Optimization design method of zoom cam curve

Abstract

The invention relates to an optimal design method of a zoom cam curve. The method comprises the following steps: acquiring a motion group position corresponding to a discrete focal length value of the optical system; performing interpolation fitting on the position data, and calculating to obtain discrete displacement data according to the interpolated position data; the maximum pressure angle is set, the motion group moves in sequence according to the interpolated position data, and the cam rotation angle corresponding to the discrete displacement is obtained; the sum of the driving torque of the cam to the motion group in the rotating process is kept constant; calculating the sum of the driving torques of the motion group in the motion process, selecting the minimum value of the sum of the driving torques, calculating the inverse function of the driving torques under the minimum value, replacing the interpolated position data with the calculation result of the inverse function, and solving the cam rotation angle and the cam total rotation angle after replacement; and judging whether the total cam rotation angle meets the requirement. The method facilitates stable rotation of the motor, prevents clamping stagnation, and is of great significance to reduction of the jerk value of the optical axis.

Description

Technical Field

[0001] The invention belongs to the technical field of zoom optical instruments, and in particular relates to an optimization design method for a zoom cam curve. Background Art

[0002] The cam structure in a zoom lens is the core mechanical component that drives continuous focal length adjustment. Its design directly determines the lens's response speed, stability, and lifespan. Optimizing the cam curve is a key design challenge in this system. An ideal curve must not only precisely match the trajectory of the optical components but also ensure smooth driving torque through mechanical properties, ensuring a smooth, lag-free zooming process.

[0003] In traditional design processes, initial cam curves generated by optical design software (such as Zemax or CodeV) are typically designed to eliminate aberrations and improve image quality. However, these curves have potential mechanical flaws: for example, the local pressure angle can significantly increase due to sudden changes in the curve's curvature. Excessively large pressure angles can lead to a surge in contact stress between the cam and the follower, and in severe cases, can even cause surface wear or structural deformation of the cam.

[0004] To overcome this bottleneck, academia and industry have proposed a variety of optimization strategies. For example, the article "Optimization of the Pressure Rise Angle of the Cam Curve of a Continuous Zoom Lens" in Volume 28, Issue 1, 2021, of the journal Electro-Optics and Control analyzes the effect of the cam curve's pressure angle on the system's transmission torque. Using Gaussian function optimization, the article proposes an optimization method for the non-uniform widening of the cam curve perpendicular to the optical axis, while ensuring the smoothness of the curve. However, the optimization technique described in this paper does not directly use the pressure angle as the dependent variable for optimization and requires multiple iterations for verification, making it less practical.

[0005] Patent CN117192771A discloses a method for optimizing the cam curve of a zoom lens. This method primarily uses pressure angle design requirements to guide the entire optimization process, processes raw data point by point, and then uses curve fitting to convert the optimized discrete data into a smooth cam curve. This method relies heavily on the degree of optimization of the initial structure and does not consider the mechanical properties of the cam.

[0006] In engineering practice, increasing the cam's rotation angle or diameter is often used to alleviate the pressure angle problem. However, both methods face significant trade-offs: increasing the rotation angle weakens the cam's torsional stiffness; while increasing the diameter runs counter to the trend of lightweight and miniaturization of lenses. Summary of the Invention

[0007] The object of the present invention is to provide a method for optimizing the pressure angle of a cam curve of a continuous zoom lens, which takes the maximum pressure angle as a constraint condition and realizes rapid optimization of the cam curve.

[0008] The technical solution to achieve the purpose of the present invention is: a method for optimizing the design of a zoom cam curve with a pressure angle as a constraint condition, wherein the zoom optical system is a dual motion group consisting of a magnification group and a compensation group, and the method comprises the following steps:

[0009] Step (1): obtaining the motion group position corresponding to the discrete focal length value of the zoom optical system, wherein the motion group position is the zoom group position data and the compensation group position data;

[0010] Step (2): performing interpolation fitting on the zoom group position data and the compensation group position data of step (1) to obtain interpolated position data, and calculating discrete displacement data based on the interpolated position data;

[0011] Step (3): Assuming the maximum pressure angle is α, the zoom group and the compensation group move in sequence according to the interpolated position data, and the cam rotation angle θ corresponding to the discrete displacement is obtained. A polynomial fitting is performed on the interpolated position data and the cam rotation angle corresponding to the discrete displacement;

[0012] Step (4): Assume that the sum of the driving torques of the cams of the zoom group and the compensation group on the motion group remains constant during the rotation process, which is used as a constraint condition for cam curve optimization;

[0013] Step (5): Calculate the sum of the driving torques of the zoom group and the compensation group during the movement of step (3), and select the minimum value T of the sum of the driving torques min , calculate the inverse function of the driving torque at the minimum value, use the calculation result of the inverse function to replace the interpolated position data in step (3), and solve to obtain the replaced cam rotation angle and the total cam rotation angle;

[0014] Step (6): Determine whether the total cam rotation angle obtained in step (5) meets the requirements. If not, increase the pressure angle α and repeat steps (3)-(5) until the requirements are met.

[0015] Furthermore, the position data of the zoom group in step (1) are (1, x1), (2, x2)...(n, x n ), the compensation group position data is (1, y1), (2, y2)... (n, y n ), where n is the serial number corresponding to different focal length values.

[0016] Furthermore, in step (2), interpolation fitting is performed through Origin, and the interpolated zoom group position data are (1, x′1), (2, x′2)...(n, x′ n ), the interpolated compensation group position data is (1, y′1), (2, y′2)...(n, y′ n), where n is the serial number corresponding to different focal length values; the calculated discrete displacement data are: (1, dx′1), (2, dx′2)...(n-1, dx′ n-1 ) and (1, dy′1), (2, dy′2)...(n, dy′ n-1 ), where dx′1=x′2-x′1, dx′2=x′3-x′2...dx′ n-1 =x n -x′ n-1 , dy′1=y′2-y′1, dy′2=y′3-y′2...dy′ n-1 =y′ n -y′ n-1 .

[0017] Furthermore, the calculation formula for the cam rotation angle corresponding to the discrete displacement in step (3) is as follows:

[0018]

[0019] Where r is the inner radius of the cam.

[0020] Furthermore, the driving torque calculation formula in step (4) is as follows:

[0021]

[0022] Where m is the mass of the motion group, s(θ) is the cam displacement curve, and “~” is proportional to.

[0023] Furthermore, the sum of the pressure angles of the dual motion groups is assumed to be constant and replaces the constraint condition in step (4).

[0024] The above method is used to optimize the pressure angle of the cam curve of a zoom lens with three motion groups or more.

[0025] Compared with the prior art, the present invention has the following significant advantages:

[0026] The present invention provides a method for optimizing the cam curve of a continuous zoom lens. The motion groups all perform nonlinear motion, which solves the problem that the pressure angle is difficult to control due to the linear motion of the zoom group in the past. The pressure angle of the cam curve provided by the present invention changes continuously, ensuring the smooth motion of the curve. The driving torque of the cam motion process is also kept constant, which is beneficial to the smooth rotation of the motor, prevents jamming, and is of great significance for reducing the amount of optical axis runout. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The original cam curve and the corresponding pressure angle diagram; (a) is the zoom group, (b) is the compensation group, and (c) is the pressure angle.

[0028] Figure 2 The cam curve and corresponding pressure angle diagram of the present invention with pressure angle as the constraint condition; (a) is the zoom group, (b) is the compensation group, and (c) is the pressure angle. DETAILED DESCRIPTION

[0029] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0030] A method for optimizing a zoom cam curve comprises the following steps:

[0031] (1) Taking the zoom optical system with dual motion groups (zoom group and compensation group) as an example, through initial structure optimization and using the macro language ZPL programming of Zemax software, the positions of the motion groups (1, x1), (2, x2) ... (n, x) corresponding to the discrete focal length values of the zoom optical system are obtained according to the decreasing focal length of the zoom lens at the long focal end (or increasing at the short focal end). n ) and (1, y1), (2, y2)...(n, y n ), where n is the serial number corresponding to different focal length values, x n is the position data of the zoom group, y n To compensate for the position data of the group, outliers are deleted.

[0032] (2) The above two sets of data are scatter plotted using Origin software and interpolated and fitted to obtain two sets of interpolated position data (1, x′1), (2, x′2)...(n, x′ n ) and (1, y′1), (2, y′2)...(n, y′ n ), the amount of data can be appropriately increased or decreased, and the discrete displacement data (1, dx′1), (2, dx′2)...(n-1, dx′ n-1 ) and (1, dy′1), (2, dy′2)...(n, dy′ n-1 ), where dx′1=x′2-x′1, dx′2=x′3-x′2...dx′ n-1 =x n -x′ n-1 , dy′1=y′2-y′1, dy′2=y′3-y′2...dy′ n-1 =y′ n -y′ n-1 .

[0033] (3) Assuming the maximum pressure angle is 30°, let the two motion groups change their positions in sequence according to the interpolated position data, and the corresponding cam rotation angle is obtained.

[0034]

[0035] Where r is the inner radius of the cam, and the rotation angle of the cam corresponding to all discrete displacements can be obtained, and then the rotation arc length dn of the cam can be obtained. The step lengths are added together to obtain D1=0, D2=D1+d1, D3=D2+d2, ..., D n =D n-1 +d n-1 , take the position data of the zoom group and compensation group as the horizontal coordinate and D as the middle coordinate to draw the curve Figure 1 The original cam curve shown in the figure meets the maximum pressure angle requirement but does not meet the requirements of continuous pressure angle change and constant driving torque.

[0036] (4) ZPL programming obtains the data of the sum of the driving torque of the two motion groups during (3) the movement process, thereby obtaining the minimum value T of the sum of the driving torque values during the entire zoom process min , calculate the inverse function of the driving torque at the minimum value, replace the inverse function with the condition in (3), and solve to obtain the latest rotation step and the total rotation angle of the cam. The new curve is as follows: Figure 2 shown.

[0037] (5) Determine whether the total cam rotation angle meets the requirements, for example, less than 160°. If not, increase the maximum pressure angle α and recalculate until the requirements are met.

[0038] In addition, the following requirements are required during implementation:

[0039] The above optimization method can not only make the cam curve pressure angle change according to the law of constant driving torque, but also make the sum of the pressure angles constant.

[0040] The above optimization method is not only applicable to double-action groups, but also to the pressure angle optimization of the cam curve of triple-action zoom lenses and above.

Claims

1. A method for optimizing the zoom cam curve with pressure angle as a constraint, characterized in that: The zoom optical system is a dual motion group consisting of a zoom group and a compensation group. The method includes the following steps: Step (1): obtaining the motion group position corresponding to the discrete focal length value of the zoom optical system, wherein the motion group position is the zoom group position data and the compensation group position data; Step (2): performing interpolation fitting on the zoom group position data and the compensation group position data of step (1) to obtain interpolated position data, and calculating discrete displacement data based on the interpolated position data; Step (3): Assuming the maximum pressure angle is α, the zoom group and the compensation group move in sequence according to the interpolated position data, and the cam rotation angle θ corresponding to the discrete displacement is obtained. A polynomial fitting is performed on the interpolated position data and the cam rotation angle corresponding to the discrete displacement; Step (4): Assume that the sum of the driving torques of the cams of the zoom group and the compensation group on the motion group remains constant during the rotation process, which is used as a constraint condition for cam curve optimization; Step (5): Calculate the sum of the driving torques of the zoom group and the compensation group during the movement of step (3), and select the minimum value T of the sum of the driving torques min , calculate the inverse function of the driving torque at the minimum value, use the calculation result of the inverse function to replace the interpolated position data in step (3), and solve to obtain the replaced cam rotation angle and the total cam rotation angle; Step (6): Determine whether the total cam rotation angle obtained in step (5) meets the requirements. If not, increase the pressure angle α and repeat steps (3)-(5) until the requirements are met.

2. The method according to claim 1, characterized in that The position data of the zoom group in step (1) are (1, x1), (2, x2)...(n, x n ), the compensation group position data is (1, y1), (2, y2)... (n, y n ), where n is the serial number corresponding to different focal length values.

3. The method according to claim 2, characterized in that In step (2), interpolation fitting is performed through Origin, and the interpolated zoom group position data is (1, x′1), (2, x′2)...(n, x′ n ), the interpolated compensation group position data is (1, y′1), (2, y′2)...(n, y′ n ), where n is the serial number corresponding to different focal length values; the calculated discrete displacement data are: (1, dx′1), (2, dx′2)...(n-1, dx′ n-1 ) and (1, dy′1), (2, dy′2)...(n, dy′ n-1 ), where dx′1=x′2-x′1, dx′2=x′3-x′2...dx′ n-1 =x n -x′ n-1 , dy′1=y′2-y′1, dy′2=y′3-y′2...dy′ n-1 =y′ n -y′ n-1 .

4. The method according to claim 3, characterized in that The calculation formula for the cam rotation angle corresponding to the discrete displacement in step (3) is as follows: ... Where r is the inner radius of the cam.

5. The method according to claim 4, characterized in that The driving torque calculation formula in step (4) is as follows: Where m is the mass of the motion group, s(θ) is the cam displacement curve, and "~" is proportional to.

6. The method according to claim 5, characterized in that Assume that the sum of the pressure angles of the dual motion group is constant and replace the constraint condition in step (4).

7. The method according to any one of claims 1 to 6, characterized in that Used for optimizing the pressure angle of the cam curve of zoom lenses with three motion groups or more.

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