A method for calculating acceleration and deceleration of each motion axis by stroke and shock limitation

Abstract

The present application relates to the technical fields of multi-axis cooperative motion control, and discloses a method for calculating acceleration and deceleration of each motion axis by stroke and vibration limitation, comprising the following steps: S1, obtaining stroke data (Sx, Sy) of each motion axis and a preset acceleration resultant vector limitation value; S2, determining total motion time T satisfying multi-axis synchronous start and stop based on the stroke data of each axis and the acceleration resultant vector limitation value; S3, calculating acceleration and deceleration time (Tx0, Ty0) corresponding to each motion axis according to the total motion time T, and verifying whether the acceleration resultant vector satisfies the limitation condition. By combining real-time iterative optimization of total motion time T and acceleration and deceleration time, instantaneous acceleration and braking caused by step-shaped trajectory under high-speed motion are effectively inhibited, structural resonance and noise are reduced, uniform speed stage time and acceleration mutation rate are limited, speed curve is further smoothed, high-frequency vibration energy transmission is reduced, and thus equipment running stability is improved and mechanical life is prolonged.

Description

Technical Field

[0001] This invention relates to the field of multi-axis cooperative motion control technology, specifically a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations. Background Technology

[0002] Multi-axis interpolation technology, as a key method in the field of precision motion control such as CNC machine tools and robots, aims to achieve high-precision motion along a predetermined trajectory by coordinating the displacement and speed of multiple motion axes. Traditional linear interpolation technology adopts a split-axis alternating micro-step approximation mechanism: after moving a small distance along a certain axis from the starting point, it switches to another axis to continue moving based on the deviation of the endpoint position, and iterates until the target endpoint is reached.

[0003] However, this method can still meet the requirements in low-speed and low-precision scenarios. Frequent inter-axis start-stop causes the motion trajectory to be stepped. The motor generates high-frequency impact force due to instantaneous acceleration and braking, which exceeds the vibration threshold allowed by the mechanical system, causing structural resonance and noise, thus reducing the service life of the equipment. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations, thus solving the problem of high-frequency impact forces generating significant resonance and noise.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations, comprising the following steps:

[0006] S1. Obtain the travel data (Sx, Sy) of each motion axis and the preset acceleration resultant vector limit value;

[0007] S2. Based on the travel data of each axis and the acceleration resultant vector limit value, determine the total motion time T that satisfies the multi-axis synchronous start and stop.

[0008] S3. Based on the total motion time T, calculate the acceleration and deceleration times (Tx0, Ty0) corresponding to each motion axis, and verify whether the resultant acceleration vector satisfies the constraint conditions.

[0009] S4. If the verification result in S3 does not meet the constraints, the total motion time T is iteratively adjusted and the acceleration and deceleration time is recalculated until the shortest total motion time Tmin that meets the constraints is obtained.

[0010] S5. Based on the shortest total motion time Tmin and the corresponding acceleration and deceleration time, generate acceleration commands and velocity curves for each motion axis;

[0011] S6. Output the acceleration command and velocity curve to the motion controller to drive multi-axis synchronous motion and reach the endpoint simultaneously.

[0012] During the iterations from S2 to S4, the data stream includes the input travel of each axis, the real-time calculated resultant acceleration vector value, and the adjusted total time parameter. The output result is the optimal time that meets the vibration limit and the corresponding acceleration distribution scheme.

[0013] The above technical solution involves collecting travel data (Sx, Sy) and preset acceleration limits (Amax) for each axis to provide basic parameter inputs for subsequent calculations, ensuring accurate physical constraints during the optimization process. Then, based on travel and acceleration constraints, the initial value of the total start-stop time T for multi-axis synchronization is quickly determined, avoiding motion asynchrony or inefficiency caused by unreasonable time allocation. This is achieved through the formula...

[0014] Calculate the acceleration components along each axis and verify whether their resultant vector satisfies the following conditions: To ensure that the acceleration is within the vibration tolerance of the mechanical system and prevent excessive impact, a combination of lookup table method and iterative adjustment is used to quickly approximate the shortest total time Tmin that satisfies the constraints, significantly reducing real-time calculation time and improving dynamic optimization efficiency. A trapezoidal velocity curve is generated and the uniform velocity time Tmin is forced to be ≥0.5s to ensure motion stability and reduce mechanical vibration and positioning errors caused by frequent speed changes. By limiting the acceleration mutation rate, high-frequency noise is suppressed, and a synchronization signal is used to ensure strict synchronization of multiple axes, thereby improving the endpoint positioning accuracy.

[0015] Preferably, in step S3, the acceleration resultant vector verification condition is: the sum of the squares of the acceleration components (ax, ay) along each axis does not exceed a preset acceleration resultant vector threshold, i.e., it satisfies ax 2 +ay 2 ≤Amax 2 , where Amax is the constraint value of the resultant acceleration vector.

[0016] The above technical solution uses vector synthesis to constrain global acceleration, avoiding uniaxial overload and reducing the risk of mechanical resonance.

[0017] Preferably, the acceleration components of each axis are calculated as follows:

[0018] ax = Sx / [Tx0·(T-Tx0)];

[0019] ay = Sy / [Ty0·(T-Ty0)];

[0020] Where Sx and Sy are the travel distances of each axis, and Tx0 and Ty0 are the acceleration and deceleration times of each axis, with Tx0 = Ty0.

[0021] The above technical solution, based on a uniform acceleration motion model, accurately matches the physical relationship between acceleration, travel distance, and time.

[0022] Preferably, in step S4, the iterative adjustment of the total motion time T is achieved by a lookup table method. The optimal acceleration / deceleration time and total time corresponding to different travel intervals are stored in advance as a lookup table, and the program directly calls the lookup table data during runtime to shorten the calculation time.

[0023] The above technical solution pre-stores the optimal parameters for typical journeys, reducing the burden of online calculations and adapting to the low-latency requirements of real-time control systems.

[0024] Preferably, the acceleration resultant vector limit value is dynamically adjusted based on the vibration threshold, and the vibration threshold is positively correlated with the motion speed.

[0025] The above technical solution achieves a balance between vibration suppression and motion efficiency at high speeds by adaptively adjusting the threshold based on speed.

[0026] Preferably, in step S5, the generated velocity curves of each axis satisfy that the uniform velocity phase time of each axis is not less than the preset minimum stabilization time tmin, and tmin ≥ 0.5 seconds.

[0027] The above technical solution aims to reduce the duration of the constant speed segment, eliminate control jitter caused by short-term speed changes, and improve motion stability.

[0028] Preferably, in S2, the initial value of the total motion time T is solved by a quartic equation, which is established based on the constraints of the combined vector of travel and acceleration of each axis.

[0029] The above technical solution allows for the rapid acquisition of feasible solutions through mathematical modeling, avoiding blind trial and error and improving the rationality of initial parameters.

[0030] Preferably, in S6, the output velocity curve is further used to reduce noise under high-speed motion, and the noise control is achieved by limiting the abrupt change rate of the resultant acceleration vector.

[0031] The above technical solutions can smooth acceleration transitions, reduce high-frequency mechanical noise, improve the working environment, and extend equipment life.

[0032] Preferably, in step S3, when verifying the resultant acceleration vector, the smallest real root greater than zero is selected as the candidate acceleration / deceleration time using the function graph analysis method.

[0033] The above technical solution enables rapid location of valid solutions through visual analysis, avoids invalid iterations, and improves computational efficiency.

[0034] Preferably, the method is applicable to multi-axis motion control scenarios of CNC machine tools, industrial robots, or 3D printing equipment.

[0035] The above technical solutions clarify technology adaptability, guide the precise parameter configuration of CNC machine tools and robots in various scenarios, and enhance the value of technology implementation.

[0036] This invention provides a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations. It has the following beneficial effects:

[0037] 1. This invention dynamically constrains the combined acceleration of multiple axes to ensure that the acceleration components of each axis are within the permissible vibration threshold of the mechanical system, avoiding excessive impact force caused by excessive acceleration of a single axis. Combined with real-time iterative optimization of the total motion time T and acceleration and deceleration time, it effectively suppresses instantaneous acceleration and braking caused by the stepped trajectory under high-speed motion, reduces structural resonance and noise, and further smooths the velocity curve by limiting the uniform velocity phase time and acceleration mutation rate, reducing the transmission of high-frequency vibration energy, thereby improving the stability of equipment operation and extending mechanical life.

[0038] 2. This invention utilizes a global optimization algorithm based on travel and vibration constraints to quickly solve for the shortest total time Tmin for synchronous start-stop under preset constraints, avoiding redundant cycles caused by traditional fixed time allocation. It calculates the initial T value in real time using a univariate quartic equation and pre-stores optimal parameters using a lookup table method, significantly reducing iterative calculation time. While ensuring acceleration and vector compliance, it dynamically balances the motion time of each axis, achieving shortest path planning in high-speed scenarios and significantly improving the motion efficiency of multi-axis interpolation. This is particularly suitable for time-sensitive high-precision scenarios such as CNC machining and 3D printing.

[0039] 3. This invention eliminates trajectory deviations and cumulative errors caused by asynchronous actions in traditional split-axis interpolation by forcing multi-axis synchronous start-stop and generating continuous and smooth speed curves. It also selects the optimal acceleration and deceleration times by combining function graph analysis to ensure uniform acceleration distribution across axes and avoid single-axis overload or sudden speed changes. In addition, the vibration threshold is dynamically adjusted with the motion speed to further adapt to different working conditions. It can maintain stable acceleration constraints even under high speed and high load, achieve a high degree of coordination of multi-axis motion, improve terminal positioning accuracy and repeatability, and meet the stringent requirements of motion control in the precision manufacturing field. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to the present invention.

[0041] Figure 2 This is a schematic diagram illustrating the interpolation motion of a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to the present invention.

[0042] Figure 3 This is a schematic diagram of the linear interpolation motion path for a method of calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to the present invention.

[0043] Figure 4 This is a schematic diagram of the linear interpolation motion resultant acceleration of a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to the present invention.

[0044] Figure 5 This is a schematic diagram of multi-axis motion velocity and acceleration, illustrating a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to the present invention.

[0045] Figure 6 This is a schematic diagram illustrating the method of continuously calculating the shortest time for estimating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to the present invention.

[0046] Figure 7 This is a schematic diagram of the initial time calculation function of a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to the present invention.

[0047] Figure 8 This is a schematic diagram of accelerometer data function for a method of calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to the present invention. Detailed Implementation

[0048] The technical solution of the present invention will now be clearly and completely described 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.

[0049] Please see the appendix Figure 1 - Appendix Figure 8 This invention provides a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations, comprising the following steps:

[0050] S1. Obtain the travel data (Sx, Sy) of each motion axis of the interpolation motion and the preset acceleration resultant vector limit value;

[0051] S2. Based on the travel data of each axis and the acceleration resultant vector limit value, determine the linear interpolation motion path that satisfies the total motion time T of multi-axis synchronous start and stop;

[0052] S3. Based on the total motion time T, calculate the acceleration and deceleration times (Tx0, Ty0) corresponding to each motion axis, and verify whether the resultant acceleration vector satisfies the constraints.

[0053] S4. If the verification result in S3 does not meet the constraints, the total motion time T is iteratively adjusted and the acceleration and deceleration time is recalculated until the shortest total motion time Tmin that meets the constraints is obtained.

[0054] S5. Based on the shortest total motion time Tmin and the corresponding acceleration and deceleration time, generate multi-axis motion velocity and acceleration curves;

[0055] S6 outputs acceleration commands and velocity curves to the motion controller, driving multi-axis synchronous motion to reach the endpoint simultaneously.

[0056] During the iterations from S2 to S4, the data stream includes the input travel of each axis, the real-time calculated resultant acceleration vector value, and the adjusted total time parameter. The output result is the optimal time that meets the vibration limit and the corresponding acceleration distribution scheme.

[0057] In S3, the verification condition for the resultant acceleration vector is: the sum of the squares of the acceleration components (ax, ay) along each axis does not exceed the preset threshold for the resultant acceleration vector, which satisfies the condition for the resultant acceleration ax in linear interpolation motion. 2 +ay 2 ≤Amax 2 , where Amax is the constraint value of the resultant acceleration vector.

[0058] The calculation method for the acceleration components of each axis is as follows:

[0059] ax = Sx / [Tx0·(T-Tx0)];

[0060] ay = Sy / [Ty0·(T-Ty0)];

[0061] Where Sx and Sy are the travel distances of each axis, and Tx0 and Ty0 are the acceleration and deceleration times of each axis, with Tx0 = Ty0.

[0062] In S4, the iterative adjustment of the total motion time T is achieved by using a lookup table method. The optimal acceleration and deceleration times and total times corresponding to different travel intervals are stored in advance as a lookup table. When the program runs, it directly calls the lookup table data to shorten the calculation time.

[0063] The acceleration resultant vector limit is dynamically adjusted based on the vibration threshold, continuously calculating the shortest time, and the vibration threshold is positively correlated with the motion speed.

[0064] Based on real-time vibration sensor feedback and accelerometer data, according to formula A max =A base -k·V dynamically reduces the acceleration threshold at high speeds to achieve dynamic adjustment, where A base The base acceleration threshold is given by k, where k is the ratio coefficient between velocity and acceleration threshold, and V is the current velocity.

[0065] The root screening method, on the other hand, draws... For the curve, the first positive real root crossing the zero point is selected as a candidate solution, where a x ,a yThese are the acceleration components along the X and Y axes.

[0066] In S5, the generated velocity curves of each axis satisfy the condition that the uniform velocity phase time of each axis is not less than the preset minimum stable time tmin, and tmin ≥ 0.5 seconds.

[0067] In S2, the initial value of the total motion time T is solved by a quartic equation, which is based on the constraints of the combined vector of travel and acceleration of each axis.

[0068] In S6, the output velocity curve is further used to reduce noise under high-speed motion. Noise control is achieved by limiting the mutation rate of the resultant acceleration vector.

[0069] In S3, when verifying the resultant acceleration vector, the function graph analysis method is used to select the smallest real root greater than zero as the candidate acceleration / deceleration time.

[0070] The method is applicable to multi-axis motion control scenarios in CNC machine tools, industrial robots, or 3D printing equipment.

[0071] Acceleration limit setting: The maximum allowable acceleration is determined based on the mechanical structure resonance frequency test or finite element analysis, and the linear relationship between the dynamic threshold and the velocity is verified by experiment.

[0072] The initial time calculation is performed using a quartic equation. Combined with constraint T x0 =T y0 The initial value of T is obtained by solving the Newton-Synchronous iteration method. The physical meaning is that the root of the equation corresponds to a feasible solution that satisfies the acceleration constraint. Negative roots and overshoot roots need to be excluded. T < S x / V max , among which, S x Sy represents the travel distance along the X and Y axes, and T represents the travel distance along the Y and X axes, respectively. x0 T y0 Let X and Y represent the acceleration and deceleration times along the X and Y axes, respectively, and T represent the total motion time. This is the constraint value for the resultant acceleration vector;

[0073] Derivation of the acceleration / deceleration time formula: from the uniform acceleration motion model The derivation is If the verification logic is Mark the current T as an invalid solution and trigger S4 iteration adjustment, where ax is the acceleration along the X-axis, and S... x This represents the travel distance along the X-axis;

[0074] The lookup table method pre-stores the Tmin and corresponding T{x0} of common travel intervals as a two-dimensional matrix, and matches the actual travel interval through bilinear interpolation at runtime;

[0075] The iteration terminates when the difference between two consecutive calculated values ​​of T is less than the preset precision.

[0076] The velocity curve is generated using a trapezoidal velocity curve, with the velocity in the uniform segment being... Ensure that Tmin = T - 2T{x0} ≥ 0.5s, where V is the velocity of the uniform segment, S is the total stroke of the single axis, and Tmin is the minimum settling time of the uniform segment;

[0077] The instruction format is an acceleration command output in pulse frequency or analog voltage signal format, which is compatible with different driver interfaces;

[0078] Synchronization control sends synchronization periodic signals via the EtherCAT bus to ensure clock alignment for each axis controller.

[0079] Noise suppression adds a limit to the rate of change of acceleration in the velocity curve, employing... To avoid high-frequency impacts, among which, Let be the rate of change of the resultant acceleration vector.

[0080] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations, characterized in that, Includes the following steps: S1. Obtain the travel data of each motion axis ( , ) and preset acceleration resultant vector limit values; S2. Based on the travel data of each motion axis and the acceleration resultant vector limit value, determine the total motion time to satisfy multi-axis synchronous start and stop. ; S3, based on the total motion time Calculate the acceleration and deceleration times corresponding to each motion axis. , And verify whether the resultant acceleration vector satisfies the constraints; S4. If the verification result in S3 does not meet the constraints, then the total motion time... Perform iterative adjustments and recalculate acceleration and deceleration times until the shortest total motion time Tmin that satisfies the constraints is obtained; S5. Based on the shortest total motion time Tmin and the corresponding acceleration and deceleration time, generate acceleration commands and velocity curves for each motion axis; S6. Output the acceleration command and velocity curve to the motion controller to drive multi-axis synchronous motion and reach the endpoint simultaneously. During the iterations from S2 to S4, the data stream includes the input travel of each motion axis, the real-time calculated resultant acceleration vector value, and the adjusted total time parameter. The output result is the optimal time to meet the vibration limit and the corresponding acceleration distribution scheme. In S3, the verification condition for the resultant acceleration vector is: the acceleration components of each motion axis ( , The sum of the squares of the accelerations does not exceed a preset threshold for the resultant acceleration vector, i.e., it satisfies... ,in This is the constraint value for the resultant acceleration vector; The acceleration components of each motion axis are calculated as follows: ； ； in, , The acceleration and deceleration times for each motion axis are given, and ; In S4, the total motion time The iterative adjustment is implemented using a lookup table method. The optimal acceleration / deceleration time and total time corresponding to different travel intervals are stored in advance as a lookup table. When the program runs, it directly calls the lookup table data to shorten the calculation time. In S2, the total motion time The initial values ​​are solved by a quartic equation, which is established based on the constraints of the combined vector of the travel and acceleration of each motion axis. The initial time calculation is performed using a quartic equation. Combined with constraints Solve using Newton's iteration method The initial value, in physical terms, represents the feasible solution that satisfies the acceleration constraints corresponding to the roots of the equation, and negative roots and overshoot roots must be excluded. ,in, , This represents the travel distance along the X and Y axes.

2. The method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to claim 1, characterized in that: The acceleration resultant vector limit value is dynamically adjusted based on the vibration threshold, and the vibration threshold is positively correlated with the motion speed.

3. The method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to claim 1, characterized in that: In S5, the generated velocity curves of each motion axis satisfy the condition that the uniform speed phase time of each motion axis is not less than the preset minimum stable time tmin, and tmin ≥ 0.5 seconds.

4. The method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to claim 1, characterized in that: In S6, the output velocity curve is further used to reduce noise under high-speed motion. The noise control is achieved by limiting the abrupt change rate of the resultant acceleration vector.

5. The method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to claim 1, characterized in that: In step S3, when verifying the resultant acceleration vector, the function graph analysis method is used to select the smallest real root greater than zero as the candidate acceleration / deceleration time.

6. The method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limitations according to claim 1, characterized in that: The method is applicable to multi-axis motion control scenarios for CNC machine tools, industrial robots, or 3D printing equipment.

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