Method for rail impact and dynamic analysis of three-degree-of-freedom flat-bottom push rod cam mechanism

Abstract

The present application relates to the technical fields of mechanical dynamics analysis and mechanism simulation, and discloses a guide rail impact and dynamic analysis method of a three-degree-of-freedom flat push rod cam mechanism, comprising the following steps: establishing global and local coordinate systems, and defining the push rod as a rigid body with three degrees of freedom of lateral, longitudinal and rotation; correcting the effective input displacement of the cam according to the rotation angle, and calculating the normal contact force, friction force and total cam contact moment; at the same time, monitoring the collision of the four corner points of the push rod with the guide rail, and calculating the guide rail impact force and total guide rail impact moment; and constructing coupled dynamics differential equations by comprehensively using the above forces and moments, and solving the motion state by using numerical integration. Further, the dynamics behavior of the system is identified by using Poincaré section and five-element impact mode code recognition system. The present application realizes the simulation of push rod tilting, overturning and multi-point impact, can effectively identify the periodic, bifurcation and chaotic motion state of the system, and provides theoretical support for mechanism optimization design.

Description

Technical Field

[0001] This invention relates to the field of mechanical dynamics analysis and mechanism simulation technology, specifically to a method for guide rail impact and dynamic analysis of a three-degree-of-freedom flat-bottomed pushrod cam mechanism. Background Technology

[0002] As a core transmission component of internal combustion engine valve train and automated machinery, the flat-bottomed pushrod cam mechanism is widely used to convert the rotational motion of the cam into the linear reciprocating motion of the pushrod. In the traditional dynamic modeling and analysis system, the theoretical assumption restricts the pushrod to a single-degree-of-freedom translational motion along the longitudinal axis of the guide rail. The engineering design method mainly relies on this idealized geometric constraint to calculate kinematic parameters such as displacement, velocity and acceleration, and treats the pushrod and the guide rail as an ideal kinematic pair without backlash for mechanical solution.

[0003] However, in actual mechanical systems, there is an objective clearance between the push rod and the guide rail. The eccentric load generated by the interaction between the cam and the flat-bottomed push rod drives the push rod to produce lateral displacement and rotational tendency within the guide rail clearance. Existing single-degree-of-freedom analysis models neglect the lateral motion and rotational degrees of freedom of the push rod, and cannot characterize the complex contact dynamics behavior of the periodic impact of the push rod's sidewall corner against the guide rail sidewall. This theoretical deficiency prevents existing methods from calculating the high-frequency impact load at the guide rail and the coupling effect of the push rod tilt on the effective input displacement of the cam, resulting in deviations between the predicted dynamic performance and the actual operating conditions, making it difficult to assess the wear risk and vibration noise level of the mechanism.

[0004] Therefore, this invention proposes a guide rail impact and dynamic analysis method for a three-degree-of-freedom flat-bottom push rod cam mechanism to address the shortcomings of existing technologies. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a guide rail impact and dynamic analysis method for a three-degree-of-freedom flat-bottom push rod cam mechanism. This method solves the problem that existing cam mechanism dynamic analysis methods typically only consider single-degree-of-freedom motion, neglecting the tilting and flipping of the push rod in the guide rail gap and the resulting multi-point impact vibration, leading to insufficient accuracy in dynamic prediction.

[0006] To achieve the above objectives, the present invention provides the following technical solution: The first aspect of the present invention provides a method for analyzing the guide rail impact and dynamics of a three-degree-of-freedom flat-bottomed pushrod cam mechanism, comprising the following steps:

[0007] Read the parameters of the cam mechanism, define the global coordinate system and the local coordinate system, and define the push rod as a rigid body with three degrees of freedom: lateral displacement along the x-axis of the global coordinate system, longitudinal displacement along the y-axis of the global coordinate system, and rotation angle about the center of mass.

[0008] The effective input displacement of the cam in the normal direction of the push rod flat bottom plane is corrected according to the rotation angle, and the normal displacement difference between the push rod flat bottom plane and the cam profile is calculated.

[0009] The contact state is determined based on the normal displacement difference, and the normal contact force, tangential friction force and total cam contact torque between the push rod flat bottom plane and the cam profile are calculated.

[0010] Monitor the physical collision state between the four corners of the push rod sidewall and the guide rail sidewall, calculate the guide rail impact force for the corners where physical collision occurs, and synthesize the total guide rail impact torque;

[0011] By combining the normal contact force, the tangential friction force, the total contact torque of the cam, the impact force of the guide rail, the total impact torque of the guide rail, and the elastic constraint force and the constraint torque generated by the elastic constraint force on the push rod, a coupled dynamic differential equation system including lateral translation, longitudinal translation and planar rotation is constructed, and the motion state of the push rod is updated using a numerical integration algorithm.

[0012] The motion trajectory of the push rod is monitored to see if it crosses the Poincaré section. The characteristic points at the crossing time are recorded, and an impact mode code is generated based on the characteristic points to identify the dynamic motion state of the system.

[0013] Preferably, to address the kinematic distortion caused by pushrod tilt, the process of correcting the effective input displacement of the cam in the normal direction of the pushrod flat-bottom plane based on the rotation angle employs a geometric iterative solution strategy. Specifically, utilizing the geometric constraint that the normal vector of the pushrod flat-bottom plane is parallel to the normal vector of the cam profile at the contact point, the position coordinates of the actual contact point on the cam profile in the global coordinate system are solved numerically through iteration, thereby correcting the effective input displacement of the cam in the normal direction of the pushrod flat-bottom plane. Simultaneously, the calculation of the normal displacement difference between the pushrod flat-bottom plane and the cam profile is based on the geometric overlap between the spatial linear equation of the pushrod flat-bottom plane and the cam profile in the normal direction of the contact point, thus accurately reflecting the influence of pushrod rotation on the actual contact compression.

[0014] Preferably, the present invention fully considers the torque effect caused by changes in contact position in the dynamic modeling. The calculation of the normal contact force between the flat bottom plane of the push rod and the cam profile is based on a nonlinear contact stiffness damping model. The calculation of the total cam contact torque between the flat bottom plane of the push rod and the cam profile is based on the lateral and longitudinal offsets of the actual contact point relative to the center of mass of the push rod. The torque components generated by the normal contact force and the tangential friction force on the center of mass of the push rod are calculated separately and summed to obtain the total cam contact torque. This step establishes a direct mechanical relationship between the cam contact force and the rotational degree of freedom of the push rod.

[0015] Preferably, for the complex collision behavior of the push rod within the guide rail gap, this invention constructs a four-corner impact model. The four corner points of the push rod sidewall specifically refer to: the lower right corner point, the upper left corner point, the upper right corner point, and the lower left corner point. The monitoring process utilizes rigid body geometric projection relationships to calculate the lateral coordinates of the four corner points in the global coordinate system in real time, and compares the absolute values ​​of the lateral coordinates with the single-sided guide rail gap threshold to determine whether a physical collision has occurred.

[0016] Preferably, to quantify the impact of guide rail impact on system stability, the guide rail impact force is calculated based on the Hertzian contact theory model, utilizing the depth of the corner point of physical collision embedded in the guide rail sidewall and the instantaneous lateral velocity of the corner point. When synthesizing the total guide rail impact torque, the effective longitudinal lever arm corresponding to each corner point is determined based on the Euclidean distance from the push rod's center of mass to each corner point of physical collision and the rotation angle. The vector sum of the products of the guide rail impact force at each corner point and the corresponding effective longitudinal lever arm is then calculated to obtain the total guide rail impact torque. This total guide rail impact torque is the primary excitation source causing the push rod to oscillate at high frequencies.

[0017] Preferably, the elastic constraint force and the constraint torque generated by the elastic constraint force on the push rod are calculated in the following way: based on the rotation angle and displacement of the push rod, the spatial position change of the spring attachment point at the top of the push rod is determined, the total elastic force generated by the top spring is calculated and decomposed into lateral and longitudinal components to obtain the elastic constraint force on the push rod; based on the lever arms of the lateral and longitudinal components relative to the center of mass of the push rod, the constraint torque of the elastic constraint force is calculated; at the same time, based on the lateral displacement and lateral velocity of the push rod, the auxiliary constraint force acting on the side of the push rod is calculated.

[0018] Preferably, the coupled dynamic differential equations constructed in this invention achieve fully coupled solution for all three degrees of freedom. Specifically, they include: a lateral dynamic equation relating to the push rod mass, lateral acceleration, the lateral component of the top spring force, the lateral component of the normal contact force, the lateral component of the tangential friction force, the auxiliary constraint force, and the lateral component of the guide rail impact force; a longitudinal dynamic equation relating to the push rod mass, longitudinal acceleration, the longitudinal component of the top spring force, the longitudinal component of the normal contact force, the longitudinal component of the tangential friction force, and the initial preload; and a rotational dynamic equation relating to the push rod moment of inertia, angular acceleration, the constraint torque generated by the top spring force, the total contact torque of the cam, and the total impact torque of the guide rail.

[0019] Preferably, to identify the nonlinear dynamic characteristics of the system, the Poincaré section is defined by a set of hypersurfaces corresponding to the critical geometric positions where the corner points of the push rod are about to contact the guide rail sidewall. Monitoring whether the motion trajectory of the push rod crosses the Poincaré section is achieved by monitoring whether the discriminant function value defining the hypersurface undergoes a sign flip between adjacent time steps.

[0020] Preferably, the impact mode code adopts the rpijf five-tuple symbol encoding system, which specifically includes: parameter r representing the reference number of cam rotation cycles; parameter p representing the total number of physical collisions at the lower right corner of the push rod within r reference cycles; parameter i representing the total number of physical collisions at the upper right corner of the push rod within r reference cycles; parameter j representing the total number of physical collisions at the lower left corner of the push rod within r reference cycles; and parameter f representing the total number of physical collisions at the upper left corner of the push rod within r reference cycles.

[0021] Preferably, the specific logic for identifying the dynamic motion state of the system includes: comparing the impact pattern codes generated over multiple consecutive reference periods; if the impact pattern codes remain unchanged, the system is determined to be in a periodic motion state; if the impact pattern codes exhibit periodic alternation between consecutive periods, the system is determined to be in a period-doubling bifurcation state; if the impact pattern codes show no repetition pattern, the system is determined to be in a chaotic motion state. This method can intuitively map complex dynamic behaviors into digital feature sequences, facilitating system stability assessment.

[0022] This invention provides a method for analyzing the guide rail impact and dynamics of a three-degree-of-freedom flat-bottomed pushrod cam mechanism. It has the following beneficial effects:

[0023] 1. This invention overcomes the limitation of traditional technologies that only consider the uniaxial motion of the push rod by constructing a three-degree-of-freedom fully coupled dynamic model that includes lateral displacement, longitudinal displacement, and the rotation angle of the push rod around its center of mass. By incorporating the normal contact force, cam contact torque, and guide rail impact torque into a unified set of differential equations, this invention can simulate the tilting and flipping behavior of the push rod caused by eccentric force within the guide rail gap. This technical solution overcomes the shortcomings of traditional models that neglect lateral and rotational degrees of freedom, and improves the prediction accuracy of the dynamic response characteristics of the cam mechanism under high-speed or large-clearance conditions.

[0024] 2. This invention utilizes a technique that tracks the physical collision states of the four corner points of the push rod sidewall with the guide rail sidewall in real time, thereby achieving a quantitative description of the gap impact effect. By calculating the instantaneous impact force at the point of physical collision and synthesizing the total impact torque of the guide rail, this invention can capture the dynamic evolution process of high-frequency impact loads. This not only provides load input for the strength design of the guide rail but also provides mechanical source data for evaluating the vibration and noise level of the mechanism, thus guiding the formulation of vibration suppression measures.

[0025] 3. This invention applies the Poincaré section technique combined with the "rpijf" quintuple symbol encoding system to establish an intuitive method for assessing system stability and lifespan. This method transforms complex nonlinear impact behavior into a visualized discrete symbol sequence. Engineers can locate high-risk areas of guide rail wear (such as specific sidewall locations) based on the statistical results of impact counts at each corner point in the sequence, and determine system stability using the periodic variation law of the impact mode. This provides a quantitative digital evaluation standard and judgment basis for solving the technical problem of unpredictable wear risk in cam mechanisms. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the system architecture of the present invention;

[0027] Figure 2 This is a schematic diagram of the overall method flow of the present invention.

[0028] Among them, 100 is the computer system; 101 is the parameter initialization module; 102 is the kinematic mapping and geometric solution module; 103 is the contact mechanics calculation module; 104 is the guide rail impact model construction module; 105 is the dynamic equation solving module; and 106 is the impact mode analysis module. Detailed Implementation

[0029] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] See attached document Figure 1This invention provides a method for analyzing the impact and dynamics of a guide rail in a three-degree-of-freedom flat-bottomed pushrod cam mechanism. This method is executed by a computer system 100, which includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, performs the following steps. From the perspective of functional module division, the computer system 100 includes: a parameter initialization module 101, a kinematic mapping and geometric solution module 102, a contact mechanics calculation module 103, a guide rail impact model construction module 104, a dynamic equation solving module 105, and an impact mode analysis module 106. The specific implementation of this invention is described in detail below with reference to the above modules.

[0031] The parameter initialization module 101 first reads the geometric and dynamic parameters of the cam mechanism, including: the concentrated mass of the pushrod. , push rod Moment of inertia of the shaft Cam base circle radius The distance between the center of mass of the putter and the ground surface Guide rail clearance Upper constraint height boundary and lower constraint height boundary Contact stiffness coefficient and Damping coefficient and and coefficient of friction In addition, the parameter initialization module 101 also needs to set the numerical simulation parameters, including the time step of numerical integration. Total simulation duration This is to ensure the convergence and completeness of the solution to the dynamic equations.

[0032] Parameter initialization module 101 defines the system's coordinate system and degrees of freedom, and the theoretical contact point between the cam and the follower during the near-rest phase. Establish a global coordinate system with the origin as the coordinate origin. ,in, The axis is defined as the main direction of motion of the push rod (longitudinal). An axis is defined as perpendicular to The transverse direction of the axis, Axis perpendicular to Plane, and simultaneously, with the center of mass of the push rod Establish a local coordinate system with the origin as the coordinate origin. Local coordinate system It moves along with the push rod.

[0033] The parameter initialization module 101 defines the push rod as a rigid body with three degrees of freedom: along the global coordinate system. Lateral displacement of the shaft Along the global coordinate system Longitudinal displacement of the shaft and around the global coordinate system Rotation angle of the shaft .

[0034] The kinematic mapping and geometric solution module 102 is used to process the influence of pushrod deflection on cam input and solve the contact geometry relationship.

[0035] When the push rod rotates around the center of mass by an angle At this time, the relative position of the pushrod's flat bottom plane with respect to the cam changes. The kinematic mapping and geometric solution module 102 first calculates based on the cam's rotational angular velocity... and time Calculate the current angular displacement of the cam .

[0036] Kinematic mapping and geometric solution module 102 calculates the rotation angle of the push rod. This corrects the effective input displacement of the cam in the direction normal to the flat-bottom plane of the pushrod. The theoretical profile curve of the cam is derived from the function... The corrected effective input displacement mapping relationship is described as follows:

[0037] ;

[0038] This mapping relationship indicates that the push rod deflects. After the angle, the cam rotation phase corresponding to the cam profile point in contact with the pushrod changed. The offset.

[0039] The kinematic mapping and geometric solution module 102 further solves for the actual contact points on the cam profile. Position coordinates in the global coordinate system. Actual contact point, based on the geometric generation principle of the cam profile. x-coordinate and ordinate The calculation is as follows:

[0040] ;

[0041] in, Indicates the current angular displacement of the cam Theoretical ascent range at that time; express right The first derivative; This indicates the base circle radius of the cam.

[0042] To determine the actual contact point The exact location is determined by the kinematic mapping and geometric solution module 102 using geometric constraints. These constraints are: the normal vector of the pushrod flat-bottom plane must coincide with the cam profile at the actual contact point. The normal vector at that point is parallel. The push rod rotates. After the angle, the direction vector of its flat bottom normal is The resulting geometric constraint equations are:

[0043] ;

[0044] in, Represents the x-coordinate of the contact point Current angular displacement of the cam Derivative; Represents the ordinate of the contact point Current angular displacement of the cam The derivative of the equation. The kinematic mapping and geometric solution module 102 solves the equation using a numerical iteration method, thereby determining the contact point parameters that satisfy the conditions.

[0045] The kinematic mapping and geometric solution module 102 is also used to calculate auxiliary parameters for the equation of the straight line on the bottom surface of the push rod. First, auxiliary points located on the tangent line of the cam's base circle are calculated. Coordinates:

[0046] ;

[0047] in, Reference This represents the theoretical displacement input of the cam at the current phase angle.

[0048] Based on auxiliary points and the slope of the flat bottom of the putter The kinematic mapping and geometric solution module 102 determines the equation of the straight line containing the bottom surface of the push rod as follows:

[0049] ;

[0050] in, The intercept of the line is given by the auxiliary point. The coordinates are substituted into the equation to obtain the line equation. This line equation is used in subsequent steps to determine the contact state between the cam and the push rod and to calculate the embedding depth.

[0051] See attached document Figure 2 After completing the coordinate system construction, the kinematic mapping and geometric solution module 102 further performs the contact geometry solution between the push rod flat-bottom plane and the cam profile. This is because the push rod has a local coordinate system... The rotational degree of freedom of the axis means that the normal vector of the flat-bottomed plane of the push rod is not always perpendicular in the global coordinate system, but rather varies with the push rod around the axis. Rotation angle of the shaft Real-time changes. Kinematic mapping and geometric solution module 102 first based on the pusher's center of mass. Along the global coordinate system Lateral displacement of the shaft Along the global coordinate system Longitudinal displacement of the shaft As the center of mass of the push rod Global coordinates in the global coordinate system And combined with push rod around Rotation angle of the shaft Determine the center point of the flat bottom of the push rod. Position in the global coordinate system. Center point of the flat bottom of the putter. x-coordinate and ordinate The following calculations were performed using rigid body kinematics transformations:

[0052] ;

[0053] in, This is the vertical distance from the center of mass of the push rod to the flat bottom plane of the push rod. This step determines the translation and rotation of the push rod's bottom surface in space using a coordinate transformation matrix.

[0054] To calculate the normal displacement difference (i.e., contact embedment depth) between the follower flat-bottom plane and the cam profile, the kinematic mapping and geometric solution module 102 constructs an auxiliary geometric solution path. The kinematic mapping and geometric solution module 102 defines an auxiliary point on the extension line of the follower flat-bottom plane. This auxiliary point The x-coordinate is set to the center point of the flat bottom of the push rod. The x-coordinates are the same. By simultaneously solving the linear equation of the push rod's flat bottom plane and the cam tangent equation, the auxiliary point is obtained through the kinematic mapping and geometric solution module 102. ordinate This auxiliary point Used to construct a geometric distance chain from the push rod to the bottom surface reference.

[0055] Based on this, the kinematic mapping and geometric solution module 102 calculates the normal displacement difference in the direction of the normal to the flat bottom plane of the push rod. Normal displacement difference This characterizes the geometric overlap or separation gap between the cam profile and the follower flat-bottom plane in the direction normal to the contact point. If the normal displacement difference... A value greater than zero indicates that physical contact and elastic deformation have occurred; a value less than or equal to zero indicates that the two have separated, with a difference in normal displacement. The calculation formula is as follows:

[0056] ;

[0057] in, For the push rod along the global coordinate system Displacement of the axis; For the push rod along the global coordinate system Displacement of the axis; This is the theoretical displacement input for the cam at the current phase angle; The base circle radius of the cam; Here are the geometric position parameters of the cam mechanism. This formula integrates the three degrees of freedom of the follower's motion with the input motion of the cam, and can capture the contact point position offset and nonlinear deformation caused by the follower's tilt.

[0058] To calculate the energy dissipation (damping force) during the contact process, the kinematic mapping and geometric solution module 102 further calculates the derivative of the normal displacement difference with respect to time, i.e., the normal relative velocity. Normal relative velocity This describes the rate at which the flat-bottomed plane of the pushrod and the cam profile approach or recede from each other in the contact normal direction; the normal relative velocity. The calculation formula is as follows:

[0059] ;

[0060] in, For the push rod along the global coordinate system The speed of the shaft; For the push rod along the global coordinate system The speed of the shaft; The first derivative of the cam lift; This is the second derivative (acceleration) of the cam lift. The formula includes Coriolis acceleration and relative motion terms. The kinematic mapping and geometric solution module 102 updates this value in real time through numerical difference or analytical differentiation, providing kinematic input for subsequent calculation of nonlinear damping force.

[0061] The kinematic mapping and geometric solution module 102, through the above calculations, outputs the normal displacement difference describing the contact state at each simulation time step. and the normal relative velocity of the motion quantity These data are then transmitted to the contact mechanics calculation module for solving the dynamic forces.

[0062] See attached document Figure 2 The contact mechanics calculation module 103 is used to solve the dynamic interaction force between the push rod flat surface and the cam profile. The contact mechanics calculation module 103 first determines the local geometric direction vector at the contact point. The contact mechanics calculation module 103 utilizes the cam profile at the contact point... Use the tangent slope information at the location to calculate the tangential unit vector. and normal unit vector Tangential unit vector The horizontal component of the sum Sum of components and normal unit vector horizontal component Sum of components The current angular displacement of the cam is determined by the cam profile coordinates. The derivative is obtained by normalizing the calculation.

[0063] The contact mechanics calculation module 103 uses a nonlinear Hunt-Crossley contact stiffness damping model to calculate the normal contact force. This model can reflect the energy dissipation characteristics during the contact process. When the kinematic mapping differs from the normal displacement output by the geometric solution module 102... When the force is greater than zero, the contact mechanics calculation module 103 determines that physical contact has occurred and calculates the normal contact force according to the following formula. :

[0064] ;

[0065] in, Indicates the contact stiffness coefficient; This represents the nonlinear stiffness exponent, typically with a value of 1.5. Indicates the damping coefficient; This represents the normal relative velocity. When the normal displacement difference... When the contact mechanics calculation module 103 calculates the normal contact force when it is less than or equal to zero. Set to zero. The contact mechanics calculation module 103 utilizes the normal unit vector. normal contact force Decomposed into global coordinate system Components of the axis and along the global coordinate system Components of the axis .

[0066] In order to accurately calculate the torque generated by the contact force, the contact mechanics calculation module 103 needs to determine the actual contact point on the push rod. Position relative to the geometric center of the push rod. Actual contact point on the push rod. The position of the push rod in the local coordinate system is determined by the offset. Confirmed. The contact mechanics calculation module 103 introduces intermediate calculation variables. and To solve for the offset intermediate calculation variables and The calculation formula is as follows:

[0067] ;

[0068] ;

[0069] Based on intermediate calculation variables and and normal displacement difference The contact mechanics calculation module 103 calculates the offset based on the geometric closed-loop vector equation. :

[0070] ;

[0071] offset The actual contact point was determined. The specific lateral position on the flat bottom plane of the push rod determines the contact force relative to the push rod's center of mass. The length of the lever arm.

[0072] Contact mechanics calculation module 103 further calculates tangential friction force. The contact mechanics calculation module 103 first calculates the actual contact point of the push rod. tangential velocity Actual contact point with the cam tangential velocity The contact mechanics calculation module 103 determines the direction of the frictional force based on the sign of the velocity difference between the two components. If the actual contact point of the push rod... tangential velocity Larger than the actual contact point of the cam tangential velocity Then the direction of the frictional force is the same as the tangential unit vector. Conversely; otherwise, they are the same. Tangential friction. The magnitude of this is calculated according to Coulomb's law of friction, i.e., the coefficient of friction. Multiplied by normal contact force The contact mechanics calculation module 103 utilizes the tangential unit vector. tangential friction force Decomposed into global coordinate system Components of the axis and along the global coordinate system Components of the axis .

[0073] The contact mechanics calculation module 103 integrates the normal contact force and frictional force to calculate their relationship with the center of mass of the push rod. Total torque generated Total torque It affects the rotational degree of freedom of the push rod. Key dynamic factors. Total torque. The calculation formula is as follows:

[0074] ;

[0075] Among them, item and item These represent the actual contact points. Relative to the putter's center of mass The longitudinal and lateral position offsets in the global coordinate system. Through this step, the contact mechanics calculation module 103 completes the conversion from contact interface geometry information to generalized forces and generalized moments.

[0076] See attached document Figure 2 The guide rail impact model construction module 104 is used to track the motion trajectory of the push rod within the guide rail gap and the location of potential collision points in real time. Because the push rod has a... Rotation angle of the shaft and along the global coordinate system Displacement of axis During its movement, the push rod will deflect and laterally move relative to the centerline of the guide rail. The guide rail impact model construction module 104 considers the push rod as the actual contact point with a fixed gap. The rigid body moving within the constrained channel is monitored, with particular attention paid to the positions of the four corner points on the side wall of the push rod. These four corner points are: the lower right corner point... Top left corner And the corresponding upper right corner point and lower left corner point.

[0077] The guide rail impact model construction module 104 first defines the geometric boundary parameters of the guide rail system, including the upper constraint height boundary of the guide rail. and lower constraint height boundary The guide rail impact model construction module 104 is based on the push rod along the global coordinate system. Displacement of axis and rotation angle The lateral coordinates of each corner point in the global coordinate system are calculated using geometric projection relationships.

[0078] For the bottom right corner of the putter The guide rail impact model construction module 104 calculates its lateral coordinates. The lower right corner of the push rod. The longitudinal geometric distance relative to the center of mass of the push rod is determined by the global coordinate system. Displacement of axis and lower constraint height boundary The impact of the guide rail impact model is calculated by module 104 based on the following formula for the lower right corner point. Horizontal coordinate :

[0079] ;

[0080] in, This indicates the vertical distance from the center of mass of the push rod to the flat bottom plane; Indicates the coordinate system around the global coordinate system The rotation angle of the axis. This formula indicates that the lower right corner point... The lateral position is determined by the push rod along the global coordinate system. Axial displacement And due to the angle of rotation The resulting transverse components are jointly determined.

[0081] For the upper left corner of the putter The guide rail impact model construction module 104 calculates its lateral coordinates. Top left corner Located in the upper region of the push rod, its longitudinal position is related to the upper constraint height of the guide rail. The guide rail impact model construction module 104 calculates the upper left corner point according to the following formula. Horizontal coordinate :

[0082] ;

[0083] in, This indicates the upper constraint height boundary of the guide rail; The height position of the upper edge of the guide rail is defined; This represents the instantaneous longitudinal distance from the center of mass of the push rod to the upper edge of the guide rail. The negative sign in the formula reflects the geometric orientation of the left corner point relative to the push rod axis.

[0084] For the upper right corner of the push rod It is located on the upper part of the push rod and is initially on the right side. The guide rail impact model construction module 104 calculates its lateral coordinates. :

[0085] ;

[0086] For the lower left corner of the push rod It is located at the bottom of the push rod and is initially on the left side. The guide rail impact model construction module 104 calculates its lateral coordinates. :

[0087] ;

[0088] The guide rail impact model construction module 104 realizes the digital reconstruction of the push rod's attitude inside the guide rail through the above calculation steps. Regardless of the complex combination of lateral movement and deflection motion of the push rod, the guide rail impact model construction module 104 can output the lateral distance of each potential impact point relative to the guide rail sidewall in real time, providing a geometric basis for subsequent judgment on whether a collision impact has occurred.

[0089] See attached document Figure 2 After determining the real-time lateral coordinates of each corner point of the push rod, the guide rail impact model construction module 104 further performs impact force calculation based on nonlinear Hertzian contact theory. The guide rail impact model construction module 104 first reads the preset single-sided gap threshold of the guide rail. Contact stiffness coefficient of the guide rail and the damping coefficient of the guide rail The guide rail impact model construction module 104 compares the absolute value of the lateral coordinate of the corner point with the single-sided gap threshold of the guide rail. The size relationship is used to determine whether a physical collision has occurred.

[0090] For the lower right corner of the putter The guide rail impact model construction module 104 calculates the instantaneous lateral velocity at that point. Instantaneous lateral velocity The lateral translation speed of the push rod Longitudinal translation speed and rotational angular velocity Jointly decided. The guide rail impact model construction module 104 is based on the lower right corner point. Horizontal coordinate Taking the derivative with respect to time yields When the lower right corner point absolute value of the horizontal coordinate Greater than or equal to the guide rail single-sided gap threshold At that time, the guide rail impact model construction module 104 determines that contact has occurred and calculates the impact force on the lower right side according to the following formula. :

[0091] ;

[0092] Among them, item Indicates the depth at which the lower right corner point is embedded in the sidewall of the guide rail; index For Hertzian contact nonlinearity exponent; terms This represents a dynamic correction factor considering the internal damping characteristics of the material; function This is a sign function used to determine the direction of the impact force (i.e., the direction pointing towards the center line of the guide rail). When the lower right corner point... absolute value of the horizontal coordinate Less than the single-sided gap threshold of the guide rail At that time, the guide rail impact model construction module 104 will generate the impact force on the lower right side. The value is assigned to zero.

[0093] For the upper left corner of the push rod The guide rail impact model construction module 104 also calculates the instantaneous lateral velocity at that point. When the upper left corner point absolute value of the horizontal coordinate Greater than or equal to the guide rail single-sided gap threshold At that time, the guide rail impact model construction module 104 calculates the impact force on the upper left side according to the following formula. :

[0094] ;

[0095] Among them, item Indicates the depth at which the upper left corner point is embedded in the sidewall of the guide rail; Item Used to calculate energy dissipation during the collision process, when the upper left corner point absolute value of the horizontal coordinate Less than the single-sided gap threshold of the guide rail At that time, the guide rail impact model construction module 104 will generate the impact force on the upper left side. The value is assigned to zero.

[0096] The guide rail impact model construction module 104 utilizes the above logic to independently handle the collision states of the four corners of the push rod. Since the push rod will simultaneously make contact with the guide rail at multiple points on different sides or at different heights, the guide rail impact model construction module 104 performs vector synthesis of all calculated non-zero impact forces to obtain the total guide rail impact force acting on the push rod. Total impact force of the guide rail It is one of the main excitation sources of the lateral vibration of the push rod. At the same time, since the point of application of each impact force does not pass through the center of mass of the push rod, the guide rail impact model construction module 104 uses each impact force and its corresponding lever arm to calculate the additional torque generated by the impact force, which directly affects the rotational acceleration of the push rod.

[0097] See attached document Figure 2 After obtaining the instantaneous impact force at each corner of the push rod, the guide rail impact model construction module 104 further performs the calculation of the guide rail impact torque. This is because the lower right corner of the push rod... and the top left corner (And other diagonal points) are not geometrically related to the center of mass of the push rod. When these corner points coincide, and are subjected to lateral impact forces from the sidewalls of the guide rail, they will generate a force relative to the center of mass of the push rod. The rotational torque, the impact torque of the guide rail It is the key dynamic driving factor that causes the push rod to oscillate and chatter in the gap between the guide rails.

[0098] The guide rail impact model construction module 104 first calculates the center of mass of the push rod. The geometric distance modulus to each potential impact point, for the lower right corner point The guide rail impact model construction module 104 constructs the model based on the coordinates of the push rod's center of mass and the lower right corner point. Calculate the Euclidean distance between the two coordinates. For the top left corner point The guide rail impact model construction module 104 also calculates the push rod's center of mass. and the top left corner point Euclidean distance between These distance moduli represent the physical rod length basis in torque calculations.

[0099] The guide rail impact model construction module 104 is based on the magnitude of the impact force, the geometric distance modulus, and the rotation angle of the push rod. The combined impact torque of the guide rail acting on the push rod The guide rail impact model construction module 104 uses the following formula for calculation:

[0100] ;

[0101] in, , , , The instantaneous impact force at the four corner points (bottom right, top right, top left, and bottom left) is 0 if there is no contact. This represents the effective longitudinal lever arm length of each corner point relative to the center of mass; This indicates the rotation angle of the push rod.

[0102] This formula, in a physical sense, characterizes the projection of the effective lever arm of the impact force application point relative to the center of mass of the push rod in the longitudinal direction. Since the impact force of the guide rail mainly acts laterally, the torque it generates about the center of mass mainly depends on the longitudinal offset distance. The guide rail impact model construction module 104 uses this formula to consider the rotation angle of the push rod's rotational attitude. The instantaneous modulation effect on the effective lever arm length. The positive and negative signs in the formula reflect the different contributions of the impact force at different points of application to the direction of rotation of the push rod (counterclockwise or clockwise).

[0103] The guide rail impact model construction module 104 calculates the total impact torque of the guide rail. As the external excitation torque of the system, it is transmitted to the dynamic equation solving module to update the angular acceleration of the push rod. Through this process, the embodiments of the present invention can accurately simulate the transient rotational effect generated by the push rod when a collision occurs, thereby achieving a complete description of the translational-rotational coupled dynamics.

[0104] See attached document Figure 2 Before assembling the overall dynamic equations of the system, the dynamic equation solving module 105 needs to calculate the elastic constraint forces acting on the push rod and the torques they generate about the center of mass. This step mainly deals with the return spring force located at the top of the push rod and the auxiliary constraint forces acting laterally on the push rod. Because the push rod introduces a rotation angle... The spring attachment point at the top of the push rod no longer moves only longitudinally, but generates lateral displacement coupling, which causes the line of action of the spring force to deflect, generating additional lateral component force and rotational torque.

[0105] The dynamic equation solving module 105 first calculates the spring attachment point at the top of the push rod. Instantaneous position in the global coordinate system. Based on the push rod's center of mass. Current displacement and the rotation angle of the push rod The dynamic equation solving module 105 uses rigid body kinematics formulas to determine the spring attachment point at the top of the push rod. Coordinates:

[0106] ;

[0107] in, Indicates the spring attachment point at the top of the push rod. Horizontal coordinate; Indicates the spring attachment point at the top of the push rod. The vertical coordinate; and This reflects the geometric modulation effect of the push rod's rotational attitude on the spatial position of the attachment point.

[0108] The dynamic equation solving module 105 is based on the spring attachment point at the top of the push rod. Using the instantaneous coordinates of the spring and the coordinates of the fixed point at the top of the spring, calculate the real-time tensile length and total elastic force of the spring. Subsequently, the dynamic equation solving module 105, based on the unit direction vector of the spring axis, calculates the total elastic force. Decomposed into global coordinate system Components of the axis and along the global coordinate system Components of the axis :

[0109] , ;

[0110] in, and These represent the unit vectors in the direction of the spring axis. shaft and Projected components on the axis. This indicates the direction in which the spring force points back to the equilibrium position. This decomposition step quantifies the lateral disturbance effect of the spring force caused by the tilt of the push rod.

[0111] The dynamic equation solving module 105 further calculates the effect of the top spring force on the center of mass of the push rod. The generated torque Because the push rod rotates, the line of action of the spring force may not pass through the center of mass of the push rod, thus creating a torque. The calculation formula is as follows:

[0112] ;

[0113] This formula integrates components. With weight The contribution of the effective lever arm in the push rod rotation coordinate system. and The term precisely describes the vertical and horizontal distances of the point of force application relative to the center of mass during rotation.

[0114] In addition, the dynamic equation solving module 105 calculates the lateral constraint force acting on the push rod. This force characterizes the elastic support and damping effects (e.g., flexible constraints from the auxiliary guide mechanism) experienced by the push rod in the lateral direction of motion; the lateral constraint force. The calculation formula is as follows:

[0115] ;

[0116] in, Indicates the lateral constraint stiffness coefficient; Indicates the lateral constraint damping coefficient; For the push rod along the global coordinate system Displacement of the axis; For the push rod along the global coordinate system The speed of the shaft. This formula shows that the lateral constraint force always prevents the push rod from deviating from the center position and from lateral vibration.

[0117] Through the above calculations, the dynamic equation solving module 105 decouples the complex elastic constraint system into a generalized force acting on the center of mass. and the top spring force on the center of mass of the push rod The generated torque This provides the necessary mechanical input terms for establishing a complete three-degree-of-freedom dynamic equation.

[0118] See attached document Figure 2After obtaining all the generalized forces and torques acting on the push rod, the dynamic equation solving module 105 is responsible for constructing a set of differential equations describing the evolution of the system's motion state, and solving them discretizedly using a numerical integration algorithm. Based on the principles of Newton-Euler dynamics, the dynamic equation solving module 105 establishes a set of coupled dynamic equations including lateral translation, longitudinal translation, and planar rotation.

[0119] The three-degree-of-freedom dynamic equations in physical space constructed by the dynamic equation solving module 105 are as follows:

[0120] ;

[0121] in, Indicates the mass of the push rod; Indicates the push rod along the global coordinate system Lateral acceleration of the axis; Indicates the push rod along the global coordinate system Longitudinal acceleration of the shaft; Indicates push rod rotation Angular acceleration of the axis; Indicates lateral constraint force; Represents the global coordinate system The components of the axis; Indicates along the global coordinate system The components of the axis; Indicates normal contact force Along the global coordinate system The components of axial decomposition; Indicates normal contact force Along the global coordinate system The components of axial decomposition; Represents tangential friction force Decomposed into global coordinate system The components of the axis; Represents tangential friction force Decomposed into global coordinate system The components of the axis; This indicates the total impact force on the guide rail; This indicates the initial preload of the system; Indicates push rod rotation Moment of inertia of the shaft; This indicates the force of the top spring relative to the center of mass of the push rod. The torque generated; This indicates the total impact torque of the guide rail; Indicates the center of mass of the putter Total torque generated .

[0122] To improve the stability of numerical calculations and enhance the generality of the results, the dynamic equation solving module 105 introduces a series of dimensionless parameters to perform dimensionless transformation on the physical equations. The dimensionless transformation parameters defined by the dynamic equation solving module 105 are as follows:

[0123] System inherent frequency parameters Defined as ,in The stiffness of the spring at the top of the push rod; dimensionless time. Defined as Dimensionless cam speed Defined as .

[0124] The dimensionless parameters of displacement and geometric dimensions are defined as follows: , , , , , , , , .

[0125] in, For the system's characteristic length parameters (such as maximum lift); Indicates the dimensionless clearance of the guide rail; Indicates the guide rail clearance; This indicates the distance between the center of mass of the putter and the bottom surface; This represents the dimensionless total clearance of the system; Indicates the actual total clearance; , The dimensionless height of the guide rail constraint boundary; This represents a dimensionless angle.

[0126] The dimensionless parameter of mechanical properties is defined as: damping ratio stiffness coefficient ratio , , Damping coefficient ratio , , .

[0127] in, , , This represents the ratio of the stiffness of each branch to the corresponding total stiffness, and is a dimensionless parameter. , , , Indicates the stiffness of the spring at different positions; , , It represents the ratio of the damping of each branch to the corresponding total damping, and is a dimensionless parameter; , , , This indicates the damping coefficient of the damper at different locations.

[0128] The dimensionless moment of inertia is defined as The dimensionless torque is defined as: , , .

[0129] in, Represents the dimensionless moment of inertia; Indicates push rod rotation The actual moment of inertia of the shaft; Representing the characteristic quality of the system The distance between the center of mass of the putter and the ground surface With the system's characteristic length parameter The reference inertia of the composition; , , This represents dimensionless torque. Indicates the stiffness of the spring and feature length parameter The reference torque is formed.

[0130] Based on the aforementioned dimensionless parameters, the dynamic equation solving module 105 transforms the physical dynamic equations into a dimensionless dynamic equations:

[0131] ;

[0132] In the above dimensionless system of equations, , , These represent dimensionless transverse acceleration, longitudinal acceleration, and angular acceleration, respectively. Various dimensionless forces (such as...) , , (etc.) are all calculated by dividing the corresponding physical force by the reference force. For example, dimensionless lateral constraint force. The calculation expression is transformed into:

[0133] ;

[0134] To solve this system of second-order differential equations in a computer, the dynamic equation solving module 105 performs a reduction process, converting it into a first-order state-space equation system. The dynamic equation solving module 105 defines the state vector. State vector time derivative It is determined by the right-hand side of the above dimensionless dynamic equations.

[0135] The dynamic equation solving module 105 uses a fourth-order Runge-Kutta numerical integration algorithm or other higher-order numerical integration algorithms for discretization. At each time step... Inside, the dynamic equation solving module 105 solves the equations based on the current state vector. Calculate the four slope coefficients to update the state vector for the next time step. The process iterates until the preset simulation cycle is completed, thus outputting the displacement, velocity, and acceleration response curves of the push rod in the entire time domain. In this way, the dynamic equation solving module 105 realizes the dynamic simulation of the cam mechanism considering the backlash impact and rotational coupling effects.

[0136] See attached document Figure 2 The impact mode analysis module 106 is used to discretize the continuous high-dimensional dynamic trajectory to capture the periodic or chaotic motion characteristics of the system within the guide rail gap. Since the collision between the push rod and the guide rail is a highly nonlinear transient process, the impact mode analysis module 106 does not record the state at all times, but instead constructs specific Poincaré sections and only records the feature points when the system state trajectory crosses these sections.

[0137] The impact mode analysis module 106 defines a set of hypersurfaces in the six-dimensional state space. These hypersurfaces physically correspond to the critical geometric positions where the corners of the push rod are about to contact the sidewalls of the guide rail. The impact mode analysis module 106 defines a set of scalar discriminant functions. To mathematically describe these hypersurfaces, where Generalized coordinates including the push rod.

[0138] For the critical contact state between the lower right corner of the push rod and the right side wall of the guide rail (positive clearance boundary), the impact mode analysis module 106 defines the first interface function. :

[0139] ;

[0140] when When the horizontal coordinate of the lower right corner point is exactly equal to the guide rail clearance boundary, it indicates that the horizontal coordinate of the lower right corner point is exactly equal to the guide rail clearance boundary. .

[0141] For the critical contact state between the lower right corner of the push rod and the left side wall of the guide rail (negative clearance boundary), the impact mode analysis module 106 defines the second interface function. :

[0142] ;

[0143] when When the horizontal coordinate of the lower right corner point is exactly equal to the negative boundary of the guide rail, it indicates that the horizontal coordinate of the lower right corner point is exactly equal to the negative boundary of the guide rail. .

[0144] For the critical contact state between the upper left corner of the push rod and the right side wall of the guide rail, the impact mode analysis module 106 defines a third interface function. :

[0145] ;

[0146] For the critical contact state between the upper left corner of the push rod and the left side wall of the guide rail, the impact mode analysis module 106 defines the fourth interface function. :

[0147] ;

[0148] During the numerical integration process in the dynamic equation solving module 105, the impact mode analysis module 106 monitors the aforementioned scalar discriminant function in real time. The sign change. When the impact mode analysis module 106 detects the scalar discriminant function. The value flips sign between two adjacent time steps (e.g., from negative to positive), indicating that the system state trajectory crosses the corresponding Poincaré section. .

[0149] To obtain the precise intersection point of the cross sections, the impact mode analysis module 106 employs an interpolation algorithm (such as the Hénon method or the bisection method) within the time interval where the sign flip is detected. This precise positioning allows... The moment The impact mode analysis module extracts time points 106. The corresponding system full state vector The full state vector is then stored in the Poincaré section point set. middle.

[0150] The impact mode analysis module 106 converts the continuous push rod motion trajectory into a series of discrete mapping points in this way:

[0151] ;

[0152] Cross-section point set By eliminating a large amount of redundant data from the non-contact phase, the system's topological structure regarding the impact boundary in phase space is directly reflected. The impact mode analysis module 106 only records crossing events with a collision velocity greater than zero (i.e., approaching the guide rail wall), thus ensuring that the physical meaning of the samples corresponds to the state just before the collision. By analyzing the distribution of these discrete points on the phase plane (e.g., clustering into a finite number of points, forming closed curves, or exhibiting fractal structures), the impact mode analysis module 106 can reveal whether the system has period-doubling bifurcations or chaotic attractors.

[0153] See attached document Figure 2 The impact mode analysis module 106, based on the constructed Poincaré mapping point set, further performs topological pattern recognition based on symbolic dynamics. In order to quantitatively describe the complex motion behavior of the push rod within the guide rail gap, especially to distinguish between periodic motion, quasi-periodic motion and chaotic motion, the impact mode analysis module 106 uses the "rpijf" quintuple symbol encoding system to classify and label the dynamic response of the system.

[0154] The impact mode analysis module 106 first defines the physical meaning of each parameter in the quintuple: Parameter This represents the number of cam rotation cycles, used to normalize the observation time window; parameter Indicates in The total number of times the lower right corner of the push rod collides with the side wall of the guide rail within each cycle; parameters Indicates in The total number of times the upper right corner of the push rod collides with the side wall of the guide rail within each cycle; parameters Indicates in The total number of times the lower left corner of the push rod collides with the side wall of the guide rail within each cycle; parameters Indicates in The total number of times the upper left corner of the push rod collides with the side wall of the guide rail within each cycle.

[0155] The impact mode analysis module 106 is configured with four independent event counters: , , , They are initialized to zero. The impact mode analysis module 106 synchronously monitors the cumulative rotation angle of the cam. Define a standard observation period interval as follows: ,in The value is typically set to 1 to detect single-cycle response.

[0156] The impact mode analysis module 106 uses the Poincaré cross-section crossing event defined in the preceding steps as a counting trigger signal. This occurs when the system state trajectory crosses the interface corresponding to the lower right corner contact point. or At that time, the impact mode analysis module 106 determined that an impact event had occurred on the lower right side and set the counter. The value is increased by 1.

[0157] When the system state trajectory crosses the interface corresponding to the upper right corner contact point (corresponding to the upper right corner coordinates exceeding the gap threshold), the impact mode analysis module 106 determines that an upper right impact event has occurred and sets the counter. The value is increased by 1.

[0158] When the system trajectory crosses the interface corresponding to the lower left corner contact point, the impact mode analysis module 106 determines that a lower left impact event has occurred and sets the counter accordingly. The value is increased by 1.

[0159] When the system state trajectory crosses the interface corresponding to the contact point at the upper left corner... or At that time, the impact mode analysis module 106 determined that an impact event had occurred on the upper left side and set the counter. The value is increased by 1.

[0160] After the cam is completed After one complete rotation cycle (i.e.) Increased The impact mode analysis module 106 reads the values ​​of each counter and generates the current impact mode code string "rpijf". For example, the code "1-2-0-0-1" means that during one revolution of the cam, there were two impacts on the lower right side of the push rod, one impact on the upper left side, and no impacts at other positions.

[0161] The impact mode analysis module 106 further compares the impact mode codes generated over multiple consecutive cycles. If the impact mode codes are consecutive... If the system remains unchanged within a certain period (e.g., always "1-1-0-1-0"), the impact mode analysis module 106 determines that the system is in a stable period. Motion State. If the impact mode code exhibits periodic changes between consecutive periods (e.g., alternating between "1-2-0-0-1" and "1-1-0-0-1"), the impact mode analysis module 106 determines that the system has undergone period-doubling bifurcation. If the impact mode code shows no repetition pattern in the long time domain, and the Poincaré cross-section point set exhibits a fractal structure, the impact mode analysis module 106 determines that the system has entered a chaotic motion state.

[0162] Through the above logic, the impact mode analysis module 106 transforms complex nonlinear dynamic time history data into a concise digital feature sequence, enabling the identification and quantitative characterization of the tilting and flipping motion and multi-point impact vibration behavior of the push rod within the guide rail gap. This process overcomes the problem of deviation between the predicted dynamic performance and the actual operating state caused by the neglect of the push rod's rotational and lateral motion degrees of freedom in traditional single-degree-of-freedom analysis methods. Simultaneously, the impact frequency and distribution information contained in the generated digital feature sequence can indicate high-risk areas of guide rail wear (i.e., corner positions with higher count values) and reflect the vibration and noise level during mechanism operation, thus providing a quantitative topological criterion based on a high-precision multidimensional coupling model for cam mechanism parameter optimization, wear risk assessment, and life prediction.

Claims

1. A method for analyzing the impact and dynamics of a guide rail in a three-degree-of-freedom flat-bottomed pushrod cam mechanism, characterized in that... Includes the following steps: Read the parameters of the cam mechanism, define the global coordinate system and the local coordinate system, and define the push rod as a rigid body with three degrees of freedom: lateral displacement along the x-axis of the global coordinate system, longitudinal displacement along the y-axis of the global coordinate system, and rotation angle about the center of mass. The effective input displacement of the cam in the normal direction of the push rod flat bottom plane is corrected according to the rotation angle of the rotation around the center of mass, and the normal displacement difference between the push rod flat bottom plane and the cam profile is calculated. The contact state is determined based on the normal displacement difference, and the normal contact force, tangential friction force and total cam contact torque between the push rod flat bottom plane and the cam profile are calculated. Monitor the physical collision state between the four corners of the push rod sidewall and the guide rail sidewall, calculate the guide rail impact force for the corners where physical collision occurs, and synthesize the total guide rail impact torque; The four corner points of the push rod sidewall specifically refer to: the lower right corner point, the upper left corner point, the upper right corner point, and the lower left corner point of the push rod; The physical collision status of the four corner points of the monitoring push rod sidewall with the guide rail sidewall specifically includes: Using the rigid body geometric projection relationship, the lateral coordinates of the four corner points in the global coordinate system are calculated in real time, and the absolute value of the lateral coordinates is compared with the single-sided gap threshold of the guide rail to determine whether a physical collision has occurred. By combining the normal contact force, the tangential friction force, the total contact torque of the cam, the impact force of the guide rail, the total impact torque of the guide rail, and the elastic constraint force and the constraint torque generated by the elastic constraint force on the push rod, a set of coupled dynamic differential equations including lateral translation, longitudinal translation and planar rotation is constructed, and the motion state of the push rod is analyzed and updated using a numerical integration algorithm. The motion trajectory of the push rod is monitored to see if it crosses the Poincaré section. The characteristic points at the crossing time are recorded, and the dynamic motion state of the impact pattern code recognition system is generated based on the characteristic points.

2. The method for analyzing the guide rail impact and dynamics of the three-degree-of-freedom flat-bottomed pushrod cam mechanism according to claim 1, characterized in that, The step of correcting the effective input displacement of the cam in the normal direction of the pushrod flat-bottom plane based on the rotation angle about the center of mass specifically includes: By utilizing the geometric constraint that the normal vector of the push rod flat bottom plane is parallel to the normal vector of the cam profile at the contact point, the position coordinates of the actual contact point on the cam profile in the global coordinate system are solved numerically through iteration, thereby correcting the effective input displacement of the cam in the normal direction of the push rod flat bottom plane. The calculation of the normal displacement difference between the push rod flat bottom plane and the cam profile is based on the spatial linear equation of the push rod flat bottom plane and the geometric overlap of the cam profile in the contact point normal direction.

3. The method for analyzing the guide rail impact and dynamics of the three-degree-of-freedom flat-bottomed pushrod cam mechanism according to claim 1, characterized in that, The calculation of the normal contact force between the flat bottom plane of the push rod and the cam profile is based on a nonlinear contact stiffness damping model. The specific logic for calculating the total cam contact torque between the flat bottom plane of the push rod and the cam profile is as follows: based on the lateral and longitudinal offsets of the actual contact point relative to the center of mass of the push rod, the torque components generated by the normal contact force and the tangential friction force on the center of mass of the push rod are calculated and summed to obtain the total cam contact torque.

4. The method for analyzing the guide rail impact and dynamics of the three-degree-of-freedom flat-bottomed pushrod cam mechanism according to claim 1, characterized in that, The impact force of the guide rail is based on the Hertzian contact theory model and is calculated using the depth of the corner point of the physical collision embedded in the side wall of the guide rail and the instantaneous lateral velocity of the corner point of the physical collision. The specific logic for synthesizing the total impact torque of the guide rail is as follows: based on the Euclidean distance from the center of mass of the push rod to each corner point where physical collision occurs and the rotation angle, determine the effective longitudinal lever arm corresponding to each corner point, and calculate the vector sum of the product of the guide rail impact force at each corner point and the corresponding effective longitudinal lever arm to obtain the total impact torque of the guide rail.

5. The method for analyzing the guide rail impact and dynamics of the three-degree-of-freedom flat-bottomed pushrod cam mechanism according to claim 1, characterized in that, The elastic constraint force on the push rod and the constraint torque generated by the elastic constraint force are calculated in the following way: Based on the rotation angle and displacement of the push rod, determine the spatial position change of the spring attachment point at the top of the push rod, calculate the total elastic force generated by the top spring and decompose it into lateral and longitudinal components to obtain the elastic constraint force on the push rod. The constraint torque of the elastic constraint force is calculated based on the lever arms of the lateral component and the longitudinal component relative to the center of mass of the push rod. Based on the lateral displacement and lateral velocity of the push rod, calculate the auxiliary constraint force acting on the side of the push rod.

6. The method for guide rail impact and dynamic analysis of the three-degree-of-freedom flat-bottomed pushrod cam mechanism according to claim 1, characterized in that, The coupled dynamic differential equations specifically include: Lateral dynamic equations: relating to the push rod mass, lateral acceleration, lateral component of the top spring force, lateral component of the normal contact force, lateral component of the tangential friction force, auxiliary constraint force, and lateral component of the guide rail impact force; Longitudinal dynamic equations: relating the push rod mass, longitudinal acceleration, longitudinal component of the top spring force, longitudinal component of the normal contact force, longitudinal component of the tangential friction force, and initial preload; Rotational dynamics equations: related to the moment of inertia of the push rod, angular acceleration, constraint torque generated by the top spring force, total contact torque of the cam, and total impact torque of the guide rail.

7. The method for analyzing the guide rail impact and dynamics of the three-degree-of-freedom flat-bottomed pushrod cam mechanism according to claim 1, characterized in that, The Poincaré section is defined by a set of hypersurfaces corresponding to the critical geometric positions where the corners of the push rod are about to contact the sidewall of the guide rail; The monitoring of whether the motion trajectory of the push rod crosses the Poincaré section specifically includes: monitoring whether the discriminant function value defining the hypersurface undergoes a sign flip between adjacent time steps.

8. The method for guide rail impact and dynamic analysis of the three-degree-of-freedom flat-bottomed pushrod cam mechanism according to claim 1, characterized in that, The impact mode code adopts the rpijf quintuple symbol encoding system, which specifically includes: The parameter r represents the reference number of cam rotation cycles; The parameter p represents the total number of physical collisions that occur at the lower right corner of the push rod within r reference cycles; The parameter i represents the total number of physical collisions that occur at the upper right corner of the push rod within r reference cycles; Parameter j represents the total number of physical collisions that occur at the lower left corner of the push rod within r reference cycles; The parameter f represents the total number of physical collisions that occur at the upper left corner of the push rod within r reference cycles.

9. The method for analyzing the guide rail impact and dynamics of the three-degree-of-freedom flat-bottomed pushrod cam mechanism according to claim 8, characterized in that, The specific logic of the dynamic motion state identification system includes: Compare the shock mode codes generated over multiple consecutive reference periods; If the impact mode code remains unchanged, the system is determined to be in a periodic motion state. If the impact mode code exhibits periodic alternation between consecutive periods, the system is determined to be in a period-doubling bifurcation state. If the impact mode code does not repeat in a regular pattern, the system is determined to be in a state of chaotic motion.

Images