A method for modifying the cycloid profile of an RV reducer

Abstract

The application discloses a cycloid profile secondary conjugate modification method of an RV reducer, selects three machining errors which have greater influences on transmission errors of the RV reducer, i.e., a center circle radius error of a pin gear shell, a pin gear radius error and a pin gear pin hole circle position error, establishes a machining error compensation model, equivalently replaces the part machining errors by equidistance or displacement modification amounts, determines a primary modification amount, and obtains a theoretical zero-side gap cycloid profile; and then, by taking given radial clearances and return differences as constraint conditions, the secondary modification amount is determined through the established conjugate profile optimization model, and the conjugate cycloid profile is obtained. The technical effect of the application is that the machining errors can be reasonably compensated under the conditions of single errors or combined errors of the parts, the radial clearance and return difference accuracy are effectively limited, and the transmission accuracy is improved.

Description

TECHNICAL FIELD

[0001] The application relates to a precision reducer, in particular to a RV reducer cycloid profile secondary conjugate modification method. BACKGROUND

[0002] The RV (Rotate vector) reducer has the advantages of small volume, large transmission ratio, high precision, high stiffness and the like, and is widely applied to the fields of aerospace, industrial robots and the like. The cycloid pin gear transmission is a core component of the RV reducer, and has a great influence on transmission precision, transmission efficiency and load capacity of the whole machine. In order to facilitate assembly and lubrication, the cycloid gear profile in the RV reducer needs to be modified.

[0003] The existing cycloid gear modification method and the determination of the cycloid gear modification amount are based on the theoretical design size of the pin gear, pin gear shell, crank shaft and the like, the modification amount is determined in the design stage, and in the actual assembly, different error combinations of the parts are adopted to implement grouping assembly, but the machining error has randomness, which may cause the cycloid gear modification amount to be unmatched with the part error, so that assembly interference occurs between the pin gear and the cycloid gear, or the transmission precision and the meshing performance are low due to the too large gap.

[0004] Term: 1, conjugate modification: refers to modification of the cycloid profile and the pin gear to be conjugate profiles, and the conjugate profile refers to a pair of profiles that are meshed and transmitted according to a predetermined transmission ratio.

[0005] 2, equidistance modification: when the cycloid gear is modified, the cutter radius is increased or decreased, and the cutter radius increase is positive and the cutter radius decrease is negative.

[0006] 3, displacement modification: when the cycloid gear is modified, the cutter radius and the generating (the cutter and the workpiece are relatively moved according to the determined motion relationship) relationship of the cycloid gear are unchanged, the cutter radius is radially moved inward or outward by a distance, the cutter is outwardly moved as positive displacement, and the cutter is inwardly moved as negative displacement.

[0007] 4, backlash: refers to the lag amount of the output shaft on the rotation angle when the input shaft is reversely rotated and the output shaft follows the reverse rotation. SUMMARY

[0008] In view of the problems existing in the prior art, the technical problem to be solved by the application is to provide an RV reducer cycloid profile secondary conjugate modification method based on machining error compensation, which effectively compensates for the machining error under the condition of part error combination, effectively solves the problem that the cycloid gear modification amount is unmatched with the part error, and improves the transmission precision of the RV reducer.

[0009] The technical problem to be solved by the application is solved by the technical scheme, which comprises the following steps:

[0010] Step 1, three key machining errors which have greater influence on transmission error of RV reducer are selected, machining errors are compensated by using equidistance or displacement modification, and an error compensation model of machining errors on distribution circle of cycloid is established;

[0011] Step 2, according to the error compensation model of machining errors of cycloid established in step 1, primary modification amount is calculated, and the elastic deformation between cycloid and needle tooth under load condition is compensated to obtain theoretical zero-clearance cycloid tooth profile after primary modification;

[0012] Step 3, given radial clearance and backlash design requirements are used as constraint conditions, equidistance and displacement combination modification method is adopted, secondary modification amount is determined by iteratively approximating the meshing working section of the theoretical zero-clearance cycloid tooth profile after primary modification, and then the conjugate cycloid tooth profile is obtained.

[0013] The technical effect of the application is:

[0014] The machining error and its combination are considered, a machining error compensation model is established, the machining error of the part is equivalently replaced by equidistance or displacement modification amount, the primary modification amount is determined, the theoretical zero-clearance cycloid tooth profile is obtained, then the given radial clearance and backlash are used as constraint conditions, the secondary modification amount is determined by establishing the conjugate tooth profile optimization model, and the conjugate cycloid tooth profile is obtained. BRIEF DESCRIPTION OF DRAWINGS

[0015] The brief description of drawings of the application is as follows:

[0016] Figure 1 It is a schematic diagram for needle tooth machining error compensation;

[0017] (a), the radius error of the needle tooth is positive deviation; (b), the radius error of the needle tooth is negative deviation;

[0018] Figure 2 It is a schematic diagram for needle tooth shell machining error compensation;

[0019] (a), the radius error of the center circle is positive deviation; (b), the radius error of the center circle is negative deviation;

[0020] Figure 3 It is a schematic diagram for needle tooth pin hole machining error compensation;

[0021] (a), the circumferential position error is positive deviation; (b), the circumferential position error is negative deviation;

[0022] Figure 4 It is a secondary conjugate modification principle diagram of the application;

[0023] Figure 5 Figure 1 is a comparative diagram of the one-time modification and the two-time conjugate modification of the cycloid profile for the embodiment. DETAILED DESCRIPTION

[0024] The application will be further described below in conjunction with the drawings and embodiments:

[0025] The application comprises the following steps:

[0026] Step 1: Three key machining errors that have a greater impact on the transmission error of the RV reducer are selected, and the errors are compensated by using equidistant or displacement modification, and an error compensation model of the machining error on the distribution circle of the cycloid gear is established (see Figure 1 、 Figure 2 and Figure 3 ).

[0027] The existing literature research shows that the center circle radius error of the pin gear shell, the pin gear radius error, the pin gear pin hole circular position error, the equidistant modification error, the displacement modification error and the cumulative error of the cycloid gear pitch have a greater impact on the transmission error of the RV reducer. Among them, the last three errors can be better controlled through the existing machining technology, but the first three errors can only be better compensated through the cycloid gear modification. Therefore, the three key machining errors are selected as the pin gear radius error, the center circle radius error of the pin gear shell and the pin gear pin hole circular position error.

[0028] As shown in Figure 1 (a), the standard radius of the pin gear is r rp , there is a positive deviation δrrp in machining, the actual radius of the pin gear is r rp + δrrp, the center distance between the pin gear and the cycloid gear (i.e. the center circle radius of the pin gear shell) is a fixed value r p , and there is an interference area between the pin gear and the cycloid gear. To eliminate the interference area, the cycloid gear profile is a positive equidistant modification that converges inward.

[0029] As shown in Figure 1 (b), the pin gear has a negative deviation δrrp in machining, the actual radius of the pin gear is r rp - δrrp, and there is a gap area between the pin gear and the cycloid gear. To eliminate the gap area, the cycloid gear profile is a negative equidistant modification that expands outward.

[0030] As shown in Figure 2 (a), the center circle radius of the pin gear shell is r p , there is a positive deviation δrp in machining, the actual center circle radius of the pin gear shell is r p + δrp, and there is a gap area between the pin gear and the cycloid gear. To eliminate the gap area, the cycloid gear profile is a positive displacement modification that expands outward.

[0031] As Figure 2 (b) shows, the pin tooth shell center circle radius has a negative deviation δrp in processing, and the actual pin tooth shell center circle radius is r p -δrp, there is an interference area between the pin tooth and the cycloid gear, to eliminate the interference area, the cycloid gear tooth profile is a negative shift distance modification that converges inward.

[0032] As Figure 3 (a) shows, in the counterclockwise direction, the pin tooth pin hole circle position degree has a forward positive deviation δ t , there is an interference area between the pin tooth and the cycloid gear, to eliminate the interference area, the cycloid gear tooth profile is a positive equidistant modification that converges inward.

[0033] As Figure 3 (b) shows, in the counterclockwise direction, the pin tooth pin hole circle position degree has a backward negative deviation δ t , there is a gap area between the pin tooth and the cycloid gear, to eliminate the gap area, the cycloid gear tooth profile is a negative equidistant modification that expands outward.

[0034] Step 2, according to the cycloid gear machining error compensation model established in step 1, calculate the first modification amount, and compensate the elastic deformation between the cycloid gear and the pin tooth under the load condition to obtain the theoretical zero side gap cycloid tooth profile after the first modification.

[0035] The first modification amount and the theoretical zero side gap cycloid tooth profile are obtained through the following calculation steps:

[0036] Step 2.1, in the case of ensuring that the cycloidal pin wheel meshing pair does not produce interference and zero side gap, use equidistant or shift distance modification to compensate the error, and equivalent replace the circumferential side gap caused by different errors on the distribution circle of the cycloid gear with corresponding equidistant and shift distance modification amount.

[0037] The circumferential side gap caused by the equidistant and shift distance modification amount on the distribution circle is respectively:

[0038]

[0039] In the formula, j D is the circumferential side gap caused by the equidistant modification amount on the distribution circle, Δr rp is the equidistant modification amount; j s is the circumferential side gap caused by the shift distance modification amount on the distribution circle; Δr p is the shift distance modification amount, k is the short amplitude coefficient when the cycloid gear is shifted, k = az p / (r p + Δr p ), a is the eccentricity of the crankshaft, z p is the number of pin teeth, and r p is the pin tooth shell center circle radius.

[0040] In this embodiment, the circumferential side clearance caused by three key machining errors on the distribution circle corresponds to:

[0041]

[0042] In the formula, j rp is the circumferential side clearance caused by the pin tooth radius error on the distribution circle, δr rp is the pin tooth radius error; j t is the circumferential side clearance of the pin hole position error on the distribution circle, δ t is the pin hole position error; j p is the circumferential side clearance caused by the pin shell center circle radius on the distribution circle, δr p is the pin shell center circle radius error.

[0043] When compensation is performed, let j rp =j D1 , j t =j D2 , j p =j s , the cycloid compensation modification amount of the single error can be obtained as: Δr rp1 , Δr rp2 , Δr p1 .

[0044] Step 2.2, the total compensation modification amount of the cycloid is the algebraic sum of the compensation modification amounts of each single error, and the total modification amount of the first modification can be obtained as:

[0045] Δr=Δr rp1 +Δr rp2 +Δr p1

[0046] In the formula, Δr is the total modification amount of the cycloid first modification; Δr rp1 , Δr rp2 , Δr p1 correspond to the compensation modification amounts of the pin tooth radius error δr rp , the pin hole position error δ t and the pin shell center circle radius error δr p .

[0047] The total modification amount is specifically divided into two kinds:

[0048]

[0049] Δr′ rp is the equidistance modification amount, and Δr′ p is the displacement modification amount.

[0050] Step 2.3: Under load conditions, elastic deformation will occur between the cycloidal wheel and the needle teeth. The deformation function of the cycloidal wheel and the needle teeth during the contact compression process...

[0051]

[0052] In the formula, δ is the rotation angle of the needle tooth relative to the rotating arm; max This represents the elastic deformation of the cycloidal gear tooth subjected to the greatest force.

[0053] The deformable function needs to be The compensation is incorporated into the equation of the cycloidal tooth profile modified by the combination of equal spacing and displacement.

[0054] Step 2.4: Adjust the shaping amount (Δr′) rp ,Δr′ p ) and deformable function Substituting these equations into the equation for the cycloidal tooth profile modified by a combination of equal-distance and offset methods, we obtain the theoretical zero-backlash cycloidal tooth profile equation after one modification:

[0055]

[0056] In the formula, i H This represents the relative transmission ratio between the cycloidal wheel and the pin wheel. z p z c These are the number of teeth on the pinwheel and the cycloidal wheel, respectively. k is the short-amplitude coefficient during cycloidal wheel displacement modification; x′ z y′ z These are the coordinates of the theoretical zero-backlash cycloidal tooth profile after one modification, where a is the crankshaft eccentricity and δ is the deformation function.

[0057] r p Let r be the radius of the center circle of the needle-tooth shell. rp Let Δr′ be the radius of the needle teeth. rp For equidistant shaping, Δr′ p For displacement and shaping amount, The angle of rotation of the needle tooth relative to the rotating arm.

[0058] The cycloidal gear tooth profile obtained by the first modification is a theoretically zero-backlash meshing cycloidal gear tooth profile, which is only of theoretical significance. In order to facilitate assembly, disassembly and lubrication, a certain radial clearance needs to be left at the root and tip of the cycloidal gear tooth, so a second modification is necessary.

[0059] Step 3, with the given radial clearance, the back-lash design requirements as constraint conditions, using the equal distance plus distance combination modification method, through the iterative step-by-step approximation of the theoretical zero side clearance cycloid profile meshing working section after the first modification to determine the secondary modification amount, and then get the conjugate cycloid profile. The tooth profile of the meshing working section can not only meet the requirements of the tooth root and tooth top radial clearance in the non-working section tooth profile, but also realize the conjugate transmission with the needle tooth in the meshing working section.

[0060] As shown in Figure 4 , based on the specific parameters of the reducer, the pressure angle change in the range of the cycloid gear can be calculated, and according to the allowable pressure angle, the corresponding needle tooth rotation angle of the two boundary points B' and C' of the theoretical zero side clearance cycloid profile meshing working section relative to the rotating arm is obtained , the values are and respectively. The X-axis coordinate values of the two boundary points are x b and x c . Divide this working section into m equal parts in the x-axis direction, and substitute it into the theoretical zero side clearance cycloid profile equation after the first modification in step 2.4 to obtain the coordinate point set (x' zi , y' zi ) (i=1, 2, …, m) on the B'C' section.

[0061] Set a set of equal distance plus distance combination secondary modification amount Δr * rp , Δr * p , and use step 2.4 to calculate another coordinate point set on the B * C * section The average value of the absolute value of the Y coordinate difference of the two point sets is:

[0062]

[0063] Δr * rp is the secondary equal distance modification amount, and Δr * p is the secondary distance modification amount.

[0064] Step 3.1, according to the design requirements of the back-lash γ, the circumferential clearance is constrained, and the calculation formula of the circumferential clearance j between the theoretical zero side clearance profile after the first modification and the profile obtained after the secondary modification is:

[0065]

[0066] In the formula, k1 and k2 are the short amplitude coefficients of the first modification and the secondary modification cycloid profile, respectively, k1=az p / (r p +Δr′ pk2 = az p / (r p +Δr * p );

[0067] The backlash γ of the cycloidal pinwheel drive can be calculated from the circumferential backlash j as follows:

[0068]

[0069] In the formula, a is the crankshaft eccentricity, and z c This represents the number of teeth on the cycloidal wheel.

[0070] Step 3.2: After the second shaping, the radial clearance Δj generated by the needle teeth at the root or tip of the cycloidal wheel teeth is:

[0071] Δj=(Δr * rp +Δr′ rp )-(Δr * p +Δr′ p )

[0072] Step 3.3: Based on the high-precision design requirements, use the secondary equidistant shaping amount |Δr * rp Using |≤d, radial clearance 0<Δj≤e, and backlash accuracy γ≤g as constraints, a secondary shaping optimization model is established:

[0073]

[0074] In one embodiment, d = 0.2 mm, e = 0.03 mm, and g = 1′.

[0075] The least squares method is suitable for iterative solutions with the objective of minimizing the sum of the absolute values ​​of the residuals. Here, we take minf(Δr) as an example. * r p , Δr * p Using Δr as the objective and the other three as constraints, the optimal quadratic shaping amount is obtained by iteratively solving the model using the least squares method. * rp and Δr * p .

[0076] like Figure 5 As shown, a theoretical zero-backlash cycloidal tooth profile was obtained through a single shaping process. The secondary shaping amount was determined by approximating the meshing working section of the first-shaped cycloidal tooth profile, resulting in a conjugate cycloidal tooth profile. This profile can satisfy the radial clearance requirements of the tooth root and tooth tip in the non-working section and can also achieve conjugate transmission with the needle tooth on the meshing working surface.

Claims

1. A method for cycloid profile quadratic conjugate modification of an RV reducer, characterized in that, Comprise the following steps: Step 1, three key machining errors which have greater influence on transmission error of RV reducer are selected, and the errors are compensated by using equidistant or displacement modification method, and an error compensation model of machining error on the distribution circle of cycloid is established; Step 2, according to the error compensation model of cycloid machining error established in step 1, the first modification amount is calculated, and the elastic deformation between the cycloid and the needle tooth under the load condition is compensated to obtain the theoretical zero side gap cycloid tooth profile after the first modification; The first modification amount and the theoretical zero side gap cycloid tooth profile are obtained through the following calculation steps: Step 2.1, the corresponding circumferential side gap caused by three key machining errors on the distribution circle of cycloid is: wherein is the circular side play caused by the pin tooth radius error on the distribution circle, is the pin tooth radius error; j t is the circumferential side clearance of the pin tooth pin hole circumferential position error on the distribution circle, is the pin tooth pin hole circumferential position error; j p for the pin tooth shell center circle radius caused by the distribution circle, for the pin tooth shell center circle radius error; k is the short amplitude coefficient for the cycloid wheel displacement modification, , is the eccentricity of the crankshaft, is the number of needle teeth, is the radius of the center circle of the needle tooth housing, is the displacement modification amount; Step 2.2, the total modification amount of the first modification is: In the formula, Total modification amount of the cycloid wheel once modification; 、 、 Corresponding to the compensation modification amount of the pin tooth radius error , pin tooth pin hole circumferential position error And the pin tooth shell center circle radius error ; The total modification amount is specifically divided into two kinds: is the isometric amount of correction, is the shift amount of correction; Step 2.

3. Function of deformation amount of the cycloid and pin tooth in the contact extrusion process : In the formula, is the rotation angle of the pin tooth relative to the swing arm; is the elastic deformation of the cycloid tooth with the largest force. Step 2.4, the amount of modification and the function of deformation Substituting into the equation of the modified cycloid profile with the combination of equidistance and shift distance, the theoretical zero-backlash cycloid profile equation after the first modification is obtained: wherein is the relative transmission ratio of the cycloid wheel to the pin wheel, ; , are the number of teeth of the pin wheel and the cycloid wheel, respectively; , , are the coordinates of the theoretical zero side clearance cycloid tooth profile after one correction, is the deformation variable function; Step 3, taking the given radial clearance and the design requirement of the backlash as the constraint condition, the equidistant and displacement combination modification method is used, the second modification amount is determined by iteratively approximating the meshing working section of the theoretical zero side gap cycloid tooth profile after the first modification, and then the conjugate cycloid tooth profile is obtained.

2. The method of cycloid profile secondary conjugate modification of the RV reducer according to claim 1, characterized in that: The three key machining errors are the needle tooth radius error, the needle tooth shell center circle radius error and the needle tooth pin hole circle position error.

3. The method of cycloid profile secondary conjugate modification of the RV reducer according to claim 2, characterized in that, In step 3, The m equal parts of the meshing working section of the theoretical zero-backlash cycloid profile in the X-axis direction are substituted into the theoretical zero-backlash cycloid profile equation after one modification in step 2.4 to obtain the coordinate point set on the meshing working section ​ Set a set of equidistantly combined quadratic modification amounts , , calculate Another coordinate point set on the segment is The average of the absolute values of the Y coordinate differences of the two point sets is: is a quadratic equidistant amount of shape modification, is a quadratic displacement amount of shape modification; Step 3.

1. The circumferential backlash between the theoretically zero backlash tooth profile after the first modification and the tooth profile obtained after the second modification The calculation formula is: wherein , are the short pitch coefficients of the once modified and twice modified cycloid profiles, respectively, , ; from the circumferential play The backlash of a cycloidal pin wheel transmission can be calculated is: Step 3.2, Radial clearance generated by the pin tooth at the root or tip of the cycloid tooth after the second reshaping Is: Step 3.3, with a secondary isometric amount of modification radial clearance backlash As a constraint, a secondary modification amount optimization model is established: The quadratic modification amount optimization model is solved by least square method to obtain the optimal quadratic modification amount as and .

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