CN116467843A - Cycloidal tooth profile secondary conjugate modification method of RV reducer - Google Patents

Abstract

The invention discloses a secondary conjugate modification method for the cycloidal tooth profile of an RV reducer, which selects three processing errors that have a great influence on the transmission error of the RV reducer: the center circle radius error of the pin gear housing, the pin tooth radius error, and the pin tooth pin hole circumferential position error, establishes a processing error compensation model, performs an equivalent replacement of the part processing error through the equidistant or shift distance modification amount, determines the modification amount once, and obtains the theoretical zero backlash cycloid tooth profile; The model determines the amount of secondary modification to obtain the conjugate cycloid tooth profile. The technical effect of the present invention is that the machining error can be reasonably compensated under the condition of single error or combined error of parts, the radial clearance and return difference accuracy are effectively limited, and the transmission accuracy is improved.

Description

A secondary conjugate modification method for cycloidal tooth profile of RV reducer

technical field

The invention relates to a precision reducer, in particular to a method for secondary conjugate modification of a cycloid tooth profile of an RV reducer.

Background technique

RV (Rotate vector) reducer has the advantages of small size, large transmission ratio, high precision, high rigidity, etc., and is widely used in aerospace, industrial robots and other fields. As the core component of the RV reducer, the cycloidal pinwheel drive has a major impact on the transmission accuracy, transmission efficiency and carrying capacity of the whole machine. In order to facilitate assembly and lubrication, the cycloid tooth profile in the RV reducer needs to be modified.

Existing cycloid wheel modification methods and the determination of cycloid wheel modification amount are based on the theoretical design dimensions of pin teeth, pin gear housings, crankshafts and other parts. The amount of modification is determined at the design stage. In actual assembly, different error combinations of parts are used for group assembly. However, the processing error is random, which may cause the mismatch between the cycloid wheel modification amount and the part error, resulting in assembly interference between the pin teeth and cycloid gear teeth, or the excessive clearance leading to low transmission accuracy and meshing performance.

Terminology: 1. Conjugate modification: refers to making the cycloid tooth profile and the needle tooth become a conjugate tooth profile through modification, and the conjugate tooth profile refers to a pair of tooth profiles that mesh with each other according to the predetermined transmission ratio.

2. Equidistant shape modification: When grinding the cycloidal wheel, increase or decrease the tool radius, and it is stipulated that the increase of the tool radius is positive, and the decrease is negative.

3. Distance modification: When grinding the cycloidal wheel, the relationship between the radius of the tool and the range of the cycloidal wheel (the tool and the workpiece move relative to each other according to the determined motion relationship) remains unchanged, and the radius of the tool moves inward or outward for a certain distance. The outward movement of the tool is a positive distance, and the inward movement is a negative distance.

4. Hysteresis: refers to the lag of the output shaft in the rotation angle when the input shaft starts to reversely rotate to the output shaft and then reversely rotates.

Contents of the invention

Aiming at the problems existing in the prior art, the technical problem to be solved by the present invention is to provide a method for secondary conjugate modification of cycloid tooth profile of RV reducer based on processing error compensation, which can effectively compensate the processing error under the condition of part error combination, effectively solve the problem of mismatch between cycloid wheel modification amount and part error, and improve the transmission accuracy of RV reducer.

The technical problem to be solved by the present invention is realized by such technical scheme, and it comprises the following steps:

Step 1. Select three key machining errors that have a great influence on the transmission error of the RV reducer, and use the equidistant or shifting distance modification method to compensate the error, and establish an error compensation model for the machining error on the distribution circle of the cycloid wheel;

Step 2. According to the cycloidal wheel processing error compensation model established in step 1, calculate the amount of primary modification, and compensate the elastic deformation between the cycloidal wheel and the needle teeth under the load condition to obtain the theoretical zero-backlash cycloidal tooth profile after the primary modification;

Step 3. With the given radial clearance and backlash design requirements as constraints, the method of equidistant plus displacement combination modification method is used to determine the secondary modification amount by iteratively approaching the meshing working section of the theoretical zero-backlash cycloidal tooth profile after the primary modification, and then obtain the conjugate cycloidal tooth profile.

Technical effect of the present invention is:

Considering the part machining error and its combination, a machining error compensation model is established. The machining error of the part is equivalently replaced by the equidistant or offset modification amount, and then the primary modification amount is determined to obtain the theoretical zero backlash cycloidal tooth profile. Then, with the given radial clearance and backlash as constraints, the secondary modification amount is determined through the established conjugate tooth profile optimization model, and the conjugate cycloidal tooth profile is obtained. The invention can effectively compensate the processing error under the condition of single error or combined error of the part, effectively limit the precision of the radial clearance and backlash, solve the problem in the prior art that the modification amount of the cycloid wheel does not match the error of the part, and improve the transmission accuracy of the RV reducer.

Description of drawings

The accompanying drawings of the present invention are as follows:

Figure 1 is a schematic diagram of needle tooth machining error compensation;

(a), the pin tooth radius error is a positive deviation; (b), the pin tooth radius error is a negative deviation;

Fig. 2 is a schematic diagram of machining error compensation of the pin gear housing;

(a), center circle radius error is positive deviation; (b), center circle radius error is negative deviation;

Fig. 3 is a schematic diagram of the compensation of the processing error of the pin tooth pin hole;

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

Fig. 4 is the schematic diagram of secondary conjugate modification of the present invention;

Fig. 5 is a comparison diagram of cycloidal tooth profiles of primary modification and secondary conjugate modification of the embodiment.

Detailed ways

Below in conjunction with accompanying drawing and embodiment the present invention will be further described:

The present invention comprises the following steps:

Step 1. Select three key machining errors that have a greater impact on the transmission error of the RV reducer, and use the equidistant or shifting distance modification method to compensate the error, and establish an error compensation model for the machining error on the distribution circle of the cycloid wheel (see Figure 1, Figure 2 and Figure 3).

Existing literature research shows that: the center circle radius error of the pin gear housing, the pin tooth radius error, the pin tooth pin hole circumferential position error, the equidistant modification error, the shift distance modification error and the cumulative pitch error of the cycloid wheel have a greater impact on the transmission error of the RV reducer. Among them, the latter three errors can be better controlled by existing processing technology, but the first three errors can only be better compensated by cycloid wheel modification. Therefore, the above three key machining errors are respectively selected as the pin tooth radius error, the pin tooth shell center circle radius error and the pin tooth pin hole circumferential position error.

As shown in Fig. 1(a), the standard radius of the pin tooth is r _rp , which has a positive deviation δrrp in machining, the actual radius of the pin tooth is r _rp + δrrp, the center distance between the pin tooth and the cycloid wheel (that is, the radius of the center circle of the pin gear housing) is a fixed value r _p , and there is an interference area between the pin tooth and the cycloid wheel.

As shown in Fig. 1(b), the pin tooth has a negative deviation δrrp during machining, and the actual radius of the pin tooth is r _rp - δrrp. There is a gap area between the pin tooth and the cycloid wheel. To eliminate this gap area, the cycloid wheel tooth profile is modified by negative equidistant outward expansion.

As shown in Fig. 2(a), the radius of the center circle of the pin gear housing is r _p , which has a positive deviation δrp in machining. The radius of the center circle of the pin gear housing is actually r _p + δrp, and there is a gap between the pin teeth and the cycloidal wheel. To eliminate this gap area, the tooth profile of the cycloidal wheel is modified by positive displacement extending outward.

As shown in Fig. 2(b), the radius of the center circle of the pin gear housing has a negative deviation δrp during machining, and the radius of the center circle of the pin gear housing is actually r _p −δrp. There is an interference area between the pin teeth and the cycloidal wheel. To eliminate this interference area, the tooth profile of the cycloidal wheel is modified by a negative displacement that converges inward.

As shown in Fig. 3(a), in the counterclockwise direction, the circumferential position of the pin hole of the pin tooth has a forward positive deviation _δt during processing, and there is an interference area between the pin tooth and the cycloid wheel. To eliminate this interference area, the tooth profile of the cycloid wheel is positively equidistant and converges inward.

As shown in Fig. 3(b), in the counterclockwise direction, the circumferential position of the needle pin hole has a backward negative deviation _δt during processing, and there is a gap area between the pin tooth and the cycloid wheel. To eliminate this gap area, the tooth profile of the cycloid wheel is a negative equidistant modification that expands outward.

Step 2. According to the cycloidal wheel processing error compensation model established in step 1, calculate the amount of primary modification, and compensate the elastic deformation between the cycloidal wheel and the pin teeth under the load condition to obtain the theoretical zero backlash cycloidal tooth profile after the primary modification.

The amount of primary modification and the theoretical zero-backlash cycloid tooth profile are obtained through the following calculation steps:

Step 2.1. Under the condition of ensuring no interference and zero backlash between the meshing pair of the cycloidal pinwheel, the error is compensated by means of equidistant or shift distance modification, and the circumferential backlash caused by different errors on the distribution circle of the cycloid wheel is equivalently replaced by the corresponding equidistant and shift distance modification.

The circumferential backlashes caused by the equidistant and displacement modification amounts on the distribution circle are respectively:

In the formula, the J _D is the circular side gap caused by the volume of the equidimum fixation on the distribution circle, and ΔR _RP is the amount of pitch; the _JS is the circular side gap caused by the displacement volume on the distribution circle; ΔR _P is the volume of the shift spacing, K is _the short coefficient _{of the rotation of the rotation of the line. From the distance, Z p is} the number of needle teeth, _{and R p is} the round radius in the center of the needle tooth shell.

In this embodiment, the circumferential backlash caused by the three key machining errors on the distribution circle corresponds to:

In the formula, j _rp is the circumferential backlash caused by the pin tooth radius error on the distribution circle, δr _rp is the pin tooth radius error; j _t is the circumferential backlash of the pin tooth pin hole circumferential position error on the distribution circle, δ _t is the pin tooth pin hole circumferential position error; j _p is the circumferential backlash caused by the pin tooth housing center circle radius on the distribution circle, and δr _p is the pin tooth housing center circle radius error.

When performing compensation, set j _rp = j _D1 , j _t = j _D2 , j _p = j _s , then the cycloid wheel compensation and modification amounts for single error can be obtained: Δr _rp1 , Δr _rp2 , Δr _p1 .

Step 2.2, the total compensation and modification amount of the cycloid wheel is the algebraic sum of the individual error compensation modification amounts, and the total modification amount of one-time modification can be obtained as:

Δr＝Δr _rp1 +Δr _rp2 +Δr _p1

In the formula, Δr is the total modification amount of the cycloid wheel for one modification; Δr _rp1 , Δr _rp2 , and Δr _p1 correspond to the compensation modification amount of the pin tooth radius error δr _rp , the pin hole circumferential position error δ _t and the pin tooth housing center circle radius error δr _p .

The total amount of modification is specifically divided into two types:

Δr' _rp is the amount of equidistant modification, and Δr' _p is the amount of displacement modification.

Step 2.3. Under load conditions, there will be elastic deformation between the cycloidal wheel and the pin teeth, and the deformation function of the cycloidal wheel and the pin teeth during the contact extrusion process

In the formula, is the rotation angle of the pin tooth relative to the rotating arm; δ _max is the elastic deformation of the cycloid tooth with the largest force.

Deformation function Compensation into the equidistant plus displacement combination modified cycloid tooth profile equation.

Step 2.4, the modification amount (Δr′ _rp , Δr′ _p ) and the deformation variable function Substituting it into the cycloidal tooth profile equation of the combination of equidistant plus displacement, the theoretical zero backlash cycloidal tooth profile equation after one modification is obtained:

In the formula, i ^H is the relative transmission ratio of the cycloidal wheel and the pin wheel, z _p , z _c are the teeth numbers of pin wheel and cycloid wheel respectively; /> k is the short-range coefficient of the cycloid wheel distance modification; x′ _z and y′ _z are the theoretical zero-backlash cycloid tooth profile coordinates after one practice, a is the eccentricity of the crankshaft, and δ is the deformation variable function;

r _p is the radius of the center circle of the pintooth housing, r _rp is the radius of the pintooth, Δr′ _rp is the amount of equidistant modification, Δr′ _p is the amount of displacement modification, is the rotation angle of the pin tooth relative to the arm.

The cycloid tooth profile obtained by the above-mentioned one-time modification is the cycloid tooth profile of theoretical zero backlash meshing, which has only theoretical significance. In order to facilitate assembly, disassembly and lubrication, a certain radial clearance must be left at the tooth root and tooth top of the cycloid wheel, so secondary modification is necessary.

Step 3. With the given radial clearance and backlash design requirements as constraints, the method of equidistant plus displacement combination modification method is used to determine the secondary modification amount by iteratively approaching the meshing working section of the theoretical zero-backlash cycloidal tooth profile after the primary modification, and then obtain the conjugate cycloidal tooth profile. The tooth profile of the meshing working section can not only meet the requirements of the tooth root and tooth tip radial clearance in the non-working section, but also realize conjugate transmission with the pin teeth in the meshing working section.

As shown in Figure 4, based on the specific parameters of the reducer, the change of the pressure angle within the range of a cycloid gear tooth can be calculated, and the rotation angle of the needle tooth relative to the rotating arm corresponding to the two boundary points B' and C' of the meshing working section of the theoretical zero-backlash cycloid tooth profile can be obtained according to the allowable pressure angle Its value is respectively /> and /> The X-axis coordinates of the two boundary points are x _b and x _c , and this working section is divided into m equal parts in the x-axis direction and substituted into the theoretical zero-backlash cycloidal tooth profile equation after the first modification in the above step 2.4, and the coordinate point set on the B′C′ section is (x′ _zi , y′ _zi ) (i=1, 2, ..., m).

Set a group of equidistant plus displacement combined secondary modification amount Δr ^* _rp , Δr ^* _p , and use step 2.4 to calculate another set of coordinate points on the B ^* C ^* section as The mean of the absolute value of the Y coordinate difference between the two point sets is:

Δr ^* _rp is the amount of secondary equidistant modification, and Δr ^* _p is the amount of secondary displacement modification.

Step 3.1. Constrain the circumferential backlash according to the design requirements of the return difference γ. The calculation formula for the circumferential backlash j between the theoretical zero-backlash tooth profile after the primary modification and the tooth profile obtained after the second modification is:

In the formula, k ₁ and k ₂ are the short-span coefficients of the cycloid tooth profile for primary modification and secondary modification respectively, k ₁ =az _p /(r _p +Δr′ _p ), k ₂ =az _p /(r _p +Δr ^* _p );

The hysteresis γ of the cycloidal pin wheel pair transmission can be calculated from the circumferential backlash j as:

In the formula, a is the eccentricity of the crank shaft, and z _c is the number of teeth of the cycloid wheel.

Step 3.2, after the second modification, the radial gap Δj generated by the needle teeth at the root or top of the cycloid wheel is:

Δj＝(Δr ^* _rp +Δr′ _rp )-(Δr ^* _p +Δr′ _p )

Step 3.3. According to the high-precision design requirements, with the secondary equidistant modification amount |Δr ^* _rp |≤d, the radial clearance 0<Δj≤e, and the hysteresis accuracy γ≤g as constraints, the secondary modification amount optimization model is established:

In one embodiment, d=0.2mm, e=0.03mm, g=1'.

The least one multiplication method is suitable for the iterative solution with the goal of minimizing the sum of the absolute values of the residuals. Here, minf(Δr ^* r _p , Δr ^* _p ) is the goal, and the other three are constraints. The optimization model of the secondary modification amount is solved iteratively by the least one multiplication method, and the optimal secondary modification amount can be obtained as Δr ^* _rp and Δr ^* _p .

As shown in Fig. 5, the theoretical cycloidal tooth profile with zero backlash is obtained through one-time modification, and the secondary modification amount is determined by approximating the once-modified cycloidal tooth profile meshing working section, and the conjugate cycloidal tooth profile is obtained, which can not only meet the radial clearance requirements of the tooth root and tooth top in the non-working section tooth profile, but also realize conjugate transmission with the pin teeth on the meshing working surface.

Claims (4)

1. A method for secondary conjugate modification of cycloid tooth profile of RV reducer, characterized in that, comprising the following steps: Step 1. Select three key machining errors that have a great influence on the transmission error of the RV reducer, and use the equidistant or shifting distance modification method to compensate the error, and establish an error compensation model for the machining error on the distribution circle of the cycloid wheel; Step 2. According to the cycloidal wheel processing error compensation model established in step 1, calculate the amount of primary modification, and compensate the elastic deformation between the cycloidal wheel and the needle teeth under the load condition to obtain the theoretical zero-backlash cycloidal tooth profile after the primary modification; Step 3. With the given radial clearance and backlash design requirements as constraints, the method of equidistant plus displacement combination modification method is used to determine the secondary modification amount by iteratively approaching the meshing working section of the theoretical zero-backlash cycloidal tooth profile after the primary modification, and then obtain the conjugate cycloidal tooth profile. 2. The method for secondary conjugate modification of cycloid tooth profile of RV reducer according to claim 1, characterized in that: said three key machining errors are pin tooth radius error, pin gear housing center circle radius error and pin pin hole circumferential position error. 3. The method for secondary conjugate modification of cycloidal tooth profile of RV reducer according to claim 2, characterized in that, in step 2, the amount of primary modification and the theoretical zero-backlash cycloidal tooth profile are obtained through the following calculation steps: Step 2.1, the circumferential backlash caused by the three key machining errors on the distribution circle of the cycloid wheel corresponds to: In the formula, j _rp is the circumferential backlash caused by the pin tooth radius error on the distribution circle, δr _rp is the pin tooth radius error; j _t is the circumferential backlash of the pin tooth pin hole circumferential _position error on the distribution circle, δ _{t is the pin tooth pin hole circumferential position degree error; j p is the circumferential backlash caused by the pin tooth shell center circle radius on the distribution circle, δr p is the} pin tooth shell center circle radius error; (r _p +Δr _p ), a is the eccentricity of the crank shaft, z _p is the number of pin teeth, r _p is the radius of the center circle of the pin gear housing, and Δr _p is the distance modification amount; Step 2.2, the total modification amount of one modification is: Δr＝Δr _rp1 +Δr _rp2 +Δr _p1 In the formula, Δr is the total modification amount of the cycloid wheel for one modification; Δr _rp1 , Δr _rp2 , and Δr _p1 correspond to the compensation modification amount of the pin tooth radius error δr _rp , the pin hole circumferential position error δ _t and the pin tooth housing center circle radius error δr _p . The total amount of modification is specifically divided into two types: Δr′ _rp is the amount of equidistant modification, and Δr′ _p is the amount of displacement modification; Step 2.3, the deformation function of the cycloid wheel and the pin tooth during the contact extrusion process In the formula, is the rotation angle of the pin tooth relative to the rotating arm; δ _max is the elastic deformation of the cycloid tooth with the largest force; Step 2.4, the modification amount (Δr′ _rp , Δr′ _p ) and the deformation variable function Substituting it into the cycloidal tooth profile equation of the combination of equidistant plus displacement, the theoretical zero backlash cycloidal tooth profile equation after one modification is obtained: In the formula, i ^H is the relative transmission ratio of the cycloidal wheel and the pin wheel, z _p , z _c are the teeth numbers of pin wheel and cycloid wheel respectively; x′ _z , y′ _z are the coordinates of the theoretical zero-backlash cycloid tooth profile after one practice, and δ is the deformation variable function. 4. The method for secondary conjugate modification of cycloid tooth profile of RV reducer according to claim 3, characterized in that, in step 3, Divide the theoretical zero-backlash cycloid tooth profile meshing section in the X-axis direction into m equal parts and substitute it into the theoretical zero-backlash cycloid tooth profile equation after one modification in step 2.4, and obtain the set of coordinate points on the meshing working section B'C' as (x' _zi , y' _zi ), i=1, 2,..., m; Set a group of equidistant plus displacement combined secondary modification amount Δr ^* _rp , Δr ^* _p , calculate another coordinate point set on the B ^* C ^* segment as (x ^* _zi , y ^* _zi ), i=1, 2,..., m, the mean value of the absolute value of the Y coordinate difference of the two point sets is: Δr ^* _rp is the amount of secondary equidistant modification, and Δr ^* _p is the amount of secondary displacement modification; Step 3.1, the formula for calculating the circumferential backlash j between the theoretical zero-backlash tooth profile after primary modification and the tooth profile obtained after secondary modification is: In the formula, k ₁ and k ₂ are the short-span coefficients of the cycloid tooth profile for primary modification and secondary modification respectively, k ₁ =az _p /(r _p +Δr′ _p ), k ₂ =az _p /(r _p +Δr ^* _p ); The hysteresis γ of the cycloidal pin wheel pair transmission can be calculated from the circumferential backlash j as: Step 3.2, after the second modification, the radial gap Δj generated by the needle teeth at the root or top of the cycloid wheel is: Δj＝(Δr ^* _rp +Δr′ _rp )-(Δr ^* _p +Δr′ _p ) Step 3.3. With the quadratic equidistant trimming amount |Δr ^* _rp |≤d, the radial gap 0<Δj≤e, and the hysteresis accuracy γ≤g as constraints, the secondary trimming amount optimization model is established: The optimization model of the secondary modification amount is solved iteratively by the method of least one multiplication, and the optimal secondary modification amount is obtained as Δr ^* _rp and Δr ^* _p .