A key parameter design method for a centrifugal pendulum damper containing multiple pendulums

Abstract

The present invention provides a key parameter design method for a CPVA including multiple pendulums. The vibration equations under the action of multiple pendulums and a rotor are established, and then the stability range of the system is calculated using the harmonic balance method after conversion of variables, dimensionless transformation and decoupling. The tuning order of the isochronous epicycloid is selected within the stable range, thereby improving the stability of the centrifugal pendulum system and ensuring the vibration reduction effect.

Description

Technical Field

[0001] The invention belongs to the technical field of automobile vibration and noise control, and relates to a key parameter design method of a centrifugal pendulum vibration absorber (CPVA), and specifically relates to a key parameter design method for a centrifugal pendulum vibration absorber comprising multiple pendulums. Background Art

[0002] Centrifugal pendulum vibration absorber CPVA is widely used in automobile transmission system. It can be equipped with manual transmission (MT), dual clutch transmission (DCT) and automatic transmission (AT). It is usually used on clutch driven plate, second stage flywheel of dual mass flywheel and engine flywheel, and has good control effect on torsional vibration.

[0003] The vibration reduction effect of CPVA mainly depends on the motion trajectory of the pendulum's center of mass, and the motion trajectory of the pendulum's center of mass is determined by the type of profile and the order of the trajectory. The profile types are mainly divided into arc, cycloid and epicycloid. When the pendulum's center of mass moves in an arc, the pendulum has the characteristics of a soft spring oscillator; when the pendulum's center of mass moves in a cycloid, the pendulum has the characteristics of a hard spring oscillator; there is a special epicycloid that makes the pendulum move approximately linearly, called an isochronous epicycloid. The isochronous epicycloid is an ideal profile, and theoretically has the best vibration reduction effect among all profiles. The actual tuning order of CPVA is mainly determined by the trajectory order of the pendulum. When the tuning order is equal to the excitation order, CPVA has the best vibration reduction effect in a stable state.

[0004] For a CPVA containing only a single pendulum, an isochronous epicycloid is selected and the tuning order is set to the excitation order to obtain an ideal vibration reduction effect. In actual engineering applications, a CPVA usually contains N pendulums of equal mass and uniformly distributed positions, such as N = 3, with an angle of 120° between two adjacent pendulums, or N = 4, with an angle of 90° between two adjacent pendulums. Since the pendulum is connected to the rotor through a roller, dividing a large pendulum into several uniformly distributed small pendulums can reduce the stress at the connection position on the one hand, and ensure the dynamic balance of the system on the other.

[0005] The key parameter design of the CPVA with N pendulums is slightly different from that of the CPVA with only one pendulum. If the design method of the CPVA with a single pendulum is directly used, non-uniform motion bifurcation may occur between the N pendulums. At this time, the amplitude and phase angle of each pendulum will be inconsistent and chaotic, resulting in a decrease in the vibration reduction performance of the CPVA. Therefore, it is necessary to develop a key parameter design method for the CPVA with multiple pendulums. Summary of the invention

[0006] In order to overcome the problem of insufficient stability of multiple pendulums when they are in a coherent state (the tuning order of the centrifugal pendulum vibration absorber CPVA is equal to the excitation order) and move in an isochronous epicycloidal path, the present invention provides a key parameter design method for a CPVA comprising multiple pendulums, so that each pendulum is always in a stable state to ensure its vibration reduction performance.

[0007] The technical problems to be solved by the present invention are:

[0008] The technical solution adopted by the present invention to solve the above technical problems is:

[0009] The present invention provides a key parameter design method for a CPVA including multiple pendulums, comprising:

[0010] Step S1, establishing a vibration equation of a multi-degree-of-freedom system after the rotor is connected to N pendulums;

[0011] Step S2, converting the time variable into an angle variable, and converting the vibration equation of the multi-degree-of-freedom system established in step S1;

[0012] Step S3, non-dimensionalizing the angle variable, and non-dimensionalizing the equation obtained after the conversion in step S2;

[0013] Step S4, decoupling the multi-degree-of-freedom system composed of N pendulums and the rotor, obtaining the dimensionless angular acceleration expression of the rotor and the dimensionless vibration equation of each pendulum after ignoring the high-order terms of ε;

[0014] Step S5, based on the high-order terms obtained in step S4 after omitting ε, the dimensionless angular acceleration expression of the rotor and the dimensionless vibration equation of each pendulum are obtained, and the dimensionless response of the i-th pendulum is obtained by solving using the harmonic balance method to find the stable interval;

[0015] Step S6, within the stable range, select a profile and determine the tuning order.

[0016] Preferably, step S1 comprises:

[0017] Assume that the rotor's rotation angle is θ, and the arc motion displacement of the i-th (i=1, 2, ... N) pendulum is S i , when the roller effect is ignored, the vibration equation of the multi-degree-of-freedom system is as follows:

[0018]

[0019]

[0020] Among them, m i is the mass of the i-th pendulum, J0 is the inertia of the rotor, T is the excitation torque amplitude, n is the excitation order, k rotis the rotation coefficient of the pendulum, J i is the inertia of the ith pendulum around its own center of mass, c i is the damping coefficient between the i-th pendulum and the rotor, R(S i ) is the arc motion displacement of the i-th pendulum, S i The distance from its center of mass to the center of the rotor, G(S i ) is the arc motion displacement of the i-th pendulum, S i When R(S i ) in the direction perpendicular to the pendulum motion, satisfying:

[0021] Preferably, step S2 comprises:

[0022] Convert the time variable into an angle variable, set the nominal speed of the rotor to Ω, and perform dimensionless transformation have The vibration equation of the multi-degree-of-freedom system in step A is converted as follows:

[0023]

[0024]

[0025] Preferably, step S3 comprises:

[0026] The angle variable is dimensionless. The equation obtained after the conversion in step B is dimensionless:

[0027]

[0028]

[0029] in,

[0030] s i =S i / C,g(s i )=G(S i ) / C,r(s i )=R(S i ) / C,μ i =c i / (m i Ω),Γ=T / (J0Ω 2 ),ε i =N·m i C 2 / J0, C is the distance from the pendulum's center of mass at the vertex of its trajectory to the rotor center.

[0031] Preferably, step S4 comprises:

[0032] Assume that the mechanical parameters of each pendulum are the same, that is, they satisfy: m i =m, J i = J, μ i =μ, (i=1,2,…N); Since v≈1, ε<<1, we use a small parameter ε to scale the parameters vv', μ and Γ, and let vv'=εw'+o(ε 2 ), after ignoring the high-order terms of ε, the expression of the dimensionless angular acceleration w' of the rotor is obtained as follows:

[0033]

[0034] The dimensionless vibration equation of the i-th pendulum is further obtained as:

[0035]

[0036] Preferably, step S5 comprises:

[0037] make

[0038] s i =A i ·cos(nθ)+B i sin(nθ)

[0039] Among them A i With B i are the cosine amplitude and sine amplitude of the first harmonic of the i-th pendulum respectively;

[0040] If the cosine amplitude of each pendulum is equal and the sine amplitude is equal, then the multi-degree-of-freedom system is stable and the corresponding interval is a stable interval;

[0041] If the cosine amplitude or sine amplitude of two or more pendulums are not equal, the multi-degree-of-freedom system is unstable.

[0042] Preferably, step S6 comprises:

[0043] In the stable interval, an isochronous epicycloid is selected and the tuning order is chosen to be a value greater than 0.2% of the critical point.

[0044] The present invention has the following advantages: by establishing vibration equations under the action of multiple pendulums and rotors, and then converting variables, dimensionlessization and decoupling, the harmonic balance method is used to calculate the stability range of the system, and the tuning order of the isochronous epicycloid is selected within the stable range, the stability of the centrifugal pendulum system is improved, and the vibration reduction effect is ensured. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a design idea map of the method in this embodiment;

[0046] Figure 2 Schematic diagram of the connection between the rotor and N pendulums in this embodiment;

[0047] Figure 3 Schematic diagram of the motion trajectory of the pendulum mass center in this embodiment;

[0048] Figure 4 This is a stable range analysis diagram of the four-cylinder engine in this embodiment. DETAILED DESCRIPTION

[0049] The present invention is described in detail below with reference to the accompanying drawings and specific examples.

[0050] Reference Figure 1 The embodiment of the present invention provides a key parameter design method for a centrifugal pendulum shock absorber including multiple pendulums, and its specific implementation includes the following steps:

[0051] A: Establish the vibration equation of the multi-degree-of-freedom system after the rotor is connected to N pendulums. Assume that the rotor angle is θ and the arc motion displacement of the i-th (i=1, 2, ... N) pendulum is S i , when the roller effect is ignored, the vibration equation of the multi-degree-of-freedom system is as follows:

[0052]

[0053]

[0054] Where J0 is the inertia of the rotor, T is the excitation torque amplitude, n is the excitation order, k rot is the rotation coefficient of the pendulum, m i With J i are the mass of the i-th pendulum and its inertia around its own center of mass, c i is the damping coefficient between the i-th pendulum and the rotor, R(S i ) represents the arc motion displacement of the i-th pendulum, which is S i The distance from its center of mass to the center of the rotor, G(S i ) represents R(S i ) is projected in the direction perpendicular to the pendulum's motion,

[0055] B: Convert the time variable into an angle variable, set Ω as the nominal speed of the rotor, and perform dimensionless transformation have The vibration equation of the multi-degree-of-freedom system in step A is converted as follows:

[0056]

[0057]

[0058] C: Make the angle variable dimensionless. The equation obtained after the conversion in step B is dimensionless:

[0059]

[0060]

[0061] where s i =S i / C,g(s i )=G(S i ) / C,r(s i )=R(S i ) / C,μ i =c i / (m i Ω),Γ=T / (J0Ω 2 ),ε i =N·m i C 2 / J0, C is the distance from the pendulum's center of mass at the vertex of its trajectory to the rotor center.

[0062] D: Decouple the multi-degree-of-freedom system composed of N pendulums and rotors. Assuming that the mechanical parameters of each pendulum are the same, there are m i =m,J i = J, μ i =μ, (i=1,2,…N), since v≈1, ε<<1, we can use the small parameter ε to scale the parameters vv', μ and Γ, let vv'=εw'+o(ε 2 ), ignoring the high-order terms of ε, the dimensionless angular acceleration expression of the rotor is obtained:

[0063]

[0064] The dimensionless vibration equation of the i-th pendulum is:

[0065]

[0066] E: Use the harmonic balance method to solve the dimensionless response of the ith pendulum and find the stable range.

[0067] make

[0068] s i =A i ·cos(nθ)+B i sin(nθ)

[0069] Among them A i With B iare the cosine amplitude and sine amplitude of the first harmonic of the i-th pendulum, respectively. If the cosine amplitude and sine amplitude of each pendulum are equal, the multi-degree-of-freedom system is stable. If the cosine amplitude or sine amplitude of two or more pendulums are unequal, the multi-degree-of-freedom system is unstable.

[0070] F: Select the type curve and determine the tuning order. In the stable range, select the isochronous epicycloid and set the tuning order to a value greater than 0.2% of the critical point.

[0071] Reference Figure 2 The theoretical principle adopted by the above method of the present invention is as follows:

[0072] exist Figure 2 In the multi-degree-of-freedom model shown in FIG. 1 , N pendulums are connected to a rotor, the rotation angle of the rotor is θ, the arc motion displacement of the i-th (i=1, 2, ... N) pendulum is S i The inertia of the rotor is J0, and the mass of the i-th pendulum is m i , the inertia of the i-th pendulum around its own center of mass is J i The distance from the center of mass of the i-th pendulum to the center of the rotor is R(S i ). xoy is a dynamic rotating coordinate system. The rotation speed of this dynamic rotating coordinate system is equal to the angular velocity of the rotor. The origin o of the dynamic rotating coordinate system coincides with the center of the rotor. The rotation angle of the i-th pendulum around its own center of mass in the xoy dynamic rotating coordinate system is β i , β i is the arc motion displacement S of the i-th pendulum i A linear function of β i =k rot ·S i , k rot is the rotation coefficient of the pendulum. When the roller effect is ignored, the total kinetic energy of the centrifugal pendulum vibration absorber CPVA is T tol as follows:

[0073]

[0074] Where G(S i ) represents the arc motion displacement of the i-th pendulum, which is S i When R(S i ) in the direction perpendicular to the pendulum motion, we have:

[0075]

[0076] Assume that the rotor angle θ and the arc motion displacement S of the i-th pendulum i are generalized variables, c iis the damping coefficient between the i-th pendulum and the rotor, T is the excitation torque amplitude, and n is the excitation order. Considering that the gravity on the pendulum is much smaller than the centrifugal force, the influence of gravity can be ignored, and the Lagrange equation is:

[0077]

[0078] Substituting formula (1) into formula (3), the vibration equation of the multi-degree-of-freedom system after each pendulum is connected to the rotor can be obtained:

[0079]

[0080]

[0081] Assuming there is a profile that allows the pendulum to absorb all the torsional vibration of the rotor when it runs along this profile, the rotor will rotate at a constant angular velocity Ω. and Formula (4) degenerates into:

[0082]

[0083] It can be seen that when the torsional vibration response of the rotor is zero, the vibration equation of each pendulum is consistent, so the motion state of each pendulum should be completely consistent. The pendulum acts as a vibration absorber, and it can only play the maximum vibration reduction effect when it vibrates linearly. Suppose the amplitude and phase of the i-th pendulum are With α i , t is time, Then the condition for the i-th pendulum to perform linear vibration is:

[0084]

[0085] exist Figure 3 In the above example, let n i is the trajectory order of the i-th pendulum, ρ0 is the radius of curvature at the top of the arc on the trajectory of the pendulum's center of mass, and Let λ be the profile parameter, then R 2 (S i ) can be expressed as:

[0086]

[0087] Formula (8) is used to calculate the arc motion displacement S of the i-th pendulum: i The derivative is:

[0088]

[0089] Assume that the tuning order of the i-th pendulum is According to equations (7) and (9), we can know that the trajectory order n of the i-th pendulum is i The tuning order with the i-th pendulum is Relationship:

[0090]

[0091] For the convenience of analysis, let γ be the nonlinear tuning parameter, and transform equation (8) into:

[0092]

[0093] Substituting equation (11) into the dimensionless vibration equation of the i-th pendulum, the harmonic balance method can be used to calculate the pendulum's tuning order: and the stability interval of the nonlinear tuning parameter γ.

[0094] Assuming that the mechanical parameters of each pendulum are the same, μ i =μ, (i=1,2,...N). Let n=2, ε=0.1, N=3, The calculated stability interval is as follows Figure 4 Select the isochronous epicycloid (γ = 0) and select the tuning order It is slightly larger than the critical value of inconsistency motion stability (0.2% is sufficient).

Claims

1. A method for designing key parameters of a CPVA including multiple pendulums, characterized in that: include: Step S1, establishing a vibration equation of a multi-degree-of-freedom system after the rotor is connected to N pendulums; Step S2, converting the time variable into an angle variable, and converting the vibration equation of the multi-degree-of-freedom system established in step S1; Step S3, non-dimensionalizing the angle variable, and non-dimensionalizing the equation obtained after the conversion in step S2; Step S4, decoupling the multi-degree-of-freedom system composed of N pendulums and the rotor, obtaining the dimensionless angular acceleration expression of the rotor and the dimensionless vibration equation of each pendulum after ignoring the high-order terms of ε; Step S5, based on the high-order terms obtained in step S4 after omitting ε, the dimensionless angular acceleration expression of the rotor and the dimensionless vibration equation of each pendulum are obtained, and the dimensionless response of the i-th pendulum is obtained by solving using the harmonic balance method to find the stable interval; Step S6, selecting a profile within a stable range and determining a tuning order; Step S1 includes: Assume that the rotor's rotation angle is θ, and the arc motion displacement of the i-th (i=1, 2, ... N) pendulum is S i , when the roller effect is ignored, the vibration equation of the multi-degree-of-freedom system is as follows: Among them, m i is the mass of the i-th pendulum, J0 is the inertia of the rotor, T is the excitation torque amplitude, n is the excitation order, k rot is the rotation coefficient of the pendulum, J i is the inertia of the ith pendulum around its own center of mass, c i is the damping coefficient between the i-th pendulum and the rotor, R(S i ) is the arc motion displacement of the i-th pendulum, S i The distance from its center of mass to the center of the rotor, G(S i ) is the arc motion displacement of the i-th pendulum, S i When R(S i ) in the direction perpendicular to the pendulum motion, satisfying: Step S2 includes: Convert the time variable into an angle variable, set the nominal speed of the rotor to Ω, and perform dimensionless transformation have The vibration equation of the multi-degree-of-freedom system in step A is converted as follows: Step S3 includes: The angle variable is dimensionless. The equation obtained after the conversion in step B is dimensionless: in, s i =S i / C,g(s i )=G(S i ) / C,r(s i )=R(S i ) / C,μ i =c i / (m i Ω),Γ=T / (J0Ω 2 ),ε i =N·m i C 2 / J0, C is the distance from the pendulum mass center at the vertex of its trajectory to the rotor center; Step S4 includes: Assume that the mechanical parameters of each pendulum are the same, that is, they satisfy: m i =m, J i = J, μ i =μ, (i=1,2,…N); Since v≈1, ε<<1, we use a small parameter ε to scale the parameters vv', μ and Γ, and let vv'=εw'+o(ε 2 ), after ignoring the high-order terms of ε, the expression of the dimensionless angular acceleration w' of the rotor is obtained as follows: The dimensionless vibration equation of the i-th pendulum is further obtained as: Step S5 includes: make s i =A i ·cos(nθ)+B i ·sin(nθ) Among them A i With B i are the cosine amplitude and sine amplitude of the first harmonic of the i-th pendulum respectively; If the cosine amplitude of each pendulum is equal and the sine amplitude is equal, then the multi-degree-of-freedom system is stable and the corresponding interval is a stable interval; If the cosine amplitude or sine amplitude of two or more pendulums are not equal, the multi-degree-of-freedom system is unstable; Step S6 includes: In the stable interval, an isochronous epicycloid is selected and the tuning order is chosen to be a value greater than 0.2% of the critical point.

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