A method and system for controlling the machining of a double enveloping toroidal worm

Abstract

The application provides a secondary envelope torus worm machining control method and system, and relates to the technical field of numerical control machining. The method comprises the following steps: according to a target ultrasonic frequency, an ultrasonic frequency establishment time is estimated, and an advance trigger distance of an ultrasonic frequency switching instruction is calculated; when a current position of a tool reaches the advance trigger distance, the ultrasonic frequency switching instruction is sent to an ultrasonic generator, and a running state thereof is determined; when the tool reaches a variable lead switching position, according to the running state of the ultrasonic generator, local interlocking control is performed on a current spindle speed. The method aims to solve the technical problem that, in the process of machining a variable lead secondary envelope torus worm, due to the mismatch between the response lag of ultrasonic frequency switching and the fast response of the spindle speed, the surface finish of the cutting transition zone is deteriorated, effectively avoids ultrasonic frequency mismatch, and significantly improves the machining surface quality of the variable lead cutting transition zone.

Description

Technical Field

[0001] This invention relates to the field of CNC machining technology, and more specifically, to a method and system for controlling the machining of a double-envelope toroidal worm gear. Background Technology

[0002] In the machining of double-envelope toroidal worm gears, variable lead double-envelope toroidal worm gears can adapt to more complex transmission scenarios, featuring smoother transmission and stronger load-bearing capacity. The precision requirements for tooth surface finish are far higher than those for ordinary fixed lead worm gears. To improve the surface finish after machining and reduce positioning errors and machining time caused by secondary clamping, existing technologies typically employ a dual-spindle horizontally opposed CNC lathe equipped with a main and auxiliary spindle and a dual-channel CNC system. Through the coordinated control of the two spindles, continuous machining of the worm gear rotation and connection is achieved, eliminating the need for disassembly and reclamping after machining halfway through. Simultaneously, an ultrasonic-assisted cutting device is installed to reduce cutting resistance using the auxiliary effect of ultrasonic vibration, improving the surface quality of the machined tooth surface and reducing tool wear.

[0003] When machining variable-lead double-envelope toroidal worm gears using dual-spindle collaborative control and ultrasonic-assisted cutting technology, the lead varies in different sections of the worm gear. To ensure that the cutting linear velocity and ultrasonic chatter frequency at different lead angles always match and to guarantee the ultrasonic-assisted cutting effect, existing machining programs typically require simultaneous switching of spindle speed and ultrasonic frequency at specific locations where the tooth surface lead changes. During this execution, the dual-channel CNC system interpreter simultaneously parses and issues spindle speed change commands and ultrasonic frequency switching commands in the same or adjacent program segments. However, when the machining tool reaches the transition zone where the worm gear tooth surface lead changes drastically, due to the damping characteristics of the phase-locked loop inside the ultrasonic generator, after changing the output frequency, it is necessary to rescan and capture a new resonant point. Only after completing the resonance lock can stable ultrasonic energy be output. The response and settling time of this frequency switching is usually quite long, while the speed adjustment response speed of modern servo spindles is extremely fast, often much shorter than the ultrasonic frequency settling time to complete acceleration or deceleration.

[0004] In the same program segment, regarding the interpretation and execution sequence of ultrasonic frequency switching commands and spindle speed commands, existing conventional CNC system interpreters typically do not actively wait for confirmation signals that the ultrasonic frequency has reached the new frequency after issuing the frequency switching command. Instead, they directly allow the spindle to run at the preset new speed. This results in the spindle already running at the new speed and driving the worm gear to rotate within the transition time window before the frequency switching is completed, and the cutting speed has already changed. However, the ultrasonic generator has not yet completed the switching and locking of the new frequency and is still operating at the old frequency. As a result, the ultrasonic vibration energy density deviates significantly from the design requirements during this cutting process, failing to provide ultrasonic-assisted cutting. This instantaneous mismatch between ultrasonic parameters and cutting speed leads to insufficient ultrasonic assistance on the tooth surface in the variable lead transition segment, resulting in local roughness rebound and extremely uneven overall surface quality in the variable lead segment, failing to meet the machining requirements of high-precision transmission components.

[0005] Furthermore, even if some machining schemes pre-set fixed advance trigger values ​​and pre-issue ultrasonic frequency switching commands, they do not consider the inherent differences in the setup time of ultrasonic frequencies under different frequency jumps and cutting loads. Fixed advance values ​​cannot adapt to all machining conditions; either the advance is too large, leading to unnecessary waiting and reduced machining efficiency, or the advance is insufficient, still resulting in mismatch issues. Some schemes, after issuing the pre-command, do not dynamically monitor and correct the actual matching state within the cutting transition zone. Even minor matching deviations cannot be adjusted in time, still affecting the tooth surface machining quality. More importantly, the performance of the phase-locked loops (PLLs) of ultrasonic generators in different machining equipment varies. Even the same equipment will change its resonance characteristics after long-term use. Fixed frequency setup prediction parameters cannot adapt to these changes, gradually leading to accumulated prediction deviations and ultimately a decline in machining quality.

[0006] Existing conventional CNC systems typically treat ultrasonic frequency switching as a routine auxiliary function parameter, lacking a compensation mechanism for the time difference between the physical locking state of the ultrasonic generator and the rapid response of the spindle servo. Furthermore, they lack hierarchical interlocking control and dynamic correction mechanisms for ultrasonic states, making it easy to overlook mismatch issues during the dynamic transition process in machining complex surfaces with varying leads. Therefore, when machining variable lead double-envelope toroidal worm gears, a major challenge in practical applications is how to address the technical problem of the ultrasonic frequency switching and spindle speed linkage command failing to confirm the ultrasonic parameter locking completion in the interpreter, resulting in a temporary deterioration of the tooth surface finish in the cutting transition zone due to a delayed ultrasonic frequency switching even after the spindle speed has changed.

[0007] There is currently no effective technical solution to the above problems. Summary of the Invention

[0008] The purpose of this invention is to provide a machining control method and system for a double-envelope toroidal worm gear, which aims to solve the technical problem of deterioration of the tooth surface finish in the cutting transition zone due to the mismatch between the lag in ultrasonic frequency switching response and the rapid response of the spindle speed during the machining of a double-envelope toroidal worm gear with variable lead. By establishing an interlocking and dynamic compensation mechanism between the ultrasonic locking state and the spindle response, ultrasonic frequency mismatch is effectively avoided, and the machining surface quality of the cutting transition zone with variable lead is significantly improved.

[0009] In a first aspect, the present invention provides a method for controlling the machining of a double-envelope toroidal worm gear, applied to the control system of a dual-spindle horizontally opposed CNC lathe. This CNC lathe is equipped with a main spindle and a secondary spindle, and a cutting tool, and is fitted with an ultrasonic-assisted cutting device. The main spindle and secondary spindle can simultaneously clamp the worm gear and achieve worm gear rotational docking through coordinated control. The ultrasonic-assisted cutting device includes an ultrasonic generator for emitting ultrasonic waves. The method for controlling the machining of the double-envelope toroidal worm gear includes the following steps: S1. Obtain the target spindle speed and target ultrasonic frequency of the target segment in the worm gear machining path; S2. Based on the target ultrasonic frequency, estimate the ultrasonic frequency establishment time, and based on the estimated ultrasonic frequency establishment time and the preset tool feed speed, calculate the advance trigger distance of the ultrasonic frequency switching command. S3. When the current position of the tool reaches the pre-trigger distance, an ultrasonic frequency switching command is sent to the ultrasonic generator, and the operating status of the ultrasonic generator is determined by monitoring the physical operating parameters of the ultrasonic generator; the operating status includes switching state, locked but unstable state, and locked and stable state. S4. When the tool reaches the preset variable lead switching position in the target section, the current spindle speed is locally interlocked according to the operating state of the ultrasonic generator; The local interlock control includes the following steps S41-S43: S41. When the ultrasonic generator is in a locked and stable operating state, the current spindle speed is allowed to switch to the target spindle speed; S42. When the ultrasonic generator is in a locked but unstable operating state, the current spindle speed is allowed to switch to the target spindle speed, and the spindle speed transition curve is dynamically adjusted. S43. When the ultrasonic generator is in a switching state, prevent the current spindle speed from switching to the target spindle speed and reduce the tool feed rate; S5. When the tool is in the cutting transition zone of the target section, evaluate the matching degree between the cutting linear speed of the tool and the tracking frequency of the phase-locked loop in the physical operating parameters, and dynamically correct the current spindle speed according to the matching degree; S6. Update the basic frequency locking time constant based on the actual time taken from the actual triggering time of the ultrasonic frequency switching command to when the ultrasonic generator reaches a locked and stable state; the basic frequency locking time constant is used to estimate the ultrasonic frequency establishment time.

[0010] The secondary envelope toroidal worm gear machining control method provided by this invention can solve the problem of mismatch between cutting speed and ultrasonic frequency caused by the switch of spindle speed and the instability of ultrasonic frequency during the machining of variable lead secondary envelope toroidal worm gears. It has the advantages of improving the surface finish of the tooth surface in the transition zone of variable lead, ensuring uniform machining quality, adapting to different machining conditions, and balancing machining efficiency and machining quality.

[0011] Secondly, the present invention provides a secondary envelope toroidal worm gear machining control system, applied to the control system of a dual-spindle horizontally opposed CNC lathe. This CNC lathe is equipped with a main spindle and a secondary spindle, and a cutting tool, and is fitted with an ultrasonic-assisted cutting device. The main spindle and secondary spindle can simultaneously clamp the worm gear and achieve worm gear rotational docking through coordinated control. The ultrasonic-assisted cutting device includes an ultrasonic generator for emitting ultrasonic waves. The secondary envelope toroidal worm gear machining control system includes: The acquisition module is used to acquire the target spindle speed and target ultrasonic frequency of the target segment in the worm gear machining path; The calculation module is used to estimate the ultrasonic frequency establishment time based on the target ultrasonic frequency, and to calculate the advance trigger distance of the ultrasonic frequency switching command based on the estimated ultrasonic frequency establishment time and the preset tool feed speed. The monitoring module is used to send an ultrasonic frequency switching command to the ultrasonic generator when the current position of the tool reaches the pre-triggered distance, and to determine the operating status of the ultrasonic generator by monitoring the physical operating parameters of the ultrasonic generator; the operating status includes switching state, locked but unstable state, and locked and stable state. The control module is used to perform local interlock control on the current spindle speed according to the operating status of the ultrasonic generator when the tool reaches the preset variable lead switching position in the target section. The local interlock control includes the following steps S41-S43: S41. When the ultrasonic generator is in a locked and stable operating state, the current spindle speed is allowed to switch to the target spindle speed; S42. When the ultrasonic generator is in a locked but unstable operating state, the current spindle speed is allowed to switch to the target spindle speed, and the spindle speed transition curve is dynamically adjusted: S43. When the ultrasonic generator is in a switching state, prevent the current spindle speed from switching to the target spindle speed and reduce the tool feed rate; The correction module is used to evaluate the matching degree between the actual cutting line speed of the tool and the actual tracking frequency of the ultrasonic generator when the tool is in the cutting transition zone of the target section, and dynamically correct the current spindle speed according to the matching degree. The update module is used to update the basic frequency locking time constant based on the actual time taken from the actual triggering time of the ultrasonic frequency switching command to the time when the ultrasonic generator reaches a locked and stable state; the basic frequency locking time constant is used to estimate the ultrasonic frequency establishment time.

[0012] As can be seen from the above, the secondary envelope toroidal worm gear machining control method provided by this invention effectively solves the technical problem of cutting speed mismatch caused by ultrasonic frequency switching lag in the machining of variable lead secondary envelope toroidal worm gears by establishing a spindle speed interlock control strategy based on ultrasonic generator frequency locking status feedback in the CNC system. By real-time estimation of frequency settling time and calculation of command trigger advance, combined with dynamic monitoring of the operating status, this application actively restricts the spindle frequency conversion action when the ultrasonic generator is not locked or the state is unstable, and introduces linear speed and ultrasonic frequency matching degree evaluation and adaptive correction in the transition zone, realizing efficient synchronization between ultrasonic-assisted machining and spindle response, significantly improving the tooth surface finish of the variable lead machining section, avoiding the consistency problem caused by dynamic transition, and improving machining accuracy and process reliability.

[0013] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description and the accompanying drawings. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the structure of a dual-spindle horizontally opposed CNC lathe in an embodiment of the present invention.

[0015] Figure 2 This is a simplified structural diagram of a dual-spindle horizontally opposed CNC lathe in an embodiment of the present invention.

[0016] Figure 3 This is a flowchart of a secondary envelope toroidal worm gear machining control method provided in an embodiment of the present invention.

[0017] Figure 4 This is a schematic diagram of a secondary envelope toroidal worm gear machining control system provided in an embodiment of the present invention.

[0018] Label Explanation: 1. Main spindle; 2. Sub-spindle; 3. Ultrasonic assisted cutting device; 4. Worm gear; 5. Ultrasonic generator; 6. Cutting tool; 100. Acquisition module; 200. Calculation module; 300. Monitoring module; 400. Control module; 500. First correction module; 600. Update module; 700. Second correction module. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0020] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0021] In the machining of double-envelope toroidal worm gears, when using a dual-spindle horizontally opposed CNC lathe with an ultrasonic-assisted cutting device for variable lead machining, the ultrasonic generator experiences a response delay during frequency switching, while the spindle speed adjustment responds rapidly. The CNC system interpreter, after issuing the ultrasonic frequency switching command, allows the spindle speed to change without waiting for confirmation of ultrasonic parameter locking completion. This results in the spindle operating at the new speed before the ultrasonic frequency has stabilized, causing the ultrasonic vibration energy density in the cutting transition zone to deviate from the design value. This leads to localized tooth surface roughness rebound, affecting surface quality uniformity. Furthermore, the high damping of the phase-locked loop inside the ultrasonic generator results in a long frequency switching setup time, while the servo spindle speed adjustment responds extremely quickly. This timing mismatch directly leads to cutting parameter mismatch, making the tooth surface finish in the variable lead section unable to meet machining requirements.

[0022] For example, when machining the transition zone of a double-envelope toroidal worm gear with abrupt lead changes, the CNC system simultaneously interprets the spindle speed change command and the ultrasonic frequency switching command when the tool reaches the lead-change switching position. Due to the damping characteristics of the phase-locked loop, the frequency switching setup time of the ultrasonic generator is typically tens to hundreds of milliseconds, while the servo spindle speed adjustment response is completed within a few milliseconds. During this process, when the tool is cutting in the transition zone, the ultrasonic generator is still operating at the old frequency, while the spindle has already rotated the worm at the new speed. This results in insufficient ultrasonic assistance in this section of the cut, manifesting as a decrease in the surface finish of local areas of the tooth surface and the formation of uneven surface texture. Specifically, during tool feed, the instantaneous shift in ultrasonic vibration energy density causes abnormal material removal behavior, resulting in periodic rough bands on the tooth surface in the transition zone, affecting the continuity and consistency of the worm tooth surface.

[0023] If the above problems are not solved, the tooth surface quality of the variable lead section will continue to be substandard, affecting the transmission accuracy and wear resistance of the worm gear. In precision machinery applications, local deterioration of surface roughness may lead to increased vibration and noise and concentration of contact stress, shortening the service life of the worm gear. In addition, repeated machining quality problems will increase the risk of workpiece rework or scrap, reduce production efficiency, and restrict the application expansion of the double-envelope toroidal worm gear in the field of high-precision transmission.

[0024] For reference, see the appendix. Figure 1 Appendix Figure 2 and attached Figure 3 This invention provides a secondary envelope toroidal worm gear machining control method, applied to the control system of a dual-spindle horizontally opposed CNC lathe. The CNC lathe is equipped with a main spindle and a secondary spindle (main spindle 1 and secondary spindle 2) and a cutting tool 6, and is equipped with an ultrasonic-assisted cutting device 3. The main spindle and the secondary spindle can simultaneously clamp the worm gear 4 and achieve the rotational docking of the worm gear 4 through coordinated control. The ultrasonic-assisted cutting device 3 includes an ultrasonic generator 5 for emitting ultrasonic waves. The machining control method for secondary envelope toroidal worm gears includes the following steps: S1. Obtain the target spindle speed and target ultrasonic frequency of the target segment in the worm gear machining path; S2. Based on the target ultrasonic frequency, estimate the ultrasonic frequency settling time, and based on the estimated ultrasonic frequency settling time and the preset tool feed rate, calculate the advance trigger distance of the ultrasonic frequency switching command. S3. When the current position of the tool reaches the advance trigger distance, an ultrasonic frequency switching command is sent to the ultrasonic generator, and the operating status of the ultrasonic generator is determined by monitoring the physical operating parameters of the ultrasonic generator. The physical operating parameters include the effective value of the output voltage and the effective value of the output current of the piezoelectric transducer and the voltage-current phase difference, as well as the tracking frequency and frequency change rate of the phase-locked loop, and the resonance capture error status word inside the ultrasonic generator used to indicate the state of the resonance point capture process. The operating status includes the switching state, the locked but unstable state, and the locked and stable state. S4. When the tool reaches the preset variable lead switching position in the target section, the current spindle speed is locally interlocked according to the operating status of the ultrasonic generator; Local interlock control includes the following steps S41-S43: S41. When the ultrasonic generator is in a locked and stable operating state, the current spindle speed is allowed to switch to the target spindle speed; S42. When the ultrasonic generator is in a locked but unstable operating state, allow the current spindle speed to switch to the target spindle speed, and dynamically adjust the spindle speed transition curve according to the following steps S421: S421. During the spindle speed transition (i.e., before the current spindle speed reaches the target spindle speed), if the ultrasonic generator's operating state reverts to the switching state, the current spindle speed is frozen (i.e., the current spindle speed remains unchanged) and the tool feed rate is reduced; when the ultrasonic generator's operating state returns to the locked but unstable state, the original tool feed rate is restored, and the transition curve is replanned based on the current spindle speed to complete the switch from the current spindle speed to the target spindle speed; S43. When the ultrasonic generator is in a switching state, prevent the current spindle speed from switching to the target spindle speed and reduce the tool feed rate; S5. When the tool is in the cutting transition zone of the target section, evaluate the matching degree between the tool's cutting linear speed and the tracking frequency of the phase-locked loop in the physical operating parameters, and dynamically correct the current spindle speed based on the matching degree. S6. Update the base frequency locking time constant based on the actual time taken from the actual triggering time of the ultrasonic frequency switching command to when the ultrasonic generator reaches a locked and stable state; the base frequency locking time constant is used to estimate the ultrasonic frequency setup time.

[0025] To more clearly explain the technical solution of this application, the basic concepts involved are explained here. "Ultrasonic frequency setup time" refers to the time span required from when the ultrasonic generator receives the frequency switching command until its internal phase-locked loop (PLL) recaptures the new resonant point and stabilizes the output. "Stable output" here is not limited to the tracking frequency value reaching near the target frequency; it also includes the effective value of the transducer output voltage, the effective value of the output current, and the voltage-current phase difference entering the allowable fluctuation range, and no longer exhibiting significant repeated oscillations within several consecutive sampling cycles. For example, when the ultrasonic generator switches from the operating frequency corresponding to the previous processing section to the operating frequency corresponding to the next processing section, the PLL typically undergoes several consecutive stages: frequency sweep search, resonant point capture, lock-in, and amplitude recovery. Only after all these stages are completed can the ultrasonic frequency setup be considered complete. "Local interlock control" refers to logically binding the spindle speed switching action with the actual operating state of the ultrasonic generator within a specific processing section. Spindle speed switching is only allowed or executed in a specific manner when the ultrasonic state meets specific conditions. The term "local" here emphasizes that the control does not force a wait for the entire program, but only takes effect in the variable lead switching position and the sections before and after which mismatch is likely to occur, thus balancing machining quality and cycle time. The "basic frequency locking time constant" reflects the basic time reference value required for the ultrasonic generator to complete frequency locking under standard operating conditions. Standard operating conditions typically refer to the locking time reference when the machine tool is in a stable cutting or no-load calibration state, the ultrasonic generator temperature rise is within the normal range, the transducer and tool are fixed in their clamping state, and the frequency switching amplitude is within a preset reference range. This basic time reference can be obtained by repeatedly performing frequency switching tests during the equipment debugging phase, or it can be continuously corrected based on the actual time consumption during subsequent machining processes.

[0026] The information acquisition and execution path in the above steps can be implemented in the following way: The target spindle speed and target ultrasonic frequency in step S1 are preferably obtained by combining the CNC machining program, the worm gear tooth surface trajectory parameter table, and the ultrasonic process parameter table. Specifically, the worm gear machining program usually already contains the axial position, rotation angle position, or program segment number corresponding to each tool position point. The control system can read the target spindle speed corresponding to the program segment where the current tool is located. At the same time, a "machining segment - ultrasonic frequency" correspondence table is established in advance, and the target ultrasonic frequencies corresponding to different lead change segments are written into the process database. The control system retrieves the table before the program runs to the target segment. The correspondence table can be established by performing surface quality verification on several typical lead segments during the process trial cutting stage, recording the ultrasonic frequency setting value when the surface quality is better in each segment, and storing it in the form of a one-to-one correspondence between the segment number and the frequency setting value. The acquisition of physical operating parameters in step S3 is preferably achieved through the industrial communication interface between the ultrasonic generator and the CNC system. For example, the ultrasonic generator periodically uploads status register data frames, which at least include the effective value of the output voltage, the effective value of the output current, the phase difference, the tracking frequency, the rate of change of frequency, and the resonance capture error status word. If the ultrasonic generator itself does not directly output all parameters, an external acquisition module can sample the transducer drive circuit, and the controller can convert the sampling results to form the corresponding parameters. The spindle speed freezing, recovery, and replanning of the transition curve in steps S4 to S5, as well as the feed rate reduction and recovery, can all be executed by the dual-channel linkage control module of the CNC system. Spindle speed freezing can be understood as temporarily maintaining the current speed setpoint and not continuing to change towards the target value. Feed rate reduction can be understood as switching the current feed rate to a preset protection rate range to shorten the surface quality fluctuation caused by unit length cutting under mismatch conditions.

[0027] The aforementioned overall technical solution breaks away from the rigid mode of traditional CNC systems that simultaneously issue spindle and ultrasonic commands within the same program segment. Firstly, steps S1 and S2 advance the ultrasonic frequency switching command in the spatial dimension, using the physical displacement time of the tool travel to mask the time delay in ultrasonic frequency establishment. Next, step S3 monitors the actual physical state of the ultrasonic generator in real time. When the tool actually reaches the physical position requiring a change in lead (step S4), instead of blindly switching the spindle speed, interlock control is implemented based on the actual ultrasonic preparation status to ensure stable synchronization between the spindle speed change and the ultrasonic frequency. Subsequently, dynamic fine-tuning is performed within the cutting transition zone in step S5, and finally, step S6 forms a closed-loop learning mechanism to optimize the prediction accuracy for the next iteration. The reason why this technical approach can improve the tooth surface quality in the variable lead transition zone is that it transforms the original "open-loop linkage" that relied solely on program timing into a "closed-loop linkage" based on actual physical conditions: on the one hand, early triggering allows the ultrasonic system to complete most of the frequency locking process before the tool reaches the critical position; on the other hand, local interlocking blocks the mismatch chain of "spindle changes first, ultrasonic arrives later"; furthermore, dynamic correction in the cutting transition zone compensates for residual deviations, thus continuously suppressing the conditions for roughness rebound.

[0028] In one possible example, the method for estimating the ultrasonic frequency setup time in step S2 can be achieved by consulting a historical experience database. This involves pre-recording the average time required for generator locking at different target ultrasonic frequencies and directly using this average time as the estimated value. Combining this with the current constant feed rate of the tool, multiplying this time value by the feed rate yields the advance trigger distance. To ensure this method can be readily implemented, the historical experience database can be established during the equipment debugging phase: First, keeping the tool, transducer, tool holder, and clamping state unchanged, under no-cutting or light-load stable cutting conditions, sequentially issue multiple target ultrasonic frequency switching commands to the ultrasonic generator. Record the time of each command issuance and continuously collect the tracking frequency, frequency change rate, phase difference, and resonance capture error status word. When the tracking frequency enters the allowable range corresponding to the target frequency, the frequency change rate decreases to a stable range, the phase difference enters the allowable range near resonance, and the resonance capture error status word indicates capture completion, this moment is recorded as the locking completion moment. The time difference between these two times is the actual setup time for this switch. After repeatedly recording the same target ultrasonic frequency, obviously abnormal individual values ​​are removed, and the representative times of the remaining records are written into the database. The database recording format can be "target ultrasonic frequency - setup time" or further refined to "starting frequency - target ultrasonic frequency - setup time" to improve the accuracy of retrieval when the frequency switching direction or span is different. Before the machining program reaches a certain target segment, the control system reads the target ultrasonic frequency to be switched to, retrieves the corresponding setup time from the database, and calculates how much path distance the tool should advance before issuing the frequency switching command, based on the feed rate of the current program segment. If the current feed rate is not strictly constant but varies slowly within the segment, the actual average feed rate within a short path before the variable lead switching position can be used as the calculation basis to avoid excessive deviation in advance distance due to instantaneous speed fluctuations.

[0029] In some implementations, the monitoring of the physical operating parameters of the ultrasonic generator in step S3 can be achieved by acquiring a single electrical signal from the power supply circuit of the ultrasonic generator. For example, the effective value of the output current can be acquired in real time using a current transformer. When the effective value of the current reaches a certain fixed threshold, it is determined that the state has changed. To more clearly illustrate the applicable boundaries of this method, it should be noted that this method can be used as a basic implementation method in scenarios with simplified structures. For example, in a modification scenario where the interface capability of the ultrasonic generator is limited and only a small number of state quantities can be output, a preliminary judgment can be made using the trend of the change in the effective value of the current: after the frequency switching command is issued, the effective value of the output current usually experiences significant fluctuations and then gradually returns to a new stable range. The control system can temporarily define the "significant fluctuation stage" as the switching state, the "stage that has entered the target range but still has fluctuations" as the locked but unstable state, and the "stage that remains stable for multiple consecutive sampling cycles" as the locked and stable state. To reduce the risk of misjudgment, this single-signal scheme is preferably used in conjunction with a time-hold condition. That is, the state does not change immediately once the effective current value crosses a certain threshold; instead, it is required that the corresponding condition be continuously met for several consecutive sampling periods before a state switch is confirmed. Furthermore, the slope of the effective current value change can be used as an auxiliary criterion: if the effective current value reaches the target range but its trend is still significant, it remains in a locked but unstable state and is not immediately determined to be locked and stable. With this approach, even using a single electrical signal can meet basic interlocking control requirements to a certain extent. However, this method is more suitable as a simplified implementation or degraded operation scheme. In the variable lead transition zone where high processing quality is required, a multi-parameter joint judgment method is preferred.

[0030] The local interlock control in step S4 is the core mechanism of this scheme. Step S41 represents the ideal situation: the ultrasonic waves are fully ready, and the spindle is changing speed normally. Step S42 represents the transition situation: the ultrasonic waves have locked the resonant point, but the energy output is not fully stable. At this time, the spindle is allowed to start changing speed, but dynamic monitoring is required. In step S421, if the ultrasonic wave condition deteriorates (reverting to switching), the spindle speed is immediately "frozen" and the feed is reduced to prevent forced cutting in a mismatched state; after the ultrasonic waves recover, a smooth transition curve is replanned based on the currently frozen speed. Step S43 is the worst-case scenario: the ultrasonic waves are not keeping up at all. At this time, spindle speed change is strictly prohibited, and a forced wait is initiated. To facilitate the implementation of this local interlock control, the following further explanation is provided: The "preset variable lead switching position" can be obtained through offline analysis of the worm gear tooth surface geometry model and machining trajectory. Specifically, during the programming phase, positions where the lead change rate significantly increases are identified, and the corresponding program segment number, tool position number, or axial coordinate is written into the control table. During runtime, the control system compares the current position with this control table, triggering the interlock logic when the tool reaches that position. The "replanning of the transition curve" does not require complex mathematical solutions. In practice, the existing acceleration / deceleration planning function of the CNC system can be used. Using the current frozen spindle speed as a new starting point and the target spindle speed as the endpoint, a smooth speed change process that satisfies the machine tool's acceleration / deceleration constraints can be regenerated. The "reduction of tool feed rate" is preferably achieved by switching the feed rate. During interlock protection, the feed rate is switched to a protection rate lower than the normal machining rate, and then restored to the original rate after the ultrasonic condition recovers. The reason for this design is that freezing the spindle speed can only prevent the mismatch from expanding further, while reducing the feed rate can reduce the amount of cutting progress per unit time, so that the tool cuts as few critical surfaces as possible during the period of ultrasonic instability, thereby further mitigating the deterioration of local roughness.

[0031] Through the aforementioned overall technical solution, the ultrasonic frequency switching command is triggered in advance on the spatial axis, and the time delay of the ultrasonic generator's phase-locked loop capturing the resonant point is compensated by the physical displacement time of the tool feed. Simultaneously, a local interlock control mechanism is introduced, ensuring that the spindle speed switching no longer depends solely on the timing of the CNC program, but is strictly controlled by the actual physical locking state of the ultrasonic generator. This mechanism effectively avoids the mismatch phenomenon where the spindle speed has completed switching while the ultrasonic frequency is still being established. Even when the ultrasonic state fluctuates, it can dynamically adapt by freezing the speed and replanning the transition curve. Ultimately, this solution ensures a strict match between the cutting linear velocity and ultrasonic vibration parameters in the variable lead transition zone, completely eliminating local roughness rebound caused by ultrasonic energy density shifts, and significantly improving the overall surface machining quality of the variable lead double-envelope toroidal worm gear. Further analysis reveals that the improvement in surface quality does not stem from a single action, but rather from the continuous coordination of multiple actions: early triggering reduces the probability of ultrasonic lag, status monitoring identifies whether the ultrasonic equipment is truly ready, local interlocking blocks spindle speed changes at incorrect times, and dynamic correction in the transition zone converges and controls the remaining deviation. Therefore, a stable process protection zone can be formed in the section where the lead changes most drastically and where surface quality inhomogeneity is most likely to occur.

[0032] In practical applications, the frequency settling time of an ultrasonic generator is not a static, constant value. If the ultrasonic frequency settling time is estimated solely by referring to historical average values, the estimated time will often deviate significantly when faced with dynamic changes in spindle load torque during machining and large differences in the amplitude of ultrasonic frequency jumps in different machining sections. This deviation will lead to inaccurate calculation of the advance trigger distance, resulting in problems such as premature or delayed ultrasonic frequency locking.

[0033] In some embodiments, the specific steps in step S2 include: S21. Based on the target ultrasonic frequency, obtain the ultrasonic frequency jump difference value, and based on the jump difference value, obtain the phase-locked loop sweep frequency coefficient from the preset frequency jump time coefficient table; S22. Obtain the current spindle load torque, and based on the current spindle load torque, obtain the amplitude damping coefficient from the preset load torque damping coefficient table; S23. Based on the ultrasonic frequency jump difference, the phase-locked loop sweep time coefficient, the spindle load torque, the amplitude damping coefficient, and the foundation frequency locking time constant, the ultrasonic frequency settling time is calculated according to the following formula: T = S + α*β*D*M; Where T is the ultrasonic frequency settling time, S is the basic frequency locking time constant, α is the phase-locked loop sweep frequency time coefficient, β is the amplitude damping coefficient, D is the ultrasonic frequency jump difference, and M is the load torque of the main shaft. S24. Multiply the ultrasonic frequency settling time by the tool feed rate to obtain the basic space advance distance, and add a safety compensation margin to the basic space advance distance to obtain the advance trigger distance.

[0034] This specific implementation plan constructs a multi-dimensional dynamic prediction model. In step S21, the jump difference in ultrasonic frequency directly determines the bandwidth that the phase-locked loop (PLL) needs to traverse. The wider the bandwidth, the longer the sweep time. Therefore, the corresponding PLL sweep time coefficient is obtained by looking up a table. To more clearly illustrate the source of this coefficient table, the frequency jump time coefficient table can be established during the equipment calibration stage: First, select several representative frequency jump intervals, for example, gradually covering from smaller jump intervals to larger jump intervals. Then, under the same clamping conditions, the same tool assembly, and similar temperature rise conditions, perform multiple frequency switching tests and record the relative time change trend required for the PLL to complete stable locking from the start of the search in each jump interval. Then, organize these test results into a correspondence table of "frequency jump interval - PLL sweep time coefficient". The coefficients in this table do not need to be limited to a certain absolute value system; their essence is to reflect the relative weight of the influence of different frequency jump amplitudes on the establishment time. During operation, the control system first determines the jump range to which it belongs based on the difference between the current operating frequency and the target ultrasonic frequency, and then retrieves the corresponding phase-locked loop sweep frequency time coefficient from the table.

[0035] In step S22, the spindle load torque reflects the magnitude of the current cutting resistance. This cutting resistance is transmitted to the ultrasonic transducer through the tool, altering its mechanical damping characteristics and thus affecting the resonant point's capture speed. Therefore, an amplitude damping coefficient is introduced. The current spindle load torque can be obtained using the real-time load monitoring value from the machine tool servo drive or the torque estimation value output by the spindle drive unit. If the machine tool control system can directly read the spindle load percentage, a correspondence table of "spindle load range - load torque damping coefficient" can be established during the equipment debugging phase. Under different cutting depths, different feed states, and different material cutting stages, the correspondence between spindle load changes and ultrasonic frequency locking time changes is recorded. The load level is then divided into several intervals, and a corresponding amplitude damping coefficient is assigned to each interval. Thus, when the current spindle load falls into a certain interval during operation, the corresponding amplitude damping coefficient can be directly invoked. The significance of this approach is that the ultrasonic frequency locking process is no longer considered an independent process unrelated to the cutting load. Instead, the influence of the cutting mechanical load on the dynamic response of the ultrasonic system is incorporated into the prediction model, making the prediction results closer to the actual working conditions.

[0036] Step S23 integrates the basic frequency locking time constant, the phase-locked loop sweep time coefficient, the amplitude damping coefficient, the ultrasonic frequency jump difference, and the spindle load torque to obtain the ultrasonic frequency settling time under the current operating condition. This "integration" can be understood as: starting with the basic frequency locking time constant, and then progressively correcting the basic time based on the increasing sweep time trend caused by the increase in frequency jump amplitude and the increasing damping trend caused by the increase in load torque. If the current frequency jump difference is small and the spindle load is light, the correction amount is small, and the obtained settling time is close to the basic frequency locking time constant; if the current frequency jump difference is large and the spindle load is heavy, the correction amount is correspondingly increased, and the obtained settling time is also extended. After this processing, the prediction result can simultaneously reflect the combined effect of two key factors: "frequency switching span" and "cutting load state."

[0037] Step S24 adds a safety compensation margin to the basic spatial advance distance to address factors such as minor backlashes in the machine tool's mechanical transmission, differences in communication refresh cycles, minor delays in servo response, and lag in the ultrasonic generator's internal state refresh. This safety compensation margin can be obtained through repeated verification during the trial cutting phase. Specifically, it can be achieved by performing several switching tests at the basic spatial advance distance and observing whether the ultrasonic frequency has stabilized when the tool reaches the variable lead switching position. If the ultrasonic frequency still occasionally lags slightly behind the spindle speed change, the compensation margin is gradually increased until the ultrasonic frequency stabilizes before or at least no later than the spindle speed change in multiple consecutive tests. Through the above multivariate coupling processing method, this specific implementation scheme can adaptively calculate a more realistic ultrasonic frequency settling time based on the current specific cutting load and frequency range. This makes the advance trigger distance setting more consistent with the current real physical conditions, effectively avoiding excessively long interlocking waiting times or insufficient advance due to estimation errors, and maximizing the machine tool's operational continuity while ensuring machining quality.

[0038] In some embodiments, step S3, which involves determining the operating status of the ultrasonic generator by monitoring its physical operating parameters, includes the following specific steps: S31. When the voltage-current phase difference is outside the preset resonant phase window and the tracking frequency fluctuates drastically, it is determined that the ultrasonic generator is in a switching state. S32. When the voltage-current phase difference is within the resonant phase window, the frequency change rate is lower than the first preset threshold, and the effective value of the output current is lower than the first percentage of the target rated current value, the ultrasonic generator is determined to be in a locked but unstable state. S33. When the voltage-current phase difference is within the resonant phase window, the frequency change rate is lower than the second preset threshold, the effective value of the output current is higher than the second percentage of the target rated current value, and the current state is maintained for multiple consecutive interpolation cycles, it is determined that the ultrasonic generator is in a locked and stable state; the second preset threshold is less than the first preset threshold; the second percentage is greater than the first percentage.

[0039] The resonant phase window refers to the allowable phase difference fluctuation range when the piezoelectric transducer is in an ideal resonant state. This "window" is not a single fixed point, but rather an acceptable deviation band reserved around the ideal resonant phase to accommodate load fluctuations, device variability, and measurement errors. The first and second preset thresholds distinguish between the "convergence has begun" and "sufficiently stable" stages, respectively; therefore, the second preset threshold is usually stricter than the first. The first and second percentages reflect the degree of ultrasonic energy buildup; the former identifies the state of "locked but energy not yet fully built up," and the latter identifies the state of "approaching rated operating energy." These preset conditions can be obtained through no-load commissioning, standard trial cutting, and process calibration before formal processing. Specifically, this can be done by repeatedly switching frequencies under non-cutting conditions, recording the distribution range of the phase difference when it enters the stable region, and then recording the frequency convergence trend and current buildup level at different stages under typical cutting loads, thereby determining the resonant phase window, the first preset threshold, the second preset threshold, the first percentage, and the second percentage. This setting aims to ensure that the judgment rules retain sufficient sensitivity without causing frequent false alarms due to overly tight parameter settings.

[0040] The resonant phase window refers to the allowable phase difference fluctuation range when the piezoelectric transducer is in an ideal resonant state. In the initial stage of frequency switching, the phase-locked loop (PLL) is sweeping frequencies over a wide range, and the phase difference will inevitably deviate from this window, with the tracking frequency jumping significantly; this corresponds to the switching state. Once the PLL initially captures the resonant point, the phase difference enters the window, the frequency change rate begins to decrease and falls below the first preset threshold, but at this point, the ultrasonic energy has not yet been fully established, and the effective value of the output current is low, below the first percentage; this corresponds to a locked but unstable state. As the energy gradually stabilizes, the frequency change rate further decreases and falls below the more stringent second preset threshold, and the effective value of the current reaches a higher level, above the second percentage. This stable state needs to be confirmed in the time dimension, i.e., remaining unchanged for multiple consecutive interpolation cycles, before it is finally confirmed as a locked and stable state. Maintaining the current state for multiple consecutive interpolation cycles is preferably achieved through synchronization determination using the interpolation clock of the CNC system; that is, the state determination result is read once at the arrival of each interpolation cycle. Only when multiple consecutive read results meet the conditions listed in S33 is a "locked and stable state" confirmation signal output to the subsequent interlock control module. This configuration effectively avoids false confirmations caused by a single sample falling within the stability window. For example, after a cutting impact, the phase difference and current may briefly meet the stability condition, but if they immediately deviate in the next interpolation cycle, it will not be considered a truly stable state. Therefore, continuous confirmation in the time dimension is actually a further screening of the state's reliability.

[0041] In one specific embodiment, the resonant phase window is set to [-5°, +5°], the first preset threshold is 50Hz / s, the second preset threshold is 10Hz / s, the first percentage is 60%, and the second percentage is 90%. When the frequency switching command is issued, the system detects a phase difference of 30° and a rapid frequency jump between 20kHz and 22kHz, and then determines that the ultrasonic generator is in a switching state. Subsequently, the phase difference enters 2°, the frequency change rate drops to 30Hz / s, and the current reaches 70% of the rated value, at which point the system determines that it has entered a locked but unstable state. After several tens of milliseconds of adjustment, the phase difference stabilizes at 1°, the frequency change rate drops to 5Hz / s, and the current reaches 95% of the rated value, and this state lasts for 20 milliseconds (equivalent to multiple interpolation cycles). The control system finally determines that the ultrasonic generator is in a locked and stable state. To further illustrate the process, it can be understood as follows: In the first stage, the controller continuously reads the phase difference and tracking frequency from the sampling module. It detects that the phase difference deviates significantly from the resonant phase window, and the frequency register reading fluctuates rapidly, thus immediately outputting a "switching state." In the second stage, the phase-locked loop (PLL) has pulled the frequency near resonance, and the phase difference reading returns to the window range, indicating that the resonant point has been captured. However, the output current has not yet reached the level required for stable high-power operation, so it is identified as a "locked but not stable state." In the third stage, the frequency change rate further decreases, indicating that the PLL's adjustment action has significantly weakened, and the effective value of the output current reaches near the rated level and remains unchanged for several interpolation cycles. Only then is a final confirmation signal of "locked and stable state" issued. The parameters in this embodiment are applicable to typical scenarios of 20kHz-level ultrasonic systems. The same judgment logic can be used under different ultrasonic frequency bands, different transducer structures, or different load conditions, with only the window and threshold values ​​calibrated accordingly.

[0042] This specific implementation scheme forms a progressive state determination mechanism by logically combining phase difference, frequency change rate, and effective current value in a hierarchical manner. First, it uses phase difference and frequency fluctuations to quickly identify the chaotic state at the initial switching stage. Then, it uses the initial convergence of the frequency change rate and the initial establishment of the current to accurately capture the intermediate transition state where the resonance point is locked but the energy is not yet full. Finally, through stricter frequency change rate, higher current threshold, and continuous confirmation over time, it ensures the absolute reliability of the final stable state. This mechanism effectively solves the state definition problem caused by multi-parameter fluctuations under complex operating conditions, providing extremely precise triggering conditions for subsequent local interlock control and completely eliminating incorrect spindle speed switching due to state misjudgment. Its technical effect can be further understood as follows: if only phase difference is used as the criterion, it may be mistakenly considered stable when the phase-locked loop just enters the vicinity of resonance; if only current is used as the criterion, a short-term current surge may occur under cutting impact, causing misjudgment; if only the frequency change rate is used as the criterion, it may prematurely release the loop during certain transient convergences. Using these three types of parameters in combination is equivalent to simultaneously verifying the ultrasonic generator's state from three perspectives: resonant position, convergence trend, and energy buildup. Therefore, it can better reflect the true physical state. Adding a confirmation step with multiple consecutive interpolation cycles further filters out occasional fluctuations, thus ensuring that subsequent spindle linkage control is based on a reliable state.

[0043] In some embodiments, the cutting speed in step S5 is calculated based on the following steps: A1. Obtain the current spindle load torque; A2. Based on the current position of the tool, calculate the radius of rotation of the tool tip contact point in the radial direction of the spindle; A3. Based on the current spindle load torque, adjust the slewing radius to obtain the cutting slewing radius; A4. Calculate the cutting linear velocity based on the cutting radius of rotation and the current spindle speed.

[0044] The current spindle load torque in step A1 can be obtained through the real-time feedback value of the spindle servo drive. Preferably, the CNC system periodically reads the load rate, output torque percentage, or equivalent torque feedback from the drive via the bus and converts it into the current spindle load torque. If the drive system directly provides torque values ​​in engineering form, they can be read directly; if only the relative load percentage is provided, the current spindle load torque can be calculated by combining it with the spindle's rated torque. The radius of rotation calculated in step A2 is actually the theoretical radius of rotation based on the CNC program and tool geometry parameters. It can be obtained by reading the current tool-compensated spatial coordinates, workpiece mounting coordinate system, spindle center position, and tool tip geometry parameters, and then obtaining the theoretical radius of rotation at that moment based on the projection relationship of the current contact position of the tool tip in the radial direction of the spindle. The core of the correction process in step A3 is to establish a mapping relationship between the spindle load torque and the system's radial elastic deformation. The larger the load torque, the greater the cutting force, and the greater the elastic deformation of the tool outward, the larger the actual cutting radius of rotation will be than the theoretical radius of rotation. By introducing spindle load torque to dynamically compensate for the theoretical turning radius, the true physical position of the tool tip under cutting force can be restored. This mapping relationship is preferably obtained through pre-calibration rather than temporary estimation during machining. During calibration, conditions similar to the actual machining material, tool overhang, clamping method, and cutting depth can be selected. Different loads are applied step-by-step, and the corresponding radial deflection of the tool tip is measured. The "load torque - radial deformation compensation value" are recorded in pairs to form a compensation coefficient table or segmented compensation rules. During actual machining, the control system looks up the compensation value from the table based on the current spindle load torque, and then superimposes this compensation value onto the theoretical turning radius to obtain the cutting turning radius. The cutting speed in step A4 can be generated in real-time by the control system based on the cutting turning radius and the current spindle speed, used for subsequent matching evaluation with the actual tracking frequency of the ultrasonic generator. To avoid frequent jumps in cutting speed caused by transient jitter in the torque signal, it is preferable to perform short-time filtering on the current spindle load torque before table lookup compensation.

[0045] In one specific embodiment, before actual machining, a cutting force calibration experiment is conducted to determine the radial deflection of the tool tip under different spindle load torques, and a compensation coefficient table of "load torque - radial deformation compensation value" is established. During the machining transition zone, the CNC system reads the current spindle load torque fed back by the servo drive in real time, assuming the current load torque is 40% of the rated torque. Based on the current tool coordinates, the theoretical turning radius is calculated to be 150.000 mm. Referring to the compensation coefficient table, it is found that under 40% load torque, the radial deformation compensation value is 0.025 mm. The control system adds this compensation value to the theoretical turning radius to obtain a corrected cutting turning radius of 150.025 mm. Finally, using the formula for circumferential motion linear velocity, combined with the corrected cutting turning radius and the current spindle speed, the current actual cutting linear velocity is accurately calculated. To more clearly disclose how the compensation coefficient table is obtained, the following specific process can be adopted: Select the same cutting tools, clamping methods, and workpiece materials as in the actual machining, and perform short-range trial cuts at low, medium, and high load levels; at each load level, record the load torque fed back by the spindle servo, and determine the actual radial deflection of the tool tip using a high-precision displacement measuring device or a surface back-calculation method after trial cuts; compile each set of load torques and corresponding deflection values ​​into a table. For example, the following recording relationship can be formed: 20% of the rated torque corresponds to a compensation value of approximately 0.010 mm, 40% of the rated torque corresponds to a compensation value of approximately 0.025 mm, and 60% of the rated torque corresponds to a compensation value of approximately 0.040 mm. In actual use, when the current spindle load torque is between the recorded gears, the compensation value of the nearest gear can be selected, or an intermediate compensation value can be obtained using a piecewise interpolation method. This makes the compensation coefficient table an engineering implementation basis that is obtainable, updatable, and directly callable.

[0046] This specific implementation scheme cleverly incorporates the mechanical elastic deformation factor during the cutting process into the linear velocity calculation model by introducing the real-time dynamic parameter of the spindle load torque to correct the tool's rotation radius online. This approach breaks through the limitation of traditional CNC systems that rely solely on pure geometric kinematics to calculate linear velocity, significantly improving the estimation accuracy of the actual cutting linear velocity. The high-precision linear velocity data provides an extremely reliable benchmark for subsequent evaluation of its matching with the ultrasonic frequency, enabling the dynamic correction of the spindle speed to sensitively respond to minute changes in the cutting state. This completely solves the problem of localized deterioration of the tooth surface finish in the transition zone caused by distortion in linear velocity estimation, ensuring the ultimate uniformity of machining quality in the variable lead section. Furthermore, the reason for achieving the above technical effects is that in the cutting transition zone of the variable lead double-envelope toroidal worm gear, the change in spindle load torque is directly related to the tool's stress state, which in turn directly determines whether the tool tip undergoes radial elastic displacement. After introducing the spindle load torque into the compensation link, the actual cutting position is no longer considered an ideal rigid body position, but rather a real working position that dynamically changes with the load. The cutting speed obtained in this way is closer to the actual cutting state. Therefore, the subsequent matching evaluation and spindle speed correction are based on more realistic data, which naturally improves the pertinence and effectiveness of the correction.

[0047] In some embodiments, the specific steps in step S5 include: S51. Calculate the matching error between the cutting line speed of the tool and the tracking frequency; S52. Compare the matching error with multiple preset error thresholds; S53. Based on the threshold range of the matching error, select the corresponding correction strategy from the preset correction strategy library, and dynamically adjust the current spindle speed by executing the selected correction strategy; the correction strategy includes the spindle speed correction amount, correction rate, and correction duration.

[0048] Matching error reflects the degree to which the current actual cutting speed deviates from the ideal ultrasonic cutting speed. It can be obtained as follows: the CNC system first reads the current cutting speed obtained in step A4, then reads the actual tracking frequency of the ultrasonic generator. Based on the pre-established correspondence between "tracking frequency and ideal cutting speed," the ideal cutting speed at the current frequency is obtained. The degree of deviation between the two is then compared to form the matching error. The "tracking frequency-ideal cutting speed" correspondence can be pre-established through process experiments. For example, standard samples are machined at different ultrasonic frequencies, and surface roughness, cutting stability, and tool wear are recorded. The optimal cutting speed range is then selected and compiled into a table showing the correspondence between frequency and ideal cutting speed. Multiple preset error thresholds divide the error range into different intervals, such as a small error zone, a medium error zone, and a severe error zone. Different combinations of adjustment parameters are pre-set for different intervals in the correction strategy library. Among them, the spindle speed correction amount determines the final magnitude of the speed adjustment, the correction rate determines the speed of the adjustment process, and the correction duration is used to limit the action cycle of a single adjustment to prevent frequent adjustments from causing system instability. The correction strategy library can be established during the equipment commissioning phase. The establishment method can be as follows: first, artificially create different degrees of matching deviation under typical operating conditions, and test the effects of different combinations of correction amounts, correction rates, and correction durations on surface quality and system vibration. Then, organize and store the combinations with better effects as strategy entries. Preferably, after each correction strategy is executed, the control system re-enters step S51 to re-evaluate the current matching degree error, thereby forming a rolling closed-loop correction, rather than keeping it unchanged for a long period after a single correction.

[0049] In one specific embodiment, the matching error thresholds are set to 2% and 5%, thus dividing the system into three intervals: [0, 2%] is the small error zone, (2%, 5%] is the medium error zone, and greater than 5% is the severe error zone. The correction strategy library is configured accordingly: no correction is applied to the small error zone (correction amount is 0); a mild correction strategy is used in the medium error zone (correction amount is ±1% of the target speed, correction rate is 5 rpm / s, duration is 0.5 seconds); and a rapid correction strategy is used in the severe error zone (correction amount is ±3% of the target speed, correction rate is 20 rpm / s, duration is 0.2 seconds). During processing, the system calculates the current matching error to be 3.5%, falling into the medium error zone. The control system then invokes the mild correction strategy, slowly fine-tuning the spindle speed at a rate of 5 rpm / s, with an adjustment increment of 1%, maintaining this correction trend for 0.5 seconds, and then... The second evaluation assesses the convergence of the error. To further illustrate the execution method, it can be understood as follows: When the error is 3.5%, the controller first determines whether the current spindle speed should be increased or decreased based on the error direction, and then retrieves the corresponding medium error zone strategy entry from the correction strategy library. Next, within the 0.5-second strategy activation cycle, the spindle speed is gradually pushed towards the correction direction at a rate of 5 rpm / s, rather than jumping to the target correction value instantaneously. After 0.5 seconds, the new cutting line speed and tracking frequency are read again, and the matching degree error is recalculated. If the error has fallen back to the small error zone, the correction stops; if it is still in the medium error zone, the mild correction strategy can be called again; if the error further increases to the severe error zone, the fast correction strategy is switched to. Through this implementation method, the correction action can have the closed-loop characteristics of being phased, directional, and reusable.

[0050] This specific implementation scheme achieves refined closed-loop control of the spindle speed by establishing an adaptive correction mechanism based on the error range. When the error is small, ineffective and frequent interventions are avoided to maintain system stability; when the error is moderate, a gradual correction parameter is used to ensure a smooth speed transition and prevent the initiation of new mechanical vibrations; when the error is large, rapid intervention is initiated to pull the linear velocity back to the matching range at a large rate and amplitude. This multi-dimensional correction strategy, combining correction amount, rate, and time, effectively solves the oscillation or hysteresis problems caused by a single correction method, ensuring that the cutting linear velocity always maintains the optimal dynamic matching state with the ultrasonic frequency throughout the entire cutting transition zone, further consolidating the high-precision surface machining quality of the variable lead double-envelope toroidal worm gear. The principle is that dividing the error range is equivalent to first classifying the severity of the deviation, and then selecting control methods of different intensities according to the level, thus enabling the correction action to match the actual deviation degree. By not correcting minor errors, the control system can avoid repeated actions around very small deviations that cause jitter. Moderate errors are corrected gently, gradually converging the error without compromising mechanical stability. Severe errors are corrected rapidly, shortening the duration of mismatch and reducing the length of defective surfaces. Combined with correction duration limits and periodic reassessment, the entire system maintains closed-loop response capability while avoiding instability caused by continuous, uncontrolled corrections, thus achieving more reliable machining quality control in complex cutting transition zones.

[0051] In some embodiments, the specific steps in step S6 include: S61. Calculate the difference between the actual time consumed and the ultrasonic frequency establishment time calculated in this case to obtain the time deviation value for this case; S62. When the time deviation value is within the preset trust range, update the basic frequency locking time constant by performing the following steps S621-S623: S621. Evaluate the system operational stability during this ultrasonic frequency switching process; S622. Determine the weighting factor based on the time deviation value and the system's operational stability; S623. Based on the actual time consumption and weighting factor, the basic frequency locking time constant is adjusted using a dynamic weighted moving average method according to the following formula: S = S_new = (1-δ)*S_old + δ*H; Where S is the base frequency locking time constant, S_new is the adjusted base frequency locking time constant, δ is the weighting factor, S_old is the base frequency locking time constant before adjustment, and H is the actual time consumption; S63. When the time deviation value exceeds the preset trust range, it is judged as an abnormal working condition sample and the data is discarded.

[0052] The above steps construct a closed-loop iterative learning mechanism based on historical operating data. In actual processing, the locking time of the ultrasonic generator will slowly drift with the increase of equipment operating time, changes in ambient temperature, and aging of internal components. If the basic frequency locking time constant remains at the fixed value at the factory or during debugging, the benchmark of the prediction model will gradually become inaccurate. To solve this problem, the control system records the actual time consumption after each ultrasonic frequency switch and calculates the time deviation value between it and the predicted time. A preset trust interval is used to filter out extreme abnormal data caused by accidental strong interference or extreme cutting impact. When the time deviation value exceeds this interval, it indicates that the switching process has been interfered with by atypical factors, and its time consumption data is not representative, so it is directly discarded to prevent abnormal data from polluting the time benchmark.

[0053] When the time deviation value is within the preset trust interval, the system enters the update process. First, the system's operational stability during this ultrasonic frequency switching process is evaluated. This stability can be comprehensively assessed by monitoring the spindle current fluctuation rate, cutting vibration amplitude, and the number of status word transitions within the ultrasonic generator during the switching period. The smoother the operation, the more accurately the actual time consumption reflects the inherent characteristics of the ultrasonic system. Next, based on the time deviation value and system operational stability, a weighting factor δ is dynamically determined. The weighting factor determines the proportion of the actual time consumption in updating the baseline frequency locking time constant. Specifically, if the system's operational stability is high and the time deviation value is small, it indicates good data quality, and a larger weighting factor can be assigned; conversely, if the stability is average or the deviation is large, a smaller weighting factor is assigned to reduce the impact of a single fluctuation on the global benchmark. Finally, a dynamic weighted moving average method is used to merge the actual time consumption with the baseline frequency locking time constant before adjustment to calculate the new baseline frequency locking time constant. Through this adaptive closed-loop update mechanism, the control system can keenly detect the long-term, slow changes in the physical characteristics of the ultrasonic system and automatically correct the baseline parameters of the prediction model. This not only eliminates the tedious work of manually recalibrating parameters periodically, but also ensures that the prediction of ultrasonic frequency settling time remains highly accurate throughout the entire life cycle of the equipment, thus providing a long-term guarantee for the accurate calculation of the advance trigger distance.

[0054] In some embodiments, it also includes: S71. With the ultrasonic generator in a locked and stable state, obtain the real-time amplitude feedback value of the ultrasonic generator; S72. Calculate the ratio between the real-time amplitude feedback value and the effective value of the piezoelectric transducer's output current in the physical operating parameters to obtain the system's equivalent damping rate; S73. Based on the system's equivalent damping ratio, the amplitude damping coefficient in the load torque damping coefficient table is corrected according to the following formula: β=β_new=β_old+γ*(R_1-R_0); Where β is the amplitude damping coefficient, β_new is the corrected amplitude damping coefficient, β_old is the original amplitude damping coefficient, γ is the preset correction gain, R_1 is the system equivalent damping rate, and R_0 is the preset standard damping rate.

[0055] In ultrasonic-assisted cutting systems, the effective value of the piezoelectric transducer's output current represents the system's input electrical power level, while the real-time amplitude feedback value represents the system's output mechanical vibration level. The real-time amplitude feedback value can be directly measured by a miniature high-frequency displacement sensor installed at the transducer's front end, or indirectly estimated using a dynamic capacitance compensation model within the ultrasonic generator. Ideally, a given input current should generate a corresponding mechanical amplitude. However, when the system's mechanical damping increases (e.g., tool wear leading to increased cutting resistance, or transducer heating causing a decrease in piezoelectric ceramic performance), the amplitude generated by the same input current decreases. Therefore, by calculating the ratio between the real-time amplitude feedback value and the effective value of the output current, the system's equivalent damping ratio can be obtained. This damping ratio directly reflects the efficiency of the current ultrasonic system in converting electrical energy into mechanical energy, i.e., the true physical damping state experienced by the system.

[0056] After obtaining the system's equivalent damping rate, the control system compares it with the preset standard damping rate. The preset standard damping rate refers to the reference damping rate measured during the equipment calibration phase when the tool is sharp and the system is in good condition. If the current system's equivalent damping rate is lower than the preset standard damping rate, it indicates that the actual damping of the system has increased. At this time, through the proportional adjustment of the preset correction gain γ, the original amplitude damping coefficient β_old is appropriately increased to obtain the corrected amplitude damping coefficient β_new, which is then updated in the load torque damping coefficient table. Through this online correction mechanism, the control system can sense and quantify the damping drift of the ultrasonic mechanical system in real time and directly feed it back to the prediction model of the ultrasonic frequency settling time. This deep linkage from the underlying physical state to the upper-level control parameters completely eliminates the prediction error caused by changes in mechanical characteristics. This ensures that the triggering timing of the local interlock control remains accurate even when facing complex and variable cutting conditions and tool wear conditions, further improving the robustness and surface quality consistency of the variable lead secondary envelope toroidal worm gear machining process.

[0057] Reference Appendix Figure 4This invention provides a secondary envelope toroidal worm gear machining control system (the secondary envelope toroidal worm gear machining control system adopts the secondary envelope toroidal worm gear machining control method of the above embodiment, and the specific process is referred to the corresponding steps above), which is applied to the control system of a dual-spindle horizontally opposed CNC lathe. The CNC lathe is equipped with a main spindle and a secondary spindle (main spindle 1 and secondary spindle 2) and a cutting tool 6, and is equipped with an ultrasonic-assisted cutting device 3. The main spindle and the secondary spindle can simultaneously clamp the worm gear 4 and achieve the rotational docking of the worm gear 4 through cooperative control. The ultrasonic-assisted cutting device 3 includes an ultrasonic generator 5 for emitting ultrasonic waves. The secondary envelope toroidal worm gear machining control system includes: The acquisition module 100 is used to acquire the target spindle speed and target ultrasonic frequency of the target section in the worm gear machining path; The calculation module 200 is used to estimate the ultrasonic frequency set-up time based on the target ultrasonic frequency, and to calculate the advance trigger distance of the ultrasonic frequency switching command based on the estimated ultrasonic frequency set-up time and the preset tool feed speed. The monitoring module 300 is used to send an ultrasonic frequency switching command to the ultrasonic generator when the current position of the tool reaches the advance trigger distance, and to determine the operating status of the ultrasonic generator by monitoring the physical operating parameters of the ultrasonic generator; the operating status includes the switching state, the locked but unstable state, and the locked and stable state. The control module 400 is used to perform local interlock control on the current spindle speed according to the operating status of the ultrasonic generator when the tool reaches the preset variable lead switching position in the target section. Local interlock control includes the following steps S41-S43: S41. When the ultrasonic generator is in a locked and stable operating state, the current spindle speed is allowed to switch to the target spindle speed; S42. When the ultrasonic generator is in a locked but unstable operating state, the current spindle speed is allowed to switch to the target spindle speed, and the spindle speed transition curve is dynamically adjusted: S43. When the ultrasonic generator is in a switching state, prevent the current spindle speed from switching to the target spindle speed and reduce the tool feed rate; The first correction module 500 is used to evaluate the matching degree between the actual cutting line speed of the tool and the actual tracking frequency of the ultrasonic generator when the tool is in the cutting transition zone of the target section, and dynamically correct the current spindle speed according to the matching degree. The update module 600 is used to update the basic frequency locking time constant based on the actual time taken from the actual triggering time of the ultrasonic frequency switching command to the time when the ultrasonic generator reaches a locked and stable state; the basic frequency locking time constant is used to estimate the ultrasonic frequency setup time.

[0058] In some embodiments, a second correction module 700 is also included, for performing the following steps: S71. With the ultrasonic generator in a locked and stable state, obtain the real-time amplitude feedback value of the ultrasonic generator; S72. Calculate the ratio between the real-time amplitude feedback value and the effective value of the piezoelectric transducer's output current in the physical operating parameters to obtain the system's equivalent damping rate; S73. Based on the system's equivalent damping ratio, the amplitude damping coefficient in the load torque damping coefficient table is corrected.

[0059] In this context, the units described as separate components may or may not be physically separate. Similarly, the components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0060] Furthermore, the functional modules in the various embodiments of the present invention can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0061] In this document, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, without necessarily requiring or implying any such actual relationship or order between these entities or operations.

[0062] The above description is merely an embodiment of the present invention and is not intended to limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for controlling the machining of a secondary envelope toroidal worm gear, applied to the control system of a dual-spindle horizontally opposed CNC lathe, the CNC lathe being equipped with a main spindle and a secondary spindle and a cutting tool, and having an ultrasonic-assisted cutting device installed, wherein the main spindle and the secondary spindle can simultaneously clamp the worm gear and achieve worm gear rotational docking through coordinated control, and the ultrasonic-assisted cutting device includes an ultrasonic generator for emitting ultrasonic waves; Its features are, The secondary envelope toroidal worm gear machining control method includes the following steps: S1. Obtain the target spindle speed and target ultrasonic frequency of the target segment in the worm gear machining path; S2. Based on the target ultrasonic frequency, estimate the ultrasonic frequency establishment time, and based on the estimated ultrasonic frequency establishment time and the preset tool feed speed, calculate the advance trigger distance of the ultrasonic frequency switching command. S3. When the current position of the tool reaches the pre-trigger distance, an ultrasonic frequency switching command is sent to the ultrasonic generator, and the operating status of the ultrasonic generator is determined by monitoring the physical operating parameters of the ultrasonic generator; the operating status includes the switching state, the locked but unstable state, and the locked and stable state; the physical operating parameters include the effective value of the output current of the piezoelectric transducer and the voltage-current phase difference, as well as the tracking frequency and frequency change rate of the phase-locked loop; S4. When the tool reaches the preset variable lead switching position in the target section, the current spindle speed is locally interlocked according to the operating state of the ultrasonic generator; The local interlock control includes the following steps S41-S43: S41. When the ultrasonic generator is in a locked and stable operating state, the current spindle speed is allowed to switch to the target spindle speed; S42. When the ultrasonic generator is in a locked but unstable operating state, the current spindle speed is allowed to switch to the target spindle speed, and the spindle speed transition curve is dynamically adjusted. S43. When the ultrasonic generator is in a switching state, prevent the current spindle speed from switching to the target spindle speed and reduce the tool feed rate; S5. When the tool is in the cutting transition zone of the target section, evaluate the matching degree between the cutting linear speed of the tool and the tracking frequency of the phase-locked loop in the physical operating parameters, and dynamically correct the current spindle speed according to the matching degree; S6. Update the basic frequency locking time constant based on the actual time taken from the actual triggering time of the ultrasonic frequency switching command to when the ultrasonic generator reaches a locked and stable state; the basic frequency locking time constant is used to estimate the ultrasonic frequency setup time; The specific steps in step S2 include: S21. Based on the target ultrasonic frequency, obtain the jump difference value of the ultrasonic frequency, and based on the jump difference value, obtain the phase-locked loop sweep frequency coefficient from the preset frequency jump time coefficient table; S22. Obtain the current spindle load torque, and based on the current spindle load torque, obtain the amplitude damping coefficient from the preset load torque damping coefficient table; S23. Based on the jump difference of the ultrasonic frequency, the sweep frequency time coefficient of the phase-locked loop, the load torque of the spindle, the amplitude damping coefficient, and the basic frequency locking time constant, the ultrasonic frequency settling time is calculated. S24. Multiply the ultrasonic frequency establishment time by the tool feed speed to obtain the basic spatial advance distance, and add a safety compensation margin to the basic spatial advance distance to obtain the advance trigger distance.

2. The machining control method for a secondary envelope toroidal worm gear according to claim 1, characterized in that, In step S3, the specific steps for determining the operating status of the ultrasonic generator by monitoring its physical operating parameters include: S31. When the voltage-current phase difference is outside the preset resonant phase window and the tracking frequency fluctuates drastically, it is determined that the ultrasonic generator is in a switching state. S32. When the voltage-current phase difference is within the resonant phase window, the frequency change rate is lower than a first preset threshold, and the effective value of the output current is lower than a first percentage of the target rated current value, the ultrasonic generator is determined to be in a locked but unstable state. S33. When the voltage-current phase difference is within the resonant phase window, the frequency change rate is lower than the second preset threshold, the effective value of the output current is higher than the second percentage of the target rated current value, and the current state is maintained for multiple consecutive interpolation cycles, it is determined that the ultrasonic generator is in a locked and stable state; the second preset threshold is less than the first preset threshold; the second percentage is greater than the first percentage.

3. The machining control method for a secondary envelope toroidal worm gear according to claim 1, characterized in that, In step S42, the specific steps for dynamically adjusting the spindle speed transition curve include: S421. During the spindle speed transition, if the ultrasonic generator's operating state reverts to the switching state, the current spindle speed is frozen and the tool feed rate is reduced; when the ultrasonic generator's operating state returns to the locked but unstable state, the original tool feed rate is restored, and the transition curve is replanned based on the current spindle speed to complete the switch from the current spindle speed to the target spindle speed.

4. The machining control method for a secondary envelope toroidal worm gear according to claim 1, characterized in that, In step S5, the cutting linear velocity is calculated according to the following steps: A1. Obtain the current spindle load torque; A2. Based on the current position of the tool, calculate the radius of rotation of the tool tip contact point in the radial direction of the spindle; A3. Based on the current spindle load torque, correct the slewing radius to obtain the cutting slewing radius; A4. The cutting linear velocity is calculated based on the cutting radius of rotation and the current spindle speed.

5. The machining control method for a secondary envelope toroidal worm gear according to claim 4, characterized in that, The specific steps in step S5 include: S51. Calculate the matching error between the cutting linear velocity of the tool and the tracking frequency; S52. Compare the matching error with a plurality of preset error thresholds; S53. Based on the threshold range where the matching error is located, select the corresponding correction strategy from the preset correction strategy library, and dynamically adjust the current spindle speed by executing the selected correction strategy.

6. The machining control method for a secondary envelope toroidal worm gear according to claim 1, characterized in that, The specific steps in step S6 include: S61. Calculate the difference between the actual time consumed and the ultrasonic frequency establishment time calculated in this instance to obtain the time deviation value for this instance; S62. When the time deviation value is within a preset trust interval, the basic frequency locking time constant is updated by performing the following steps S621-S623: S621. Evaluate the system operational stability during this ultrasonic frequency switching process; S622. Determine the weighting factor based on the time deviation value and the system's operational stability; S623. Based on the actual time consumption and the weighting factor, the basic frequency locking time constant is adjusted using a dynamic weighted moving average method; S63. When the time deviation value exceeds the preset trust interval, it is determined to be an abnormal working condition sample and the data is discarded.

7. The machining control method for a secondary envelope toroidal worm gear according to claim 1, characterized in that, Also includes: S71. When the ultrasonic generator is in a locked and stable state, obtain the real-time amplitude feedback value of the ultrasonic generator; S72. Calculate the ratio between the real-time amplitude feedback value and the effective value of the piezoelectric transducer output current in the physical operating parameters to obtain the system equivalent damping rate; S73. Based on the equivalent damping ratio of the system, the amplitude damping coefficient in the load torque damping coefficient table is corrected.

8. A control system for machining a secondary envelope toroidal worm gear, which operates the secondary envelope toroidal worm gear machining control method as described in any one of claims 1-7, is applied to the control system of a dual-spindle horizontally opposed CNC lathe, the CNC lathe being equipped with a main spindle and a secondary spindle and a cutting tool, and having an ultrasonic-assisted cutting device installed, wherein the main spindle and the secondary spindle can simultaneously clamp the worm gear and achieve worm gear rotational docking through coordinated control, and the ultrasonic-assisted cutting device includes an ultrasonic generator for emitting ultrasonic waves; Its features are, The secondary envelope toroidal worm gear machining control system includes: The acquisition module is used to acquire the target spindle speed and target ultrasonic frequency of the target segment in the worm gear machining path; The calculation module is used to estimate the ultrasonic frequency establishment time based on the target ultrasonic frequency, and to calculate the advance trigger distance of the ultrasonic frequency switching command based on the estimated ultrasonic frequency establishment time and the preset tool feed speed. The monitoring module is used to send an ultrasonic frequency switching command to the ultrasonic generator when the current position of the tool reaches the pre-triggered distance, and to determine the operating status of the ultrasonic generator by monitoring the physical operating parameters of the ultrasonic generator; the operating status includes switching state, locked but unstable state, and locked and stable state. The control module is used to perform local interlock control on the current spindle speed according to the operating status of the ultrasonic generator when the tool reaches the preset variable lead switching position in the target section. The local interlock control includes the following steps S41-S43: S41. When the ultrasonic generator is in a locked and stable operating state, the current spindle speed is allowed to switch to the target spindle speed; S42. When the ultrasonic generator is in a locked but unstable operating state, the current spindle speed is allowed to switch to the target spindle speed, and the spindle speed transition curve is dynamically adjusted. S43. When the ultrasonic generator is in a switching state, prevent the current spindle speed from switching to the target spindle speed and reduce the tool feed rate; The correction module is used to evaluate the matching degree between the actual cutting line speed of the tool and the actual tracking frequency of the ultrasonic generator when the tool is in the cutting transition zone of the target section, and dynamically correct the current spindle speed according to the matching degree. The update module is used to update the basic frequency locking time constant based on the actual time taken from the actual triggering time of the ultrasonic frequency switching command to when the ultrasonic generator reaches a locked and stable state; the basic frequency locking time constant is used to estimate the ultrasonic frequency establishment time.

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