This variable-pitch limited-slip differential features a friction ring extending from the planetary gear body outwards from the gear carrier. The gear carrier has a friction boss at a corresponding position to the friction ring. When the planetary gear is subjected to radial force, the friction ring and friction boss abut against each other, causing a shift in the force transmission point of the planetary gear, thus achieving the limited-slip function of the differential. However, the extension of the friction ring outwards from the gear carrier makes the planetary gear susceptible to centrifugal force and prone to detachment, while also increasing the overall size of the differential. Furthermore, the externally mounted planetary gear requires a limiting shaft for radial support. The radius of this limiting shaft is smaller than the root circle radius of the planetary gear and significantly smaller than the radius of the friction ring, resulting in a decrease in limited-slip performance.

[0005] Furthermore, in mechanical principles, the "friction circle" is a classic theoretical model for analyzing friction in rotating pairs. In this model, when the net external force on the journal in the radial plane can be simplified to a single external force (i.e., a "single force"), it will compress the bearing bore wall, and the bearing will generate a total reaction force that balances this force on the journal. This total reaction force is the resultant force of the normal support force and the friction force, and its effect can be equivalent to a frictional torque that opposes the rotation of the journal. The friction circle theory simplifies this complex force system into a clear geometric constraint—assuming that the line of action of this total reaction force is always tangent to a virtual circle (called the "friction circle") with the center of the rotating pair as its center and a radius of ρ. The radius ρ of the friction circle is calculated by the formula ρ = f · r, where r is the journal radius and f is the equivalent friction coefficient (its value is greater than the material sliding friction coefficient μ; for point contact or unbroken bearings, f ≈ (π / 2)μ is usually taken to equivalently characterize the comprehensive effect of distributed friction).

[0006] In determining the self-locking phenomenon of rotating pairs, the friction circle theory provides clear geometric and quantitative criteria. The critical state of self-locking is when the line of action of the net external force is tangent to the friction circle, i.e., the lever arm l... 合 It is equal to the radius ρ of the friction circle. The self-locking condition derived from this is: the line of action of the resultant external force is tangent to or intersects the friction circle, and its mathematical criterion is l. 合 ≤ f · r (where the lever arm l) 合 (This is the perpendicular distance from the line of action of the resultant external force to the center of the revolute joint). Conversely, the condition for the mechanism to transmit power normally is l. 合 > f ·r.

[0007] In the evaluation of transmission efficiency, this theory reveals the lever arm l of the net external force. 合 The qualitative relationship between transmission efficiency η and the actual force arm l. For a single rotating pair, its transmission efficiency η can be expressed as the ratio of output work to input work. Considering the friction circle, the transmission efficiency η varies with the actual force arm l. 合 The decrease is due to the reduction of the lever arm l. 合 As the friction circle radius ρ approaches, the efficiency η approaches zero, at which point the mechanism tends to self-lock; when the self-locking condition l is met... 合 When ≤ f · r, the efficiency η ≤ 0, which confirms the occurrence of self-locking from an energy point of view. That is, the input work cannot overcome frictional dissipation and cannot output effective work.

[0008] The applicant's patent application No. 202610462605.5 provides a self-locking transmission mechanism and its self-locking method, which realizes mechanical self-locking transmission based on the friction circle theory. In Embodiments 1 and 2 of paragraphs 0033-0043 of the specification of this application, a self-locking transmission mechanism is provided that transmits a single force through a force-transmitting side. The self-locking transmission mechanism includes a support member and a rotating body rotatably mounted to each other, with a contact radius r between the rotating body and the support member. It also includes a single-force member that contacts and transmits power synchronously with the rotating body through a force-transmitting side, and the force F exerted by the single-force member on the rotating body can be simplified to a single force. The rotating body is configured such that the ratio l / r of the lever arm l of the force F exerted by the single-force member on the rotating body to the corresponding contact radius r is less than or equal to a self-locking threshold, thereby giving the self-locking transmission mechanism self-locking characteristics. Furthermore, when the self-locking threshold is set to the equivalent friction coefficient f between the rotating body and the supporting member, the self-locking condition l ≤ f · r of the friction circle theory is satisfied.

[0009] In addition to transmitting single force through the force transmission side, in Embodiment 4 of paragraphs 0048-0050 of the specification of this application, a self-locking transmission mechanism that transmits single force through gear meshing is also proposed. Summary of the Invention

[0010] This invention provides a limited-slip differential, which aims to at least partially solve the above-mentioned technical problems in the prior art.

[0011] To achieve the above objectives, the present invention provides a limited-slip differential, comprising a housing, a first half-shaft gear, a second half-shaft gear, and planetary gears, wherein: The housing is configured to rotate about a main axis; Both the first half-shaft gear and the second half-shaft gear are rotatably mounted on the housing, and their axes coincide with the main axis. The planetary gear is disposed between the first half-shaft gear and the second half-shaft gear, and the planetary gear meshes with both the first half-shaft gear and the second half-shaft gear simultaneously; The housing is provided with a mounting cavity for mounting the planetary gear, and the mounting cavity has a support portion for supporting the planetary gear; The planetary gear has a planetary gear shaft and planetary gear teeth. The side of the planetary gear shaft is rotatably supported on the support, and the axis of the planetary gear is perpendicular to the main axis. The planetary gear is configured such that, within the radial plane of the planetary gear, the ratio l / r of the lever arm l of the force F exerted by either the first half-shaft gear or the second half-shaft gear on the planetary gear to the engagement radius r between the side surface and the support is less than or equal to a self-locking threshold.

[0012] In addition, the limited-slip differential according to embodiments of the present invention may also have the following additional technical features.

[0013] According to some embodiments of the present invention, the housing is provided with a limiting part for restricting the movement of the planetary gear along its axial direction, and the end of the planetary gear away from the planetary gear teeth is provided with a limiting engagement part that abuts against the limiting part.

[0014] Furthermore, the limiting part and / or the limiting mating part are provided with raised curved surfaces, so that the housing limits the planetary gear through point contact to reduce friction.

[0015] According to some embodiments of the present invention, the housing comprises a first housing and a second housing connected to each other, wherein: The mounting cavity is disposed on the first housing and has a radial opening, through which the planetary gear is inserted into the mounting cavity; The limiting part is disposed on the second housing, and the limiting part abuts against the limiting mating part at the radial opening.

[0016] Furthermore, both the first half-shaft gear and the second half-shaft gear can be rotatably mounted on the first housing, and the first housing is an integrally formed structure.

[0017] Furthermore, the first housing is configured such that the first half-shaft gear and the second half-shaft gear can be inserted into the first housing through the radial opening.

[0018] According to some embodiments of the present invention, the edge of the planetary gear shaft extends into an annular flange toward one side of the planetary gear teeth.

[0019] Furthermore, the side surface includes an outer side surface and an inner side surface, wherein the outer side surface is the outer peripheral surface of the planetary gear shaft, and the inner side surface is the inner wall of the flange; the support portion includes an inner support portion and an outer support portion, wherein the inner support portion supports and cooperates with the outer side surface, and the outer support portion supports and cooperates with the inner side surface; the space between the inner support portion and the outer support portion is used to accommodate the flange.

[0020] According to some embodiments of the present invention, the planetary gear is configured such that its addendum circle radius r a The ratio r to the mating radius ra / r is less than or equal to the self-locking threshold.

[0021] According to some embodiments of the present invention, the self-locking threshold is set to the equivalent friction coefficient f between the side and the corresponding support, so as to satisfy the self-locking condition l ≤ f · r in the friction circle theory.

[0022] Beneficial effects: 1. The planetary gears of the limited-slip differential provided according to some embodiments of the present invention are installed inside the housing, resulting in a more robust structure; 2. In some embodiments of the present invention, instead of using a limiting shaft passing through the planetary gear to limit the planetary gear, a housing is used to limit the planetary gear to move along its axial direction, which can avoid the problem of reduced slip performance caused by the radial support force of the limiting shaft. 3. In some embodiments of the present invention, the planetary gear extends a flange axially in the direction of its teeth, which can shorten the axial length of the planetary gear and thus reduce the size of the differential; 4. In some embodiments of the present invention, only the outer side of the planetary gear shaft is rotatably supported on the housing, which has a larger engagement radius and is easier to achieve limited slip compared to the technical solution of using the inner side to rotatably support the housing; 5. In some embodiments of the present invention, planetary gears and half-shaft gears are installed from radial openings, eliminating the need for end caps and resulting in higher structural strength of the housing. Attached Figure Description

[0023] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a cross-sectional view of a limited-slip differential according to an embodiment of the present invention; Figure 2 This is an exploded view of the limited-slip differential according to an embodiment of the present invention; Figure 3 This is a top view of the first housing in a limited-slip differential according to an embodiment of the present invention; Figure 4 This is a cross-sectional view of the first housing in a limited-slip differential according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of the second housing in a limited-slip differential according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the planetary gears in a limited-slip differential according to an embodiment of the present invention.

[0025] Figure label: 1. Shell; 11. First shell; 12. Second shell; 2. Installation cavity; 3. Support section; 31. Inner support section; 32. Outer support section; 4. Limiting part; 51. First half-shaft gear; 52. Second half-shaft gear; 6. Planetary gear; 61. Planetary gear shaft; 62. Planetary gear teeth; 7. Side view; 71. Outer side view; 72. Inner side view; 8. Flange; 9. Limiting and fitting parts. Detailed Implementation

[0026] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0027] like Figures 1-6 As shown, an embodiment of the present invention provides a limited-slip differential, comprising a housing 1, a first half-shaft gear 51, a second half-shaft gear 52, and a planetary gear 6; wherein, the housing 1 is configured to rotate about a main axis, and the housing 1 includes a first housing 11 and a second housing 12 connected to each other; the first half-shaft gear 51 and the second half-shaft gear 52 are rotatably mounted on the first housing 11, and their axes coincide with the main axis; the planetary gear 6 is disposed between the first half-shaft gear 51 and the second half-shaft gear 52, and the planetary gear 6 meshes with both the first half-shaft gear 51 and the second half-shaft gear 52 simultaneously.

[0028] like Figure 3 , Figure 4 As shown, in this embodiment, the first housing 11 is provided with a mounting cavity 2 for mounting the planetary gear 6. The mounting cavity 2 has a support portion 3 for supporting the planetary gear 6, and the mounting cavity 2 has a radial opening. The planetary gear 6 is inserted into the mounting cavity 2 through the radial opening. Figure 6 As shown, the planetary gear 6 has a planetary gear shaft 61 and planetary gear teeth 62. The side 7 of the planetary gear shaft 61 is rotatably supported on the support part 3, and the axis of the planetary gear 6 is perpendicular to the main axis.

[0029] like Figure 2 , Figure 5As shown, in this embodiment, the second housing 12 is provided with a limiting part 4, which is used to restrict the movement of the planetary gear 6 along its axial direction. The end of the planetary gear 6 away from the planetary gear teeth 62 is provided with a limiting engagement part 9 that abuts against the limiting part 4, and the limiting part 4 and the limiting engagement part 9 abut against each other at the radial opening. Figure 1 , Figure 2 and Figure 5 As shown, in this embodiment, the limiting part 4 is set as a plane, and the limiting mating part 9 is set as a raised curved surface, so that the second housing 12 limits the planetary gear 6 by point contact to reduce friction; in other embodiments, the limiting part 4 can also be set as a raised curved surface.

[0030] like Figures 1-4 As shown, in this embodiment, the first housing 11 is an integrally formed structure, and the first housing 11 is configured such that the first half-shaft gear 51 and the second half-shaft gear 52 can be inserted into the first housing 11 through the radial opening.

[0031] like Figure 1 and Figure 2 As shown, in this embodiment, the second housing 12 is sleeved on the first housing 11; in other embodiments, the second housing 12 can be set as a side cover parallel to the main axis and fixedly connected to the first housing 11 by bolts.

[0032] like Figure 6 As shown, in this embodiment, the side surface 7 of the planetary gear shaft 61 includes an outer side surface 71 and an inner side surface 72, wherein the outer side surface 71 is the outer peripheral surface of the planetary gear shaft 61; the edge of the planetary gear shaft 61 extends an annular flange 8 towards the planetary gear teeth 62, and the inner side surface 72 is the inner wall of the flange 8. Figure 3 , Figure 4 As shown, the support portion 3 includes an inner support portion 31 and an outer support portion 32, wherein the inner support portion 31 supports and cooperates with the outer side surface 71, and the outer support portion 32 supports and cooperates with the inner side surface 72; the space between the inner support portion 31 and the outer support portion 32 is used to accommodate the flange 8.

[0033] In this embodiment, by increasing the axial length of the outer side surface 71 by setting the flange 8, the axial length of the planetary gear 6 can be made shorter, thereby reducing the size of the limited-slip differential; in addition, supporting the outer side surface 71 and the inner side surface 72 on the first housing 11 at the same time can improve the overall structural stability.

[0034] According to some embodiments of the present invention, during the process of the limited-slip differential distributing power to the first half-shaft gear 51 and / or the second half-shaft gear 52, the first half-shaft gear 51 and / or the second half-shaft gear 52 generate a reaction force on the planetary gear 6; in the radial plane of the planetary gear 6, the force F exerted by either the first half-shaft gear 51 or the second half-shaft gear 52 on the planetary gear 6 can be simplified to a single external force; the planetary gear 6 is configured such that the ratio l / r of the lever arm l of the force F to the engagement radius r between the side surface 7 and the corresponding support 3 is less than or equal to a self-locking threshold. The magnitude of the lever arm l of the force F dynamically changes with the rotation angle of the planetary gear 6, by limiting the addendum circle radius r of the planetary gear 6. a The maximum value of the lever arm l can be limited, thereby allowing the planetary gear 6 to be configured such that its tip circle radius r a The ratio r to the mating radius r a / r is less than or equal to the self-locking threshold to achieve self-locking.

[0035] According to some embodiments of the present invention, the self-locking threshold can be set to the equivalent friction coefficient f between the side surface 7 and the corresponding support portion 3, so as to satisfy the self-locking condition l ≤ f · r in the friction circle theory.

[0036] The working process of the limited-slip differential according to an embodiment of the present invention will be briefly described below.

[0037] Taking the use of the limited-slip differential in an automobile wheel differential as an example, the housing 1 constitutes the input end of the limited-slip differential, which is used to receive the power transmitted by the engine; the first half-shaft gear 51 and the second half-shaft gear 52 constitute the two output ends of the limited-slip differential, and the two are respectively connected to the left wheel and the right wheel.

[0038] When the vehicle is traveling straight or one wheel slips, the torque generated by the force F exerted by the first half-shaft gear 51 and the second half-shaft gear 52 on the planetary gear 6 is in opposite directions, or only one of the first half-shaft gear 51 and the second half-shaft gear 52 exerts a force F greater than 0 on the planetary gear 6; the resultant force F of the forces F exerted by the first half-shaft gear 51 and the second half-shaft gear 52 on the planetary gear 6 is... 合 lever arm l 合 Satisfying relation l 合 ≤ l; The limited-slip differential distributes the power input from the housing 1 to the first half-shaft gear 51 and / or the second half-shaft gear 52, and drives the vehicle forward.

[0039] When the vehicle turns, the torque generated by the force F exerted by the first half-shaft gear 51 and the second half-shaft gear 52 on the planetary gear 6 is in the same direction; the force F exerted by the first half-shaft gear 51 and the second half-shaft gear 52 on the planetary gear 6 forms a couple, or the resultant force F of the force F exerted by the first half-shaft gear 51 and the second half-shaft gear 52 on the planetary gear 6 is... 合 It can be simplified to a single external force and l 合 > l; The limited-slip differential enters the differential transmission state.

[0040] It should be noted that in the description of this invention, the term "shell" should be interpreted broadly, and its shape is not limited to traditional shells and cavities; for example, it can be a non-enclosed support structure.

[0041] In this invention, the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0042] In this invention, the terms "first," "second," "third," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first," "second," "third," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0043] In this invention, unless otherwise explicitly specified and limited, terms such as "installation," "connection," "linking," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a connection that allows communication between them; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0044] In this invention, terms such as “component,” “part,” and “section” should be interpreted broadly. For example, they can refer to a single element, multiple elements fixedly connected together, or a mechanism composed of multiple connected elements.

[0045] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A limited-slip differential, characterized in that, It includes a housing, a first half-shaft gear, a second half-shaft gear, and planetary gears, wherein: The housing is configured to rotate about a main axis; Both the first half-shaft gear and the second half-shaft gear are rotatably mounted on the housing, and their axes coincide with the main axis. The planetary gear is disposed between the first half-shaft gear and the second half-shaft gear, and the planetary gear meshes with both the first half-shaft gear and the second half-shaft gear simultaneously; The housing is provided with a mounting cavity for mounting the planetary gear, and the mounting cavity has a support portion for supporting the planetary gear; The planetary gear has a planetary gear shaft and planetary gear teeth. The side of the planetary gear shaft is rotatably supported on the support, and the axis of the planetary gear is perpendicular to the main axis. The planetary gear is configured such that, within the radial plane of the planetary gear, the ratio l / r of the lever arm l of the force F exerted by either the first half-shaft gear or the second half-shaft gear on the planetary gear to the engagement radius r between the side surface and the support is less than or equal to a self-locking threshold.

2. The limited-slip differential according to claim 1, characterized in that, The housing is provided with a limiting part, which is used to restrict the movement of the planetary gear along its axial direction. The end of the planetary gear away from the planetary gear teeth is provided with a limiting engagement part that abuts against the limiting part.

3. The limited-slip differential according to claim 2, characterized in that, The limiting part and / or the limiting mating part are provided with raised curved surfaces, so that the housing limits the planetary gear by point contact, thereby reducing friction.

4. The limited-slip differential according to claim 2, characterized in that, The housing comprises a first housing and a second housing connected to each other, wherein: The mounting cavity is disposed on the first housing and has a radial opening, through which the planetary gear is inserted into the mounting cavity; The limiting part is disposed on the second housing, and the limiting part abuts against the limiting mating part at the radial opening.

5. The limited-slip differential according to claim 4, characterized in that, Both the first half-shaft gear and the second half-shaft gear are rotatably mounted on the first housing, and the first housing is a one-piece molded structure.

6. The limited-slip differential according to claim 4, characterized in that, The first housing is configured such that the first half-shaft gear and the second half-shaft gear can be inserted into the first housing through the radial opening.

7. The limited-slip differential according to claim 1, characterized in that, The edge of the planetary gear shaft extends into an annular flange toward one side of the planetary gear teeth.

8. The limited-slip differential according to claim 7, characterized in that: The side surface includes an outer side surface and an inner side surface, wherein the outer side surface is the outer peripheral surface of the planetary gear shaft, and the inner side surface is the inner wall of the flange. The support portion includes an inner support portion and an outer support portion, wherein the inner support portion cooperates with the outer side support, and the outer support portion cooperates with the inner side support; The space between the inner support and the outer support is used to accommodate the flange.

9. The limited-slip differential according to claim 1, characterized in that, The planetary gear is configured such that its tip circle radius r a The ratio r to the mating radius r a / r is less than or equal to the self-locking threshold.

10. The limited-slip differential according to any one of claims 1-9, characterized in that, The self-locking threshold is set as the equivalent friction coefficient f between the side and the corresponding support.