A cycloid gear tooth profile modification method

Abstract

The present invention discloses a method for modifying the cycloid tooth profile of a cycloid gear, comprising the following steps: obtaining the standard tooth profile equation of the cycloid gear; obtaining the minimum positive displacement modification amount and the positive equidistant modification amount that minimize the maximum contact force F within the meshing region between the cycloid gear and the pin gear, and modifying the cycloid gear into an "inverted bow" tooth profile by using the "positive displacement + positive equidistant" modification; obtaining the tooth profile curve equation of the cycloid gear under the "positive displacement + positive equidistant" modification method; using the "negative displacement + negative equidistant" modified tooth profile to fit the "positive displacement + positive equidistant" modified tooth profile curve, and taking the minimum deviation value within the range of the teeth that are simultaneously meshing when the cycloid gear and the pin gear are working between the "negative displacement + negative equidistant" modified tooth profile curve and the "positive displacement + positive equidistant" modified tooth profile curve as the target, obtaining the optimal "negative displacement + negative equidistant" modification amount, and performing secondary modification by using the "negative displacement + negative equidistant" to obtain the modified tooth profile equation. By adopting optimized modification parameters, the force transmission and accuracy transmission performance of the cycloid gear are improved. max The present invention discloses a method for modifying the cycloid tooth profile of a cycloid gear, comprising the following steps: obtaining the standard tooth profile equation of the cycloid gear; obtaining the minimum positive displacement modification amount and the positive equidistant modification amount that minimize the maximum contact force F within the meshing region between the cycloid gear and the pin gear, and modifying the cycloid gear into an "inverted bow" tooth profile by using the "positive displacement + positive equidistant" modification; obtaining the tooth profile curve equation of the cycloid gear under the "positive displacement + positive equidistant" modification method; using the "negative displacement + negative equidistant" modified tooth profile to fit the "positive displacement + positive equidistant" modified tooth profile curve, and taking the minimum deviation value within the range of the teeth that are simultaneously meshing when the cycloid gear and the pin gear are working between the "negative displacement + negative equidistant" modified tooth profile curve and the "positive displacement + positive equidistant" modified tooth profile curve as the target, obtaining the optimal "negative displacement + negative equidistant" modification amount, and performing secondary modification by using the "negative displacement + negative equidistant" to obtain the modified tooth profile equation. By adopting optimized modification parameters, the force transmission and accuracy transmission performance of the cycloid gear are improved.

Description

Technical Field

[0001] The present invention is used in the field of cycloid gear profile modification, and particularly relates to a cycloid gear profile modification method for a cycloid gear. Background Art

[0002] The cycloid pinwheel planetary reducer has significant characteristics such as a large transmission ratio range, a compact structure, high reliability, and a long service life. It is not only widely used in the field of general transmission, but also has great application potential in robot transmission devices, precision mechanical transmissions, aerospace equipment, measuring instruments, etc.

[0003] As the core transmission component of the cycloid pinwheel planetary reducer, in order to compensate for manufacturing errors, maintain a reasonable backlash, facilitate loading and unloading, ensure lubrication, and more importantly, to obtain a reasonable tooth profile required for transmission, the standard cycloid gear must be modified. There are three common modification methods for cycloid gears: shift modification (modification amount is Δr p ), equal-distance modification (modification amount is Δr rp ), and rotation angle modification (modification amount is δ). Among them, shift modification and equal-distance modification cannot form a conjugate tooth profile with the pinwheel teeth well, thus affecting the transmission smoothness; although rotation angle modification is conjugate with the pinwheel teeth, there will be a non-clearance contact at the tooth tip and tooth root parts, thus unable to compensate for the manufacturing errors of the radial dimension chain and meet the lubrication requirements. The above three methods cannot well meet the actual use requirements. Summary of the Invention

[0004] An object of the present invention is to at least solve one of the technical problems existing in the prior art, and provide a cycloid gear profile modification method for a cycloid gear to improve the load-bearing capacity and rotational accuracy of the cycloid gear.

[0005] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0006] A cycloid gear profile modification method for a cycloid gear includes the following steps:

[0007] Obtain the standard tooth profile equation of the cycloid gear;

[0008] Obtain the minimum positive shift modification amount and positive equal-distance modification amount that minimize the maximum contact force F max within the meshing area between the cycloid gear and the pinwheel, and use "positive shift + positive equal-distance" modification to modify the cycloid gear into an "inverted bow" tooth profile;

[0009] Obtain the tooth profile curve equation of the cycloid gear under the "positive shift + positive equal-distance" modification method;

[0010] The modified tooth profile with "negative shift distance + negative equal distance" is used to fit the modified tooth profile curve with "positive shift distance + positive equal distance". Taking the minimum deviation value within the range of the simultaneously meshing teeth of the modified tooth profile curve with "negative shift distance + negative equal distance" and the modified tooth profile curve with "positive shift distance + positive equal distance" during the operation of the cycloid gear and the pin gear as the goal, the optimal "negative shift distance + negative equal distance" modification amount is obtained, and secondary modification is carried out using "negative shift distance + negative equal distance" to obtain the modified tooth profile equation.

[0011] In some embodiments, the standard tooth profile equation of the cycloid gear is:

[0012] Xc = (r p - r rp * S) * cos((1 - i H ) * ψ) - (a - K 1 * r rp * S) * cos(i H * ψ);

[0013] Yc = (r p - r rp * S) * sin((1 - i H ) * ψ) + (a - K 1 * r rp * S) * sin(i H * ψ);

[0014] In the formula:

[0015] Xc - The abscissa of the standard cycloid gear tooth profile curve;

[0016] Yc - The ordinate of the standard cycloid gear tooth profile curve;

[0017] r p - The radius of the center circle of the pin teeth;

[0018] r rp - The radius of the roller pin;

[0019] i H - The relative transmission ratio of the cycloid gear and the pin gear;

[0020] ψ - The rotation angle of the arm relative to the vector radius of a certain pin tooth center;

[0021] a - The eccentricity;

[0022] K 1 - The stub factor, K 1 = a * z p / r p ;

[0023] S = [1 + K 1 2 - 2 * K 1*cos(ψ)] -0.5 .

[0024] In some embodiments, the maximum contact force F in the meshing area between the cycloid wheel and the pin wheel is obtained. max The minimum positive displacement and positive isometric corrections are made using the following steps:

[0025] Calculate the minimum meshing clearance Q(ψ) at the first contact point between the cycloid wheel and the pin wheel T );

[0026] Find the maximum deformation δ between the cycloid wheel and the pinwheel teeth T ;

[0027] Find the number of teeth that mesh simultaneously when the cycloid wheel and the pin wheel are working;

[0028] Calculate the contact force F between the cycloid wheel and the needle teeth at the point of maximum deformation T ;

[0029] Calculate the force F on the i-th tooth when the cycloid wheel and the pin wheel are meshing and transmitting force at the same time i ;

[0030] Find the minimum value of the maximum contact force between the cycloid wheel and the pin wheel in the entire meshing area;

[0031] Correction amount Δr by positive isometric rp1 is the independent variable, and the minimum value F of the maximum contact force between the cycloid wheel and the pin wheel in the entire meshing area max is the dependent variable, find Δr rp1 With F max The change relationship between the cycloid wheel and the pin wheel is used to obtain the maximum contact force F in the meshing area between the cycloid wheel and the pin wheel. max The minimum positive isometric modification value Δr rp1 , positive displacement modification amount Δr p1 =Δr rp1 -Δ 1 , Δr p1 >0,Δr rp1 >0.

[0032] In some embodiments, the following formula is used to calculate the minimum meshing clearance Q (ψ T ):

[0033] V=-Δr rp1 / Δr p1 ;

[0034] ψ T1 =arccos{(V 2 -1) / (V 2 *K 1 )+[(1-V 2 )2 -V 2 *(V 2 -1-K 1 2 )] 0.5 / (V 2 *K 1 )};

[0035] ψ T2 =arccos{(V 2 -1) / (V 2 *K 1 )-[(1-V 2 ) 2 -V 2 *(V 2 -1-K 1 2 )] 0.5 / (V 2 *K 1 )};

[0036] Calculate the initial backlash of the cycloid gear at points ψ T1 、ψ T2 :

[0037] Q(ψ T1 )=Δr rp1 *[1 - sin(ψ T1 )*S] - Δr p1 *[1 - K 1 *cos(ψ T1 ) - (1 - K 1 2 ) 0.5 *sin(ψ T1 )]*S;

[0038] Q(ψ T2 )=Δr rp1 *[1 - sin(ψ T2 )*S] - Δr p1 *[1 - K 1 *cos(ψ T2 ) - (1 - K 1 2 ) 0.5 *sin(ψ T2 )]*S;

[0039] Where: S = (1 + K 1 2 - 2*K 1 *cos(ψ)) -0.5 , ψ are substituted by ψ T1 、ψ T2 respectively;

[0040] Compare Q(ψ T1 ) with Q(ψ T2 ). The first contact point ψ T of the cycloid gear and the pin gear in mesh is the rotation angle value of the smaller value between Q(ψ T1 ) and Q(ψ T2 ); The minimum meshing clearance Q(ψ T ) = min[Q(ψ T1 ), Q(ψ T2 )];

[0041] The following formula is used to obtain the maximum deformation δ T between the cycloid gear and the pin gear teeth:

[0042] δ T = 2*(1 - μ 2 ) / E*F T / (π*b)*(2 / 3 + ln(16*r rp *|ρ| / c 2 ));

[0043] In the formula:

[0044] δ T ——The maximum deformation between the cycloid gear and the pin teeth;

[0045] μ——Poisson's ratio;

[0046] E——Elastic modulus;

[0047] F T ——The contact force of the pin teeth at the maximum deformation between the cycloid gear and the pin gear teeth;

[0048] b——The tooth width of the cycloid gear;

[0049] ρ——The radius of curvature of the tooth profile of the cycloid gear at ψ T ;

[0050] ρ = r p *(1 + K 1 2 - 2*K 1 *cos(ψ T )) 1.5 / [K 1 *(z P + 1)*cos(ψ T ) - (1 + z p *K 1 2 )] + r rp , z p ——The number of teeth of the pin gear;

[0051] c = 9.98*10 -3*[(1-μ 2 ) / E*F T / b*|ρ|*r rp / (|ρ|+r rp )] 0.5 。

[0052] In some embodiments, obtaining the number of simultaneously meshing teeth between the cycloid gear and the pin gear during operation includes the following steps:

[0053] Obtain the initial meshing clearance at any position of the cycloid gear:

[0054] Q(ψ) = Δr rp1 *[1 - sin(ψ)*S] - Δr p1 *[1 - K 1 *cos(ψ) - (1 - K 1 2 ) 0.5 *sin(ψ)]*S - Q(ψ T );

[0055] Where: S = (1 + K 1 2 - 2*K 1 *cos(ψ)) -0.5 ;

[0056] Obtain the deformation between the pin teeth and the cycloid gear at any position:

[0057] δ(ψ) = δ T *sin(ψ)*(1 + K 1 2 - 2*K 1 *cos(ψ T )) 0.5 / [sin(ψ T )*(1 + K 1 2 - 2*K 1 *cos(ψ)) 0.5 ;

[0058] At any moment, the criterion for determining whether a certain pin tooth can participate in transmission is:

[0059] δ(ψ i ) - Q(ψ i ) > 0, participate in meshing;

[0060] δ(ψ i ) - Q(ψ i ) < 0, do not participate in meshing;

[0061] Through the judgment of the above two states, the number j of the first contacting tooth and the number k of the last contacting tooth can be obtained, and the number of simultaneously contacting teeth is j - k + 1.

[0062] In some embodiments, the following formula is used to calculate the contact force F of the pin teeth at the maximum deformation between the cycloid gear and the pin teeth T :

[0063]

[0064] In the formula:

[0065] L(i) — the distance from the common normal of the i-th pin tooth meshing point or the normal of the to-be-meshing point to the center O of the cycloid gear c of;

[0066] L(i) = a * z c * sin(ψ) * (1 + K 1 2 - 2 * K 1 * cos(ψ)) -0.5 ;

[0067] In the formula:

[0068] z c — the number of teeth of the cycloid gear;

[0069] Use the iterative method to find F T ;

[0070] The following formula is used to calculate the force F of the i-th tooth when the cycloid gear and the pin gear are meshing and transmitting force simultaneously i :

[0071] F i = (δ(ψ i ) - Q(ψ i )) * F T / δ T

[0072] In the formula:

[0073] F i — the force on any i-th tooth;

[0074] Find the minimum value F max = min(F i )

[0075] In some embodiments, the cycloid gear tooth profile curve equation in the modification method of "positive shift + positive equal distance" is:

[0076] Xc1 = [r p + Δr p1 - (r rp + Δr rp1 ) * S 1 -0.5 * cos((1 - iH ) * ψ) - a / (r p + Δr p1 ) * [r p + Δr p1 - z p *(r rp + Δr rp1 ) * S 1 -0.5 * cos(i H * ψ);

[0077] Yc1 = [r p + Δr p1 -(r rp + Δr rp1 ) * S 1 -0.5 * sin((1 - i H ) * ψ) + a / (r p + Δr p1 ) * [r p + Δr p1 - z p *(r rp + Δr rp1 ) * S 1 -0.5 * sin(i H * ψ);

[0078] Wherein:

[0079] Δr p1 —— Positive shift modification amount;

[0080] Δr rp1 —— Positive equal distance modification amount;

[0081] S 1 = 1 + K 1 ’ 2 - 2 * K 1 ’* cos(ψ);

[0082] K 1 ’ = a * z p / (r p + Δr p1 ).

[0083] In some embodiments, the cycloid gear tooth profile curve equation under the modification method of "negative shift + negative equal distance" is:

[0084] Xc2 = [r p + Δr p2 -(r rp + Δr rp2 ) * S 2 -0.5*cos((1 - i H )*ψ) - a / (r p +Δr p2 )*[r p +Δr p2 -z p *(r rp +Δr rp2 )*S 2 -0.5 *cos(i H *ψ);

[0085] Yc2 = [r p +Δr p2 -(r rp +Δr rp2 )*S 2 -0.5 *sin((1 - i H )*ψ) + a / (r p +Δr p2 )*[r p +Δr p2 -z p *(r rp +Δr rp2 )*S 2 -0.5 *sin(i H *ψ);

[0086] Wherein:

[0087] Δr p2 —— Negative shift modification amount;

[0088] Δr rp2 —— Negative equal-distance modification amount;

[0089] S 2 = 1 + K 2 ’ 2 -2*K 2 ’*cos(ψ);

[0090] K 2 ’ = a*z p / (r p +Δr p2 );

[0091] Let Yc2 = Yc1, and it is required that the tooth profile curve in the "negative shift + negative equal-distance" modification method coincides with the tooth profile curve in the "positive shift + positive equal-distance" modification method within the j-k range. The coincidence index algorithm is as follows:

[0092]

[0093] Wherein:

[0094] λ —— The deviation value between the modified tooth profile curve of "negative shift + negative equal addendum" and the modified tooth profile curve of "positive shift + positive equal addendum" within the range of j - k.

[0095] In some embodiments,

[0096] Δr that makes λ obtain the minimum value p2 , Δr rp2 is the optimal "negative shift + negative equal addendum" modification amount, and the objective function and constraint conditions are established:

[0097]

[0098] Δr p2 < 0;

[0099] Δr rp2 < 0;

[0100] Δr rp2 -Δr p2 = Δ 2 ;

[0101] The obtained Δr p2 , Δr rp2 is the optimal "negative shift + negative equal addendum" modification amount.

[0102] One of the technical solutions in the above technical solutions has at least the following advantages or beneficial effects: First, find the positive shift modification amount and positive equal addendum modification amount that minimize the maximum contact force F max in the meshing area between the cycloid gear and the pin gear. Use the "positive shift + positive equal addendum" modification to shape the cycloid gear into an "inverted bow" tooth profile. However, the single "positive shift + positive equal addendum" modification method can only improve its load - carrying capacity. In order to obtain a precision cycloid speed reducer with high load - carrying capacity and certain rotational accuracy, further secondary modification is carried out on the cycloid gear modified by "positive shift + positive equal addendum". The combination modification method of "negative shift + negative equal addendum" will cause the middle part of the cycloid gear to bulge significantly, thereby reducing the geometric rotation angle and improving the rotational accuracy of the speed reducer. By adopting optimized modification parameters, the present invention improves the force transmission and precision transmission performance of the cycloid gear.

[0103] The additional aspects and advantages of the present invention will be partly given in the following description, partly will become obvious from the following description, or will be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] The above - mentioned and / or additional aspects and advantages of the present invention will become obvious and easy to understand from the description of the embodiments in conjunction with the following drawings, wherein:

[0105] Figure 1 is the meshing distribution diagram of the cycloid gear and the pin teeth;

[0106] Figure 2 This is a schematic diagram of the force distribution of the positive shift + positive equidistant shaping cycloid wheel according to an embodiment of the present invention;

[0107] Figure 3 This is an embodiment of the present invention Δr rp1 With F max The change relationship curve of

[0108] Figure 4 It is a positive shift + positive equidistant modified cycloid gear tooth profile in one embodiment of the present invention;

[0109] Figure 5 It is a "negative displacement + negative equidistance" tooth profile curve fitting the "positive displacement + positive equidistance" modified tooth profile in one embodiment of the present invention;

[0110] Figure 6 It is a curve showing the relationship between the equidistant shaping amount and the minimum rotation angle of the cycloid wheel in one embodiment of the present invention. DETAILED DESCRIPTION

[0111] This section will describe in detail the specific embodiments of the present invention. The preferred embodiments of the present invention are shown in the accompanying drawings. The purpose of the accompanying drawings is to supplement the description of the text part of the specification with graphics, so that people can intuitively and vividly understand each technical feature and the overall technical solution of the present invention, but it cannot be understood as a limitation on the scope of protection of the present invention.

[0112] See also Figure 1 , Figure 4 , Figure 5 , an embodiment of the present invention provides a cycloidal gear cycloidal tooth profile modification method, comprising the following steps:

[0113] S1 obtains the standard tooth profile equation of the cycloid gear;

[0114] S2 obtains the maximum contact force F in the meshing area between the cycloid wheel and the pin wheel max The minimum positive shift and positive equidistance shaping amount, using "positive shift + positive equidistance" shaping to shape the cycloid gear into a "reverse bow" tooth profile;

[0115] S3 obtains the cycloid gear tooth profile curve equation under the “positive shift + positive equidistance” modification mode;

[0116] S4 adopts the "negative shift + negative equidistance" modified tooth profile to fit the "positive shift + positive equidistance" modified tooth profile curve. The goal is to minimize the deviation between the "negative shift + negative equidistance" modified tooth profile curve and the "positive shift + positive equidistance" modified tooth profile curve within the range of simultaneously meshing teeth when the cycloid wheel and the pin wheel are working. The optimal "negative shift + negative equidistance" modification amount is obtained, and the "negative shift + negative equidistance" is used for secondary modification to obtain the tooth profile equation after modification.

[0117] In the embodiments of the present invention, first, the positive displacement modification amount and the positive equal distance modification amount that minimize the maximum contact force F within the meshing region between the cycloid gear and the pin gear are obtained. The cycloid gear is modified into an "inverted bow" tooth profile by using the "positive displacement + positive equal distance" modification. However, the modification method of only "positive displacement + positive equal distance" can only improve its load-carrying capacity. In order to obtain a precision cycloid reducer with high load-carrying capacity and certain rotational accuracy, the cycloid gear modified by "positive displacement + positive equal distance" is further modified. The combination modification method of "negative displacement + negative equal distance" will cause the middle part of the cycloid gear to bulge significantly, thereby reducing the geometric rotation angle and improving the rotational accuracy of the reducer. By adopting optimized modification parameters, the present invention improves the force transmission and accuracy transmission performance of the cycloid gear. max Combined with ,

[0118] , the standard tooth profile equation of the cycloid gear is:

[0118] Combined Figure 1 , the standard tooth profile equation of the cycloid gear is:

[0119] Xc = (r p -r rp *S)*cos((1 - i H )*ψ) - (a - K 1 *r rp *S)*cos(i H *ψ);

[0120] Yc = (r p -r rp *S)*sin((1 - i H )*ψ) + (a - K 1 *r rp *S)*sin(i H *ψ);

[0121] In the formula:

[0122] Xc - the abscissa of the standard cycloid gear tooth profile curve;

[0123] Yc - the ordinate of the standard cycloid gear tooth profile curve;

[0124] r p - the radius of the center circle of the pin teeth;

[0125] r rp - the radius of the roller needle;

[0126] i H - the relative transmission ratio between the cycloid gear and the pin gear;

[0127] ψ - the rotation angle of the swing arm relative to the vector radius of a certain pin tooth center;

[0128] a - the eccentricity;

[0129] K 1 - the short amplitude coefficient, K 1= a * z p / r p ;

[0130] S = [1 + K 1 2 - 2 * K 1 * cos(ψ)] -0.5 .

[0131] In some embodiments, to obtain the positive displacement modification amount and the positive equal addendum modification amount that minimize the maximum contact force F in the meshing region between the cycloid gear and the pin gear, the following steps are adopted: max S2.1 Obtain the minimum meshing clearance Q(ψ

[0132] ) at the first contact point of the meshing between the cycloid gear and the pin gear: T :

[0133] Combined with Figure 2 , there are two first contact points ψ T1 , ψ T2 in the meshing between the cycloid gear and the pin gear. The following formula is used to obtain the minimum meshing clearance Q(ψ T ) at the first contact point of the meshing between the cycloid gear and the pin gear:

[0134] V = -Δr rp1 / Δr p1 ;

[0135] ψ T1 = arccos{(V 2 - 1) / (V 2 * K 1 ) + [(1 - V 2 ) 2 - V 2 *(V 2 - 1 - K 1 2 )] 0.5 / (V 2 * K 1 )};

[0136] ψ T2 = arccos{(V 2 - 1) / (V 2 * K 1 ) - [(1 - V 2 ) 2 - V 2 *(V 2 - 1 - K 1 2 )] 0.5 / (V 2 * K 1 )};

[0137] Calculate the initial backlash of the cycloid gear at points ψ T1 and ψ T2 :

[0138] Q(ψ T1 ) = Δr rp1 *[1 - sin(ψ T1 ) * S] - Δr p1 *[1 - K 1 * cos(ψ T1 ) - (1 - K 1 2 ) 0.5 * sin(ψ T1 )] * S;

[0139] Q(ψ T2 ) = Δr rp1 *[1 - sin(ψ T2 ) * S] - Δr p1 *[1 - K 1 * cos(ψ T2 ) - (1 - K 1 2 ) 0.5 * sin(ψ T2 )] * S;

[0140] Where: S = (1 + K 1 2 - 2 * K 1 * cos(ψ)) -0.5 , and ψ are respectively substituted by ψ T1 and ψ T2 ;

[0141] Compare Q(ψ T1 ) with Q(ψ T2 ). The first contact point ψ T of the cycloid gear and the pin gear meshing is the rotation angle value of the smaller value between Q(ψ T1 ) and Q(ψ T2 ); The minimum meshing clearance Q(ψ T ) = min[Q(ψ T1 ), Q(ψ T2 )].

[0142] S2.2 Obtain the maximum deformation δ T between the teeth of the cycloid gear and the pin gear:

[0143] Combined with Figure 2 , the following formula is used to obtain the maximum deformation δ T between the teeth of the cycloid gear and the pin gear:

[0144] δ T = 2 * (1 - μ 2) / E*F T / (π*b)*(2 / 3+ln(16*r rp *|ρ| / c 2 ));

[0145] Where:

[0146] δ T ——The maximum deformation between the cycloid wheel and the needle teeth;

[0147] μ——Poisson’s ratio;

[0148] E——elastic modulus;

[0149] F T ——The contact force between the cycloid wheel and the needle teeth at the point of maximum deformation;

[0150] b——cycloid gear tooth width;

[0151] ρ——cycloid wheel at ψ T The radius of curvature of the tooth profile at ;

[0152] ρ=r p *(1+K 1 2 -2*K 1 *cos(ψ T )) 1.5 / [K 1 *(z P +1)*cos(ψ T )-(1+z p *K 1 2 )]+r rp , z p ——Number of pinwheel teeth;

[0153] c=9.98*10 -3 *[(1-μ 2 ) / E*F T / b*|ρ|*r rp / (|ρ|+r rp )] 0.5 .

[0154] S2.3 Calculate the number of teeth that mesh simultaneously when the cycloid wheel and the pin wheel are working:

[0155] Calculate the initial meshing clearance of the cycloid wheel at any position:

[0156] Q(ψ)=Δr rp1 *[1-sin(ψ)*S]-Δr p1 *[1-K 1 *cos(ψ)-(1-K 1 2) 0.5 *sin(ψ)]*S - Q(ψ T );

[0157] Where: S = (1 + K 1 2 - 2*K 1 *cos(ψ)) -0.5 ;

[0158] Obtain the deformation between the pin teeth and the cycloid gear at any position:

[0159] δ(ψ) = δ T *sin(ψ)*(1 + K 1 2 - 2*K 1 *cos(ψ T )) 0.5 / [sin(ψ T )*(1 + K 1 2 - 2*K 1 *cos(ψ)) 0.5 ;

[0160] At any moment, the criterion for judging whether a certain pin tooth can participate in transmission is:

[0161] δ(ψ i ) - Q(ψ i ) > 0, it participates in meshing;

[0162] δ(ψ i ) - Q(ψ i ) < 0, it does not participate in meshing;

[0163] By judging the above two states, the first contact tooth number j and the last contact tooth number k can be obtained, and the number of simultaneously contacting teeth is j - k + 1.

[0164] S2.4 Obtain the pin tooth contact force F at the maximum deformation position between the cycloid gear and the pin teeth T :

[0165]

[0166] Where:

[0167] L(i) - The distance from the common normal of the i-th pin tooth meshing point or the normal of the to-be-meshing point to the center O of the cycloid gear c of;

[0168] L(i) = a*z c *sin(ψ)*(1 + K 1 2 - 2*K 1 *cos(ψ))-0.5 ;

[0169] Wherein:

[0170] z c —— Number of teeth of the cycloid gear;

[0171] Use the iterative method to find F T .

[0172] S2.5 Obtain the force F on the i-th tooth when the cycloid gear and the pin gear are meshing and transmitting force simultaneously i :

[0173] F i =(δ(ψ i ) - Q(ψ i )) * F T / δ T

[0174] Wherein:

[0175] F i —— Force on any i-th tooth.

[0176] S2.6 Obtain the minimum value F of the maximum contact force between the cycloid gear and the pin gear in the entire meshing region max = min(F i );

[0177] Wherein:

[0178] F max —— Minimum value of the maximum contact force between the cycloid gear and the pin gear in the entire meshing region.

[0179] S2.7 Obtain the modification amount of "positive shift + positive equal addendum" that minimizes the maximum contact force F in the meshing region between the cycloid gear and the pin gear max Minimum:

[0180] Taking the positive equal addendum modification amount Δr rp1 as the independent variable and the minimum value F of the maximum contact force between the cycloid gear and the pin gear in the entire meshing region max as the dependent variable, find the variation relationship between Δr rp1 and F max to obtain the positive equal addendum modification amount Δr max that minimizes the maximum contact force F in the meshing region between the cycloid gear and the pin gear rp1 . Specifically, combined with Figure 3 , use Matlab to plot the variation relationship curve between Δr rp1 and F max . There is a minimum value in this variation curve. Use the golden section method in Matlab to find the optimal Δr rp1 , and the positive shift modification amount Δr p1 = Δr rp1-Δ 1 , Δr p1 > 0, Δr rp1 > 0.

[0181] Among them, in the above steps S2.1 to S2.7, the specific calculation method is as follows:

[0182] 1. Determine the range [a, b] of Δr rp1 according to experience;

[0183] 2. Take the initial value of Δr rp1 as a;

[0184] 3. According to the flow of S2.1 to S2.7, 1) obtain the minimum meshing clearance Q(ψ T ) at the first contact point of the cycloid gear and the pin gear; 2) obtain the maximum deformation δ T between the cycloid gear and the pin gear teeth. During the process of obtaining δ T , first give an initial value to F T , and the accurate value can be obtained by the iterative method later; 3) obtain the number of simultaneously meshing teeth when the cycloid gear and the pin gear are working; 4) obtain the pin tooth contact force F T at the maximum deformation between the cycloid gear and the pin teeth. At this time, the obtained F T is not equal to the value obtained in step "2)"; 5) substitute the F T obtained in step "4)" into steps "2)", "3)", and "4)" (iterative method) until the difference between the input F T and the output F T meets certain requirements, then the iteration ends. At this time, F T is what we want; obtain the force F i on the i-th tooth where the cycloid gear and the pin gear are simultaneously meshing and transmitting force;

[0185] 4. Obtain the minimum value of the maximum contact force between the cycloid gear and the pin gear in the entire meshing region, F max = min(F i );

[0186] 5. In the interval [a, b], each Δr rp1 corresponds to a unique F max . The Δr rp1 and F max variation curves can be obtained. The Δr max when F rp1 takes the minimum value is the optimal positive equal-distance modification amount.

[0187] The modification method of "positive shift + positive equal-distance" can obtain more pin teeth participating in meshing, but it is difficult to meet the requirement of small backlash. Therefore, it is generally applied to large torque transmission with low precision requirements.

[0188] In step S3, the cycloid gear tooth profile curve equation under the modification method of "positive shift + positive equal distance" is as follows:

[0189] Xc1 = [r p +Δr p1 -(r rp +Δr rp1 )*S 1 -0.5 *cos((1 - i H )*ψ) - a / (r p +Δr p1 )*[r p +Δr p1 - z p *(r rp +Δr rp1 )*S 1 -0.5 *cos(i H *ψ);

[0190] Yc1 = [r p +Δr p1 -(r rp +Δr rp1 )*S 1 -0.5 *sin((1 - i H )*ψ) + a / (r p +Δr p1 )*[r p +Δr p1 - z p *(r rp +Δr rp1 )*S 1 -0.5 *sin(i H *ψ);

[0191] In the formula:

[0192] Δr p1 —— Positive shift modification amount;

[0193] Δr rp1 —— Positive equal distance modification amount;

[0194] S 1 = 1 + K 1 ’ 2 - 2*K 1 ’*cos(ψ);

[0195] K 1 ’ = a*z p / (r p +Δr p1 ).

[0196] Step S4 further includes the following steps:

[0197] S4.1 Obtain the cycloid gear tooth profile curve equation under the modification method of "negative shift + negative equal distance":

[0198] Xc2 = [r p +Δr p2 -(r rp +Δr rp2 )*S 2 -0.5 *cos((1 - i H )*ψ)-a / (r p +Δr p2 )*[r p +Δr p2 -z p *(r rp +Δr rp2 )*S 2 -0.5 *cos(i H *ψ);

[0199] Yc2 = [r p +Δr p2 -(r rp +Δr rp2 )*S 2 -0.5 *sin((1 - i H )*ψ)+a / (r p +Δr p2 )*[r p +Δr p2 -z p *(r rp +Δr rp2 )*S 2 -0.5 *sin(i H *ψ);

[0200] In the formula:

[0201] Δr p2 —— Negative shift modification amount;

[0202] Δr rp2 —— Negative equal distance modification amount;

[0203] S 2 = 1 + K 2 ’ 2 - 2*K 2 ’*cos(ψ);

[0204] K 2 ’ = a*z p / (r p +Δr p2 ).

[0205] S4.2 "Negative shift + negative equal addendum modification" profile fitting for "positive shift + positive equal addendum modification" profile curve

[0206] Let Yc2 = Yc1, and require the profile curve under the "negative shift + negative equal addendum modification" method to coincide with the profile curve under the "positive shift + positive equal addendum modification" method within the range of j - k. The coincidence index algorithm is as follows:

[0207]

[0208] In the formula:

[0209] λ —— Deviation value between the "negative shift + negative equal addendum modification" profile curve and the "positive shift + positive equal addendum modification" profile curve within the range of j - k.

[0210] S4.3 Using the Matlab optimization toolbox to obtain the optimal "negative shift + negative equal addendum modification" amount

[0211] The Δr p2 , Δr rp2 that makes λ reach the minimum value is the optimal "negative shift + negative equal addendum modification" amount. Establish the objective function and constraint conditions:

[0212]

[0213] Δr p2 < 0;

[0214] Δr rp2 < 0;

[0215] Δr rp2 -Δr p2 = Δ 2 ;

[0216] The obtained Δr p2 , Δr rp2 is the optimal "negative shift + negative equal addendum modification" amount.

[0217] The embodiments of the present invention may further include the following steps:

[0218] S5 Verifying the load - bearing capacity and rotational accuracy of the final modified profile curve

[0219] Since the Δr p2 , Δr rp2It has a high degree of fitting with the tooth profile curve under the "positive shift + positive equal distance" modification method. It has been proven that the tooth profile curve under the "positive shift + positive equal distance" modification method has the ability to increase the load-carrying capacity. Now, it is proven that the "negative shift + negative equal distance" modification can improve the rotational accuracy of the cycloid gear. The calculation of the minimum rotation angle of the cycloid gear is as follows:

[0220] β min =[-Δr p* (1 - K 1 2 ) 0.5 +Δr rp / (a * z c )

[0221] Combined with Figure 6 , Δr rp and β min are in a direct proportional relationship. The smaller Δr rp , the smaller β min is also.

[0222] The cycloid tooth profile modified by the method described in the present invention can ensure a certain rotational accuracy of the precision cycloid speed reducer while reducing the contact force of the cycloid gear, thereby improving the load-carrying capacity of the speed reducer.

[0223] In the description of this specification, the descriptions referring to terms such as "example", "embodiment" or "some embodiments" etc. mean that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0224] Certainly, the present invention is not limited to the above embodiments. Those skilled in the art can also make equivalent deformations or substitutions without departing from the spirit of the present invention, and these equivalent deformations or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A method for modifying the cycloid tooth profile of a cycloid wheel, It is characterized in that The following steps are involved: Obtain the standard tooth profile equation of the cycloid gear; Find the maximum contact force F within the meshing area between the cycloid gear and the pin gear max The minimum positive shift modification amount and positive equal addendum modification amount, and use the "positive shift + positive equal addendum" modification to modify the cycloid gear into an "inverted bow" tooth profile; Obtain the equation of the cycloid gear tooth profile curve under the "positive shift + positive equidistance" modification method; The "negative shift + negative equidistance" modified tooth profile is used to fit the "positive shift + positive equidistance" modified tooth profile curve. The goal is to minimize the deviation between the "negative shift + negative equidistance" modified tooth profile curve and the "positive shift + positive equidistance" modified tooth profile curve within the range of simultaneously meshing teeth when the cycloid wheel and the pin wheel are working. The optimal "negative shift + negative equidistance" modification amount is obtained, and the "negative shift + negative equidistance" is used for secondary modification to obtain the tooth profile equation after modification.

2. The cycloid gear cycloid tooth profile modification method according to claim 1, It is characterized in that The standard tooth profile equation of the cycloid gear is: Xc = (r p - r rp * S) * cos((1 - i H ) * ψ) - (a - K 1 * r rp * S) * cos(i H * ψ); Yc = (r p - r rp * S) * sin((1 - i H ) * ψ) + (a - K 1 * r rp * S) * sin(i H * ψ); Where: Xc——abscissa of standard cycloid gear tooth profile curve; Yc——the ordinate of the standard cycloid gear tooth profile curve; r p ——Radius of the center circle of the pin teeth; r rp —— Needle roller radius; i H —— relative transmission ratio between cycloid gear and pin gear; ψ——the rotation angle of the rotating arm relative to the central vector radius of a certain needle tooth; a——eccentricity; K 1 —— Shortening coefficient, K 1 = a * z p / r p ; S = [1 + K 1 2 - 2 * K 1 * cos(ψ)] -0.5 。 3. The cycloid gear cycloid tooth profile modification method according to claim 2, It is characterized in that Find the maximum contact force F within the meshing region between the cycloid gear and the pin gear max The minimum positive shift modification amount and positive equal-distance modification amount are obtained by the following steps: Obtain the minimum meshing clearance Q(ψ T ) at the first contact point of the cycloid gear and the pin gear; Obtain the maximum deformation δ between the cycloid gear and the pin gear teeth T ; Find the number of teeth that mesh simultaneously when the cycloid wheel and the pin wheel are working; Obtain the pin tooth contact force F at the maximum deformation between the cycloid gear and the pin teeth T ; Obtain the force \(F\) on the \(i\)-th tooth where the cycloid gear and the pin gear are simultaneously meshing and transmitting force i ; Find the minimum value of the maximum contact force between the cycloid wheel and the pin wheel in the entire meshing area; With the positive equidistant modification amount Δr rp1 as the independent variable and the minimum value F of the maximum contact force between the cycloid gear and the pin gear in the entire meshing region max as the dependent variable, find Δr rp1 and F max 's variation relationship, and obtain the positive equidistant modification amount Δr that minimizes the maximum contact force F in the meshing region between the cycloid gear and the pin gear max . The positive shift modification amount Δr rp1 =Δr p1 -Δ rp1 , where Δr 1 >0 and Δr p1 >0. rp1 >0.

4. The cycloid gear cycloid tooth profile modification method according to claim 3, It is characterized in that The minimum meshing clearance Q(ψ T ) at the first contact point of the cycloid gear and the pin gear is obtained by using the following formula: V = -Δr rp1 / Δr p1 ; ψ T1 = arccos{(V 2 - 1) / (V 2 * K 1 ) + [(1 - V 2 ) 2 - V 2 *(V 2 - 1 - K 1 2 )] 0.5 / (V 2 * K 1 )}; ψ T2 = arccos{(V 2 - 1) / (V 2 * K 1 ) - [(1 - V 2 ) 2 - V 2 *(V 2 - 1 - K 1 2 )] 0.5 / (V 2 * K 1 )}; Calculate the initial backlash of the cycloid gear at the point ψ T1 , ψ T2 : Q(ψ T1 ) = Δr rp1 * [1 - sin(ψ T1 ) * S] - Δr p1 * [1 - K 1 * cos(ψ T1 ) - (1 - K 1 2 ) 0.5 * sin(ψ T1 )] * S; Q(ψ T2 ) = Δr rp1 * [1 - sin(ψ T2 ) * S] - Δr p1 * [1 - K 1 * cos(ψ T2 ) - (1 - K 1 2 ) 0.5 * sin(ψ T2 )] * S; Where: S = (1 + K 1 2 - 2 * K 1 * cos(ψ)) -0.5 , ψ are respectively substituted by ψ T1 , ψ T2 ; Compare Q(ψ T1 ), with Q(ψ T2 ). The first contact point ψ T of the cycloid gear and the pin gear engagement is the rotation angle value of the smaller value in Q(ψ T1 ) and Q(ψ T2 ); The minimum engagement clearance Q(ψ T ) = min[Q(ψ T1 ), Q(ψ T2 )]; The maximum deformation δ between the cycloid gear and the pin gear teeth is obtained by using the following formula T :[[-END]] δ T = 2 * (1 - μ 2 ) / E * F T / (π * b) * (2 / 3 + ln(16 * r rp * |ρ| / c 2 )); Where: δ T —— The maximum deformation between the cycloid gear and the pin teeth; μ——Poisson’s ratio; E——elastic modulus; F T —— Contact force of the pin tooth at the maximum deformation between the cycloid gear and the pin teeth; b——cycloid gear tooth width; ρ——The radius of curvature of the tooth profile of the cycloid gear at ψ T ; ρ = r p *(1 + K 1 2 - 2*K 1 *cos(ψ T )) 1.5 / [K 1 *(z P + 1)*cos(ψ T ) - (1 + z p *K 1 2 )] + r rp , z p —— Number of teeth of the pinwheel; c = 9.98*10 -3 *[(1 - μ 2 ) / E * F T / b * |ρ| * r rp / (|ρ| + r rp )] 0.5 。 5. The cycloid gear cycloid tooth profile modification method according to claim 4, It is characterized in that The following steps are involved in obtaining the number of teeth that are simultaneously engaged when the cycloid wheel and the pin wheel are working: Calculate the initial meshing clearance of the cycloid wheel at any position: Q(ψ) = Δr rp1 *[1 - sin(ψ)*S] - Δr p1 *[1 - K 1 *cos(ψ) - (1 - K 1 2 ) 0.5 *sin(ψ)]*S - Q(ψ T ); Where: S = (1 + K 1 2 - 2 * K 1 * cos(ψ)) -0.5 ; Find the deformation between the pin teeth and the cycloid wheel at any position: δ(ψ) = δ T *sin(ψ)*(1 + K 1 2 -2*K 1 *cos(ψ T )) 0.5 / [sin(ψ T )*(1 + K 1 2 -2*K 1 *cos(ψ)) 0.5 ; At any time, the sign of whether a certain needle tooth can participate in the transmission is: δ(ψ i ) - Q(ψ i ) > 0, engage in meshing; δ(ψ i ) - Q(ψ i ) < 0, does not participate in meshing; By judging the above two states, the first contact tooth number j and the last contact tooth number k can be obtained, and the number of contact teeth is j-k+1.

6. The cycloid gear cycloid tooth profile modification method according to claim 5, It is characterized in that The following formula is used to calculate the pin tooth contact force F at the maximum deformation between the cycloid gear and the pin teeth T :[[]]END]] Where: L(i) —— The distance from the common normal line of the i-th pin engagement point or the normal line of the to-be-engaged point to the center O of the cycloid gear c ; L(i) = a * z c * sin(ψ) * (1 + K 1 2 - 2 * K 1 * cos(ψ)) -0.5 ; Where: z c —— number of teeth of cycloid gear; Use the iterative method to find F T ; The force \(F\) on the \(i\)-th tooth when the cycloid gear and the pin gear are meshing and transmitting force simultaneously is obtained by using the following formula i : F i = (δ(ψ i ) - Q(ψ i )) * F T / δ T Where: F i —— the force on any ith tooth; Obtain the minimum value F of the maximum contact force between the cycloid gear and the pin gear in the entire meshing region max = min(F i ).

7. The cycloid gear cycloid tooth profile modification method according to claim 2, It is characterized in that The equation of the cycloid gear tooth profile curve under the "positive shift + positive equidistance" modification method is: Xc1 = [r p + Δr p1 -(r rp + Δr rp1 ) * S 1 -0.5 * cos((1 - i H ) * ψ) - a / (r p + Δr p1 ) * [r p + Δr p1 - z p *(r rp + Δr rp1 ) * S 1 -0.5 * cos(i H * ψ); Yc1 = [r p +Δr p1 -(r rp +Δr rp1 )*S 1 -0.5 *sin((1 - i H )*ψ)+a / (r p +Δr p1 )*[r p +Δr p1 -z p *(r rp +Δr rp1 )*S 1 -0.5 *sin(i H *ψ); Where: Δr p1 —— Positive shift modification amount; Δr rp1 —— Positive equal-spacing modification amount; S 1 = 1 + K 1 ’ 2 - 2 * K 1 ’ * cos(ψ); K 1 ’ = a * z p / (r p + Δr p1 )。 8. The cycloid gear cycloid tooth profile modification method according to claim 7, It is characterized in that The equation of the cycloid gear tooth profile curve under the modification method of "negative displacement + negative equidistance" is: Xc2 = [r p +Δr p2 -(r rp +Δr rp2 )*S 2 -0.5 *cos((1 - i H )*ψ) - a / (r p +Δr p2 )*[r p +Δr p2 -z p *(r rp +Δr rp2 )*S 2 -0.5 *cos(i H *ψ); Yc2 = [r p +Δr p2 -(r rp +Δr rp2 )*S 2 -0.5 *sin((1 - i H )*ψ)+a / (r p +Δr p2 )*[r p +Δr p2 -z p *(r rp +Δr rp2 )*S 2 -0.5 *sin(i H *ψ); Where: Δr p2 —— Negative shift modification amount; Δr rp2 —— Negative equal-spacing modification amount; S 2 = 1 + K 2 ’ 2 - 2 * K 2 ’ * cos(ψ); K 2 ’ = a * z p / (r p + Δr p2 ); Let Yc2 = Yc1, and require the tooth profile curve under the "negative displacement + negative equidistance" modification mode to be consistent with the tooth profile curve under the "positive displacement + positive equidistance" modification mode in the jk range. The matching index algorithm is as follows: Where: λ——The deviation value between the modified tooth profile curve of "negative displacement + negative equidistance" and the modified tooth profile curve of "positive displacement + positive equidistance" within the range of jk.

9. The method for modifying the cycloid tooth profile of a cycloid wheel according to claim 8, It is characterized in that Δr that minimizes λ p2 and Δr rp2 are the optimal "negative shift + negative equal distance" modification amounts. Establish the objective function and constraint conditions: Δr p2 < 0; Δr rp2 < 0; Δr rp2 -Δr p2 =Δ 2 ; The obtained Δr p2 , Δr rp2 is the optimal modification amount of "negative shift + negative equal distance".

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