Method for solving the kinematical fidelity solution domain of a negative radius roller cam mechanism

Abstract

The application discloses a solving method of a motion fidelity solution domain of a negative radius roller cam mechanism, and comprises the following steps: determining motion information according to the design requirement of motion output in an actual engineering; determining a region in which a cam shaft center is allowed to be selected according to the space size constraint of the mechanism in the actual engineering; setting a step distance according to a cam theoretical profile equation, and obtaining the cam profile of each cam shaft center position in the region in which the cam shaft center is allowed to be selected by using a discrete-traversal method; setting a step distance of a rotation angle according to the curvature radius of the theoretical profile, and calculating the curvature radius of each rotation angle position in a 360-degree rotation angle according to the cam theoretical profile of each cam shaft center position by using the discrete-traversal method; obtaining the shaft center position and the curvature radius family of all cam profiles which satisfy the condition that the curvature radius of the theoretical profile is greater than 0; obtaining the maximum curvature radius of each cam profile in the curvature radius family by cyclic comparison; and obtaining the motion fidelity solution domain of the negative radius roller cam mechanism based on a new criterion of motion fidelity.

Description

Technical Field

[0001] This invention belongs to the field of motion fidelity technology, and particularly relates to a method for solving the motion fidelity solution domain of a negative radius roller cam mechanism. Background Technology

[0002] Motion fidelity is the first constraint to be considered in the design of cam mechanisms. Only by satisfying motion fidelity can subsequent design and verification of transmission performance, contact strength, etc. be carried out. Compared with ordinary positive radius roller cam mechanisms, negative radius roller cam mechanisms can withstand large loads and have simple structure and compact size, showing broad engineering application prospects. However, the problem of "motion distortion" is very easy to occur and very prominent, which has become an important bottleneck and key to its design. The shortcomings and problems of existing motion fidelity criteria and judgment methods are as follows: (1) Based on the intuitiveness of recognizing "motion distortion" from the appearance of the "swallowtail cross" of the working profile, the existing "motion distortion" judgment method is based on the working profile of the cam. (2) Due to the insufficient understanding of the essence of "motion distortion", the judgment method based on the working profile mentioned in (1) can only judge whether the cam has motion distortion after the design is completed. If it is distorted, it needs to be redesigned. Therefore, it cannot be well used to guide analysis and design. (3) In the design process of negative radius roller cam mechanism, the theoretical profile of the cam is designed first, then the roller radius is selected, and then the working profile of the cam is determined. There is currently no relevant design method for selecting parameters at each design stage to avoid "motion distortion". Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a method for solving the motion fidelity domain of a negative radius roller cam mechanism. The method solves for the motion fidelity domains of the theoretical profile parameters and the roller radius parameters from two aspects: the theoretical profile and the roller radius. This yields the motion fidelity domain, which can then be used for the design and analysis of cam motion fidelity.

[0004] To achieve the above objectives, the present invention provides a method for solving the motion fidelity solution domain of a negative radius roller cam mechanism, including: determining motion information based on the design requirements of motion output in actual engineering;

[0005] Based on the spatial dimensional constraints of the mechanism in the actual engineering, determine the area where the camshaft center can be selected;

[0006] Based on the cam theoretical profile equation, the step distance is set, and the discrete-traversal method is used to obtain the cam profile of each cam axis position within the allowed selectable area;

[0007] Based on the theoretical profile radius of curvature, the step size of the rotation angle is set. Using the discrete-traversal method, the radius of curvature at each rotation angle within 360° is calculated based on the cam profile at each cam axis center position.

[0008] Obtain the pivot position and family of curvature radii for all cam profiles that satisfy the theoretical profile curvature radius greater than 0;

[0009] The maximum radius of curvature of each cam profile in the family of radii of curvature is obtained by iterative comparison.

[0010] Based on the new motion fidelity criterion, the motion fidelity solution domain of the negative radius roller cam mechanism is obtained.

[0011] According to the method for solving the motion fidelity solution domain of a negative radius roller cam mechanism provided by the present invention, the motion information includes push rod stroke, forward and return displacement law, forward and return motion angle, and near and far rest angle.

[0012] According to the method for solving the motion-fidelity solution domain of a negative radius roller cam mechanism provided by the present invention, the theoretical profile equation of the cam is calculated as follows:

[0013]

[0014] Where, x p y is the abscissa of the theoretical profile of the cam; p denoted as the ordinate of the theoretical profile of the cam; h is the follower stroke; s is the center displacement of the roller. y is the rotation angle; x is the horizontal coordinate of the camshaft center position; y is the vertical coordinate of the camshaft center position.

[0015] According to the method for solving the motion fidelity solution domain of a negative radius roller cam mechanism provided by the present invention, the theoretical profile radius of curvature is calculated as follows:

[0016]

[0017] Where ρ is the theoretical profile radius of curvature; x p y is the abscissa of the theoretical profile of the cam; p The vertical coordinate of the theoretical profile of the cam; For the turning angle; x p ′,y p ′, x p "and y p "Represents x respectively" p and y p Variable pairs The first and second derivatives.

[0018] According to the method for solving the motion fidelity solution domain of a negative radius roller cam mechanism provided by the present invention, the method for obtaining the new motion fidelity criterion is as follows:

[0019] ρ+ρ w =R

[0020] 0<ρ w <R

[0021] 0<ρ <R

[0022] Where ρ is the theoretical profile radius of curvature; ρ w R is the radius of curvature of the working profile; R is the roller radius.

[0023] According to the method for solving the motion fidelity solution domain of a negative radius roller cam mechanism provided by the present invention, the method for obtaining the motion fidelity solution domain of a negative radius roller cam mechanism is as follows:

[0024] ρ min >0

[0025] ρ max <R

[0026] Where, ρ min The minimum value of the theoretical profile radius of curvature ρ; ρ max R is the maximum value of the theoretical profile curvature radius ρ; R is the roller radius.

[0027] Technical advantages of this invention: This invention discloses a method for solving the motion fidelity domain of a negative radius roller cam mechanism. Based on the discovery of a quantitative relationship between the theoretical profile and the working profile, a new motion fidelity criterion based on the curvature radius of the theoretical profile is proposed. According to this new criterion, and combined with the actual process of engineering design (first designing the theoretical profile, then selecting the roller radius to obtain the working profile), this invention solves for the motion fidelity domains of the theoretical profile parameters and the roller radius parameters from both the theoretical profile and roller radius perspectives, obtaining the motion fidelity domain for use in the design and analysis of cam motion fidelity. Attached Figure Description

[0028] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0029] Figure 1 This is a schematic diagram of a negative radius roller direct-acting push rod disc cam mechanism according to an embodiment of the present invention, wherein (a) is a quasi-structural diagram and (b) is a simplified kinematic diagram;

[0030] Figure 2 This is a schematic diagram of the working profile and theoretical profile of a common positive radius roller cam according to an embodiment of the present invention;

[0031] Figure 3 This is a schematic diagram illustrating the inherent regularity relationship between the theoretical profile and the working profile in the embodiments of the present invention, wherein (a) is the envelope showing the cam profile, and (b) is the cam profile solved by the "reverse method".

[0032] Figure 4This is a flowchart illustrating the method for solving the motion fidelity solution domain of a negative radius roller cam mechanism according to an embodiment of the present invention.

[0033] Figure 5 This is a schematic diagram of the O(x,y) / R three-dimensional spatial model of an embodiment of the present invention;

[0034] Figure 6 This is a schematic diagram of the motion-fidelity solution domain Ω* of O(x,y) / R according to an embodiment of the present invention;

[0035] Figure 7 This is a schematic diagram of the motion-fidelity solution domain for an embodiment of the present invention with x = 15mm and R ≤ 350mm. Detailed Implementation

[0036] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0037] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0038] Based on the discovered quantitative relationship between the theoretical profile and the working profile, this invention proposes a new motion fidelity criterion based on the radius of curvature of the theoretical profile of the cam.

[0039] Based on the actual situation in the engineering design of cam mechanisms, this invention constructs a mechanism with the push rod at its top dead center C. e With the origin as the coordinate system and the camshaft center position O(x,y) as the design parameter, C e xy coordinate system.

[0040] This invention relies on the constructed C e Using the xy coordinate system, the equations for the theoretical and working profiles of the cam were derived.

[0041] This invention employs a discrete-ergodic method to obtain the range of values ​​for the cam shaft center O(x,y) and roller radius R that satisfy the motion fidelity condition, thus constructing a motion-fidelity (x,y,R) solution domain. This solution domain elucidates the range of values ​​for O(x,y) and R that satisfy the motion fidelity condition, as well as the method for determining the shaft center position and roller radius during cam profile design.

[0042] The method and solution domain used in this invention have practical engineering value for the analysis and design of cam profiles and the design of minimum cam profile dimensions in engineering design.

[0043] Object mechanism and C e xy coordinate system

[0044] like Figure 1 The diagram shown is a structural diagram and a simplified kinematic diagram of a negative radius roller direct-acting follower disc cam mechanism, using cylindrical roller bearings for the rollers. It consists of a disc cam 1, a direct-acting follower 2, a negative radius roller 3, and a frame 0. The driving cam 1 (input component) rotates at a constant speed, driving the direct-acting follower 2 (output component) along guide path C via the negative radius roller 3. b C e The direction can be moved back and forth and paused at near and far distances to achieve the expected output motion.

[0045] like Figure 1 As shown in (a), O—camshaft center, C b C e —The forward journey is always instantaneously centered on the roller, K b K e —The instantaneous contact point between the roller and cam during the forward stroke. C—The center of any instantaneous roller, K—The contact point between any instantaneous roller and cam. OK b =r0,C b K b =C e K e =R, r0—cam base circle radius, R—roller radius.

[0046] The preset motion information of the mechanism is as follows: push rod 2 stroke h, forward and return motion angle Φ g and Φ r Forward and return displacement patterns and Near and far rest angles Φ n and Φ f Cam rotation angle The cam rotates in the direction ω1.

[0047] In practical engineering design, the motion information of a direct-acting push rod is usually partially or completely defined by given constraints, such as the constraint stroke h, the starting and ending points C of the rollers fixed to the push rod. b C e Based on this, the known endpoint C of the push rod's forward stroke is selected. e With the origin of the coordinate system as the x-axis, the x-axis points horizontally to the right, and the y-axis points vertically upwards (along C). b C e ), establish C e Using an xy coordinate system, the unknown position of the camshaft center can be denoted as O(x,y).

[0048] The position of the camshaft center O must also satisfy the following motion connectivity constraint: it must be located at point C. e Point of reference C b C e The plane above the vertical line, i.e., C eQuadrants I and II of the xy coordinate system, such as Figure 1 As shown in (b).

[0049] Cam theoretical profile, working profile and their conjugate relationship

[0050] like Figure 2 As shown, in a typical positive radius roller cam mechanism, the cam working profile η' is an equidistant curve (also called a parallel curve) of the theoretical profile η, and its theoretical profile radius of curvature ρ and working profile radius of curvature ρ w The relationship between the roller radius r and the roller radius r is as follows:

[0051] ρ-ρ w =r(1)

[0052] Any pair of conjugate points on this curve shares a common center of curvature, a common normal, and the same direction of the normal vector; the two conjugate points are located on the same side of the center of curvature. This invention refers to this curve as a "co-directional equidistant curve".

[0053] like Figure 3 As shown in (a), unlike ordinary positive radius roller cams, in negative radius roller cams, the cam profiles Γ and Γ w Any pair of conjugate points (such as C) b and K b (C1 and K1, C2 and K2), common normal (e.g., n) b -n b The cam profiles Γ and Γ2 are conjugate points (n1-n1, n2-n2) sharing a common curvature center (e.g., O, O1, O2), but with opposite normal vector directions, and the two conjugate points are located on opposite sides of the curvature center. This invention refers to these as "opposite equidistant curves". Based on the above, the cam profiles Γ and Γ2 can be obtained. w The sum of the radii of curvature equals the radius of the roller, that is...

[0054] ρ+ρ w =R(2)

[0055] Equation (2) reveals the quantitative relationship between the theoretical profile and the working profile of the negative radius roller cam.

[0056] Therefore, the theoretical profile Γ is the reverse trajectory of the roller center C around the cam shaft center O, and the working profile Γ is... w It is the envelope of the family of roller circles centered at each point on Γ.

[0057] like Figure 3 As shown in (b), the cam rotates clockwise. Roller center from C b Point movement To any instantaneous position C. According to the principle of the reversal method, the roller center rotates around the cam shaft center O. Reverse from point C to point C'.

[0058] Based on the predicted motion information of the mechanism and coordinate system C e Using the inversion method, the theoretical profile equation and radius of curvature formula of the cam are derived:

[0059]

[0060] Based on the aforementioned understanding of "opposite equidistant curves," and using the principle of differential geometric envelope, similar to that of a positive radius roller cam, the equation for the cam's working profile is derived:

[0061]

[0062] In equations (3) to (5), x p ′,y p ′, x p "and y p "Represents x respectively" p and y p Variable pairs The first and second derivatives.

[0063] According to equations (2) to (5), under the condition that the predicted motion information is certain, the following conclusions can be drawn:

[0064] 1) The theoretical profile Γ of the cam and its radius of curvature ρ depend on the position of the cam axis O(x,y).

[0065] 2) Cam working profile Γ w and its radius of curvature ρ w It depends on the camshaft center position O(x,y) and the roller radius R.

[0066] New Criteria for Sports Fidelity

[0067] "Motion distortion" refers to a mechanism's inability or failure to achieve the expected motion output. Based on current understanding, this manifests as a "dovetail crossing" phenomenon in the cam's working profile. Therefore, the existing motion fidelity criterion is:

[0068] 0<ρ w <R(6)

[0069] The working profile of the cam is used as the target.

[0070] In the design, the theoretical profile of the cam is first determined. After selecting the roller radius R, the working profile of the cam can be obtained. From equations (2) and (5), it can be seen that ρ w =ρ w(x,y,R) contains two types of parameters: cam shaft center O(x,y) and roller radius R. Obviously, Equation (6) expresses the criterion through two types of parameters. Based on Equation (6), it can only judge whether distortion will occur from the combined result of the two. It cannot directly and accurately reflect whether the cause of distortion is the cam shaft center position or the roller radius. Therefore, it cannot provide good guidance for cam design, cam distortion cause analysis and improvement.

[0071] Combining equations (2) and (6), we obtain a new criterion for motion fidelity:

[0072] 0<ρ <R(7)

[0073] Equation (7) can be further written as

[0074] ρ min >0(8a)

[0075] ρ max <R(8b)

[0076] In the formula, ρ min ρ max —Minimum and maximum values ​​of the theoretical profile radius of curvature ρ.

[0077] Equation (8a) reveals that the value of the theoretical profile curvature radius must be positive (the cam is not concave), and Equation (8b) reveals that the value of the roller radius must be greater than the maximum value of the theoretical profile curvature radius.

[0078] Thus, the present invention employs a method of sequentially solving the motion-fidelity solution domain from the theoretical profile (i.e., the position of the camshaft center) and the roller radius R.

[0079] The solution process for the motion-fidelity solution domain is as follows: Figure 4 As shown, based on the theoretical profile and its radius of curvature, the solution formulas (3) and (4), and the motion fidelity criteria (8a) and (8b), the solution method and steps for the motion fidelity solution domain are as follows:

[0080] 1. Based on the design requirements of motion output in actual engineering, determine the motion information: push rod stroke h, forward and return displacement patterns. and Angle of motion Φ for both outward and return journeys g and Φ r Near and far rest angle Φ n and Φ f ;

[0081] 2. Based on the spatial dimensional constraints of the mechanism in actual engineering, determine the allowable selection range of the camshaft center O(x,y), that is, determine the lower limit and upper limit of the values ​​of x and y [(x...y ... min ,x max ),(y min ,y max)];

[0082] 3. According to equation (3), set the step size x. step y step The discrete-traversal method is used to obtain the cam profiles of each cam shaft center position O(x,y) in the above region;

[0083] 4. Set the corner according to equation (4). step size Using a discrete-time traversal method, the 360° rotation angle is calculated for the cam profile at each camshaft center position. The radius of curvature at each corner position within the interior;

[0084] 5. Obtain the pivot position O(x,y) of all cam profiles that satisfy the curvature radius ρ>0, and their family of curvature radii {ρ};

[0085] 6. By iterative comparison, obtain the maximum radius of curvature ρ of each cam profile in the above family of radii of curvature {ρ}. max ;

[0086] 7. Output the axis position and maximum radius of curvature (x, y, ρ) of each cam profile that satisfies the condition of radius of curvature ρ > 0. max ).

[0087] According to equations (8a) and (8b), the axis position O(x,y) of each cam profile with a curvature radius ρ > 0 is the selectable region for the cam axis position that satisfies motion fidelity, and the corresponding ρ max This is the lower limit of the minimum roller radius value for the camshaft center position.

[0088] like Figure 5 As shown, in a two-dimensional coordinate system C e Origin C of xy e With the origin as the coordinate point and the roller radius R as the vertical coordinate axis, construct C... e The xyR three-dimensional coordinate system. All (x, y, ρ) coordinates generated using the method described above. max A point can construct a surface S ρmax Then S ρmax The space above is the solution domain Ω* of O(x,y) and R that satisfies motion fidelity.

[0089] like Figure 6 As shown, the solution domain Ω*—the green part—is presented in a 3D visualization with motion fidelity. Within the horizontal coordinate plane, the gray area represents the region where the camshaft center position is measured, and the black area represents the region where the camshaft center position is not measured.

[0090] When designing a cam mechanism, if actual engineering requirements constrain the selection range of the cam shaft center, the feasibility of achieving the design under this constraint can be determined in advance. Furthermore, based on the motion-fidelity solution domain Ω*, the solution space corresponding to the roller radius R and the minimum roller radius R are obtained. min If the range of roller radius R is constrained, the selectable region of the camshaft center can be obtained from Ω*, providing a basis for subsequent design to meet constraints such as pressure angle and contact fatigue strength, as well as structural optimization.

[0091] Design Example: The motion information of the cam mechanism required by the actual engineering requirements is shown in Table 1. Due to the constraint of the relative position of the direct-acting follower and the camshaft, x is limited to 15mm. Due to the constraint of the relative position of the direct-acting follower and the frame, and the size of the mechanism space, the roller radius is set to R≤350mm. Design a range of basic cam dimensions that satisfy the motion fidelity requirements.

[0092] Table 1

[0093]

[0094] The motion-fidelity solution domain Ω* is generated using the above method. Taking a plane with x = 15 mm as the intercept for the solution domain Ω*, we can obtain... Figure 7 The boundary curve abc in the yR coordinate system is shown, where b(150.60, 310.85). The planar region above the boundary curve is the solution surface D satisfying x = 15 mm. x Take R = 350mm and cut D. x We obtain the line segment de, where d(112.01,350) and e(228.45,350). The region enclosed by the dbe curve and the line segment de is the range D of the basic dimensions of the cam that satisfies x=15mm, R≤350mm, and meets the motion fidelity condition. xR The corresponding y values ​​range from y∈(112.01,228.45), and the R values ​​range from R∈(310.85,350). The minimum structural size solution satisfying the motion fidelity condition is point b(150.60,310.85).

[0095] It is worth noting that when (y,R) is located on the dbe curve, the minimum radius of curvature of the cam working profile is zero (at this time, R = ρ). max When the cam profile is in a critical distortion / fidelity state, it develops sharp points and is prone to wear. Typically, the actual value of R is increased appropriately.

[0096] Based on the discovery of a quantitative relationship between the theoretical profile and the working profile, this invention proposes a new criterion for motion fidelity based on the radius of curvature of the theoretical profile. According to this new criterion, and combined with the actual process of engineering design (first designing the theoretical profile, then selecting the roller radius to obtain the working profile), this invention solves for the motion fidelity domains of the theoretical profile parameters and the roller radius parameters from both aspects, obtaining the motion fidelity solution domain for the design and analysis of cam motion fidelity. This invention proposes a new equidistant curve (“opposite equidistant curve”), and derives the new motion fidelity criterion based on the radius of curvature of the theoretical profile through derivation. Based on the above new criterion, a discrete-ergodic approach is used to solve for the solution domain satisfying the motion fidelity condition from the ranges of the cam shaft center position and the roller radius, respectively.

[0097] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for solving the motion-fidelity solution domain of a negative radius roller cam mechanism, characterized in that, include: Determine the motion information based on the design requirements of motion output in actual engineering; Based on the spatial dimensional constraints of the mechanism in the actual engineering, determine the area where the camshaft center can be selected; Based on the theoretical profile equation of the cam, the step distance is set, and the theoretical profile of the cam axis position of each cam axis position in the allowed selectable area is obtained by using the discrete-traversal method. Based on the theoretical profile radius of curvature, the step size of the rotation angle is set. Using the discrete-traversal method, the radius of curvature at each rotation angle within 360° is calculated based on the theoretical profile of the cam at each cam axis position. Obtain the pivot position and family of curvature radii for all cam profiles that satisfy the theoretical profile curvature radius greater than 0; The maximum radius of curvature of each cam profile in the family of radii of curvature is obtained by iterative comparison. Based on the new motion fidelity criterion, the motion fidelity solution domain of the negative radius roller cam mechanism is obtained; The method for obtaining the new motion fidelity criterion is as follows: p+p w =R 0<ρ w <R 0<ρ <R Where ρ is the theoretical profile radius of curvature; ρ w R is the radius of curvature of the working profile; R is the roller radius. The method for obtaining the motion-fidelity solution domain of a negative radius roller cam mechanism is as follows: r min >0 r max <R Where, ρ min The minimum value of the theoretical profile radius of curvature ρ; ρ max R is the maximum value of the theoretical profile curvature radius ρ; R is the roller radius.

2. The method for solving the motion-fidelity solution domain of a negative radius roller cam mechanism as described in claim 1, characterized in that, The motion information includes push rod stroke, forward and return displacement patterns, forward and return motion angles, and near and far rest angles.

3. The method for solving the motion-fidelity solution domain of a negative radius roller cam mechanism as described in claim 1, characterized in that, The theoretical profile equation of the cam is calculated as follows: Where, x p y is the abscissa of the theoretical profile of the cam; p denoted as the ordinate of the theoretical profile of the cam; h is the follower stroke; s is the roller center displacement. y is the rotation angle; x is the horizontal coordinate of the camshaft center position; y is the vertical coordinate of the camshaft center position.

4. The method for solving the motion-fidelity solution domain of a negative radius roller cam mechanism as described in claim 1, characterized in that, The theoretical contour radius of curvature is calculated as follows: Where ρ is the theoretical profile radius of curvature; x p y is the abscissa of the theoretical profile of the cam; p The vertical coordinate of the theoretical profile of the cam; For the turning angle; x p ′,y p ′, x p "and y p "Represents x respectively" p and y p Variable pairs The first and second derivatives.

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