Method and system for planning feeding speed of cam grinding machine tool

Abstract

The invention belongs to the related technical field of numerical control machine tools, and discloses a cam grinding machine tool feeding speed planning method and system. The maximum allowable machining speed curve of the cam grinding machine tool is divided into a plurality of intervals, peak intervals are combined, and the maximum speed of each combined interval and the speed accessibility of a right end point are both larger than or equal to zero; a forward planning speed curve and a reverse speed planning curve of each acceleration overrun interval are obtained; and combining the forward planning speed curve and the reverse planning speed curve to obtain a combined planning curve corresponding to the acceleration overrun intervals, and replacing the curve of each acceleration overrun interval with the combined planning curve in the maximum allowable processing speed curve to obtain the required cam speed planning curve. According to the invention, the feed speed planning calculation efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to numerical control machine tools, and more specifically, relates to a method and system for planning the feed speed of a cam grinding machine tool. Background Art

[0002] The camshaft is one of the key components in transmission machinery and is widely used in equipment such as automobile engines and precision machinery. With the development of the manufacturing industry, the functions to be realized by the camshaft are becoming more and more complex, resulting in more variable cam profiles and larger changes in profile curvature. The C-X two-axis linkage numerical control grinding is the main method for camshaft machining. Under the currently commonly used constant linear speed machining method, when the rotational speed of the workpiece rotation axis C-axis reaches more than one hundred revolutions per minute, the acceleration of the following motion of the grinding wheel feed axis X-axis is extremely easy to exceed the physical constraint limit, causing the machine tool to vibrate. Therefore, to improve the machining efficiency and running stability, a new speed planning method is needed.

[0003] Although only two axes are involved in cam grinding for machining, for speed planning, there is still a complex non-linear synthesis problem. The commonly used speed planning method based on the acceleration and deceleration model has a simple algorithm and high calculation efficiency, but it cannot make full use of the machine tool performance and has a low machining efficiency. The speed planning method based on two-way scanning can make full use of the physical properties of each axis and has a high machining efficiency, but has a high calculation complexity and low calculation efficiency. So far, there is still a lack of a speed planning method that can be used in actual machining and has both a high machining efficiency and a high calculation efficiency. Summary of the Invention

[0004] In view of the above defects or improvement requirements of the prior art, the present invention provides a method and system for planning the feed speed of a cam grinding machine tool, which solves the problem that the existing speed planning methods cannot have both a high machining efficiency and a high calculation efficiency.

[0005] To achieve the above object, according to one aspect of the present invention, a method for planning the feed speed of a cam grinding machine tool is provided, and the method includes the following steps:

[0006] Divide the maximum allowable machining speed curve of the cam grinding machine tool into multiple peak intervals, merge the peak intervals and make the reachability from the left endpoint of each merged peak interval to the maximum speed and from the maximum speed to the right endpoint speed greater than or equal to zero;

[0007] Judge whether the acceleration of each merged peak interval exceeds the maximum acceleration, and use the peak interval with the acceleration exceeding the maximum acceleration as the acceleration overrun interval;

[0008] For each acceleration overrun interval, update the speeds of each point on the curve in the forward and reverse directions respectively, while ensuring that the speed of each point after the update does not exceed the speed of that point on the maximum allowable machining speed curve, so as to obtain the forward planning speed curve and the reverse speed planning curve for each acceleration overrun interval;

[0009] Merge the forward planning speed curve and the reverse speed planning curve to obtain the merged planning curve corresponding to the acceleration overrun interval, and use the merged planning curve to replace the curve of each acceleration overrun interval in the maximum allowable machining speed curve, so as to obtain the required cam speed planning curve.

[0010] Further preferably, the merging of the peak intervals is carried out according to the following steps:

[0011] (1) When the reachability from the left-end point speed to the maximum speed or from the maximum speed to the right-end point speed within each peak interval is less than zero, calculate the global reachability from the left-end point speed to the right-end point speed. When the global reachability is less than or equal to zero, update the right-end point speed; when the global reachability is greater than zero, update the maximum speed; update the speeds of the points within each peak interval except the left-end point, the right-end point, and the maximum speed point, so as to realize the update of the speeds of all points within the peak interval;

[0012] (2) Repeat (1) until the reachability from the left-end point speed to the maximum speed and from the maximum speed to the right-end point speed within each peak interval is greater than or equal to zero;

[0013] (3) Re-divide the peak intervals according to the updated speeds of each point, and return to step (1) until the reachability from the left-end point speed to the maximum speed and from the maximum speed to the right-end point speed within each peak interval is greater than or equal to zero.

[0014] Further preferably, in (1), the calculation formula for the reachability from the left-end point speed to the maximum speed is as follows:

[0015]

[0016] where ψ left-maxv is the speed reachability from the left-end point speed to the maximum speed, Δc left-maxv is the C-axis rotation angle corresponding to the speed from the left-end point speed to the maximum speed, v left and v max are the left-end point speed and the maximum speed respectively, and a cmax is the maximum acceleration of the C-axis;

[0017] Further preferably, in (1), the calculation formula for the reachability from the maximum speed to the right-end point speed is as follows:

[0018]

[0019] Among them, ψ maxv-right is the velocity reachability from the maximum velocity to the right endpoint velocity, and Δc maxv-right is the C-axis rotation angle corresponding to the velocity from the maximum velocity to the right endpoint velocity, v right , v max are the right endpoint velocity and the maximum velocity respectively, and a cmax is the maximum acceleration of the C-axis.

[0020] Further preferably, in (1), the calculation formula of the global reachability is as follows:

[0021]

[0022] Among them, ψ left-right is the global reachability from the left endpoint velocity to the right endpoint velocity, and Δc left-right is the C-axis rotation angle corresponding to the velocity from the left endpoint velocity to the right endpoint velocity, v left , v right are the left endpoint velocity and the right endpoint velocity respectively, and a cmax is the maximum acceleration of the C-axis.

[0023] Further preferably, in (1), the calculation formula for updating the right endpoint velocity is as follows:

[0024]

[0025] The formula for updating the maximum velocity is as follows:

[0026]

[0027] Among them, Δc left-right is the C-axis rotation angle corresponding to the velocity from the left endpoint velocity to the right endpoint velocity, Δc right-maxv is the C-axis rotation angle corresponding to the velocity from the left endpoint velocity to the maximum velocity, v left is the left endpoint velocity, v maxv , v right represent the updated maximum velocity and the right endpoint velocity respectively, and a cmax is the maximum acceleration of the C-axis.

[0028] Further preferably, the velocities of each point on the forward update curve are calculated according to the following formula:

[0029]

[0030] If then is the forward iterative calculation velocity of the i-th sampling point, is the forward iterative calculation velocity of the (i - 1)-th discrete point, is the maximum feasible acceleration of the C-axis at the (i - 1)-th sampling point, c i is the C-axis rotation angle corresponding to the i-th sampling point, c i-1 is the C-axis rotation angle corresponding to the (i - 1)-th sampling point is the speed at the corresponding sampling point on the VLC curve

[0031] The speed of each point on the reverse update curve is calculated according to the following formula:

[0032]

[0033] If then let is the reverse iterative calculation speed at the i-th sampling point is the reverse iterative calculation speed at the (i + 1)-th discrete point is the minimum feasible acceleration of the C-axis at the (i + 1)-th sampling point, c i is the C-axis rotation angle corresponding to the i-th sampling point, c i+1 is the C-axis rotation angle corresponding to the (i + 1)-th sampling point is the speed at the corresponding sampling point on the VLC curve

[0034] Further preferably, the formula for merging the planning curves is as follows:

[0035]

[0036] where, c cs is the intersection point of the forward planning curve and the reverse planning curve, c s 、c e respectively represent the left and right endpoints of the acceleration overrun interval, v cf 、v cb are the forward planning curve and the reverse planning curve respectively, v vlc represents the VLC curve

[0037] Further preferably, the construction model of the maximum allowable machining speed curve is as follows:

[0038]

[0039] where, v c 、a c 、j c are the C-axis speed, acceleration and jerk respectively, f′(c), f″(c), f″′(c) are the first, second and third order derivatives of the spline relationship of the X-axis displacement relative to the C-axis rotation angle respectively, v cmax 、a cmax 、j cmax are the maximum speed, acceleration and jerk of the C-axis respectively, v xmax 、axmax and j xmax are the maximum speed, acceleration, and jerk of the X-axis, respectively.

[0040] According to another aspect of the present invention, a feed speed planning system for a cam grinding machine tool is provided. The system includes an actuator for executing the feed speed planning method for a cam grinding machine tool described above.

[0041] Generally speaking, compared with the prior art, the above technical solutions conceived by the present invention have the following beneficial effects:

[0042] 1. The feed speed planning method used in the present invention first preliminarily adjusts the speeds of points on the maximum allowable machining speed curve as a whole to merge the peak intervals, and then locally adjusts the speeds in the acceleration overrun intervals. The maximum allowable machining speed curve is modified in two steps. In actual production, after modifying the machining trajectory and parameters, a speed planning curve for machining can be quickly generated, with high calculation efficiency, greatly improving the actual production efficiency and reducing the time cost.

[0043] 2. In the present invention, since the number of initially divided peak intervals is too large and the interval size is small, it is necessary to merge the initially divided peak intervals to reduce the number of speed points in subsequent forward and reverse iterative calculations. During the merging process, the acceleration of the maximum allowable machining speed curve is initially constrained by adjusting the speed, reducing the acceleration overrun intervals; in addition, only the maximum point speed and the right endpoint speed need to be adjusted during merging, with simple calculations and high calculation efficiency.

[0044] 3. The feed speed planning method used in the present invention has high machining efficiency. An optimization problem model is constructed considering the physical axis performance limits, and at the same time, the speed, acceleration, and jerk limits of the C-axis and X-axis are considered, enabling full utilization of the physical performance of the machine tool and achieving a high machining efficiency.

[0045] 4. The feed speed planning method used in the present invention has high machining accuracy. Considering the speed, acceleration, and jerk limits of the C-axis and X-axis, it ensures that there are no drastic fluctuations in speed and acceleration in the planned speed curve, avoiding problems such as vibration marks and increased contour errors in the machining area, and having high machining accuracy.

[0046] 5. The feed speed reachability planning method for the cam grinding machine tool of the present invention is universal and can be used for any numerically controlled machine tool with the coordinated machining of a linear axis and a rotating axis. The method has strong scalability and strong engineering practicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a flowchart of the feed speed planning method for a cam grinding machine tool constructed according to a preferred embodiment of the present invention;

[0048] Figure 2 is a schematic diagram of speed spike interval division constructed according to the preferred embodiment of the present invention;

[0049] Figure 3 is a schematic diagram of speed recalculation within the speed spike interval constructed according to the preferred embodiment of the present invention, where (a) is a schematic diagram of the maximum speed in the update interval, and (b) is a schematic diagram of the speed at the right endpoint of the update interval;

[0050] Figure 4 is a flow chart of speed interval merging according to reachability constructed according to the preferred embodiment of the present invention;

[0051] Figure 5 is a schematic diagram of forward and backward iteration constructed according to the preferred embodiment of the present invention. Detailed implementation manners

[0052] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0053] As Figure 1 shown, the present invention provides a feed speed planning method for a cam grinding machine tool, which can realize the feed speed planning of the cam grinding machine tool, including the following steps:

[0054] S1 Obtain the limit speed curve VLC curve

[0055] (1) Establish a high-order spline relationship between the X-axis displacement and the C-axis rotation angle:

[0056] X = f(c)

[0057] where X represents the X-axis displacement and c represents the C-axis rotation angle. And take the first, second, and third derivatives f′(c), f″(c), f″′(c) of the above relationship with respect to c.

[0058] (2) Establish the relationship between the X-axis speed, acceleration, jerk and the C-axis rotation angle, first derivative and second derivative:

[0059]

[0060] where, v c , a c , j c respectively represent the C-axis speed, acceleration and jerk, v x , a x , j xThey respectively represent the X-axis speed, acceleration, and jerk, and f′(c), f″(c), and f″′(c) respectively represent the first, second, and third-order derivatives of the spline relationship between the X-axis displacement and the C-axis rotation angle.

[0061] (3) Based on the speed limit, acceleration limit, and jerk limit of the C-axis and X-axis, establish a kinematic constraint optimization problem model, and take the maximum machining speed as the optimization goal to obtain the limit speed curve, the VLC curve.

[0062] Specifically, the established optimization problem model is:

[0063]

[0064] where v c , a c , and j c respectively represent the C-axis speed, acceleration, and jerk, f′(c), f″(c), and f″′(c) respectively represent the first, second, and third-order derivatives of the spline relationship between the X-axis displacement and the C-axis rotation angle, v cmax , a cmax , and j cmax respectively represent the maximum speed, acceleration, and jerk of the C-axis, v xmax , a xmax , and j xmax respectively represent the maximum speed, acceleration, and jerk of the X-axis.

[0065] Solving non-linear quadratic programming problems is generally complex and computationally intensive. Therefore, the known sequential quadratic programming (SQP) algorithm is used to simplify the calculation. Calculate the maximum achievable speed at each discrete point of the C-axis, and use the C-axis angle as the abscissa and the maximum speed as the ordinate to obtain the limit speed curve, the VLC (Velocity Limit Curve), that is, the maximum allowable machining speed curve.

[0066] S2 defines a continuous speed curve that first rises and then falls as a spike interval, and divides the VLC curve into multiple spike intervals, as shown in Figure 2 .

[0067] Based on the divided spike intervals, calculate the interval reachability of the maximum speed and the speeds at the left and right endpoints within the interval;

[0068] Specifically, the formula for calculating the interval reachability from the left endpoint to the maximum speed within the interval is:

[0069]

[0070] where ψ left-maxv represents the speed reachability from the left endpoint speed to the maximum speed, Δc left-maxv is the C-axis rotation angle corresponding to the speed from the left endpoint speed to the maximum speed, vleft and v max are the left - endpoint speed and the maximum speed respectively, and a cmax represents the maximum acceleration of the C - axis. The reachability calculation formula for the speed interval from the maximum speed to the right - endpoint speed within the interval is:

[0071]

[0072] where ψ maxv-right is the speed reachability from the maximum speed to the right - endpoint speed, Δc maxv-right is the C - axis rotation angle corresponding to the speed from the maximum speed to the right - endpoint speed, v right and v max are the right - endpoint speed and the maximum speed respectively, and a cmax is the maximum acceleration of the C - axis. Merge the speed intervals according to the interval reachability, ensure that the interval reachability is greater than 0, and obtain the acceleration over - limit interval based on the interval merging result. The process is as Figure 4 shown.

[0073] Specifically, the speed - interval merging process first adjusts the speed within the interval according to the reachability, and there are two cases:

[0074] (1) The reachability of the maximum speed within the interval and the reachability of the speed from the maximum speed to the right - endpoint speed are greater than or equal to zero, that is, the left - endpoint speed can be accelerated to the maximum speed, and the maximum speed can also be decelerated to the right - endpoint speed. Therefore, the speed within the interval does not need to be adjusted.

[0075] (2) The reachability of the maximum speed within the interval or the reachability of the speed from the maximum speed to the right - endpoint speed is less than zero, that is, the left - endpoint speed cannot be accelerated to the maximum speed or the maximum speed cannot be decelerated to the right - endpoint speed. Therefore, the speed within the interval needs to be adjusted. First, calculate the reachability of the speed from the left - endpoint to the right - endpoint speed within the interval. The calculation formula is:

[0076]

[0077] where ψ left-right is the global speed reachability from the left - endpoint speed to the right - endpoint speed, Δc left-right is the C - axis rotation angle corresponding to the speed from the left - endpoint speed to the right - endpoint speed, v left and v right are the left - endpoint speed and the right - endpoint speed respectively, and a cmax represents the maximum acceleration of the C - axis.

[0078] According to the calculation results, it can also be divided into the following two categories:

[0079] A. The reachability of the speed from the left - endpoint to the right - endpoint within the interval is less than or equal to zero, that is, the left - endpoint speed cannot be accelerated to the right - endpoint speed within the stroke, and the right - endpoint speed needs to be reduced, as Figure 3As shown in (b), the formula for the right endpoint speed is:

[0080]

[0081] where Δc left-right is the C-axis rotation angle corresponding to the left endpoint speed to the right endpoint speed, v left is the left endpoint speed, v right is the updated right endpoint speed, a cmax is the maximum acceleration of the C-axis.

[0082] B. The reachability of the right endpoint within the interval is greater than zero, that is, the left endpoint speed cannot be accelerated to the maximum speed, but can be accelerated to the right endpoint speed. Only the maximum speed needs to be reduced. As shown in (a), the formula for the maximum speed is: Figure 3 As shown in (a), the formula for the maximum speed is:

[0083]

[0084] where Δc right-maxv is the C-axis rotation angle corresponding to the left endpoint speed to the maximum speed, v left is the left endpoint speed, v maxv is the updated maximum speed, a cmax is the maximum acceleration of the C-axis.

[0085] After adjusting the right endpoint and the maximum speed, the formula for the speed of the remaining points within the interval is:

[0086]

[0087] where the parameters k and h are calculated by substituting the left and right endpoint speeds. After calculating all the speeds, re-divide the speed interval according to the new speed curve, and calculate the maximum speed within the interval and the reachability of the left and right endpoint speeds of the interval. If there is still an interval with reachability less than 0, continue to adjust the speed within the interval according to the reachability.

[0088] Repeat (2) until the reachability of the speed from the left end to the maximum speed and the reachability of the speed from the maximum speed to the right end within all intervals are both greater than or equal to zero.

[0089] S3. Obtain the acceleration overrun interval based on the interval merging result;

[0090] Specifically, when calculating the C-axis angle as c and the speed as v, the corresponding feasible maximum acceleration at this point is a max and the feasible minimum acceleration is a min , and the calculation formula is:

[0091]

[0092] where v cIndicates the C-axis speed at this time. f′(c), f″(c), and f″′(c) respectively represent the first, second, and third derivatives of the spline relationship between the X-axis displacement and the C-axis rotation angle. v cmax , a cmax respectively represent the maximum speed and acceleration of the C-axis. v xmax , a xmax respectively represent the maximum speed and acceleration of the X-axis. a c Represents the C-axis acceleration. From this formula, the set of C-axis accelerations a clarr can be obtained. Then, the maximum feasible acceleration of the C-axis a max = max(a clarr ), and the minimum feasible acceleration of the C-axis a min = min(a clarr ).

[0093] Obtain the actual acceleration a at this position, and determine whether the actual acceleration a is within the interval [a min , a max . If it is not within this interval, then this point is an over-limit point. Judge each position point in turn to obtain the over-limit interval [c s , c e .

[0094] Based on local reachability, perform forward and backward speed iteration within the acceleration over-limit interval to obtain a DC-VLC curve that satisfies the acceleration constraint;

[0095] Specifically, traverse each acceleration over-limit interval, calculate the speed at each sampling point from forward and backward iteration respectively. For forward iteration, use the maximum feasible C-axis acceleration in the positive direction of the interpolation stroke to calculate the maximum speed that the next sampling point can reach. For backward iteration, use the minimum feasible C-axis acceleration in the reverse direction of the interpolation stroke to calculate the maximum speed that the next sampling point can reach. Finally, merge the results of forward and backward iteration, as Figure 5 shown. The specific process is as follows:

[0096] (1) First, traverse each acceleration over-limit interval [c s , c e from front to back. Starting from the left endpoint c s of the acceleration over-limit interval, calculate the allowable acceleration range [a min , a max of the current sampling point. The calculation formula is the same as the acceleration calculation formula in step S3. Let the C-axis acceleration a c of the current point = a max and perform forward iteration calculation. Its recurrence formula is:

[0097]

[0098] Among them, is the forward iteration calculation speed of the i-th sampling point, is the forward iteration calculation speed of the (i - 1)-th discrete point, is the maximum feasible acceleration of the C-axis at the (i - 1)-th sampling point, and is the C-axis rotation angle corresponding to the i-th sampling point, c i-1 is the C-axis rotation angle corresponding to the (i - 1)-th sampling point.

[0099] If the result of the forward iteration speed of the current point then let Continue the forward iteration calculation until it stops when reaching the right endpoint of the acceleration overrun interval. At this time, the forward speed iteration planning is completed, and the forward speed planning curve is obtained.

[0100] (2) Traverse each acceleration overrun interval [c s , c e from back to front. Starting from the right endpoint c e , calculate the allowable acceleration range [a min , a max of the current sampling point. The calculation formula is the same as the acceleration calculation formula in step S3. Let the C-axis acceleration a c = a min and perform the backward iteration calculation. Its recurrence formula is:

[0101]

[0102] where, is the backward iteration calculation speed of the i-th sampling point, is the backward iteration calculation speed of the (i + 1)-th discrete point, is the minimum feasible acceleration of the C-axis at the (i + 1)-th sampling point, c i is the C-axis rotation angle corresponding to the i-th sampling point, c i+1 is the C-axis rotation angle corresponding to the (i + 1)-th sampling point.

[0103] If the result of the backward iteration speed of the current point then let Continue the backward planning until it stops when reaching the left endpoint of the acceleration overrun interval. At this time, the backward speed iteration planning is completed, and the backward speed planning curve is obtained.

[0104] (3) Merge the forward and backward speed iteration results. As Figure 5 shown, let the iterated speed curve be v vc , and let the intersection point of the forward iteration and backward iteration speed curves be c cs . Take min(v cf , v vlc ) on the left side of the intersection point, and take min(v cb , vvlc ) , namely

[0105]

[0106] (4) After completing the speed iteration calculation for an acceleration overrun interval, check whether there are still un-iterated overrun intervals. If there are, continue with the speed iteration calculation according to step (1). If the iteration calculation is completed for the last acceleration overrun interval, then the speed iteration planning for all intervals is completed.

[0107] Finally, perform FIR filtering on the DC-VLC curve to improve the continuity of acceleration and reduce jerk to obtain the target speed planning curve. A feed speed planning system for a cam grinding machine, the system includes an actuator, which is used to execute a feed speed planning method for a cam grinding machine described in the above embodiment. The related technical solutions are the same as those in the above embodiment and will not be repeated here.

[0108] Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for planning the feed speed of a cam grinding machine tool, characterized in that, The method includes the following steps: Divide the maximum allowable machining speed curve of the cam grinding machine into multiple peak intervals, update the speeds of the peak intervals, and merge the peak intervals according to the updated speeds, while ensuring that the reachability from the left endpoint to the maximum speed and from the maximum speed to the right endpoint speed of each merged peak interval is greater than or equal to zero; Judge whether the acceleration of each merged peak interval exceeds the maximum acceleration, and the peak interval with acceleration exceeding the maximum acceleration is used as the acceleration overrun interval; For each acceleration overrun interval, update the speeds of the points on the curve in the forward and reverse directions respectively, while ensuring that the updated speeds of each point are not greater than the speed of that point on the maximum allowable machining speed curve, so as to obtain the forward planning speed curve and the reverse speed planning curve of each acceleration overrun interval; Merge the forward planning speed curve and the reverse speed planning curve to obtain the merged planning curve corresponding to the acceleration overrun interval, and use the merged planning curve to replace the curve of each acceleration overrun interval in the maximum allowable machining speed curve, so as to obtain the required cam speed planning curve.

2. The feed speed planning method of a cam grinding machine tool according to claim 1, characterized in that, The merging of the peak intervals is carried out according to the following steps: (1) When the reachability from the left endpoint speed to the maximum speed or from the maximum speed to the right endpoint speed within each peak interval is less than zero, calculate the global reachability from the left endpoint speed to the right endpoint speed. When the global reachability is less than or equal to zero, update the right endpoint speed; When the global reachability is greater than zero, update the maximum speed; Update the speeds of the points within each peak interval except the left endpoint, the right endpoint, and the maximum speed point, so as to realize the update of the speeds of all points within the peak interval; (2) Repeat (1) until the reachability from the left endpoint speed to the maximum speed and from the maximum speed to the right endpoint speed of each peak interval is greater than or equal to zero; (3) Re-divide the peak intervals according to the updated speeds of each point, and return to step (1).

3. The feed speed planning method of a cam grinding machine tool according to claim 2, characterized in that, In (1), the calculation formula for the reachability from the left endpoint speed to the maximum speed is as follows: Among them, ψ left-maxv is the velocity reachability from the left-endpoint velocity to the maximum velocity, and Δc left-maxv is the C-axis rotation angle corresponding to the velocity from the left-endpoint velocity to the maximum velocity, v left and v max are the left-endpoint velocity and the maximum velocity respectively, and a cmax is the maximum acceleration of the C-axis.

4. The feed speed planning method of a cam grinding machine tool according to claim 2, characterized in that In (1), the calculation formula for the reachability from the maximum speed to the right endpoint speed is as follows: Among them, ψ maxv-right is the velocity reachability from the maximum velocity to the velocity at the right endpoint, and Δc maxv-right is the C-axis rotation angle corresponding to the velocity from the maximum velocity to the velocity at the right endpoint. v right and v max are the velocity at the right endpoint and the maximum velocity respectively, and a cmax is the maximum acceleration of the C-axis.

5. The feed speed planning method of a cam grinding machine tool according to claim 2, characterized in that, In (1), the calculation formula for the global reachability is as follows: where, ψ left-right is the global reachability from the left-endpoint velocity to the right-endpoint velocity, and Δc left-right is the C-axis rotation angle corresponding to the left-endpoint velocity to the right-endpoint velocity, v left and v right are the left-endpoint velocity and the right-endpoint velocity respectively, and a cmax is the maximum acceleration of the C-axis.

6. The method for planning the feed speed of a cam grinding machine tool according to claim 2, characterized in that, In (1), the calculation formula for updating the right endpoint speed is as follows: The formula for updating the maximum speed is as follows: Among them, Δc left-right is the C-axis rotation angle corresponding to the left-endpoint speed to the right-endpoint speed, and Δc right-maxv is the C-axis rotation angle corresponding to the left-endpoint speed to the maximum speed, v left is the left-endpoint speed, v maxv and v right respectively represent the updated maximum speed and the right-endpoint speed, and a cmax is the maximum acceleration of the C-axis.

7. The feed speed planning method of a cam grinding machine tool according to claim 1, characterized in that, The speeds of the points on the curve updated in the forward direction are carried out according to the following formula: If then is the forward iterative calculation speed of the i-th sampling point, is the forward iterative calculation speed of the (i - 1)-th sampling point, is the maximum feasible acceleration of the C-axis at the (i - 1)-th sampling point, c i is the C-axis rotation angle corresponding to the i-th sampling point, c i-1 is the C-axis rotation angle corresponding to the (i - 1)-th sampling point, is the speed at the corresponding sampling point on the maximum allowable machining speed curve; The speeds of the points on the curve updated in the reverse direction are carried out according to the following formula: If then let be the reverse iteration calculation speed of the i-th sampling point, be the reverse iteration calculation speed of the (i + 1)-th sampling point, be the minimum feasible acceleration of the C-axis of the (i + 1)-th sampling point, c i be the C-axis rotation angle corresponding to the i-th sampling point, c i+1 be the C-axis rotation angle corresponding to the (i + 1)-th sampling point, be the speed of the corresponding sampling point on the maximum allowable machining speed curve.

8. A method for planning the feed speed of a cam grinding machine tool according to claim 7, characterized in that, The formula for the merged planning curve is as follows: Among them, c cs is the intersection point of the forward planning curve and the reverse planning curve, and c s , c e respectively represent the left and right endpoints of the acceleration overrun interval, v cf , v cb are the forward planning curve and the reverse planning curve respectively, and v vlc represents the maximum allowable machining speed curve.

9. A feed speed planning method for a cam grinding machine tool according to claim 1 or 8, characterized in that The construction model of the maximum allowable machining speed curve is as follows: Among them, v c , a c , j c are the C-axis speed, acceleration, and jerk respectively. f′(c), f″(c), f″′(c) are the first, second, and third derivatives of the spline relationship between the X-axis displacement and the C-axis rotation angle. v cmax , a cmax , j cmax are the maximum speed, acceleration, and jerk of the C-axis respectively. v xmax , a xmax , j xmax are the maximum speed, acceleration, and jerk of the X-axis respectively.

10. A feed speed planning system for a cam grinding machine tool, characterized in that, The system includes an actuator, and the actuator is used to execute a method for planning the feed speed of a cam grinding machine according to any one of claims 1-9.

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