Method for calculating acceleration and deceleration of each motion axis through stroke and vibration limitation

Abstract

The invention relates to the technical field of multi-axis cooperative motion control, and discloses a method for calculating acceleration and deceleration of each motion axis by stroke and vibration limitation, which comprises the following steps of: S1, acquiring stroke data (Sx, Sy) of each motion axis and a preset acceleration resultant vector limit value; s2, based on the stroke data of each shaft and the acceleration resultant vector limit value, determining the total motion time T meeting the requirement of multi-shaft synchronous start and stop; and S3, according to the total motion time T, calculating acceleration and deceleration time (Tx0, Ty0) corresponding to each motion axis, and verifying whether an acceleration resultant vector meets a limiting condition or not. By combining real-time iterative optimization of total motion time T and acceleration and deceleration time, instantaneous acceleration and braking caused by a stepped track under high-speed motion are effectively suppressed, structural resonance and noise are reduced, constant-speed stage time and acceleration abrupt change rate are limited, a speed curve is further smoothed, high-frequency vibration energy transfer is reduced, and the high-speed vibration performance is improved. Therefore, the equipment operation stability is improved and the mechanical life is prolonged.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-axis coordinated motion control, and in particular to a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limits. Background Art

[0002] Multi-axis interpolation technology is a key method in the field of precision motion control for CNC machine tools, robots, and other applications. It aims to achieve high-precision motion along a predetermined trajectory by coordinating the displacement and speed of multiple motion axes. Traditional linear interpolation technology uses 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 based on the end point position deviation and continues to move, repeating the cycle until the target end point is reached.

[0003] However, this method can still meet the needs in low-speed, low-precision scenarios. Frequent starting and stopping between axes causes the motion trajectory to be step-like. 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, and reducing the operating life of the equipment. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the present invention provides a method for calculating the acceleration and deceleration of each motion axis based on the stroke and vibration limit, which solves the problem of high-frequency impact force, large resonance and noise.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solutions: A method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limit, comprising the following steps:

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

[0007] S2. Determine the total motion time T that satisfies multi-axis synchronous start and stop based on the stroke data of each axis and the acceleration vector limit value;

[0008] S3. Calculate the acceleration and deceleration time (Tx0, Ty0) corresponding to each motion axis based on the total motion time T, and verify whether the acceleration vector satisfies the restriction conditions;

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

[0010] S5. Generate acceleration instructions and speed curves for each motion axis based on the shortest total motion time Tmin and corresponding acceleration and deceleration times;

[0011] S6, outputting the acceleration command and speed curve to the motion controller to drive the multi-axis synchronous motion and reach the end point at the same time;

[0012] Among them, during the iterative process from S2 to S4, the data stream includes the input stroke of each axis, the real-time calculated 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 plan.

[0013] Through the above technical solution: by collecting the stroke data (Sx, Sy) of each axis and the preset acceleration limit value (Amax), basic parameter input is provided for subsequent calculations to ensure that the optimization process has accurate physical constraints. Then, based on the stroke and acceleration constraints, the total time T initial value of the multi-axis synchronous start and stop is quickly determined to avoid motion asynchrony or inefficiency caused by unreasonable time allocation. Through the formula

[0014] Calculate the acceleration components of each axis and verify whether their resultant vector satisfies Ensure that the acceleration is within the vibration tolerance of the mechanical system and prevent over-limit impact. Use a combination of table lookup and iterative adjustment to quickly approximate the shortest total time Tmin that meets the constraints, significantly reduce real-time calculation time, improve dynamic optimization efficiency, generate a trapezoidal velocity curve and force a uniform speed time Tmin ≥ 0.5s to ensure motion smoothness and reduce mechanical jitter and positioning errors caused by frequent speed changes. By limiting the acceleration mutation rate and suppressing high-frequency noise, the synchronization signal is used to ensure strict synchronization of multiple axes and improve end point positioning accuracy.

[0015] Preferably, in said S3, the acceleration vector verification condition is: the sum of the squares of the acceleration components (ax, ay) of each axis does not exceed the preset acceleration vector threshold, that is, ax is satisfied. 2 +ay 2 ≤Amax 2 , where Amax is the acceleration vector limit value.

[0016] Through the above technical solution: global acceleration is constrained by vector synthesis, single-axis overload is avoided, and the risk of mechanical resonance is reduced.

[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 strokes of each axis, Tx0 and Ty0 are the acceleration and deceleration times of each axis, and Tx0 = Ty0.

[0021] Through the above technical solution: based on the uniform acceleration motion model, the physical relationship between acceleration, stroke and time is accurately matched.

[0022] Preferably, in said S4, the iterative adjustment of the total motion time T is implemented by a table lookup method, and the optimal acceleration and deceleration times and the total time corresponding to different travel intervals are stored in advance as a lookup table, and the lookup table data is directly called when the program is running to shorten the calculation time.

[0023] Through the above technical solution: the optimal parameters of typical trips are pre-stored, the online computing burden is reduced, and the low latency requirements of real-time control systems are adapted.

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

[0025] Through the above technical solution: the threshold is adaptively adjusted according to the speed to balance vibration suppression and motion efficiency at high speed.

[0026] Preferably, in said S5, the speed curve of each axis generated satisfies that the time of the uniform speed stage of each axis is not less than the preset minimum stabilization time tmin, and tmin≥0.5 seconds.

[0027] Through the above technical solution: the duration of the forced uniform speed section is increased, the control jitter caused by short-term speed changes is eliminated, and the movement stability is improved.

[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 the stroke and acceleration of each axis.

[0029] Through the above technical solution: fast obtain feasible solutions through mathematical modeling, avoid blind trial and error, and improve the rationality of initial parameters.

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

[0031] Through the above technical solutions: smooth acceleration transition, reduce high-frequency mechanical noise, improve the working environment and extend the life of the equipment.

[0032] Preferably, in said S3, when verifying the acceleration resultant vector, a function graph analysis method is used to screen the smallest real root greater than zero as the candidate acceleration and deceleration time.

[0033] Through the above technical solution: quickly locate the effective solution through visual analysis, avoid invalid iterations, and improve computing efficiency.

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

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

[0036] The present invention provides a method for calculating the acceleration and deceleration of each motion axis based on travel and vibration limits. It has the following beneficial effects:

[0037] 1. The present invention dynamically constrains the combined acceleration of multiple axes to ensure that the acceleration components of each axis are within the vibration threshold allowed by the mechanical system, avoiding excessive impact forces caused by excessive uniaxial acceleration. Combined with real-time iterative optimization of the total motion time T and acceleration and deceleration times, it effectively suppresses instantaneous acceleration and braking caused by step-like trajectories under high-speed motion, reduces structural resonance and noise, and further smoothes the speed curve by limiting the uniform speed stage time and the acceleration mutation rate, reducing high-frequency vibration energy transmission, thereby improving the smoothness of equipment operation and extending the mechanical life.

[0038] 2. This invention uses a global optimization algorithm based on travel and vibration limits to rapidly determine the minimum total time Tmin required for synchronized start and stop, subject to preset constraints, avoiding the redundant cycles caused by traditional fixed time allocations. By using a quartic equation to calculate the initial T value in real time and combining it with a table lookup to store optimal parameters, it significantly reduces iterative calculation time. While ensuring acceleration and vector compliance, it dynamically balances the motion time of each axis, achieving the shortest path planning in high-speed scenarios and significantly improving the motion efficiency of multi-axis interpolation. This approach is particularly suitable for time-sensitive, high-precision applications such as CNC machining and 3D printing.

[0039] 3. The present invention eliminates trajectory deviations and accumulated errors caused by asynchronous motion in traditional split-axis interpolation by forcing multi-axis synchronous start and stop and generating a continuous and smooth speed curve. It also combines function image analysis to screen the optimal acceleration and deceleration times, ensuring uniform acceleration distribution across all axes and avoiding single-axis overload or speed mutations. In addition, the vibration threshold is dynamically adjusted with the movement speed to further adapt to different working conditions. It can still maintain stable acceleration constraints under high speed and high load, achieve high coordination of multi-axis motion, improve terminal positioning accuracy and repeatability, and meet the stringent requirements of motion control in the field of precision manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Schematic diagram of a method flow of the present invention for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limit;

[0041] Figure 2 Schematic diagram of interpolation action description of a method for calculating acceleration and deceleration of each motion axis based on stroke and vibration limit according to the present invention;

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

[0043] Figure 4 Schematic diagram of linear interpolation motion combined acceleration according to a method of calculating acceleration and deceleration of each motion axis based on stroke and vibration limit of the present invention;

[0044] Figure 5 A schematic diagram of multi-axis motion speed and acceleration of a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limits according to the present invention;

[0045] Figure 6 A schematic diagram of continuously calculating the shortest time for a method of calculating the acceleration and deceleration of each motion axis based on stroke and vibration limits according to the present invention;

[0046] Figure 7 Schematic diagram of an initial time calculation function image of a method for calculating the acceleration and deceleration of each motion axis based on stroke and vibration limit of the present invention;

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

[0048] The following will clearly and completely describe the technical solution of the present invention in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0049] Please see the attached Figure 1 -Attached Figure 8 , an embodiment of the present invention provides a method for calculating the acceleration and deceleration of each motion axis based on the stroke and vibration limit, comprising the following steps:

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

[0051] S2. Determine a linear interpolation motion path that satisfies the total motion time T required for multi-axis synchronous start and stop based on the stroke data of each axis and the acceleration vector limit value;

[0052] S3. Calculate the acceleration and deceleration time (Tx0, Ty0) corresponding to each motion axis based on the total motion time T, and verify whether the acceleration vector meets the restriction conditions;

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

[0054] S5. Generate multi-axis motion speed and acceleration curves based on the shortest total motion time Tmin and the corresponding acceleration and deceleration times;

[0055] S6, output acceleration command and speed curve to the motion controller, drive multiple axes to move synchronously and reach the end point at the same time;

[0056] Among them, during the iterative process from S2 to S4, the data stream includes the input stroke of each axis, the real-time calculated 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 plan.

[0057] In S3, the acceleration vector verification condition is: the sum of the squares of the acceleration components of each axis (ax, ay) does not exceed the preset acceleration vector threshold, that is, the linear interpolation motion acceleration ax is satisfied. 2 +ay 2 ≤Amax 2 , where Amax is the acceleration vector limit value.

[0058] The calculation method of the acceleration component of each axis is:

[0059] ax=Sx / [Tx0·(T−Tx0)];

[0060] ay=Sy / [Ty0·(T−Ty0)];

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

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

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

[0064] According to the real-time vibration sensor feedback and accelerometer data, according to formula A max =A base -k·V dynamically reduces the acceleration threshold at high speed to complete dynamic adjustment, where A base is the basic acceleration threshold, k is the proportional coefficient between speed and acceleration threshold, and V is the current motion speed;

[0065] The root screening method is to draw The first positive real root crossing zero is selected as the candidate solution, where a x ,a yare the acceleration components of the X and Y axes.

[0066] In S5, the generated speed curve of each axis satisfies that the uniform speed stage time of each axis is not less than the preset minimum stabilization 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 established based on the constraints of the stroke and acceleration vector 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 acceleration vector.

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

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

[0071] Acceleration limit value setting: Determine the maximum allowable acceleration based on mechanical structure resonance frequency testing or finite element analysis, and verify the linear relationship between the dynamic threshold and speed through experiments;

[0072] The initial time calculation is based on the quartic equation Combined with the constraint T x0 =T y0 , solve the initial value of T by Newton 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 , where S x , Sy is the travel distance of X axis and Y axis, T x0 , T y0 is the acceleration and deceleration time of the X-axis and Y-axis, T is the total motion time, is the acceleration vector limit value;

[0073] Derivation of acceleration and deceleration time formula: from uniform acceleration motion model Derived When verifying the logic Mark the current T as an invalid solution and trigger S4 iterative adjustment, where ax is the acceleration of the X axis, S x is the travel distance of the X axis;

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

[0075] Iteration termination: When the difference between two consecutive T calculations is less than the preset accuracy, the iteration is stopped;

[0076] When generating the speed curve, a trapezoidal speed curve is used, and the speed of the uniform speed section is Ensure that Tmin = T-2T{x0} ≥ 0.5s, where V is the speed of the uniform speed section, S is the total stroke of the single axis, and Tmin is the minimum stabilization time of the uniform speed stage;

[0077] The instruction format is that the acceleration instruction is output as a pulse frequency or analog voltage signal, which is adapted to different drive interfaces;

[0078] Synchronous control sends synchronous cycle signals through the EtherCAT bus to align the clocks of each axis controller;

[0079] Noise suppression adds acceleration rate limit to the speed curve, using Avoid high frequency shocks, among which, is the rate of change of the acceleration vector.

[0080] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention 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 limit, characterized in that: The following steps are involved: S1. Obtain the travel data (Sx, Sy) of each motion axis and the preset acceleration vector limit value; S2. Determine the total motion time T that satisfies multi-axis synchronous start and stop based on the stroke data of each axis and the acceleration vector limit value; S3. Calculate the acceleration and deceleration time (Tx0, Ty0) corresponding to each motion axis based on the total motion time T, and verify whether the acceleration vector satisfies the restriction conditions; S4. When the verification result in S3 does not meet the constraint conditions, the total motion time T is iteratively adjusted and the acceleration and deceleration times are recalculated until the shortest total motion time Tmin that meets the constraints is obtained; S5. Generate acceleration instructions and speed curves for each motion axis based on the shortest total motion time Tmin and corresponding acceleration and deceleration times; S6, outputting the acceleration command and speed curve to the motion controller to drive the multi-axis synchronous motion and reach the end point at the same time; Among them, during the iterative process from S2 to S4, the data stream includes the input stroke of each axis, the real-time calculated 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 plan.

2. The method of calculating the acceleration and deceleration of each motion axis based on travel and vibration limits according to claim 1, characterized in that: In S3, the acceleration vector verification condition is: the sum of the squares of the acceleration components of each axis (ax, ay) does not exceed the preset acceleration vector threshold, that is, ax is satisfied. 2 +ay 2 ≤Amax 2 , where Amax is the acceleration vector limit value.

3. The method of calculating the acceleration and deceleration of each motion axis based on travel and vibration limits according to claim 2, characterized in that: The calculation method of the acceleration components of each axis is: ax=Sx / [Tx0·(T−Tx0)]; ay=Sy / [Ty0·(T−Ty0)]; Where Sx and Sy are the strokes of each axis, Tx0 and Ty0 are the acceleration and deceleration times of each axis, and Tx0 = Ty0.

4. The method of calculating the acceleration and deceleration of each motion axis based on travel and vibration limits according to claim 1, characterized in that: In S4, the iterative adjustment of the total motion time T is implemented by using a lookup table method. The optimal acceleration and deceleration times and the total time corresponding to different travel intervals are stored in a lookup table in advance. When the program is running, the lookup table data is directly called to shorten the calculation time.

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

6. The method of calculating the acceleration and deceleration of each motion axis based on travel and vibration limits according to claim 1, characterized in that: In the above S5, the generated speed curves of each axis satisfy that the time of the uniform speed stage of each axis is not less than the preset minimum stabilization time tmin, and tmin≥0.5 seconds.

7. The method of calculating the acceleration and deceleration of each motion axis based on travel and vibration limits according to claim 1, characterized in that: 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 the stroke and acceleration of each axis.

8. The method of calculating the acceleration and deceleration of each motion axis based on travel and vibration limits according to claim 1, characterized in that: In S6, the outputted velocity curve is further used to reduce noise under high-speed motion, and the noise control is achieved by limiting the mutation rate of the acceleration resultant vector.

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

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

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