Cam curve pressure angle optimization method of continuous zooming infrared lens

Abstract

The invention discloses a cam curve pressure angle optimization method of a continuous zooming infrared lens. The method comprises the following steps: S1, obtaining cam curve digital coordinate data of a to-be-optimized part; s2, pressure angle distribution characteristics are obtained; s3, selecting an optimization strategy according to the pressure angle distribution characteristics; s4, performing global piecewise function angle redistribution on the cam curve to be optimized; and S5, processing constraint inspection, motion constraint inspection, smoothness constraint inspection and pressure angle constraint inspection are performed according to the constraint conditions, and an optimized result is output after target requirements are met. According to the method, the cam curve can be accurately detected, and various parameters of the curve can be effectively optimized.

Description

Technical Field

[0001] This application relates to the field of infrared lens generation technology, and in particular to a method and apparatus for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens. Background Technology

[0002] Continuous zoom infrared lenses are widely used in military reconnaissance, security monitoring, industrial inspection and other fields. In a continuous zoom system, the cam mechanism is the core driving component, and the design quality of its cam curve directly affects the smoothness, stability and imaging quality of the zoom system.

[0003] The existing technology has the following problems: 1. There is a lack of an effective cam curve pressure angle detection device, which makes it impossible to accurately obtain the digital data of the physical cam curve; 2. Traditional cam curve design methods result in excessive pressure angles, generating excessive torque at inflection points, which affects zoom smoothness; 3. Existing optimization methods are limited and cannot adaptively optimize for different pressure angle distribution characteristics; 4. Lack of comprehensive optimization solutions that consider machining accuracy and motion constraints; 5. For systems with large zoom magnification, traditional methods have limited optimization effects.

[0004] The information disclosed in the background section is intended only to enhance the understanding of the overall background of the invention and should not be construed as an admission or in any way implying that such information constitutes prior art known to those skilled in the art. Summary of the Invention

[0005] This application addresses the aforementioned technical problems by providing a method and apparatus for optimizing the pressure angle of a cam curve in a continuous zoom infrared lens. This method can accurately detect the cam curve and effectively optimize various parameters of the curve.

[0006] This application provides a method for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens, including the following steps: Step S1: After obtaining the digital coordinate data of the cam curve of the part to be optimized, calculate the initial pressure angle α_i and construct the mathematical model of the cam curve; Step S2: Obtain the pressure angle distribution characteristics, including: maximum pressure angle α_man, minimum pressure angle α_min, average pressure angle α_mean, and standard deviation of pressure angle σ_α; obtain the high pressure angle region in the cam curve mathematical model, obtain the coordinates of the inflection points in the cam curve mathematical model and the pressure angle value at the inflection points, and calculate the pressure angle change rate α% between adjacent coordinate points of each inflection point. Step S3: Select an optimization strategy based on the pressure angle distribution characteristics and optimize the mathematical model of the cam curve to be optimized; Obtain the standard deviation σ_α of the cam curve to be optimized. When the standard deviation σ_α < threshold T1 and α_max < threshold T2, use Gaussian function to smooth and optimize the cam curve. T1 is 10° and T2 is 80°. When the standard deviation σ_α ≥ threshold T1 or the maximum pressure angle α_max ≥ threshold T2, optimization is performed by redistributing the piecewise function angle of the cam curve mathematical model. Obtain the number of inflection points in the cam curve to be optimized. When the number of inflection points is ≥3, a hybrid optimization strategy is adopted. Establish a decision matrix, automatically select an optimization strategy to optimize the cam curve, and output the optimized cam curve. Step S4: After global piecewise function angle redistribution of the cam curve to be optimized, local Gaussian function fine optimization is performed, followed by iterative optimization. The maximum number of iterations N_max is set, and iteration stops when the improvement is less than the threshold ε2 for 3 consecutive iterations. The maximum number of iterations N_max is 20~50. Step S5: Perform machining constraint checks, motion constraint checks, smoothness constraint checks, and pressure angle constraint checks according to the constraints. After the checks are completed, obtain the cam rotation angle and pressure angle corresponding to each coordinate point on the optimized cam curve. Obtain the optimization effect verification parameters based on the obtained cam rotation angle and pressure angle. Compare the optimization effect verification parameters with the target cam curve requirements to see if they meet the target cam curve requirements. If they do, output the cam rotation angle and pressure angle corresponding to each coordinate point on the optimized cam curve.

[0007] Preferably, the optimized cam curve results are the cam rotation angle and pressure angle corresponding to each coordinate point on the optimized cam curve of each component. Based on the cam rotation angle and pressure angle corresponding to each coordinate point on the optimized cam curve of each component, the optimized maximum pressure angle α_max_new, the optimized pressure angle value standard deviation σ_α_new, and the optimized pressure angle at the inflection point α_inflection_new are obtained. The reduction in maximum pressure angle η1: η1=(α_max_old-α_max_new) / α_max_old×100%; where α_max_old is the original maximum pressure angle; α_max_new is the optimized maximum pressure angle; The rate of change of the standard deviation of the pressure angle η2: η2=(σ_α_old-σ_α_new) / σ_α_old×100%, where σ_α_old is the standard deviation of the pressure angle value before optimization; σ_α_new is the standard deviation of the pressure angle value after optimization; The rate of change of pressure angle at the inflection point η3: η3=(α_inflection_old-α_inflection_new) / α_inflection_old×100%; where α_inflection_old is the pressure angle at the inflection point before optimization; α_inflection_new is the pressure angle at the inflection point after optimization.

[0008] Preferably, the device used for “acquiring digital coordinate data of the cam curve of the part to be optimized” includes: a mounting platform, a height measuring instrument (2), a Y-axis manual translation stage (22), an X-axis manual translation stage (23), and a claw-equipped electric rotary table (21); the height measuring instrument (2) is suspended on the mounting platform and is positioned directly opposite the claw-equipped electric rotary table (21), the X-axis manual translation stage (23), and the Y-axis manual translation stage (22) stacked in sequence; The part to be tested is clamped on a claw-equipped electric rotary table (21); the height measuring instrument (2) is set to contact the cam curve detection of the part to be tested; During measurement, the electric rotary table with claw (21) is started, and the part to be measured is rotated while the coordinate data (x_i, z_i) of each coordinate on the cam curve of the part to be measured is measured.

[0009] Preferably, the height measuring instrument (2) includes: a data interface, a host, a displacement sensor, and a probe; the host is provided with a data interface; a probe is provided below the host, and a displacement sensor is provided on the extension end of the probe as a probe.

[0010] Preferably, the installation platform includes: a base (11), a support arm (12), and an installation arm (13). An mounting arm (13) is provided on one side of the base (11); the mounting arm (13) is set vertically to the base (11); a support arm (12) is provided on the top of the mounting arm (13); the support arm (12) extends outward vertically to the mounting arm (13), and a height measuring instrument (2) is provided on the extended end.

[0011] Preferably, step S1 includes the following steps: Step S1.1: Filter the obtained coordinate data (x_i, z_i) to obtain the coordinate data; Step S1.2: Calculate the initial pressure angle α_i according to the formula, α_i = arctan((z_{i+1} - z_i) / (x_{i+1}- x_i)), where z_{i+1} is the z-axis coordinate value of the (i+1)th point and x_{i+1} is the x-axis coordinate value of the (i+1)th point; Step S1.3: Establish a mathematical model of the cam curve based on the initial pressure angle α_i and coordinate data.

[0012] Preferably, step S2 includes the following steps: Step S2.1: Obtain the high pressure angle region in the mathematical model of the cam curve. Specifically, iterate through the pressure angle values ​​of each coordinate in the mathematical model of the cam curve, obtain the pressure angle value α_i of the i-th point, and mark the i-th point as a high pressure angle point when α_i > α_mean + 2σ_α. Step S2.2: Obtain the coordinates of the inflection points and the pressure angle value at the inflection points in the mathematical model of the cam curve; Step S2.3: Calculate the rate of change of pressure angle α between adjacent coordinate points according to the following formula, and analyze the gradient of pressure angle change in the mathematical model of the cam curve: α%=(α_i —α_i -1) / α_i *100%, where α_i is the pressure angle α at point i; α_i -1 is the pressure angle α at point i-1.

[0013] Preferably, the Gaussian function smoothing optimization in step S3 includes the following steps: Step S3.1: Construct the Gaussian function: G(x) = A·exp[-(xb)² / c²] Step S3.2: Adaptive parameter setting: Amplitude parameter A: A=k1·(α_max—α_min), where k1 is the adjustment coefficient, usually taken as 0.5~1.0; Central parameter b: b = x_{α_max}, where x_{α_max} is the x-coordinate of the point corresponding to the maximum pressure angle; Width parameter c: c=k2·|x_{α_max}—x_{α_min}|, where k2 is the adjustment coefficient, usually taken as 0.3~0.8, and x_{α_min} is the x-coordinate position of the coordinate point corresponding to the minimum pressure angle; Step S3.3: Perform lateral widening processing on each coordinate point on the cam curve to be optimized. Specifically, update the x-coordinate value of each coordinate point on the cam curve to be optimized to obtain the updated x-coordinate value x_new, x_new=x·G(x); where x is the x-axis coordinate value of each coordinate point on the cam curve to be optimized. After traversing and updating, the optimized cam curve coordinates and pressure angle distribution are obtained. Step S3.4 Recalculate the optimized cam curve coordinates and pressure angle distribution, and iteratively optimize the pressure angle until the convergence condition is met: |α_max^(k+1)—α_max^(k)|<ε1, where ε1 is the convergence threshold, usually set to 1 degree, and k is the number of iterations.

[0014] Preferably, the piecewise function angle redistribution in step S3 includes the following steps: Step S3.5: Construct a piecewise function from the cam curve rotation angle data of the part to be optimized: The first function segment is: y(i)-y(i-1)=r·θ2 / (nm)+(m+1-i)·δ(i=2:m); The second function is: y(i) = r·θ1 + r·θ2 / (nm)·i (i = m:n); Set the constraint: θ1 + θ2 = θ_total (total rotation angle); Where θ1 is the rotation angle assigned to the first segment, θ2 is the rotation angle assigned to the second segment, r is the cam radius, n is the total number of data points, m is the index position of the segment point, and δ is the adjustment parameter used to control the intensity and fineness of the optimization. Based on the pressure angle distribution characteristics, segment point m is selected, and the angle allocation ratio θ1:θ2 is determined according to the length of the high and low pressure angle regions; the parameter δ is adjusted to control the smoothness of the transition region of the cam curve; a larger rotation angle θ2 is allocated to the high pressure angle region, and the rotation angle θ1 is compressed to the low pressure angle region. Step S3.6: Obtain the number of high-pressure angle regions of the cam curve of the part to be optimized. When the number of high-pressure angle regions is less than or equal to 1, use Gaussian function to smooth and optimize the cam curve. When the number of high-pressure angle regions is greater than 1, use piecewise function to optimize the cam curve piecewise. The piecewise strategy is as follows: first calculate the first derivative of the cam curve, find all points where the first derivative is 0 (assuming the total number of points is k), and divide the cam into k+1 segments, that is, optimize the cam curve of k+1 segments respectively.

[0015] Preferably, the "hybrid optimization strategy" in step S3 includes the following steps: Step S3.7: Identify all high-pressure angle regions, coarsely adjust the overall curve to reduce the global maximum pressure angle to 80-45% of the original pressure angle, and establish a multi-segment function model to handle multiple problem regions; Step S3.8: Use an adaptive window size to smooth the remaining local high-pressure angle regions with a Gaussian function, ensuring the overall continuity and differentiability of the curve.

[0016] The beneficial effects that this application can produce include: 1) The cam curve pressure angle optimization method of the continuous zoom infrared lens provided in this application can obtain micron-level cam curve displacement detection results through the collaborative work of the nine-module integrated detection device. The angle detection accuracy reaches 0.01°, the displacement detection accuracy reaches 1μm, and the data acquisition frequency is as high as 100Hz, which ensures the complete capture and high-precision digital conversion of the details of the cam curve to be optimized.

[0017] 2) The cam curve pressure angle optimization method for continuous zoom infrared lens provided in this application has the following optimization effect: the method uses an adaptive dual optimization algorithm to optimize the obtained cam curve. The maximum pressure angle of the optimized cam curve can be reduced by 20-60%, effectively suppressing the pressure angle abrupt change at the inflection point, improving the effect by 30-50%, significantly improving the smoothness of the zoom process, and fundamentally improving the imaging quality of the optimized infrared lens.

[0018] 3) The cam curve pressure angle optimization method for continuous zoom infrared lenses provided in this application has strong intelligent features in terms of adaptability. The algorithm can automatically select the optimal optimization strategy according to different cam curve characteristics, supports pressure angle optimization in the range of 5~80°, adapts to the optimization needs of different zoom magnifications, and has the characteristics of automatic optimization.

[0019] 4) The cam curve pressure angle optimization method for the continuous zoom infrared lens provided in this application fully considers the actual engineering conditions such as machining accuracy (0.02mm) and motion constraints in terms of practicality, ensuring the engineering feasibility of the optimization results. When the optimization results are applied to physical devices, the optimized parameters can maintain the above-mentioned optimized performance in a wide operating temperature range of -45~60℃.

[0020] 5) The cam curve pressure angle optimization method for continuous zoom infrared lenses provided in this application has the following advantages in terms of versatility. This detection system is not only applicable to infrared zoom systems, but can also be extended to various zoom systems such as visible light and laser. It supports various cam types such as linear cams and helical cams, and can be extended to the optimization of multiple sets of linkage cam systems. It has broad application prospects and promotion value. Attached Figure Description

[0021] Figure 1 A schematic diagram of a method for optimizing the pressure angle of a cam curve of a continuous zoom infrared lens in at least one embodiment provided in this application; Figure 2 A three-dimensional structural schematic diagram of the cam curve pressure angle testing device for a continuous zoom infrared lens in at least one embodiment provided in this application; Figure 3 This application provides cam curve diagrams of the optimized lens components before and after the optimization obtained in Embodiment 2. The gray lines represent the cam curves of the zoom group, compensation group, and aberration stabilization group of the optimized lens; the red lines represent the cam curve of the zoom group; the green lines represent the cam curve of the compensation group; and the blue lines represent the cam curve of the aberration stabilization group. Figure 4This application provides a diagram showing the relationship between the pressure angle and cam rotation angle of the optimized lens obtained in Example 2; wherein, gray represents the overall pressure angle curve; red represents the pressure angle and cam rotation angle relationship curve of the zoom group; green represents the pressure angle and cam rotation angle relationship curve of the compensation group; and blue represents the pressure angle and cam rotation angle relationship curve of the aberration stabilization group; a) is the lens relationship diagram before optimization; and b) is the lens relationship diagram after optimization. Legend: Base 11, support arm 12, mounting arm 13, height measuring instrument 2, Y-axis manual translation stage 22, electric rotary table with claw 21, X-axis manual translation stage 23, probe 211. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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.

[0023] Therefore, the following detailed description of the embodiments of the 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 invention without inventive effort are within the scope of protection of the invention.

[0024] Technical means not detailed in this application and not used to solve the technical problems of this application are all set according to common general knowledge in the field, and multiple common general knowledge setting methods can be implemented.

[0025] See Figure 1 This application provides a cam curve pressure angle detection device for a continuous zoom infrared lens, comprising: The mounting platform includes a base 11, a support arm 12, and a mounting arm 13. The mounting arm 13 is vertically mounted on the top surface of the base 11. The support arm 12 is mounted at the top of the mounting arm 13, with one end of the support arm 12 extending outward perpendicularly to the mounting arm 13. The height gauge 2 is mounted on the extended end of the support arm 12. Using this platform to mount the height gauge 2 ensures its stability during measurement, preventing displacement and enabling accurate measurement of the cam curve of the infrared lens. The platform is made of high-rigidity materials and has excellent vibration resistance.

[0026] The lower part of the height measuring instrument 2 extends out a support arm 12 to set the height measuring instrument probe 211: the height measuring instrument displacement sensor probe is installed on the side wall of the height measuring instrument probe 211, the probe makes contact with the cam groove of the infrared lens being measured, and realizes the displacement transmission of the cam curve of the infrared lens being measured. The probe material is a high-hardness alloy to ensure long-term accuracy; the probe used is a displacement sensor.

[0027] Altimeter 2: Used for real-time, high-precision acquisition of the relative displacement of the cam curve of the infrared lens under test, and output of displacement data. The measurement accuracy is not less than 1μm and the sampling frequency is not less than 100Hz. The altimeter is a commercially available product.

[0028] The top of the altimeter 2 is equipped with a data interface for connecting the altimeter's displacement sensor and a computer, enabling real-time acquisition and transmission of displacement data, and supporting high-speed data transmission protocols.

[0029] Y-axis manual translation stage 22: The Y-axis manual translation stage 22 is set on the top surface of the base 1 and is set directly opposite the lower part of the height measuring instrument 2; during measurement, the operator manually adjusts the Y-axis manual translation stage 22 to adjust the position of the infrared lens to be measured placed on it in the Y-axis direction, and the adjustment accuracy is not less than 0.01mm. X-axis manual translation stage 23: The X-axis manual translation stage 23 is set on the top surface of the Y-axis manual translation stage 22. During measurement, the operator manually adjusts the X-axis manual translation stage 23 to control the position of the infrared lens under test in the X-axis direction. The adjustment accuracy is not less than 0.01mm. The electric rotary stage 21 with claws is mounted on the top surface of the X-axis manual translation stage 23. A rotating claw is set in the central area of ​​the X-axis manual translation stage 23 to fix the infrared lens under test. The rotating claw rotates relative to the X-axis manual translation stage 23, thereby driving the infrared lens under test to achieve axial rotation. The rotation accuracy is not less than 0.01°, and the repeatability is not less than 0.005°. A data interface is set on one side of the electric rotary stage 21. Through the data interface, it can be electrically connected to a computer to realize real-time high-precision acquisition of the rotation angle of the electric rotary stage and realize remote communication control of the rotation angle of the rotating claw on the electric rotary stage 21. This interface supports multiple communication protocols such as RS485 and USB.

[0030] The part under test can be an infrared lens with cams, including multiple cam curves such as zoom group, compensation group, and aberration stabilization group.

[0031] The above-mentioned device can be used to accurately measure the cam curve on the part to be tested, so as to detect the actual situation of the cam curve on the part before and after optimization.

[0032] Another aspect of this application provides a method for optimizing the cam curve of a continuous zoom infrared lens, comprising the following steps: Step S1: After obtaining the digital coordinate data of the cam curve of the part to be tested, calculate the initial pressure angle α_i and construct the mathematical model of the cam curve; Step S1.1 Obtain the digital coordinate data (x_i, z_i) of the cam curve of the part to be optimized through the cam curve detection device, where the i-th coordinate point = 1, 2, ..., n, x_i is the x-axis coordinate value of the i-th point, and z_i is the z-axis coordinate value of the i-th point; Step S1.2 Filter the raw data to remove noise from the obtained coordinate measurement results and obtain coordinate data; Step S1.3 Calculate the initial pressure angle α_i based on the obtained coordinate data using the following formula: α_i = arctan((z_{i+1} - z_i) / (x_{i+1} - x_i)), where z_{i+1} is the z-axis coordinate value of the (i+1)th point and x_{i+1} is the x-axis coordinate value of the (i+1)th point. Step S1.4 Establish a mathematical model of the cam curve based on the initial pressure angle α_i and coordinate data; Step S2: Obtain the pressure angle distribution characteristics: Step S2.1 Iterate through the pressure angle values ​​of each coordinate point in the obtained cam curve mathematical model. Each time a comparison is made, select the maximum pressure angle in the current comparison data, and then compare the obtained maximum pressure angle with the other pressure angle values ​​to obtain the maximum pressure angle value α_man: α_max = max{α_i}. The pressure angle values ​​of each coordinate point in the obtained cam curve mathematical model are traversed. The minimum pressure angle in the current comparison data is selected each time. The obtained minimum pressure angle is then compared with the other pressure angle values ​​to obtain the minimum pressure angle value α_min: α_min = min{α_i}. Calculate the average pressure angle α_mean at each coordinate point in the mathematical model of the cam curve: α_mean = (1 / n)∑α_i; Calculate the standard deviation of the pressure angle σ_α at each coordinate point in the mathematical model of the cam curve: σ_α = √[(1 / n)∑(α_i- α_mean)²]; Step S2.2 Obtain the high pressure angle region in the mathematical model of the cam curve. Specifically, iterate through the pressure angle values ​​of each coordinate in the mathematical model of the cam curve, obtain the pressure angle value α_i of the i-th point, and mark the i-th point as a high pressure angle point when α_i > α_mean + 2σ_α. Step S2.3 Obtain the coordinates of the inflection point and the pressure angle value at the inflection point in the mathematical model of the cam curve; the calculation method of the inflection point is: calculate the second derivative of the cam curve, find all points where the value of the second derivative is zero, and among all points, traverse and select the point where the product of the second derivatives of the two points before and after a specific point is negative, which is the inflection point of the cam curve; Step S2.4 Calculate the rate of change of pressure angle α% between adjacent coordinate points of the inflection point according to the following formula, and analyze the gradient of pressure angle change in the mathematical model of the cam curve: α%=(α_i —α_i -1) / α_i *100%, where α_i is the pressure angle α at point i; α_i-1 is the pressure angle α at point i-1; Step S3: Adaptive optimization strategy selection: Step S3.1 Based on the pressure angle distribution characteristics obtained in step S2, after acquiring the characteristic parameters, compare each characteristic parameter with the index, select an optimization strategy based on the comparison results, and then perform optimization processing accordingly: Obtain the standard deviation σ_α of the cam curve to be optimized. When the standard deviation σ_α < threshold T1 (usually 10°) and α_max < threshold T2 (usually 80°), use Gaussian function smoothing optimization. When the standard deviation σ_α ≥ threshold T1 or α_max ≥ threshold T2, optimization is performed by redistributing the piecewise function angle of the cam curve mathematical model. Obtain the number of inflection points in the cam curve to be optimized. When the number of inflection points is ≥3, adopt a hybrid optimization strategy. Step S3.2: Establish a decision matrix and automatically select an optimization strategy; Step S4: When Gaussian function smoothing optimization is required, the following steps are performed: Step S4.1 Construct the Gaussian function: G(x) = A·exp[-(xb)² / c²] Step S4.2 Parameter adaptive setting: Amplitude parameter: A = k1·(α_max—α_min), where k1 is the adjustment coefficient, usually taken as 0.5~1.0; Central parameter: b = x_{α_max}, where x_{α_max} is the x-coordinate of the point corresponding to the maximum pressure angle; Width parameter: c=k2·|x_{α_max}—x_{α_min}|, where k2 is the adjustment coefficient, usually taken as 0.3~0.8, and x_{α_min} is the x-coordinate position of the coordinate point corresponding to the minimum pressure angle; Step S4.3 Perform lateral widening processing on each coordinate point on the cam curve to be optimized. Specifically, update the x-coordinate value of each coordinate point on the cam curve to be optimized to obtain the updated x-coordinate value x_new, x_new=x·G(x); where x is the x-axis coordinate value of each coordinate point on the cam curve to be optimized. After traversing and updating, the optimized cam curve coordinates and pressure angle distribution are obtained. Step S4.4 Recalculate the optimized cam curve coordinates and pressure angle distribution, and iteratively optimize the pressure angle until the convergence condition is met: |α_max^(k+1)—α_max^(k)|<ε1, where ε1 is the convergence threshold, usually set to 1 degree, and k is the number of iterations; Step S5: Piecewise function angle redistribution optimization: Step S5.1: After probe 211 contacts the cam curve of the part to be optimized, start the jaw electric rotary table 21 to rotate. During the rotation, read the rotation angle data in real time, and construct the obtained rotation angle as a piecewise function: The first function segment is: y(i)-y(i-1)=r·θ2 / (nm)+(m+1-i)·δ(i=2:m); The second function is: y(i) = r·θ1 + r·θ2 / (nm)·i (i = m:n); Set the constraint: θ1 + θ2 = θ_total (total rotation angle); Where θ1 is the rotation angle assigned to the first segment, θ2 is the rotation angle assigned to the second segment, r is the cam radius, n is the total number of data points, m is the index position of the segment point, and δ is the adjustment parameter used to control the intensity and fineness of the optimization. Based on the pressure angle distribution characteristics obtained in step S2, segment point m is selected, and the angle allocation ratio θ1:θ2 is determined according to the length of the high and low pressure angle regions; the parameter δ is adjusted to control the smoothness of the transition region of the cam curve; a larger rotation angle θ2 is allocated to the high pressure angle region, and the rotation angle θ1 is compressed to the low pressure angle region.

[0033] Step S5.3 Multi-segment optimization: Obtain the number of high-pressure angle regions on the cam curve of the part to be optimized. When the number of high-pressure angle regions is less than or equal to 1, use a Gaussian function to smooth and optimize the cam curve; when the number of high-pressure angle regions is greater than 1, use a piecewise function to optimize the cam curve piecewise. The piecewise strategy is as follows: first calculate the first derivative of the cam curve, find all points where the first derivative is 0 (assuming a total number of points is k), and divide the cam into k+1 segments, that is, optimize the cam curve of k+1 segments separately. Step S6: Hybrid optimization strategy; Step S6.1 Global piecewise function angle redistribution: Identify all high pressure angle regions, coarsely adjust the overall curve to reduce the global maximum pressure angle to 80-45% of the original pressure angle, and establish a multi-piece function model to handle multiple problem regions; this value needs to be determined in conjunction with the uniformity of the pressure angle distribution of the cam curve, and it is necessary to ensure the uniform distribution of pressure angles as much as possible while ensuring the reduction of the global maximum pressure angle. Step S6.2 Local Gaussian function fine optimization: Adaptive window size is used to smooth the remaining local high pressure angle region with Gaussian function, ensuring the overall continuity and differentiability of the curve; Step S6.3 Iterative optimization strategy: Set the maximum number of iterations N_max (usually 20~50); stop when the improvement is less than the threshold ε2 after 3 consecutive iterations.

[0034] Step S7: Constraint verification and correction Step S7.1 Machining constraint check, minimum spacing constraint: min{x_{i}-x_{i-1}}>δ_machine; where δ_machine is the machining accuracy requirement, usually taken as 0.02mm; x_{i} is the x-coordinate value of the i-th point on the cam curve; x_{i-1} is the x-1 coordinate value of the i-th point on the cam curve; min is the minimum value of x_{i}-x_{i-1}. Step S7.2 Motion constraint check: Motor accuracy constraint: min{x_{i}-x_{i-1}}>δ_motor Where δ_motor is the motor stepping accuracy, which is usually taken as 0.01mm; Step S7.3 Smoothness constraint check: Curvature continuity: |x_{i}-x_{i-1}|>nD_max, where n is the safety factor and D_max is the maximum allowable radius of curvature; Step S7.4 Pressure Angle Constraint Verification: Iterate through the pressure angle values ​​of each coordinate point on the cam curve, compare the pressure angle values, obtain α_max, and set the maximum pressure angle α_max < α_limit, where α_limit is usually taken as 30~50°; set the pressure angle gradient |α_{i+1}-α_i| < Δα_max; where Δα_max is usually taken as 0.5°, and use it as a constraint condition for iterative optimization, outputting the optimized cam curve parameters, including the optimized coordinate data (x_new, z_new), pressure angle distribution α_new, and optimization effect evaluation index; the variable Δα_max determines the density of the optimized cam curve data points, which is determined by the accuracy of the machining tool.

[0035] Step S8: Optimize the output of results and verify the optimization effect parameters. The optimized cam curve results are the cam rotation angle and pressure angle corresponding to each coordinate point on the optimized cam curve of each component. Based on the cam rotation angle and pressure angle corresponding to each coordinate point on the optimized cam curve of each component, obtain the optimized maximum pressure angle α_max_new, the optimized pressure angle value standard deviation σ_α_new, and the optimized pressure angle at the inflection point α_inflection_new.

[0036] The parameters for verifying the optimization effect include: the reduction in the maximum pressure angle η1: η1=(α_max_old-α_max_new) / α_max_old×100%; where α_max_old is the original maximum pressure angle; α_max_new is the optimized maximum pressure angle; The rate of change of the standard deviation of the pressure angle η2: η2=(σ_α_old-σ_α_new) / σ_α_old×100%, where σ_α_old is the standard deviation of the pressure angle value before optimization; σ_α_new is the standard deviation of the pressure angle value after optimization; The rate of change of pressure angle at the inflection point η3: η3=(α_inflection_old-α_inflection_new) / α_inflection_old×100%; where α_inflection_old is the pressure angle at the inflection point before optimization; α_inflection_new is the pressure angle at the inflection point after optimization. Example 1: Detection of Cam Curve of 25~225mm Long-Wave Uncooled Infrared Lens Assemble according to the aforementioned structure as follows: Figure 2 The detection device shown in this embodiment details the specific implementation process of cam curve pressure angle detection and optimization for 25~225mm long-wave uncooled infrared zoom lenses. Through the coordinated work of nine core modules, micron-level precision digital detection of cam curves is achieved. The height gauge 2 uses a high-precision digital display height gauge from Mitutoyo, with a measurement accuracy of ±1μm, a measurement range of 0~300mm, an electric rotary table angle accuracy of ±0.005°, a repeatability accuracy of ±0.002°, a maximum load of 15kg, an adjustable rotation speed of 0.05~10° / s, an encoder resolution of 0.0001°, and a manual translation stage with X and Y axis adjustment accuracy of 0.05mm and a stroke of ±40mm. The Y-axis manual translation stage 22 and the X-axis manual translation stage 23 use precision crossed roller guides. The data acquisition system uses an STM32F407 data acquisition module with a sampling frequency of 100Hz, 16-bit resolution, and an accuracy of ±0.02%.

[0037] Developed based on the STM32F407 platform, it integrates noise filtering algorithms, cubic spline interpolation, and least squares fitting algorithms. The user interface adopts a graphical design, including a real-time data display area, a parameter setting area, and a status monitoring area. It supports one-click automatic measurement, and the communication protocols support RS485, Ethernet, and USB.

[0038] System initialization includes hardware self-test, coordinate system establishment, and environmental parameter settings. The lens to be tested and optimized is mounted on a three-jaw chuck fixed to the electric rotary table 21, with a clamping force set to 10N±1N. A laser collimator is used to align the optical axis with an accuracy ≤0.01mm. Measurement parameters are set as follows: starting angle 0°, ending angle 135°, angle step 0.12°, a total of 1125 measurement points, and a rotation speed of 0.6° / s. The displacement measurement range is 0~55mm, with a resolution of 0.1μm and a sampling frequency of 100Hz. Environmental conditions are strictly controlled at 20℃±2℃ and 50%±5%RH for measurement.

[0039] The automated measurement program executes the following steps: parameter verification, equipment inspection, data acquisition, anomaly monitoring, and result saving. Real-time display functions include cam curve plotting and pressure angle distribution calculation. Data output supports multiple formats such as Excel, CSV, and JSON, covering raw data, processed data, pressure angle calculation results, and statistical parameters.

[0040] This embodiment uses the detection device with the above-described structure to detect the cam curve of the lens under test, realizing the digital detection of the cam curve with micron-level precision, providing a reliable technical basis for pressure angle optimization, and significantly improving product quality and production efficiency.

[0041] Example 2: Optimizing the cam curve of a 25~225mm long-wavelength uncooled infrared lens The optimization target is a high-precision 9x zoom infrared lens. This lens system has extremely high requirements for image quality and needs to approach the diffraction-limited optical performance. Therefore, more stringent requirements are placed on the pressure angle control of the cam curve. The focal length range of this high-precision zoom lens is 25-225mm, achieving 9x continuous zoom. Compared with the conventional 4x zoom system, its zoom magnification is significantly increased, which poses a greater challenge to the design of the cam curve.

[0042] The system's imaging quality must approach the diffraction limit, meaning that all aberrations in the optical system must be controlled at extremely low levels. Even minor vibrations or uneven movements caused by any mechanical structure can significantly affect image quality. Based on this stringent requirement, the system imposes a constraint of ≤50° on the pressure angle of the cam curve.

[0043] The lens cam curve was digitally acquired and analyzed using the aforementioned detection device, yielding detailed initial state data. Measurement results showed that before optimization, the pressure angle distribution range of the lens was 28–70°, with a maximum pressure angle of 70°, exceeding the system's stringent 50° requirement. The standard deviation of the pressure angle was 8.5°, indicating uneven pressure angle distribution. Second-derivative analysis identified a significant inflection point; the pressure angle changes drastically at these inflection points, affecting zoom smoothness.

[0044] The adaptive optimization strategy provided in this application is used to select the optimization method and obtain the pressure angle distribution characteristics of the lens to be optimized. The feature analysis results show that the pressure angle standard deviation σ_α=8.5° is less than the first threshold T1=10°, indicating that the pressure angle distribution has discreteness and needs to be optimized.

[0045] However, the maximum pressure angle α_max = 70° is less than the second threshold T2 = 80°, indicating that the lens does not have extremely high pressure angles. Based on the above feature analysis results, the decision algorithm adopts a Gaussian function smoothing optimization strategy, which is particularly suitable for handling situations where the pressure angle distribution is relatively discrete but has local fluctuations.

[0046] The key to Gaussian function optimization lies in setting the function parameters appropriately to achieve the best smoothing effect. The amplitude parameter A is set based on the dynamic range of the pressure angle, calculated as A = 0.8 × (70° - 28°) = 33.6. The coefficient 0.8 ensures a moderate optimization intensity, effectively reducing the pressure angle without excessively altering the original curve characteristics. The center parameter b is set to the abscissa position corresponding to the maximum pressure angle of 70°, ensuring that the optimization focuses on the area most in need of improvement. The width parameter c considers the entire abscissa range of the curve, calculated as c = 0.5 × 94 mm = 47 mm. This setting allows the Gaussian function's influence range to cover the main problem areas while maintaining sufficient locality.

[0047] The optimization process employs an iterative algorithm to gradually improve the pressure angle distribution. Each iteration recalculates the pressure angle distribution, evaluates the optimization effect, and determines whether to continue iterating based on a convergence criterion. After eight iterations, the algorithm reaches convergence, with the improvement margin for three consecutive iterations being less than the set threshold of 0.1°. During the iteration process, the maximum pressure angle gradually decreases, converging from an initial 70° to 50° after eight iterations. The entire iterative process converges smoothly without oscillations or divergence, indicating that the parameter settings are reasonable and the algorithm is stable and reliable.

[0048] After optimization, the lens was fabricated according to the optimized parameters. The pressure angle data was directly calculated from the optimized data, and the rest were measured results. The optimized pressure angle distribution of the lens was obtained using the aforementioned device. The pressure angle range was improved from the original 28°~70° to 32°~50°. Not only was the maximum pressure angle significantly reduced, but the minimum pressure angle was also improved, resulting in a more uniform overall distribution. The maximum pressure angle decreased from 70° to 50°, an improvement of 28.57%, successfully meeting the requirement of ≤50°. The standard deviation of the pressure angle decreased from 8.5° to 5.2°, an improvement of 38.8%, indicating a significant improvement in the uniformity of the pressure angle distribution.

[0049] Using the axial position coordinates of the cam curves of the front and rear lenses as the horizontal axis and the cam rotation angle as the vertical axis, the cam curve diagram is drawn as follows: Figure 3 As shown, by Figure 3 As can be seen, the cam curves of each part after optimization by the method provided in this application have all changed significantly compared to the original optimization. Figure 3 Explanation: The gray dashed lines represent the original cam curves for the zoom group, compensation group, and aberration stabilization group. After cam curve optimization, the red, green, and blue lines represent the optimized curves for the zoom group, compensation group, and aberration stabilization group, respectively. The slope of the curves shows that the zoom group curve changed from a straight line to a curve. The biggest advantage of this is reducing the slope of the compensation group and aberration stabilization group curves, resulting in a smaller overall pressure angle.

[0050] A graph is plotted with the pressure angles of the front and rear lenses optimized as the vertical axis and the cam rotation angle as the horizontal axis, as shown below. Figure 4 As shown in (a~b), it can be seen from the figure. Figure 4 illustrate: Figure 4 'a' represents the pressure angle of the curves corresponding to the zoom group, compensation group, and aberration stabilization group in the original cam curve. Red, green, and blue represent the pressure angles corresponding to the zoom group, compensation group, and aberration stabilization group, respectively, while gray represents the combined pressure angle, which is the sum of the pressure angles corresponding to the zoom group, compensation group, and aberration stabilization group. Figure 4 b represents the pressure angle of the curves corresponding to the zoom group, compensation group, and aberration stabilization group in the optimized cam curve. Red, green, and blue represent the pressure angles corresponding to the optimized zoom group, compensation group, and aberration stabilization group, respectively, while gray represents the optimized overall pressure angle, which is the sum of the pressure angles corresponding to the optimized zoom group, compensation group, and aberration stabilization group. From the gray curve in the figure, it can be seen that the original overall pressure angle curve has a minimum value of 26, a maximum value of 70, and a pressure angle amplitude of 44; the optimized overall pressure angle curve has a minimum value of 34, a maximum value of 52, and a pressure angle amplitude of 18. This indicates that after optimization, the maximum value of the overall pressure angle decreases from 70 to 52, a reduction of approximately 25%, and the amplitude decreases from 44 to 18, a reduction of approximately 59%. This means the uniformity of the overall pressure angle distribution improves by 59%, resulting in a 25% reduction in the maximum pressure angle and a 59% improvement in distribution uniformity in the optimized cam curve. Ultimately, this leads to a smoother and more effortless zooming of the infrared lens drive motor, greatly improving the optical axis consistency and stability of the infrared lens.

[0051] Of particular note is that the abrupt change in pressure angle at the original inflection point has been effectively smoothed, eliminating factors that could cause uneven zooming. The optimized cam curve underwent physical machining and assembly testing, and its effectiveness was verified in practical applications.

[0052] The smoothness of the zoom process is significantly improved, the peak drive torque is reduced by 15%, and the consistency of zoom speed is improved by 25%.

[0053] Test method: The optical axis consistency test of the infrared lens is adopted. The test method is a commonly used method in the industry: a small hole target is selected, the image is adjusted to the clearest state (visual inspection and judgment), the center pixel position of the image is calculated by the image processing algorithm (marked as the starting point), the lens zoom is controlled (from small field of view to large field of view), the software collects the center pixel position of the small hole target in real time, and calculates the horizontal and vertical pixel deviations from the starting point. When the infrared lens zooms to the large field of view, it is marked as the ending point. The horizontal and vertical pixel deviations between the ending point and the starting point are the horizontal and vertical optical axis offset pixels of the infrared lens. The optical axis consistency test results of the infrared lens show that, within the entire 25-225mm zoom range, the optimized lens exhibits a visual axis stability test, with the deviation within 3 pixels during zooming, meeting the requirements for high-precision applications. Temperature adaptability tests were conducted within the range of -40℃ to +60℃, demonstrating superior resistance to temperature variations. The lens's imaging performance remained stable within this temperature range, with pressure angle changes of less than 10%.

[0054] As can be seen from the above, after optimization using the method provided in this application, the lens with the optimized cam curve has improved performance in all aspects and can better meet the actual use requirements.

[0055] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the pressure angle of a cam curve in a continuously zoom infrared lens, characterized in that, Includes the following steps: Step S1: After obtaining the digital coordinate data of the cam curve of the part to be optimized, calculate the initial pressure angle α_i and construct the mathematical model of the cam curve; Step S2: Obtain the pressure angle distribution characteristics, including: maximum pressure angle α_man, minimum pressure angle α_min, average pressure angle α_mean, and standard deviation of pressure angle σ_α; obtain the high pressure angle region in the cam curve mathematical model, obtain the coordinates of the inflection points in the cam curve mathematical model and the pressure angle value at the inflection points, and calculate the pressure angle change rate α% between adjacent coordinate points of each inflection point. Step S3: Select an optimization strategy based on the pressure angle distribution characteristics and optimize the mathematical model of the cam curve to be optimized; Obtain the standard deviation σ_α of the cam curve to be optimized. When the standard deviation σ_α < threshold T1 and α_max < threshold T2, use Gaussian function to smooth and optimize the cam curve. T1 is 10° and T2 is 80°. When the standard deviation σ_α ≥ threshold T1 or the maximum pressure angle α_max ≥ threshold T2, optimization is performed by redistributing the piecewise function angle of the cam curve mathematical model. Obtain the number of inflection points in the cam curve to be optimized. When the number of inflection points is ≥3, a hybrid optimization strategy is adopted. Establish a decision matrix, automatically select an optimization strategy to optimize the cam curve, and output the optimized cam curve. Step S4: After global piecewise function angle redistribution of the cam curve to be optimized, local Gaussian function fine optimization is performed, followed by iterative optimization. The maximum number of iterations N_max is set, and iteration stops when the improvement is less than the threshold ε2 for 3 consecutive iterations. The maximum number of iterations N_max is 20~50. Step S5: Perform machining constraint checks, motion constraint checks, smoothness constraint checks, and pressure angle constraint checks according to the constraints. After the checks are completed, obtain the cam rotation angle and pressure angle corresponding to each coordinate point on the optimized cam curve. Obtain the optimization effect verification parameters based on the obtained cam rotation angle and pressure angle. Compare the optimization effect verification parameters with the target cam curve requirements to see if they meet the target cam curve requirements. If they do, output the cam rotation angle and pressure angle corresponding to each coordinate point on the optimized cam curve.

2. The method for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens according to claim 1, characterized in that, The optimized cam curve results are the cam rotation angle and pressure angle corresponding to each coordinate point on the optimized cam curve of each component. Based on the cam rotation angle and pressure angle corresponding to each coordinate point on the optimized cam curve of each component, the optimized maximum pressure angle α_max_new, the optimized pressure angle value standard deviation σ_α_new, and the optimized pressure angle at the inflection point α_inflection_new are obtained. The reduction in maximum pressure angle η1: η1=(α_max_old-α_max_new) / α_max_old×100%; where α_max_old is the original maximum pressure angle; α_max_new is the optimized maximum pressure angle; The rate of change of the standard deviation of the pressure angle η2: η2=(σ_α_old-σ_α_new) / σ_α_old×100%, where σ_α_old is the standard deviation of the pressure angle value before optimization; σ_α_new is the standard deviation of the pressure angle value after optimization; The rate of change of pressure angle at the inflection point η3: η3=(α_inflection_old-α_inflection_new) / α_inflection_old×100%; where α_inflection_old is the pressure angle at the inflection point before optimization; α_inflection_new is the pressure angle at the inflection point after optimization.

3. The method for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens according to claim 1, characterized in that, The device used to "obtain digital coordinate data of the cam curve of the part to be optimized" includes: a mounting platform, a height measuring instrument (2), a Y-axis manual translation stage (22), an X-axis manual translation stage (23), and a claw-equipped electric rotary table (21); the height measuring instrument (2) is suspended on the mounting platform and is positioned directly opposite the claw-equipped electric rotary table (21), the X-axis manual translation stage (23), and the Y-axis manual translation stage (22) stacked in sequence; The part to be tested is clamped on a claw-equipped electric rotary table (21); the height measuring instrument (2) is set to contact the cam curve detection of the part to be tested; During measurement, the electric rotary table with claw (21) is started, and the part to be measured is rotated while the coordinate data (x_i, z_i) of each coordinate on the cam curve of the part to be measured is measured.

4. The method for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens according to claim 3, characterized in that, The height measuring instrument (2) includes: a data interface, a host, a displacement sensor, and a probe; the host is equipped with a data interface; a probe is installed below the host, and a displacement sensor is installed on the extension end of the probe as a probe.

5. The method for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens according to claim 3, characterized in that, The installation platform includes: a base (11), a support arm (12), and an installation arm (13); An mounting arm (13) is provided on one side of the base (11); the mounting arm (13) is set vertically to the base (11); a support arm (12) is provided on the top of the mounting arm (13); the support arm (12) extends outward vertically to the mounting arm (13), and a height measuring instrument (2) is provided on the extended end.

6. The method for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens according to claim 1, characterized in that, Step S1 includes the following steps: Step S1.1: Filter the obtained coordinate data (x_i, z_i) to obtain the coordinate data; Step S1.2: Calculate the initial pressure angle α_i according to the formula, α_i = arctan((z_{i+1} - z_i) / (x_{i+1} -x_i)), where z_{i+1} is the z-axis coordinate value of the (i+1)th point and x_{i+1} is the x-axis coordinate value of the (i+1)th point; Step S1.3: Establish a mathematical model of the cam curve based on the initial pressure angle α_i and coordinate data.

7. The method for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens according to claim 1, characterized in that, Step S2 includes the following steps: Step S2.1: Obtain the high pressure angle region in the mathematical model of the cam curve. Specifically, iterate through the pressure angle values ​​of each coordinate in the mathematical model of the cam curve, obtain the pressure angle value α_i of the i-th point, and mark the i-th point as a high pressure angle point when α_i > α_mean + 2σ_α. Step S2.2: Obtain the coordinates of the inflection points and the pressure angle value at the inflection points in the mathematical model of the cam curve; Step S2.3: Calculate the rate of change of pressure angle α between adjacent coordinate points according to the following formula, and analyze the gradient of pressure angle change in the mathematical model of the cam curve: α%=(α_i —α_i -1) / α_i *100%, where α_i is the pressure angle α at point i; α_i -1 is the pressure angle α at point i-1.

8. The method for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens according to claim 1, characterized in that, The Gaussian function smoothing optimization in step S3 includes the following steps: Step S3.1: Construct the Gaussian function: G(x) = A·exp[-(xb)² / c²] Step S3.2: Adaptive parameter setting: Amplitude parameter A: A=k1·(α_max—α_min), where k1 is the adjustment coefficient, usually taken as 0.5~1.0; Central parameter b: b = x_{α_max}, where x_{α_max} is the x-coordinate of the point corresponding to the maximum pressure angle; Width parameter c: c=k2·|x_{α_max}—x_{α_min}|, where k2 is the adjustment coefficient, usually taken as 0.3~0.8, and x_{α_min} is the x-coordinate position of the coordinate point corresponding to the minimum pressure angle; Step S3.3: Perform lateral widening processing on each coordinate point on the cam curve to be optimized. Specifically, update the x-coordinate value of each coordinate point on the cam curve to be optimized to obtain the updated x-coordinate value x_new, x_new=x·G(x); where x is the x-axis coordinate value of each coordinate point on the cam curve to be optimized. After traversing and updating, the optimized cam curve coordinates and pressure angle distribution are obtained. Step S3.4 Recalculate the optimized cam curve coordinates and pressure angle distribution, and iteratively optimize the pressure angle until the convergence condition is met: |α_max^(k+1)—α_max^(k)|<ε1, where ε1 is the convergence threshold, usually set to 1 degree, and k is the number of iterations.

9. The method for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens according to claim 1, characterized in that, Step S3, piecewise function angle redistribution, includes the following steps: Step S3.5: Construct a piecewise function from the cam curve rotation angle data of the part to be optimized: The first function segment is: y(i)-y(i-1)=r·θ2 / (nm)+(m+1-i)·δ(i=2:m); The second function is: y(i) = r·θ1 + r·θ2 / (nm)·i (i = m:n); Set the constraint: θ1 + θ2 = θ_total (total rotation angle); Where θ1 is the rotation angle assigned to the first segment, θ2 is the rotation angle assigned to the second segment, r is the cam radius, n is the total number of data points, m is the index position of the segment point, and δ is the adjustment parameter used to control the intensity and fineness of the optimization. Based on the pressure angle distribution characteristics, segment point m is selected, and the angle allocation ratio θ1:θ2 is determined according to the length of the high and low pressure angle regions; the parameter δ is adjusted to control the smoothness of the transition region of the cam curve; a larger rotation angle θ2 is allocated to the high pressure angle region, and the rotation angle θ1 is compressed to the low pressure angle region. Step S3.6: Obtain the number of high-pressure angle regions of the cam curve of the part to be optimized. When the number of high-pressure angle regions is less than or equal to 1, use Gaussian function to smooth and optimize the cam curve. When the number of high-pressure angle regions is greater than 1, use piecewise function to optimize the cam curve piecewise. The piecewise strategy is as follows: first calculate the first derivative of the cam curve, find all points where the first derivative is 0 (assuming the total number of points is k), and divide the cam into k+1 segments, that is, optimize the cam curve of k+1 segments respectively.

10. The method for optimizing the pressure angle of the cam curve of a continuous zoom infrared lens according to claim 1, characterized in that, Step S3, the "hybrid optimization strategy", includes the following steps: Step S3.7: Identify all high-pressure angle regions, coarsely adjust the overall curve to reduce the global maximum pressure angle to 80-45% of the original pressure angle, and establish a multi-segment function model to handle multiple problem regions; Step S3.8: Using an adaptive window size, smooth the remaining local high-pressure angle regions with a Gaussian function, ensuring the overall continuity and differentiability of the curve.

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