Method for predicting machining shearing of tooth profile curve of variable ratio tooth sector of recirculating ball type steering gear

Abstract

The present application relates to the technical field of automobile steering system, and provides a method for predicting the machining shearing of the tooth profile curve surface of a variable ratio gear sector of a circulating ball type steering gear, which comprises the following steps: 1, establishing the tooth profile geometric element and the rack profile coordinate system, and solving the instantaneous meshing point coordinates of the tooth profile and the rack profile; 2, in the tooth profile geometric element and the rack profile coordinate system, the instantaneous meshing point coordinates of the tooth profile and the rack profile are used to draw the meshing trajectory line of the intermediate tooth of the gear sector on the small end surface; 3, the meshing trajectory line of the intermediate tooth of the gear sector on the small end surface is used to calculate the size of the front point polar radius and the rear point polar radius of each meshing point on the meshing trajectory line, and then it is judged whether the tooth profile curve surface of the gear sector exists the machining shearing phenomenon; 4, according to the mapping point group, the degree of the machining shearing of the tooth profile curve surface of the gear sector is predicted. The present application can obtain the prediction result within seconds, which can greatly shorten the verification time and improve the development efficiency.

Description

Technical Field

[0001] This invention relates to the field of automotive steering system technology, and in particular to a method for predicting the shearing of the profile surface of the variable ratio sector tooth in a recirculating ball steering gear. Background Technology

[0002] Commercial vehicles, due to their heavy front axle load, require significant steering torque to steer the wheels. They typically employ recirculating ball steering systems, such as hydraulic or electric power steering. These systems share the basic transmission components of a rack and pinion (rack) and a sector rocker arm shaft (sector). Modern commercial vehicles have increasingly demanding requirements for steering system control, particularly regarding the steering gear's transmission ratio. To meet vehicle handling and stability requirements, a desired variable transmission ratio is typically used. This variable ratio steering system's ratio curve is usually achieved through meshing between the sector's special tooth profile surface (the corresponding sector can be called a variable ratio sector, and the corresponding tooth profile can be called a variable ratio tooth profile) and the rack's straight tooth profile.

[0003] The special tooth profile surface of the variable ratio gear sector is usually calculated based on the transmission relationship between the rack and the gear sector, derived from the gear ratio curve of the steering gear. This transmission relationship is then used to solve for the variable ratio tooth profile surface data using the analytical method of meshing principles, providing data support for subsequent tooth profile surface machining. However, due to the variable ratio transmission, the tooth profile surface corresponding to certain local data may be sheared off during subsequent machining. This affects the meshing transmission effect of the gear sector tooth profile surface. This phenomenon of local tooth profile surface shearing should be identified during the design phase to avoid the misuse of this data.

[0004] There are two common identification methods. The first method involves using the variable ratio tooth profile surface data after the design is completed, machining the tooth sector sample with a rack cutter, and then performing meshing transmission with the rack workpiece. The identification is then observed by using a color imprint method on the tooth profile. This method has a long verification time and is expensive. The second method involves simulating the machining of the tooth sector tooth profile surface according to the design data, and then performing simulated meshing transmission with the rack. The identification is then observed by observing the meshing distribution. However, regardless of whether 3D simulation or programming calculation-data simulation is used, a long simulation time is required to draw a conclusion. For example, the Boolean operation time for 3D simulation is about 3 to 5 hours, and the programming calculation-data simulation time is about 10 to 15 hours. Using the two common identification methods mentioned above, if it is determined that there is a phenomenon of local tooth profile surface shearing, the design parameters need to be readjusted and the judgment repeated. Usually, it takes multiple times to finalize the design parameters, which is inefficient. Although this can avoid the phenomenon of tooth profile surface shearing during machining, the cumulative time is very long. Even with simulation verification, it still takes several days. Summary of the Invention

[0005] This invention primarily addresses the problem of existing methods for judging and verifying the machining shearing of the variable ratio gear sector tooth profile surface in recirculating ball steering gears. These methods are time-consuming, and if local shearing is detected, design parameters need to be readjusted and the judgment repeated, often requiring multiple iterations to finalize the design parameters, resulting in low efficiency. The invention proposes a predictive method for the machining shearing of the variable ratio gear sector tooth profile surface in recirculating ball steering gears. This method can predict the machining shearing phenomenon of the gear sector tooth profile surface; it provides prediction results within seconds, significantly shortening verification time, improving development efficiency, and reducing verification costs.

[0006] This invention provides a method for predicting the machining shearing of the variable ratio sector tooth profile surface in a recirculating ball steering gear, comprising the following steps:

[0007] Step 1: Establish the coordinate system of the tooth profile geometry and the rack profile, and solve for the instantaneous meshing point coordinates (x, y) of the sector tooth profile and the rack tooth profile. j y j );

[0008] Step 2, in the coordinate system of tooth profile geometry and rack profile, use the instantaneous meshing point coordinates (x, y, z) of the sector tooth profile and rack tooth profile. j y j Draw the meshing trajectory line of the middle tooth of the gear sector on the small end face;

[0009] Step 3: By drawing the meshing trajectory line of the middle tooth of the tooth sector on the small end face, calculate the size of the front point extreme diameter ρ1 and the rear point extreme diameter ρ2 of each meshing point on the meshing trajectory line, and then determine whether there is a machining shearing phenomenon on the tooth profile surface of the tooth sector.

[0010] Furthermore, following step 3, the following steps are also included:

[0011] Step 4: Map all meshing points on the meshing trajectory line to the x-axis, and associate each meshing point with the previous meshing point to form a mapping point composition line; and predict the degree of machining shearing of the tooth profile surface of the tooth sector based on the mapping point composition line.

[0012] Furthermore, in step 1, a coordinate system x-0-y is established with the center point of the gear sector shaft as the origin 0;

[0013] Place the rack profile on the small end face into the coordinate system x-0-y, and make the bisector of the middle tooth groove coincide with the y-axis, so that the rack center line y = H(0) and is parallel to the x-axis; also place the main geometric elements of the tooth sector on the small end face into the coordinate system x-0-y, and obtain the tooth profile geometric elements and the rack profile coordinate system.

[0014] The pitch circle radius of the sector gear is calculated using the following formula:

[0015]

[0016] In the above formula, Indicates the pitch circle radius of the gear sector, in mm; This represents the steering gear ratio curve, given as known conditions; unit: none; P h The screw lead, in mm, is a known condition.

[0017] The rack travel is calculated using the following formula:

[0018]

[0019] In the above formula, Indicates the rack and pinion travel;

[0020] From the given conditions and formulas (1) and (2), we can obtain the meshing line of the rack moving to the left on the small end face, the right tooth profile of the rack's tooth groove, and the instantaneous engagement point (x). in y in Instantaneous disengagement point (x) out y out );

[0021] The following formula can be used to calculate the line of engagement for the rack moving to the left on the small end face:

[0022]

[0023] The right tooth profile of the rack tooth groove is calculated using the following formula:

[0024]

[0025] The coordinates of the instantaneous engagement point of the rack moving left are calculated using the following formula:

[0026]

[0027] The coordinates of the instantaneous disengagement point when the rack moves left are calculated using the following formula:

[0028]

[0029] The intersection of the meshing line of the rack moving to the left and the right profile of the tooth groove in the rack can be solved using formulas (3) and (4). When this intersection meets the x out ≤x j ≤x in Under certain conditions, it becomes the theoretical engagement point. Therefore, the instantaneous engagement point coordinates (x, y, y) are calculated using the following formula. j y j ):

[0030]

[0031] Furthermore, in step 2, the instantaneous engagement point coordinates obtained in step 1 are used to continuously rotate the gear sector with the angle change as the step size, and the coordinates (x, y, y) of each instantaneous engagement point are calculated and listed. j y j ) and the angle of the gear sector The corresponding numerical table is used to draw the meshing trajectory line.

[0032] Furthermore, in step 3, on the meshing trajectory line, from right to left are front and back, corresponding to the coordinates of the front point as (x... j1 y j1 The coordinates of the point after the point are (x j2 y j2 ), corresponding to the front point extreme diameter ρ1 and the rear point extreme diameter ρ2, calculate the magnitude of the front point extreme diameter ρ1 and the rear point extreme diameter ρ2 at each meshing point on the meshing trajectory line;

[0033] Then, based on the magnitudes of the front extreme diameter ρ1 and the rear extreme diameter ρ2, it is determined whether there is a machining shearing phenomenon on the tooth profile surface of the tooth sector. If the rear extreme diameter ρ2 is greater than the front extreme diameter ρ1, it indicates that there is a machining shearing phenomenon; conversely, if the rear extreme diameter ρ2 is less than the front extreme diameter ρ1, it indicates that there is no machining shearing phenomenon.

[0034] Furthermore, step 4 specifically includes the following steps 401 to 402:

[0035] Step 401: Map all meshing points on the meshing trajectory line to the x-axis, and associate the meshing point with the previous meshing point to form a line of mapping points;

[0036] Mapping point (x) t The expression for ,0) is as follows:

[0037]

[0038] By associating and mapping all engagement points on the engagement trajectory line with the previous engagement point, the engagement trajectory line can be mapped onto the x-axis for distribution.

[0039] When the polar radius of the rear point ρ2 > the polar radius of the front point ρ1, its mapping point (x t ,0) are distributed in the negative x-axis region; when the polar radius of the later point ρ2 < the polar radius of the earlier point ρ1, its mapping point (x t ,0) are distributed in the positive x-axis region;

[0040] Step 402: Based on the lines formed by the mapping points, predict the degree of shearing of the tooth profile surface of the tooth sector during processing;

[0041] When the meshing trajectory line is mapped onto the x-axis, forming a line of mapped points, the deeper this line extends into the negative x-axis region, the more severe the shearing phenomenon during processing. The minimum mapped point (x...) t-min The severity is indicated by 0, and the evaluation method is as follows:

[0042] When x t-min When the value is ≤-1.00, there is a very severe shearing phenomenon;

[0043] When -1.00 <x t-min When the value is ≤-0.50, there is a more severe shearing phenomenon;

[0044] When -0.50 <x t-min When the value is ≤0.00, there is a slight shearing phenomenon;

[0045] When 0.00 <x t-min When the value is less than 0.25, there is no shearing phenomenon, and the meshing transmission effect is generally poor.

[0046] When 0.25≤x t-min When the value is less than 0.50, there is no shearing phenomenon and the meshing transmission effect is better.

[0047] When 0.50≤x t-min At this time, there is no shearing phenomenon, and the meshing transmission effect is good.

[0048] Furthermore, following step 402, the following steps are also included:

[0049] Step 403: Determine the compressive damage resistance of the tooth profile surface of the tooth sector;

[0050] When x t-min When the value is large, it indicates that the front point extreme diameter ρ1 is significantly larger than the rear point extreme diameter ρ2. In this case, the distance between the two corresponding meshing points of the tooth sector profile is also large, which avoids the tooth sector rotation angle from always being concentrated in the area with a small tooth profile surface within a certain range, thus preventing the tooth profile surface from being damaged by pressure.

[0051] Minimum value of the mapping point x t-min It also represents the resistance to pressure loss of the tooth profile surface of the sector tooth, and its evaluation method is as follows:

[0052] When x t-min When the value is ≤0.00, the tooth profile surface of the tooth sector has no resistance to compressive damage;

[0053] When 0 <x t-min When the value is less than 0.25, the compressive damage resistance of the tooth profile surface of the sector tooth is relatively poor.

[0054] When 0.25≤x t-min If the value is less than 0.50, then the compressive damage resistance of the tooth profile surface of the tooth sector is qualified.

[0055] When 0.50≤xt-min When the tooth profile surface is in good condition, it has good resistance to pressure loss.

[0056] The present invention provides a method for predicting the shearing of the tooth profile surface of a variable ratio sector gear in a recirculating ball steering gear, which has the following advantages compared with the prior art:

[0057] 1. The method for predicting the shearing of the gear profile surface of the recirculating ball steering gear of the present invention, which is designed for the gear profile surface of the gear sector with concave gear ratio curve, can avoid the shearing phenomenon during processing and improve the meshing transmission effect of the gear profile surface.

[0058] 2. The method for predicting whether the tooth profile surface of the variable ratio gear sector of the recirculating ball steering gear of the present invention will be sheared during machining can be determined without the need for a physical workpiece of the gear sector, thus avoiding verification after machining the sample, reducing verification costs and improving development efficiency.

[0059] 3. The method for predicting the machining shearing of the variable ratio sector tooth profile surface of the recirculating ball steering gear proposed in this invention can obtain a predictive conclusion on the machining shearing of the sector tooth profile surface design parameters in just a few seconds. This provides a better method for repeatedly testing and matching to obtain optimal design parameters, and can significantly shorten the design verification time. The prediction method of this invention can obtain near-optimal design parameters in advance, and the results can be verified using existing methods, all of which can yield ideal meshing distribution results, avoiding the need for repeated parameter testing and re-verification.

[0060] 4. The method for predicting the machining shearing of the variable ratio sector tooth profile surface of the recirculating ball steering gear proposed in this invention can further evaluate the design of the pressure loss resistance of the tooth profile surface when it is predicted that no machining shearing phenomenon will occur, which facilitates the optimization of its associated design parameters.

[0061] 5. The method for predicting the machining shearing of the variable ratio sector tooth profile surface of the recirculating ball steering gear proposed in this invention can optimize important design parameters, such as the variable ratio, the variable ratio start and stop angles, and the variable ratio transition curve form, when it is predicted that no machining shearing phenomenon will occur and the tooth profile surface has good resistance to pressure loss. This method can serve as a basis for technical exchanges with customers, so as to promote the overall collaborative development of the vehicle steering system. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the basic structure of the rack and gear sector used in this invention.

[0063] Figure 2 This is a schematic diagram of the concave linear ratio curve structure used in this invention.

[0064] Figure 3This is a schematic diagram of the concave cosine ratio curve structure used in this invention.

[0065] Figure 4 This is a curve of the concave cosine ratio of the gear sector designated A in this invention.

[0066] Figure 5 The figure shows the simulation results of the meshing distribution state of the tooth sector A of the present invention.

[0067] Figure 6 The figure shows the simulation results of the meshing distribution state of the tooth sector code B of the present invention.

[0068] Figure 7 The figure shows the simulation results of the meshing distribution state of the gear sector code C of the present invention.

[0069] Figure 8 This is the coordinate system for the transmission relationship between the right tooth profile of the small end face of the middle tooth of the tooth sector and the tooth profile of the rack in this invention.

[0070] Figure 9 This is a flowchart illustrating the process of predicting the shearing of the tooth profile surface of the tooth sector according to the present invention.

[0071] Figure 10 The coordinate system is composed of the geometric elements of the right tooth profile of the small end face of the middle tooth of the tooth sector in this invention and the tooth rack profile.

[0072] Figure 11 This is a diagram illustrating the theoretical meshing trajectory of the right side profile of the small end face of the middle tooth of the tooth sector when the rack moves to the left.

[0073] Figure 12 This is a schematic diagram illustrating the principle of mapping the meshing point to the x-axis in this invention.

[0074] Figure 13 This is a diagram showing the distribution of mapping points of a certain tooth sector meshing trajectory line mapped to the x-axis according to the present invention.

[0075] Figure 14 This is a curve of the concave cosine ratio of the gear sector designated D in this invention.

[0076] Figure 15 The figure shows the simulation results of the meshing distribution state of the tooth sector code D of the present invention. Detailed Implementation

[0077] To make the technical problems solved by this invention, the technical solutions adopted, and the technical effects achieved clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings, not all of them.

[0078] I. Manifestations of the shearing phenomenon on the curved surface of the tooth profile of the tooth sector during machining

[0079] The gear ratio transmission of a recirculating ball steering gear is achieved through its second-stage rack and pinion gear transmission, specifically through the special tooth profile surface of the gear sector. Therefore, the gear ratio curve output by the recirculating ball steering gear mainly refers to the gear ratio curve achievable by the gear sector. For ease of understanding and analysis, this invention references the basic structural components of the rack and pinion gear as follows: Figure 1 As shown, the phenomenon of the tooth profile surface being sheared during machining of the variable ratio gear sector manifests as follows: when the rack and gear sector are driven in a variable ratio, there are local areas on the tooth profile surface of the gear sector that do not participate in meshing and are thus disengaged. Essentially, the tooth profile surface in these local areas has been machined and sheared away.

[0080] Combining the main structural parameters of the gear sector of the recirculating ball steering gear with the key parameters of the vehicle steering system, special attention should be paid to the gear ratio curve required by the vehicle steering system. The commonly used curve structure is as follows: Figure 2 The concave linear ratio curve structure shown is as follows: Figure 3 The diagram shows a concave cosine ratio curve structure, and it is typically a concave ratio curve. Figure 2 and Figure 3 In the diagram, ① represents the median fixed-ratio section, ② represents the variable-ratio transition section, and ③ represents the fixed-ratio sections on both sides. Indicates the starting angle of the ratio change (positive value, unit: °). Indicates the dead center angle of the gear ratio (positive value, unit: °), i wA This indicates the center-range transmission ratio of the steering gear (abbreviated as: center-range transmission ratio of the steering gear), i wB This indicates the gear ratio of the fixed-ratio sections on both sides of the steering gear (abbreviated as: gear ratio of both sides of the steering gear). Taking the concave cosine gear ratio curve as an example, the main parameters of the initial design of the gear sector tooth profile surface are shown in Table 1 below. The gear ratio curve of its gear sector code A is as follows: Figure 4 As shown.

[0081] Table 1: Main parameters of the tooth profile surface of the tooth sector designated A

[0082]

[0083]

[0084] In Table 1, "gear ratio" refers to the absolute value of the difference between the gear ratios on both sides and the midpoint gear ratio in the gear ratio curve, i.e., gear ratio Δi. w =|i wB -i wA The same applies below.

[0085] Using existing technology and a programming-calculation-data simulation method, the main design parameters of the variable ratio sector tooth profile surface in Table 1 above were verified. The process took approximately 15 hours and yielded the following results: Figure 5 The simulation results of the meshing distribution state are shown.

[0086] Analysis method of simulation results of meshing distribution: This simulation result diagram of meshing distribution represents the transmission of rack moving left and sector rotating counterclockwise. It shows the meshing distribution of the right tooth profile surface of sector. Since each tooth profile surface of sector is symmetrical about the middle tooth splitting surface (i.e., the central axis surface of sector), the meshing distribution of each tooth profile surface on the left and right sides of sector is also symmetrical. The horizontal values ​​at the bottom of the diagram represent the position of rack travel, and the horizontal values ​​at the top represent typical sector corner points and the specific rack travel positions corresponding to these corner points. The vertical values ​​on the right represent the sector profile code i (i = 0, 1, 2, ..., 50), where code i indicates the distance L = ixB / 50 from the small end face of the sector profile, and B is the axial width of sector. This method is used for analysis. Figure 5 When the rack travels to the left, approximately -9 to -18 mm (corresponding to a gear sector rotation angle of approximately 15° to 29°), a blank area appears on the right side of the gear sector's tooth profile surface where there is no meshing. This indicates that machining shearing has occurred. This phenomenon is more severe near the small end face and gradually extends towards the large end face, disappearing around i = 33 (L = 33 x B / 50). Therefore, the design parameters in Table 1 above are unusable.

[0087] Adjusting the initial design parameters, especially those relevant to the vehicle steering system, will improve the meshing state. This also indicates that the area to be machined and sheared on the tooth profile surface of the variable ratio gear sector can be reduced after parameter adjustment. Conversely, inappropriate parameter adjustment will increase the area to be machined and sheared. To determine the direction of improvement in parameter adjustment, repeat the above programming calculation and data simulation using the main parameters of the tooth profile surfaces of gear sector codes B and C as shown in Table 2. The results are as follows: Figure 6 The simulation results of the meshing distribution state of the tooth sector code B shown are as follows: Figure 7 The simulation results for the meshing distribution state of gear sector code C are shown. Among them, gear sector code B, compared with gear sector code A, only has a smaller ratio; gear sector code C, compared with gear sector code A, only has a smaller ratio starting angle value and an increased ratio starting and stopping angle range.

[0088] Table 2: Main parameters of the tooth profile surfaces of gear sector codes B and C

[0089]

[0090] Depend on Figure 6 and Figure 7Analysis of the simulation results of the meshing distribution shows that reducing the gear ratio can improve the shearing phenomenon during machining, and increasing the range of the gear ratio's start and stop angles can also have an improvement effect, but it still does not achieve the required effect. Therefore, the two sets of adjusted design parameters in Table 2 are also unusable. After multiple adjustments to other parameters, including adjustments to the main structural parameters of the gear sector, such as increasing the tooth profile angle and decreasing the cutting angle, the improvement effect will also be achieved. However, the improvement effects of these parameters are interactive. For example, the module and the total number of teeth will affect the median transmission ratio, and the median transmission ratio will further affect the maximum value of the gear ratio and the optimal value of the gear ratio's stop angle. When adjusting parameters, special attention should be paid to the gear ratio's stop angle parameter, as it has a critical point. The further the parameter adjustment deviates from the critical point, the worse the improvement effect will be. At the same time, the adjustment of other parameters will also cause this critical point to change. This requires repeated parameter adjustments, and each adjustment needs to be verified by simulation in order to find the best design parameters, which will consume a long design time.

[0091] In summary, for the recirculating ball steering gear with a concave gear ratio curve, and focusing on the main structural parameters of the gear sector and the key parameters of the vehicle steering system, parameter adjustments were made within acceptable limits. Then, using existing technology and programming calculations and data simulations, their meshing distribution was observed. The shearing phenomenon on all tooth profile surfaces occurred on the tooth profile surface of the middle teeth of the gear sector, and its severity gradually decreased from the small end face to the large end face of the gear sector until it disappeared. This provides a simplified direction for subsequent prediction processes.

[0092] II. Analysis of the Causes of Shearing Phenomena on the Profile Surface of the Gear Sector

[0093] First, it is necessary to understand how the variable ratio tooth profile surface is formed.

[0094] The special tooth profile surface of the variable ratio gear sector is calculated based on the gear ratio curve of the steering gear, which shows the transmission relationship between the rack and the gear sector. The analytical method based on the meshing principle is used to solve for the variable ratio tooth profile surface data. Combining the above analysis, the tooth profile curve of one side (left or right) of the small end face of the middle tooth of the gear sector, which is prone to machining shearing, is simplified to establish a... Figure 8 The coordinate system shown represents the transmission relationship between the right tooth profile of the small end face of the middle tooth of the gear sector and the tooth profile of the rack. This coordinate system is... Figure 1The coordinate system x-0-y is consistent, except that the corresponding section ii is for the small end face when i=0. The parameters associated with the small end face of section i=0 include: the radius of the addendum circle of the sector tooth is Ra(0), unit: (mm), and the distance between the center line of the rack and the center point of the sector tooth is H(0), unit: mm. The y-axis of the coordinate system of this transmission relationship coincides with the zero point of the initial position of the sector tooth and rack transmission. That is, when the sector tooth and rack transmission are at the zero point position, the reference line of the central axis surface of the sector tooth coincides with the y-axis, and the reference line of the central parting surface of the rack also coincides with the y-axis. When the rack moves and drives the sector tooth to rotate, the reference line of the central parting surface of the rack moves with the rack, and the reference line of the central axis surface of the sector tooth rotates with the sector tooth. Figure 8 Let's analyze how the tooth profile curve on the right side of the small end face of the middle tooth of this tooth sector is formed.

[0095] In theory, when the profile of the gear sector is not subjected to machining shearing, the rack moves to the left. The position will drive the gear sector to rotate to At the corner position, the right profile of the sector tooth meshes with the right profile of the rack tooth. This is the tangent point of a pair of conjugate curves, which is the meshing point (x). j y j Different racks move to the left. Position and rotation of the gear sector At the corner positions, these meshing points correspond to different tooth profile curve points of the gear sector, and all of these tooth profile curve points must participate in the meshing transmission. That is, the meshing point is the tooth profile curve point, and the meshing points are all on the meshing line. Only through this meshing transmission can the rack push the gear sector along the meshing line direction around the base circle. Rotation is used to satisfy the ratio transmission of the rack and sector gear; thinking in reverse, since the meshing point is the point of the tooth profile curve, and the meshing points are all on the meshing line, then the intersection of the meshing line and the right profile of the rack is the meshing point. As the sector gear rotates, this meshing point is developed into the point of the tooth profile curve of the sector gear, thus forming the tooth profile curve.

[0096] If the tooth profile of the sector gear undergoes machining shearing, some of the theoretically obtained meshing points will be sheared away, and these will no longer be points on the sector gear profile curve. However, to satisfy the gear ratio transmission between the rack and the sector gear, the rack travel must be satisfied at the corresponding meshing point positions. and gear sector corner When the meshing point is not a point on the profile curve of the tooth sector, the meshing transmission will experience disengagement, which means that the shearing phenomenon of the machined part occurs.

[0097] when Figure 8When the rack moves to the left, the sector gear rotates counterclockwise. Observing the extreme radii ρ1 and ρ2 at the front and rear points on the sector gear's tooth profile curve, we can always find that ρ2 < ρ1. When the rack moves to the left, the intersection of the line of action and the right profile of the rack is the engagement point. If the extreme radii ρ2 > ρ1 at the front and rear engagement points, then the rear engagement point is not a point on the sector gear's tooth profile curve. This is because the gear ratio transmission uses the sector gear's base circle... As a result of these changes, if the base circle radius of the rear point is significantly higher than that of the front point at the front and rear corner points of the gear sector, the rear line of engagement will be significantly higher than the front line of engagement, resulting in a situation where the extreme diameters ρ2 > ρ1 at the front and rear engagement points. When the gear ratio curve does not match the structural parameters of the gear sector, this is the fundamental reason for the machining shearing phenomenon on the tooth profile surface of the gear sector.

[0098] III. Predictive Method for Machining Shearing of Gear Sector Profile Surface

[0099] For a concave gear sector with a variable ratio curve, the tooth profile curve on the small end face of the gear sector, which is prone to machining shearing, is predicted. Specifically, only the small end face tooth profile curve on one side (left or right) of the middle tooth of the gear sector is predicted by equivalently converting it into a meshing point. If no machining shearing occurs at this point, it indicates that no machining shearing will occur on any of the gear sector's tooth profile surfaces. Then, the extreme radii of the front and rear points on the meshing trajectory are compared, and the meshing trajectory points are mapped onto the horizontal axis of the coordinate system. Based on their distribution, the possibility of machining shearing on the gear sector's tooth profile surfaces is predicted. Specifically, for example... Figure 9 As shown, the present invention provides a method for predicting the shearing of the tooth profile surface of a variable ratio sector gear in a recirculating ball steering gear, specifically including the following process:

[0100] Step 1: Establish the coordinate system of the tooth profile geometry and the rack profile, and solve for the instantaneous meshing point coordinates (x, y) of the sector tooth profile and the rack tooth profile. j y j ).

[0101] With the center point of the gear sector shaft as the origin 0, create an array in Excel that is parallel to... Figure 8 In a coordinate system with consistent x-0-y, such as Figure 10 As shown.

[0102] exist Figure 10 In the process, the rack profile on the small end face is placed in the coordinate system x-0-y, and the bisector of the middle tooth groove (i.e., the datum line of the rack bisector) is made to coincide with the y-axis, so that the rack center line y = H(0) and is parallel to the x-axis; the main geometric elements of the tooth sector on the small end face, such as the instantaneous meshing point, instantaneous meshing line, instantaneous base circle, etc., are also placed in the coordinate system x-0-y to obtain the tooth profile geometric elements and the rack profile coordinate system.

[0103] The basic structural parameters of the gear sector include: basic module m (mm), pressure angle of the gear sector pitch circle / tooth profile angle of the rack α (rad), axial width of the gear sector B (mm), and cutting angle of the gear sector θ. A (rad), sector small end profile displacement coefficient x0, sector tooth addendum coefficient and rack tooth addendum coefficient ha*, sector tooth dedendum coefficient and rack tooth dedendum coefficient h f *=Rack cutter tooth tip height coefficient ha0*. These basic structural parameters are initial parameters, from which we can obtain the tooth tip circle radius Ra(0) on the small end face of the tooth sector, unit: mm, the distance H(0) between the rack centerline and the center point of the tooth sector, unit: mm, and the tooth groove width P of the rack. T The unit is mm, so that these are also known conditions.

[0104] exist Figure 10 In the coordinate system shown, the meshing state of the right tooth profile curve of the sector is evaluated with the rack moving to the left as a condition.

[0105] The pitch circle radius of the sector gear is calculated using the following formula:

[0106]

[0107] In the above formula, This indicates the pitch circle radius of the gear sector (i.e., the pitch circle radius), in mm; This represents the steering gear ratio curve, given as known conditions; unit: none; P h The screw lead, in mm, is a known condition.

[0108] The rack travel is calculated using the following formula:

[0109]

[0110] In the above formula, This indicates the rack travel.

[0111] From the given conditions and formulas (1) and (2), we can obtain the meshing line of the rack moving to the left on the small end face, the right tooth profile of the rack's tooth groove, and the instantaneous engagement point (x). in y in Instantaneous disengagement point (x) out y out ),exist Figure 10 The equations or coordinates in the coordinate system x-0-y are as follows.

[0112] The following formula can be used to calculate the line of engagement for the rack moving to the left on the small end face:

[0113]

[0114] The right tooth profile of the rack tooth groove is calculated using the following formula:

[0115]

[0116] The coordinates of the instantaneous engagement point of the rack moving left are calculated using the following formula:

[0117]

[0118] The coordinates of the instantaneous disengagement point when the rack moves left are calculated using the following formula:

[0119]

[0120] The intersection of the meshing line of the rack moving to the left and the right profile of the tooth groove in the rack can be solved using formulas (3) and (4). When this intersection meets the x out ≤x j ≤x in When the condition is met, it becomes the theoretical engagement point. Therefore, the instantaneous engagement point coordinates (x, y, y) are calculated using the following formula. j y j ):

[0121]

[0122] Step 2, in the coordinate system of tooth profile geometry and rack profile, use the instantaneous meshing point coordinates (x, y, z) of the sector tooth profile and rack tooth profile. j y j Draw the meshing trajectory line of the middle tooth of the gear sector on the small end face.

[0123] The meshing trajectory is the line formed by the meshing points of the rack and pinion gears on a certain section ii to achieve the required gear ratio transmission. Theoretically, these meshing points, when unfolded according to the corresponding gear sector rotation angle, should be the tooth profile curve points on the gear sector section ii. This step only draws the theoretical meshing trajectory on the small end face of the middle tooth of the gear sector when i=0.

[0124] The instantaneous engagement point coordinates obtained in step 1 are used with the change in rotation angle as the step size. Since the change in rotation angle is relatively small, it is usually... Continuously rotate the gear sector, calculate and list the coordinates (x, y) of each instantaneous engagement point in Excel. j y j ) and the angle of the gear sector The corresponding numerical table can be used to draw a graph like this. Figure 11 The theoretical meshing trajectory is shown.

[0125] Step 3: By drawing the meshing trajectory line of the middle tooth of the tooth sector on the small end face, calculate the size of the front point extreme diameter ρ1 and the rear point extreme diameter ρ2 of each meshing point on the meshing trajectory line, and then determine whether there is a machining shearing phenomenon on the tooth profile surface of the tooth sector.

[0126] On the meshing trajectory line, from right to left are forward and backward, with the corresponding coordinates of the forward point being (x...). j1 y j1 The coordinates of the point after the point are (x j2 y j2 ), corresponding to the front point extreme diameter ρ1 and the rear point extreme diameter ρ2, calculate the size of the front point extreme diameter ρ1 and the rear point extreme diameter ρ2 of each meshing point on the meshing trajectory line.

[0127] Then, based on the magnitudes of the front extreme diameter ρ1 and the rear extreme diameter ρ2, it is determined whether there is a machining shearing phenomenon on the tooth profile surface of the tooth sector. If the rear extreme diameter ρ2 is greater than the front extreme diameter ρ1, it indicates that there is a machining shearing phenomenon; conversely, if the rear extreme diameter ρ2 is less than the front extreme diameter ρ1, it indicates that there is no machining shearing phenomenon.

[0128] However, step 3, which involves observing and comparing the front point extreme diameter ρ1 and the rear point extreme diameter ρ2, is not intuitive. It can only determine whether the tooth profile surface of the tooth sector has been subjected to machining shearing, but it is not suitable to determine the severity of the machining shearing phenomenon. Therefore, this invention uses step 4 to more intuitively determine whether the tooth profile surface of the tooth sector has been subjected to machining shearing.

[0129] Step 4: Map all meshing points on the meshing trajectory line to the x-axis, and associate each meshing point with the previous meshing point to form a mapping point composition line; based on the mapping point composition line, predict the degree of machining shearing on the tooth profile surface of the sector. Step 4 specifically includes the following steps 401 to 403:

[0130] Step 401: Map all meshing points on the meshing trajectory line to the x-axis, and associate the meshing point with the previous meshing point to form a line of mapped points.

[0131] Step 401 provides a more intuitive demonstration of the shearing process. This invention maps all meshing points on the meshing trajectory line to the x-axis and associates each meshing point with the previous meshing point, thus showing the relationship between the magnitudes of the preceding and following extreme diameters ρ1 and ρ2. The mapping principle is as follows: Figure 12 As shown, the line connecting the front and rear engagement points is perpendicular to the line drawn through the rear engagement point. The intersection of this perpendicular line with the x-axis is the mapping point (x) from the rear engagement point to the x-axis. t The mapping point (0) represents the mapping position of the rear engagement point and is also related to the state of the front engagement point. Following this step, the meshing trajectory line is mapped to the x-axis to form a line of mapping points, as shown below. Figure 13 As shown.

[0132] Mapping point (x) t The expression for ,0) is as follows:

[0133]

[0134] By associating all engagement points on the engagement trajectory line with the previous engagement point, the engagement trajectory line can be mapped onto the x-axis for distribution. For example... Figure 12 The two cases shown illustrate the rear engagement point. When the rear point radius ρ2 > the front point radius ρ1 (due to machining shearing), its mapping point (x) t ,0) are distributed in the negative x-axis region; when the rear point extreme radius ρ2 < the front point extreme radius ρ1 (there is no phenomenon of processing shearing), its mapping point (x t The positive values ​​(0) are distributed in the positive region of the x-axis. Therefore, by observing whether there is a negative region on the x-axis when the meshing trajectory line is mapped onto it, we can also predict whether there is a shearing phenomenon on the tooth profile surface of the tooth sector during machining.

[0135] Step 402: Based on the lines formed by the mapping points, predict the degree of shearing of the tooth profile surface of the tooth sector during processing.

[0136] When the meshing trajectory line is mapped onto the x-axis, forming a line of mapped points, the deeper this line extends into the negative x-axis region, the more severe the shearing phenomenon during processing. In this invention, the minimum mapped point (x... t-min The severity is indicated by 0, and the evaluation method is shown in Table 3.

[0137] Table 3: Evaluation Methods for Machining Shearing of Gear Sector Profile Surface

[0138]

[0139] As can be seen from Table 3, when x t-min When the value is ≤-1.00, there is a very severe shearing phenomenon;

[0140] When -1.00 <x t-min When the value is ≤-0.50, there is a more severe shearing phenomenon;

[0141] When -0.50 <x t-min When the value is ≤0.00, there is a slight shearing phenomenon;

[0142] When 0.00 <x t-min When the value is less than 0.25, there is no shearing phenomenon, and the meshing transmission effect is generally poor.

[0143] When 0.25≤x t-min When the value is less than 0.50, there is no shearing phenomenon and the meshing transmission effect is better.

[0144] When 0.50≤x t-min At this time, there is no shearing phenomenon, and the meshing transmission effect is good.

[0145] Step 403: Determine the compressive damage resistance of the tooth profile surface of the tooth sector.

[0146] Minimum value of the mapping point x t-min Similar to the minimum radius of curvature of conventional tooth profile surfaces, when x t-min When the value is large, it indicates that the front point extreme diameter ρ1 is significantly larger than the rear point extreme diameter ρ2. In this case, the distance between the two corresponding meshing points of the tooth sector profile is also large, which avoids the tooth sector rotation angle from always being concentrated in the area with a small tooth profile surface within a certain range, thus preventing the tooth profile surface from being damaged by pressure.

[0147] Therefore, the minimum value of the mapping point x t-min It also represents the resistance to pressure loss of the tooth profile surface of the tooth sector, and its evaluation method is shown in Table 4.

[0148] Table 4: Evaluation Methods for the Compressive Loss Resistance of the Tooth Profile Surface of a Sector

[0149]

[0150] As can be seen from Table 4, when x t-min When the value is ≤0.00, the tooth profile surface of the tooth sector has no resistance to compressive damage;

[0151] When 0 <x t-min When the value is less than 0.25, the compressive damage resistance of the tooth profile surface of the sector tooth is relatively poor.

[0152] When 0.25≤x t-min If the value is less than 0.50, then the compressive damage resistance of the tooth profile surface of the tooth sector is qualified.

[0153] When 0.50≤x t-min When the tooth profile surface is in good condition, it has good resistance to pressure loss.

[0154] IV. Verification of the Predicted Results

[0155] Based on the above prediction method, the parameters were readjusted (compared to gear sector code A, only the shift angle was adjusted to 2°~28.3°), and the main parameters of the tooth profile surface of gear sector code D are given in Table 5 below, to minimize the mapping point x. t-min =0.291.

[0156] Table 5: Main parameters of the tooth profile surface of the tooth sector designated D

[0157]

[0158] According to the parameters in Table 5, the strain ratio curve is as follows: Figure 14 As shown, by employing existing technology and utilizing programming calculations and data simulation methods, the following can be obtained: Figure 15 The simulation results of the meshing distribution state are shown. (From...) Figure 15It can be seen that this parameter adjustment has resulted in a better matching effect of the main parameters of the tooth profile surface of the tooth sector code D; combined with the above-mentioned tooth sector codes A, B, and C, their evaluation results are listed in Table 6 for comparison.

[0159] Table 6: Evaluation Results of Main Parameters of Tooth Profile Surfaces for Four Types of Gear Fans

[0160]

[0161] As shown in Table 6, the evaluation of the machining shearing phenomenon of gear sector codes A, B, C, and D using the prediction method of this invention, followed by evaluation using existing methods of programming calculation and data simulation, yields consistent results. Furthermore, the prediction method of this invention also adds an evaluation method for the compressive damage resistance of the gear sector tooth profile surface.

[0162] In summary, this invention provides a method for predicting the machining shearing of the tooth profile surface of a recirculating ball steering gear with a variable ratio. Specifically, it predicts the machining shearing phenomenon on the small end face tooth profile curve, which is prone to occur in concave variable ratio curves of the tooth profile curve. Furthermore, it only predicts the small end face tooth profile curve on one side (left or right) of the middle tooth of the tooth profile. If no shearing phenomenon occurs, it indicates that the entire tooth profile surface of the tooth profile will not experience machining shearing. Then, by comparing the extreme radii of the front and rear points on the meshing trajectory line and mapping the meshing trajectory points onto the horizontal axis of the coordinate system, the method predicts the machining shearing phenomenon of the tooth profile surface based on their distribution position.

[0163] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the shearing of the profile surface of the variable ratio sector gear in a recirculating ball steering gear, characterized in that, The tooth profile surface designed for the concave variable ratio curve includes the following process: Step 1: Establish the coordinate system of the tooth profile geometry and the rack profile, and solve for the coordinates of the instantaneous meshing point of the sector tooth profile and the rack tooth profile. x j , y j ); In step 1, a coordinate system is established with the center point of the gear sector shaft as the origin O. x -0- y ; Place the rack profile on the small end face into the coordinate system. x -0- y In the middle, and make its middle tooth groove's center line align with y The shafts coincide, making the rack centerline coincide. y = H(0) and with x The axes are parallel; the main geometric elements of the gear sector on the small end face are also placed in the coordinate system. x -0- y In this process, the tooth profile geometry and rack profile coordinate system are obtained; The pitch circle radius of the sector gear is calculated using the following formula: （1）； In the above formula, Indicates the pitch circle radius of the gear sector, in mm; This represents the steering gear ratio curve, given as known conditions; unit: none. P h The screw lead, in mm, is a known condition. The rack travel is calculated using the following formula: （2）； In the above formula, Indicates the rack and pinion travel; From the above known conditions and formulas (1) and (2), we can obtain the meshing line of the rack moving to the left on the small end face, the right tooth profile of the rack's tooth groove, and the instantaneous engagement point ( x in , y in Instantaneous disengagement point ( x out , y out ); The following formula can be used to calculate the line of engagement for the rack moving to the left on the small end face: （3）； The right tooth profile of the rack tooth groove is calculated using the following formula: （4）； The coordinates of the instantaneous engagement point of the rack moving left are calculated using the following formula: （5）； The coordinates of the instantaneous disengagement point when the rack moves left are calculated using the following formula: （6）； The intersection of the meshing line of the rack moving to the left and the right profile of the tooth groove in the rack can be obtained by using formulas (3) and (4). When this intersection meets the following conditions... Under certain conditions, it becomes the theoretical engagement point. Therefore, the instantaneous engagement point coordinates are calculated using the following formula ( x j ，y j ): （7）； Step 2, in the coordinate system of tooth profile geometry and rack profile, use the coordinates of the instantaneous meshing point of the sector tooth profile and rack tooth profile ( x j , y j Draw the meshing trajectory line of the middle tooth of the gear sector on the small end face; Step 3: Using the meshing trajectory line of the middle tooth of the gear sector on the small end face, calculate the extreme diameter of the front point of each meshing point on the meshing trajectory line. ρ 1 and the rear point polar radius ρ 2 The size of the tooth profile surface is used to determine whether the tooth sector has been sheared during processing. In step 3, on the meshing trajectory line, from right to left are front and back, and the coordinates of the corresponding front point are ( x j1 , y j1 The coordinates of the point after the point are ( x j2 , y j2 ), corresponding to the front point polar radius ρ 1 and the rear point polar radius ρ 2 Calculate the extreme radius of the front point at each meshing point on the meshing trajectory line. ρ 1 and the rear point polar radius ρ 2 Size; Then from the previous point polar radius ρ 1 and the rear point polar radius ρ 2 The size of the radius is used to determine whether there is machining shearing on the tooth profile surface of the sector tooth. If so, the rear point polar diameter... ρ 2 > Front point polarity ρ 1 In this case, it indicates that there is a phenomenon of processing and shearing; conversely, if it is the post-point polarity... ρ 2 < Front point polarity ρ 1 In this case, it indicates that there is no processing or shearing phenomenon.

2. The method for predicting the machining shearing of the variable ratio sector tooth profile surface of the recirculating ball steering gear according to claim 1, characterized in that, Following step 3, the following is also included: Step 4, move all engagement points on the engagement trajectory line towards x The axis is mapped, and the meshing point is associated with the previous meshing point to form a line of mapping points; and based on the line of mapping points, the degree of machining shearing of the tooth profile surface of the tooth sector is predicted.

3. The method for predicting the machining shearing of the variable ratio sector tooth profile surface of the recirculating ball steering gear according to claim 1, characterized in that, In step 2, the instantaneous engagement point coordinates obtained in step 1 are used to continuously rotate the gear sector with the rotation angle change as the step size, and the coordinates of each instantaneous engagement point are calculated and listed. x j ，y j ) and the angle of the gear sector The corresponding numerical table is used to draw the meshing trajectory line.

4. The method for predicting the machining shearing of the variable ratio sector tooth profile surface of the recirculating ball steering gear according to claim 3, characterized in that, Step 4 specifically includes the following steps 401 to 402: Step 401, move all engagement points on the engagement trajectory line towards x Axis mapping is performed, and the meshing point is associated with the previous meshing point to form a line of mapped points; Mapping point ( x t The expression for ,0 is as follows: （8）； By associating and mapping all engagement points on the engagement trajectory line with the previous engagement point, the engagement trajectory line can be mapped to... x Distributed along the axis; When the rear point radius ρ 2 > Front point polarity ρ 1 In this case, its mapping point ( x t ,0) distributed in x Negative region of the axis; when the rear point radius ρ 2 < Front point polarity ρ 1 In this case, its mapping point ( x t ,0) distributed in x Positive region of the axis; Step 402: Based on the lines formed by the mapping points, predict the degree of shearing of the tooth profile surface of the tooth sector during processing; When the meshing trajectory line is towards x Axis mapping forms lines composed of mapped points, which are distributed in... x The deeper the negative value region of the axis, the more severe the shearing phenomenon during machining; with the minimum mapping point ( x t-min The severity is indicated by 0, and the evaluation method is as follows: when x t-min When the value is ≤-1.00, there is a very severe shearing phenomenon; When -1.00 < x t-min When the value is ≤-0.50, there is a more severe shearing phenomenon; When -0.50 < x t-min When the value is ≤0.00, there is a slight shearing phenomenon; When 0.00 < x t-min When the value is less than 0.25, there is no shearing phenomenon, and the meshing transmission effect is generally poor. When 0.25≤ x t-min When the value is less than 0.50, there is no shearing phenomenon and the meshing transmission effect is better. When 0.50≤ x t-min At this time, there is no shearing phenomenon, and the meshing transmission effect is good.

5. The method for predicting the machining shearing of the variable ratio sector tooth profile surface of the recirculating ball steering gear according to claim 4, characterized in that, Following step 402, the following is also included: Step 403: Determine the compressive damage resistance of the tooth profile surface of the tooth sector; when x t-min A larger value indicates a larger polar radius at the front point. ρ 1 Significantly larger than the rear point polarity ρ 2 The distance between the two corresponding meshing points of the tooth profile is also relatively large, which avoids the tooth profile turning angle from always being concentrated in the area with a small tooth profile surface within a certain range, thus preventing the tooth profile surface from being damaged by pressure. Minimum value of mapping point x t-min It also represents the resistance to pressure loss of the tooth profile surface of the sector tooth, and its evaluation method is as follows: when x t-min When the value is ≤0.00, the tooth profile surface of the tooth sector has no resistance to compressive damage; When 0 < x t-min When the value is less than 0.25, the compressive damage resistance of the tooth profile surface of the sector tooth is relatively poor. When 0.25≤ x t-min If the value is less than 0.50, then the compressive damage resistance of the tooth profile surface of the tooth sector is qualified. When 0.50≤ x t-min When the tooth profile surface is in good condition, it has good resistance to pressure loss.

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