A method for stability analysis of a conjugate cam link beating-up mechanism with clearance motion

Abstract

The application discloses a kind of gap-containing kinematic stability analysis methods for conjugate cam connecting rod beating-up mechanism, including corresponding gap-containing kinematic pair geometric constraint of construction, the motion gap includes the first motion gap between roller and conjugate cam and the second motion gap between reed and mounting hole;Respectively construct the mechanics model corresponding to the first motion gap and the second motion gap;Utilize the theory of multi-rigid-body system dynamics to construct the dynamics model of gap-containing kinematic pair containing the first motion gap and the second motion gap;Optimization function for optimizing each connecting rod length and horizontal angle is constructed, and the best optimization scheme is obtained based on solving with the dynamics model of gap-containing kinematic pair.The method provided by the application can effectively reduce the influence of gap on the motion performance of conjugate cam connecting rod, so as to ensure the stable work of beating-up mechanism.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of transmission mechanism design, and particularly relates to a method for analyzing the motion stability of a gap-containing mechanism for a conjugate cam link beating-up mechanism. BACKGROUND

[0002] With the continuous development of textile engineering and precision mechanical engineering, mechanisms are moving towards the goal of high stability, high reliability, high precision and high efficiency. In engineering practice, due to the need for fitting tolerances, friction and wear, manufacturing errors and other reasons, the gap in the mechanism kinematic pair is inevitable.

[0003] The gap-containing kinematic pair will cause the object connected by the kinematic pair to collide, resulting in severe acceleration jitter and instantaneous severe impact of the mechanism. The jitter amplitude and frequency are very high, and the instantaneous impact is very large, which will cause severe vibration of the mechanism, and thus reduce the motion stability of the mechanism. For high-precision beating-up mechanisms, the influence of the gap in the kinematic pair cannot be ignored. Therefore, it is necessary to reduce the influence of the gap in the kinematic pair on the motion stability of the beating-up mechanism, which is of great significance for improving the working performance of mechanisms in important fields such as precision machinery and beating-up mechanisms.

[0004] In order to reduce the influence of the gap on the dynamic performance of the mechanism and improve the motion stability of the mechanism, previous studies have mostly focused on simple mechanisms such as planar link beating-up mechanisms, and there are few studies on conjugate cam link mechanisms. Re-distribution of link mass, external constant spring force and lubrication of the gap in the kinematic pair are mostly used to avoid separation of the elements in the kinematic pair, and thus improve the performance of the mechanism. Or the gap in the kinematic pair is simplified as a massless rigid rod, i.e. a continuous contact model, and then the original gap-containing mechanism is converted into a multi-link multi-degree-of-freedom system without gap for motion analysis and design. The disadvantage of this method is that the elastic deformation of the contact surface of the elements in the kinematic pair is ignored, which cannot truly reflect the contact and collision characteristics of the kinematic pair in the gap-containing mechanism, and is not consistent with the actual situation.

[0005] Patent document CN106055749A discloses a method for improving the motion stability of a gap-containing link mechanism, which comprises the following steps: step one, establishing a mathematical model of the gap-containing kinematic pair; step two, establishing a normal impact force model and a tangential friction force model of the gap in the kinematic pair; step three, establishing an ideal mechanism dynamics model based on the theory of multi-body system dynamics, and parameterizing the length of the link mechanism during the modeling process; step four, establishing a mechanism dynamics model considering the gap in the kinematic pair; step five, establishing an optimization design model for the motion stability of the gap-containing mechanism; and step six, performing optimization design to obtain the optimal length of the link mechanism.

[0006] Patent document CN114775146A discloses a weaving machine variable-angle weaving device, which integrates a shuttle mechanism and a beating-up mechanism on a weft insertion device rack, and a rotating mechanism is designed at the bottom of the weft insertion device rack. The rotating mechanism is composed of a planetary gear train, a ring guide rail sliding seat, a limiting mechanism and the like. The weft insertion device rack and the rotating mechanism are connected through the ring guide rail sliding seat, the sun gear in the planetary gear train is connected with the motor output shaft, a circular 3D printed part is used to connect the planetary gear train and the weft insertion device rack, an angle sensor is used to accurately control the rotation of the motor, and the integrated shuttle mechanism and beating-up mechanism on the weft insertion device rack are rotated to set an angle. At this time, the limiting mechanism fixes the weft insertion device rack after rotation for the second time to increase stability, and the function of variable-angle weaving of the fabric is realized. SUMMARY

[0007] The present application aims to provide a gap-containing motion stability analysis method for a conjugate cam connecting rod beating-up mechanism, which can effectively reduce the influence of the gap on the motion performance of the conjugate cam connecting rod, thereby ensuring the stable operation of the beating-up mechanism.

[0008] In order to achieve the purpose of the present application, the following technical scheme is provided: a gap-containing motion stability analysis method for a conjugate cam connecting rod beating-up mechanism, the conjugate cam connecting rod beating-up mechanism comprising a reed and a self-rotating conjugate cam, and a connecting rod mechanism for converting the rotary motion of the conjugate cam into the reciprocating motion of the reed, the connecting rod mechanism comprising a connecting rod set, a roller and a mounting hole provided at the oscillating end of the connecting rod set, the roller being used for the rolling surface contact between the connecting rod set and the conjugate cam, and the mounting hole being used for the articulation between the connecting rod set and the reed;

[0009] The gap-containing motion stability analysis method comprises the following steps:

[0010] According to the motion gaps between the connecting rod set and the conjugate cam and the reed respectively, corresponding gap-containing motion pair geometric constraints are constructed, the motion gaps comprising a first motion gap between the roller and the conjugate cam and a second motion gap between the reed and the mounting hole;

[0011] Based on the gap-containing motion pair geometric constraints and the motion conditions of the conjugate cam connecting rod beating-up mechanism, corresponding mechanical models of the first motion gap and the second motion gap are respectively constructed, the mechanical models comprising a normal collision force model and a tangential friction force model;

[0012] Based on the corresponding mechanical models of the first motion gap and the second motion gap, a gap-containing motion pair mechanism dynamics model containing the first motion gap and the second motion gap is constructed by using the multi-rigid-body system dynamics theory;

[0013] An optimization mathematical model for optimizing the length of each connecting rod and the horizontal included angle is constructed, and the optimization mathematical model is solved based on the dynamic model of the gap-containing motion pair to obtain an optimal optimization scheme, the optimization mathematical model takes the length of each connecting rod in the connecting rod mechanism and the included angle with the horizontal plane as the design variable, takes the stroke of the reed as the constraint, and minimizes the maximum value of the absolute value of the acceleration of the reed during reciprocating motion as the optimization target.

[0014] The present application is based on multi-rigid-body system dynamics, analyzes the influence of gap and complex surface contact on the dynamic behavior of the conjugate cam connecting rod through numerical simulation, and minimizes the maximum value of the absolute value of the acceleration of the reed during reciprocating motion as the optimization target, the stroke of the reed as the constraint function, reduces the influence of the gap by optimizing the length of the connecting rod and the included angle of the conjugate cam connecting rod beating mechanism, and improves the motion behavior of the mechanism.

[0015] Specifically, the expression of the geometric constraint of the gap-containing motion pair is as follows:

[0016]

[0017] When the first motion gap is considered, δ = e linkage -c linkage ;

[0018] When the second motion gap is considered, δ = r camfollower -e cam_max ;

[0019] In the formula, δ represents the penetration amount of the contact point in the motion gap, e linkage represents the center distance between the mounting hole and the rotating shaft of the connecting rod where the mounting hole is located, c linkage =r b -r j represents the rotation pair gap value, r b represents the radius of the rotating shaft of the connecting rod where the mounting hole is located, r j represents the radius of the assembly hole corresponding to the reed and the mounting hole, e cam_max represents the center distance between the maximum penetration contact point and the roller, r camfollwer represents the radius of the roller.

[0020] Specifically, the normal collision force model is obtained by analyzing a nonlinear spring damping model.

[0021] Specifically, the expression of the normal collision force model is as follows:

[0022]

[0023] In the formula, δ represents the penetration amount of the contact point in the motion gap, n represents the force index, represents the relative collision speed, c edenotes the restitution coefficient, denotes the initial impact velocity, and K denotes the contact stiffness coefficient of the colliding body.

[0024] Specifically, the tangential friction force model is analyzed by a modified Coulomb friction force model.

[0025] Specifically, the expression of the tangential friction force model is as follows:

[0026]

[0027]

[0028] In the formula, F n denotes the normal impact force, μ(v t ) denotes the dynamic friction coefficient, v t denotes the relative sliding velocity of two objects in contact at the impact point, i.e., the velocity component in the tangential direction, μ d is the sliding friction coefficient, μ s is the static friction coefficient, v s is the static friction critical velocity, v d is the maximum dynamic friction critical velocity.

[0029] Specifically, the dynamics model of the gap-containing kinematic pair mechanism is constructed by regarding each component in the conjugate cam connecting rod beating mechanism as a module node to construct a corresponding topological structure.

[0030] The motion equation of the conjugate cam connecting rod beating mechanism is decomposed into the topological structure characteristics in a dynamic segmentation manner, the dynamic segmentation including a free motion state in which the components connected by the kinematic pair lose the kinematic pair constraint and freely move, and a contact and impact stage when the penetration amount of the contact point of the two objects is greater than zero.

[0031] Specifically, the expression of the dynamics model of the gap-containing kinematic pair mechanism is as follows:

[0032]

[0033] wherein, and q are vectors of generalized accelerations, generalized velocities, and generalized coordinates; M represents the mass of the system, C represents the damping, and K represents the stiffness matrix, Φ q denotes the Jacobian matrix of the constraint equation, is the transpose matrix of Φ q , λ is the Lagrange operator, Q represents the vector of generalized forces, Q c represents the vector of generalized external forces.

[0034] Specifically, the expression of the optimization mathematical model is as follows:

[0035]

[0036] wherein g k (X) is a constraint function, S is the stroke of the reed, is the acceleration of the gap-containing mechanism, N is the number of links of the link set, l n is the length of the link, θ n is the included angle of the link.

[0037] Compared with the prior art, the beneficial effects of the present application are:

[0038] In order to optimize the length of the link and the horizontal included angle of the link in the link set, a kinematic model of the gap-containing mechanism is constructed, so that a more accurate and comprehensive design scheme reference is obtained through data analysis, so as to improve the motion stability of the conjugate cam link beating-up mechanism. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 is a structural schematic diagram of the conjugate cam link beating-up mechanism provided in the present embodiment;

[0040] Figure 2 is a flowchart of a gap-containing motion stability analysis method for the conjugate cam link beating-up mechanism provided in the present embodiment;

[0041] Figure 3 is a trajectory diagram of the gap motion between the reed and the link set provided in the present embodiment;

[0042] Figure 4 is a trajectory diagram of the gap motion between the roller of the link set and the conjugate cam provided in the present embodiment;

[0043] Figure 5 is a response diagram of the conjugate cam link beating-up mechanism before and after structural optimization provided in the present embodiment. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative efforts fall within the scope of protection of the present application.

[0045] As Figure 1As shown in the figure, it is a structural schematic diagram of the conjugate cam connecting rod beating-up mechanism provided in this embodiment, and the conjugate cam connecting rod beating-up mechanism includes a reed 9 and a rotating conjugate cam 2, and a connecting rod mechanism for converting the rotational motion of the conjugate cam into the reciprocating motion of the reed 9, and the connecting rod mechanism includes a connecting rod group, a roller and a mounting hole arranged at the swinging end of the connecting rod group, the roller is used for the connecting rod group to contact the rolling surface of the conjugate cam, and the mounting hole is used for the connecting rod group to be hinged to the reed 9.

[0046] Furthermore, the roller includes a main roller 3 and a secondary roller 4. The connecting rod group in this example is a four-bar connecting rod group, which includes a main rocker arm 5 that drives the main roller 3 to rotate, a secondary rocker arm 6 that drives the secondary roller 4 to rotate, a connecting rod 8 that is hinged to the reed 9 with a mounting hole at one end, and a rocker 7 for connecting the rocker arm and the connecting rod 8.

[0047] That is, the main rocker arm 5, the auxiliary rocker arm 6 and the rocker arm 7 are fixed at a certain angle and the three are hinged to the frame through a rotation center at the same time. The main roller 3 is hinged to the main rocker arm 5; the auxiliary roller 4 is hinged to the auxiliary rocker arm 6; the connecting rod 8 is hinged to the rocker arm 7; the reed 9 is hinged to the connecting rod 8; the reed 9 is connected to the frame through a translation pair. When the camshaft 1 drives the conjugate cam to rotate 2, the main rocker arm 5 and the auxiliary rocker arm 6 drive the rocker arm 7 to rotate according to the cam profile curve, and then the rocker arm 7 drives the connecting rod 8 to make a planar motion, and the connecting rod 8 drives the reed 9 to reciprocate in the vertical direction.

[0048] like Figure 2 As shown in FIG. 1 , a method for analyzing the stability of a conjugate cam-link beating-up mechanism with clearance provided in this embodiment includes:

[0049] According to the motion clearances between the connecting rod group and the conjugate cam and the reed, the corresponding geometric constraints of the motion pair with clearances are constructed. The motion clearances include a first motion clearance between the roller and the conjugate cam and a second motion clearance between the reed and the mounting hole.

[0050] like Figure 3 and Figure 4 The figure shows the trajectory diagram of the two gap motions in the conjugate cam connecting rod beating mechanism. The elements, the pin for assembling the reed 9 and the mounting hole of the connecting rod, are considered as two collision bodies. The dynamic characteristics of the gap motion pair depend on the gap contact collision force. The ideal geometric constraint is converted into a force constraint. Figure 3 The geometric constraints of the clearance revolute pair in are as follows:

[0051] δ linkage =e linkage -c linkage

[0052] Where, e linkage Indicates the center distance between the mounting hole and the connecting rod rotation axis where the mounting hole is located, c linkage= r b - r j represents the rotation pair gap value, r b represents the radius of the connecting rod rotating shaft where the mounting hole is located, r j represents the radius of the mounting hole corresponding to the reed.

[0053] e linkage is the center distance between the connecting rod hole and the pin shaft hole, and the rotation pair gap value c linkage is c linkage = r b - r j , wherein r b is the radius of the connecting rod hole, and r j is the radius of the pin shaft.

[0054] Similarly, Figure 4 the gap cam pair geometry constraint is as follows:

[0055] δ cam_max = r camfollower - e cam_max

[0056] In the formula, e cam_max represents the center distance between the maximum penetration point and the roller, r camfollwer represents the radius of the roller.

[0057] Therefore, the gap-containing motion pair geometry constraint of the conjugate cam connecting rod beating-up mechanism is as follows:

[0058]

[0059] When the first motion gap is considered, δ = e linkage - c linkage ;

[0060] When the second motion gap is considered, δ = r camfollower - e cam_max ;

[0061] In the formula, δ represents the penetration of the contact point in the motion gap.

[0062] Based on the gap-containing motion pair geometry constraint and the motion condition of the conjugate cam connecting rod beating-up mechanism, a mechanical model corresponding to the first motion gap and the second motion gap is respectively constructed, and the mechanical model includes a normal collision force model and a tangential friction force model.

[0063] Further, when the motion pair has a gap, collision of two contact objects will be caused, so the gap motion pair always contains a certain contact and collision process, and correct description of the gap contact and collision process needs to be considered. The motion pair gap normal force model adopts a nonlinear spring damping model, and the expression is as follows:

[0064]

[0065] K = E1v1v2 / (1-v12)2+ (1-v22)2 is the contact stiffness coefficient of the colliding bodies, v1 and v2 represent the Poisson's ratios of the contact bodies 1 and 2 respectively, E1 and E2 are the elastic moduli of the contact bodies 1 and 2 respectively, ± represents the contact mode, + represents the external contact, - represents the internal contact, r1 and r2 are the radii of curvature of the contact bodies 1 and 2 respectively, is the damping coefficient of the collision process, c e is the restitution coefficient, is the initial collision velocity, δ is the penetration amount of the collision process, n is the force index, and is taken as 1.5, is the relative collision velocity.

[0066] The normal collision force model F n is constructed based on the geometric constraints of the gap-containing motion pair as follows:

[0067]

[0068] where K is the contact stiffness coefficient of the colliding bodies, δ is the contact penetration amount of the collision process, n is the force index, and is taken as 1.5, c e is the restitution coefficient, is the relative collision velocity, is the initial collision velocity.

[0069] The modified Coulomb friction force model is used to establish the friction force of the gap-containing motion pair. In the modified friction force model, the concept of dynamic friction coefficient is proposed, and the formula of the tangential friction force model is

[0070]

[0071] Since μ(υ t ) is the dynamic friction coefficient, the final expression is as follows:

[0072]

[0073] where v t represents the relative sliding velocity of two mutually contacting bodies at the collision point, i.e., the velocity component in the tangential direction, μ d is the sliding friction coefficient, μ s is the static friction coefficient, v s is the static friction critical velocity, v d is the maximum dynamic friction critical velocity.

[0074] Based on the mechanical model corresponding to the first motion gap and the second motion gap, a dynamic model of the motion pair with the gap is constructed by using the multi-rigid-body system dynamics theory, the dynamic model including the first motion gap and the second motion gap;

[0075] Further, the existence of the gap causes the collision of the connected components, and the mechanism system becomes a variable topology structure. When the motion pair has the gap, the components connected with the motion pair lose the constraint of the motion pair and freely move, thereby entering the free motion state. When the penetration of the contact point of the two objects is greater than zero, the motion pair with the gap has the contact, and thus the motion state of the mechanism changes into the contact and collision stage constrained by the collision force. Therefore, the method of dynamic segmentation is adopted to process the variable topology characteristics of the mechanism with the gap.

[0076] Firstly, the dynamic model of the ideal mechanism is established, i.e. when the mechanism does not have the gap, the dynamic equation of the mechanism is based on the Lagrange multiplier method:

[0077]

[0078] wherein, and q are the vectors of generalized acceleration, generalized velocity and generalized coordinates. M, C and K are the matrices of mass, damping and stiffness of the system. Φ q is the Jacobian matrix of the constraint equation, is the transpose matrix of Φ q , λ is the Lagrange operator, and Q is the vector of generalized forces.

[0079] Based on the normal collision force model and the tangential friction force model provided in the above embodiment, the dynamic model of the mechanism with the gap is constructed, i.e. when the motion pair with the gap has the collision, the contact and collision force is generated, and the state is changed from the unconstrained state to the force constraint. Therefore, the generalized force is mainly composed of the normal contact force and the tangential friction force in the contact and collision process, and is defined as Q c When the gap of the motion pair is considered, the dynamic equation of the mechanism is:

[0080]

[0081] wherein, and q are the vectors of generalized acceleration, generalized velocity and generalized coordinates; M represents the mass of the system, C represents the damping, and K represents the stiffness matrix, Φ q represents the Jacobian matrix of the constraint equation, is the transpose matrix of Φ q , λ is the Lagrange operator, Q represents the vector of generalized forces, and Q c represents the vector of generalized external forces.

[0082] An optimization function for optimizing the length of each connecting rod and the horizontal angle is constructed, and the optimization function is solved based on the dynamic model of the gap-containing motion pair to obtain the best optimization scheme. The optimization mathematical model takes the length of each connecting rod in the connecting rod mechanism and the angle with the horizontal plane as the design variable, takes the stroke of the reed as the constraint, and minimizes the maximum value of the absolute value of the acceleration of the reed during reciprocating motion as the optimization objective.

[0083] Furthermore, the optimization design of the gap-containing planar conjugate cam connecting rod mechanism is studied, taking the length of the connecting rod as the design variable and the angle of each connecting rod as the design variable. The design variable X is:

[0084] X = [l1, l 2, ..., l N , θ1, θ2,..., θ N ]

[0085] In the formula, N is the number of connecting rods of the conjugate cam connecting rod beating mechanism, l n is the length of the connecting rod, and θ n is the angle of the connecting rod.

[0086] Since the gap-containing motion pair will cause the object connected by the motion pair to collide, the acceleration of the mechanism will fluctuate sharply and there will be a momentary sharp impact, the amplitude and frequency of the fluctuation are very high and the momentary impact is very large, which will cause the mechanism to vibrate seriously, thereby reducing the motion stability of the mechanism. Therefore, in order to reduce the influence of the gap on the motion stability of the mechanism, the minimum value of the maximum value of the absolute value of the acceleration of the reed is taken as the optimization objective, and the objective function is:

[0087]

[0088] In the formula, is the acceleration of the gap-containing mechanism.

[0089] The constraint condition is that the length of the connecting rod of the conjugate cam connecting rod mechanism, the angle of the connecting rod, and the stroke of the reed do not exceed the corresponding upper and lower limits.

[0090] As described above, the expression of the final optimization mathematical model is as follows:

[0091]

[0092] In the formula, g k (X) is a constraint function, which is a deterministic constraint function related only to the design variable X. S is the stroke of the slider.

[0093] The conjugate cam connecting rod beating mechanism provided in the embodiment is optimized, and the design variable range of the conjugate cam connecting rod is shown in Table 1.

[0094] Table 1

[0095] Design variable Initial value Maximum value Minimum value Rocker 7 (mm) 360 410 310 angle θ1 (°) 355 335 375 Link 8 (mm) 565 515 615 angle θ2 (°) 98 92 104

[0096] The theoretical profile curve of the conjugate cam is unchanged, the diameter of the cam roller is less than the theoretical cam roller diameter by 0.1 mm, and the gap size at the reed and the connecting rod is 0.5 mm. In the dynamic simulation process, the conjugate cam speed is 600 r / min, the initial state is that the swing rod position is the same as the theoretical position, that is, the initial angle of the main swing rod is 335°, and the initial angle velocity of the swing rod is 0. The pin shaft of the connecting rod and the hole of the reed are tangent in the vertical direction, and the center point is 0.5 mm apart.

[0097] As shown in Table 2, the design variables of the conjugate cam connecting rod after optimization.

[0098] Table 2

[0099] Design variable Initial value After optimization Change rate Rocker 7 (mm) 360 330.13 8.2％ angle θ1 (°) 355 345.03 2.8％ Link 8 (mm) 565 547.16 1.6％ included angle θ2 (°) 98 95.15 2.9％ Target 6424.824 m / s 2 ]] 2196.675 m / s 2 ]] 65.8％

[0100] In combination with Table 2 and Figure 5 It is shown that the optimization results show that: after the optimization design taking the minimum value of the maximum value of the reed acceleration absolute value as the objective function, the maximum peak value of the mechanism acceleration absolute value and the shaking times are obviously reduced, the acceleration peak value and the shaking times after optimization are obviously reduced, the maximum peak value of the acceleration objective function after optimization is reduced by 65.8%, and it can be seen that by optimizing the connecting rod length and the connecting rod angle of the conjugate cam connecting rod, the instantaneous impact of the mechanism is reduced, and the acceleration shaking is obviously reduced, and the stability of the mechanism motion is improved.

[0101] In summary, the present application is based on multi-rigid-body system dynamics, based on a multi-rigid-body system dynamics model, a complex surface contact collision model and a motion pair gap contact collision model, a conjugate cam connecting rod dynamics model considering complex surface contact and motion pair gap is established, the influence of gap and complex surface contact on the dynamic behavior of the conjugate cam connecting rod is analyzed by numerical simulation, and then the minimum value of the maximum value of the reed running acceleration absolute value is taken as the optimization target, the stroke of the reed is taken as the constraint function, the influence of the gap is reduced by optimizing the connecting rod length and the connecting rod angle of the conjugate cam connecting rod beating mechanism, and then the motion behavior of the mechanism is improved. The present application reduces the influence of the gap on the motion performance of the mechanism by optimizing the connecting rod length and the connecting rod angle of the mechanism, and improves the motion stability of the mechanism containing the gap.

[0102] Finally, it should be noted that the above-described embodiments are merely specific embodiments of the present application, which are used to illustrate the technical solutions of the present application, but not to limit the same. The protection scope of the present application is not limited thereto. Although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that any person skilled in the art can still modify or easily think of changes to the technical solutions recorded in the foregoing embodiments, or make equivalent replacements to some of the technical features, within the technical scope disclosed by the present application. The modifications, changes or replacements do not cause the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for analyzing the stability of backlash motion in a conjugate cam-link beating-up mechanism. The conjugate cam-link beating-up mechanism comprises a reed and a rotating conjugate cam, and a connecting rod mechanism for converting the rotational motion of the conjugate cam into reciprocating motion of the reed. The connecting rod mechanism comprises a connecting rod assembly, a roller disposed at a swinging end of the connecting rod assembly, and a mounting hole. The roller ensures contact between the rolling surface of the connecting rod assembly and the conjugate cam, and the mounting hole provides an articulated connection between the connecting rod assembly and the reed. It is characterized in that The method for analyzing the stability of motion with gaps comprises the following steps: According to the motion clearances between the connecting rod group and the conjugate cam and the reed, the corresponding geometric constraints of the motion pair with clearances are constructed. The motion clearances include a first motion clearance between the roller and the conjugate cam and a second motion clearance between the reed and the mounting hole. Based on the geometric constraints of the kinematic pair with the gap and the motion of the conjugate cam-link beating-up mechanism, mechanical models corresponding to the first motion gap and the second motion gap are respectively constructed, wherein the mechanical models include a normal collision force model and a tangential friction force model; Based on the mechanical models corresponding to the first motion gap and the second motion gap, the dynamics model of the gap-containing motion pair mechanism including the first motion gap and the second motion gap is constructed using the multi-rigid body system dynamics theory; An optimization mathematical model is constructed for optimizing the length of each connecting rod and the horizontal angle, and the best optimization solution is obtained based on the solution of the dynamic model of the motion pair with clearance. The optimization mathematical model uses the length of each connecting rod in the connecting rod mechanism and the angle with the horizontal plane as design variables, the stroke of the reed as a constraint, and the minimization of the maximum absolute value of the acceleration of the reed during reciprocating motion as the optimization goal.

2. The method for analyzing the stability of the motion with clearance for the conjugate cam connecting rod beating mechanism according to claim 1, characterized in that: The geometric constraint of the kinematic pair with clearance is expressed as follows: When considering the first motion gap, δ = e linkage -c linkage ; When the second motion gap is considered, δ = r camfollower -e cam_max ; Where δ represents the penetration of the contact point in the motion gap, e linkage Indicates the center distance between the mounting hole and the connecting rod rotation axis where the mounting hole is located, c linkage =r b -r j Indicates the clearance value of the rotating pair, r b Indicates the radius of the connecting rod's rotation axis where the mounting hole is located, r j Indicates the radius of the assembly hole corresponding to the reed and the mounting hole, e cam_max Indicates the distance between the contact point of maximum penetration and the center of the roller, r camfollwer Indicates the radius of the roller.

3. The method for analyzing the stability of the motion with clearance for the conjugate cam-link beating-up mechanism according to claim 1, characterized in that: The normal collision force model is obtained by analyzing a nonlinear spring damping model.

4. The method for analyzing the stability of the motion with clearance for the conjugate cam connecting rod beating mechanism according to claim 1 or 3, characterized in that: The expression of the normal collision force model is as follows: Where δ represents the penetration of the contact point in the motion gap, n represents the force index, represents the relative collision velocity, c e represents the coefficient of restitution, represents the initial collision velocity, and K represents the contact stiffness coefficient of the collision body.

5. The method for analyzing the stability of the motion with clearance for the conjugate cam-link beating-up mechanism according to claim 1, characterized in that: The tangential friction force model is obtained by analyzing the modified Coulomb friction force model.

6. The method for analyzing the stability of the motion with clearance for the conjugate cam connecting rod beating mechanism according to claim 1 or 5, characterized in that: The expression of the tangential friction force model is as follows: Where, F n represents the normal collision force, μ(υ t ) represents the dynamic friction coefficient, v t It represents the relative sliding velocity of two objects in contact at the collision point, that is, the velocity component in the tangential direction, μ d is the sliding friction coefficient, μ s is the static friction coefficient, v s is the critical speed of static friction, v d is the critical speed of maximum dynamic friction.

7. The method for analyzing the stability of the motion with clearance for the conjugate cam-link beating-up mechanism according to claim 1, characterized in that: The dynamic model of the kinematic pair with clearance is constructed by treating each component in the conjugate cam-link beating-up mechanism as a module node to construct a corresponding topological structure; The motion of the conjugate cam-link beating-up mechanism is decomposed into topological structural characteristics in a dynamic segmentation manner. The dynamic segmentation includes a free motion state in which the components connected by the kinematic pairs lose the kinematic pair constraints and move freely, and a contact collision stage when the penetration of the contact point of the two objects is greater than zero.

8. The method for analyzing the stability of the motion with clearance for the conjugate cam connecting rod beating mechanism according to claim 1 or 7, characterized in that: The expression of the dynamic model of the mechanism with clearance motion pair is as follows: in, and q are vectors of generalized acceleration, generalized velocity and generalized coordinates; M represents the system mass, C represents the damping and K represents the stiffness matrix, Φ q represents the Jacobian matrix of the constraint equation, is Φ q The transposed matrix, λ is the Lagrangian operator, Q represents the vector of generalized force, Q c A vector representing a generalized external force.

9. The method for analyzing the stability of the motion with clearance for the conjugate cam-link beating-up mechanism according to claim 1, characterized in that: The expression of the optimization mathematical model is as follows: Among them, g k (X) is the constraint function, S is the stroke of the reed, is the acceleration of the mechanism with clearance, N is the number of connecting rods in the connecting rod group, l n is the connecting rod length, θ n is the connecting rod angle.

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