A method for selecting cycloid gear meshing pair and needle roller specifications

Abstract

The present invention discloses a cycloid gear meshing pair and a method for selecting needle roller specifications thereof, wherein the meshing pair comprises: a cycloid gear, a needle roller and a rolling groove having double-line contact with the needle roller. The method comprises: inputting cycloid gear forming parameters, a measuring rod diameter, a distance from the center of the measuring rod to the center of the cycloid gear, a distance between two geometric centers of rolling grooves in a 180-degree direction, a radius of a cycloid gear meshing starting point and a radius of a cycloid gear meshing ending point, solving geometric parameter equidistant shaping and shifting parameters, selecting needle rollers according to equidistant shaping, a virtual tooth top circle diameter calculated according to shaping, a tooth root circle diameter, a preset interference amount and a rolling groove distribution circle diameter, and the meshing pair and method improve the reliability of the cycloid gear during operation and the stability of assembly, and achieve the effect of improving the precise control of backlash and backlash.

Description

Technical Field

[0001] The invention discloses a cycloid gear meshing pair and a method for selecting needle roller specifications, and belongs to the technical field of industrial robot reducers. Background Art

[0002] As an important part of the robot reducer, among the various factors that affect the backlash and hysteresis of the reducer, the positioning and matching relationship between the cycloid gear, the needle roller and the rolling groove are several of them. At present, the rolling groove in the reducer is a semicircular arc tooth profile with an actual diameter larger than the actual diameter of the needle roller. The needle roller swings back and forth in the rolling groove, affecting the backlash, hysteresis and transmission accuracy of the reducer. On the other hand, the tooth top and root of the cycloid gear have been modified, or there are machining errors between the tooth top and the tooth root. It is not appropriate to use the actual tooth top diameter and root diameter of the cycloid gear as the basis for selection. Blindly selecting the cross-bar distance to select the root circle diameter of the pin gear ring and the needle roller will bury the hidden danger of the instability of the backlash and hysteresis of the reducer. The tooth side of the cycloid gear hides the geometric parameter information of the equidistant modification and the shift modification, which is very important for size selection. Summary of the invention

[0003] In order to solve the above problems, the present invention adopts the following technical solutions.

[0004] The present invention first provides a cycloidal gear meshing pair, which includes a cycloidal gear, a needle roller and a rolling groove; the rolling groove and the needle roller are in double-line contact, and the rolling groove consists of two sections of elliptical curves and circular arcs connected between the two sections of the elliptical curves and tangent to the two sections of the elliptical curves at both ends; on a cross section perpendicular to the central axis of the needle roller, the angle between the line connecting the contact point of the needle roller and the rolling groove and the geometric center point of the rolling groove and the horizontal axis is β, the length of the minor semi-axis of the ellipse of the rolling groove elliptical curve segment is half of the radius of the needle roller, and the length of the major semi-axis of the ellipse is the radius of the needle roller multiplied by cosβ.

[0005] As a preferred solution of the present invention, the center of the needle roller coincides with the geometric center of the rolling groove.

[0006] The present invention also provides a method for selecting the roller specifications of the cycloid gear meshing pair, which comprises the following steps:

[0007] 1) Input the cycloid gear forming parameters and the diameters of the two measuring rods D lb1 and D lb2 , the distances M1 and M2 from the centers of the two measuring rods to the center of the cycloid gear, the distance dp between the geometric centers of the two rolling grooves in the 180-degree direction (i.e., the rolling groove distribution circle diameter dp), the radius of the cycloid gear meshing starting point and the radius of the cycloid gear meshing ending point; the cycloid gear forming parameters include the eccentricity e, the pin gear ring distribution circle radius, and the pin roller radius r p , number of teeth of the pinion ring z p , number of teeth of cycloid gear z c , needle roller radius rrp , tooth top modification amount, tooth root modification amount, on the section perpendicular to the center axis of the needle roller, the angle β between the line connecting the contact point between the needle roller and the rolling groove and the geometric center point of the rolling groove and the horizontal axis, the length of the major semi-axis of the ellipse, and the radius R of the tangent arc;

[0008] 2) Solve the nonlinear equations to obtain the isometric modification Δr rp , displacement parameter Δr p , the meshing angles corresponding to the contact points between the two measuring rods and the tooth profile and

[0009] 3) Calculate the radius of the contact point between the measuring rod and the cycloid gear tooth profile; determine whether the contact point exceeds the meshing area; if not, execute step 4); if the contact point between a measuring rod and the cycloid gear tooth profile exceeds the meshing area, return to step 1) and adjust the diameter D of the measuring rod lb , the distance M from the center of the measuring rod to the center of the cycloid wheel;

[0010] 4) Calculate the isometric modification Δr rp , displacement parameter Δr p The corresponding virtual cycloid gear root circle diameter df and cycloid gear tip circle diameter da;

[0011] 5) Select needle rollers according to the virtual cycloid gear root circle diameter df, the cycloid gear addendum circle diameter da, the preset interference and the rolling groove distribution circle diameter dp; the needle roller specifications satisfy the relationship: preset minimum interference ≤ dp-(df+da) / 2-d ≤ preset maximum interference; output the needle roller diameter.

[0012] As a preferred embodiment of the present invention, the nonlinear equations in step 2) include:

[0013] Equation 1: y E +(D lb / 2-r rp -Δr p )·cosα=M

[0014] Among them, y E D is the ordinate of the contact point between the measuring rod and the theoretical tooth profile of the cycloid gear; lb is the diameter of the measuring rod. According to the selected measuring rod, D lb Take D lb1 or D lb2 ; M is the distance from the center of the measuring rod to the center of the cycloid gear. Depending on the selected measuring rod, M is M1 or M2; α is the tangent inclination angle of the contact point between the measuring rod and the cycloid gear tooth profile. Depending on the selected measuring rod, α is α1 or α2;

[0015]

[0016]

[0017] x E is the horizontal coordinate of the contact point between the measuring rod and the theoretical tooth profile of the cycloid gear;

[0018]

[0019] Equation 2:

[0020] Among them, the parameters

[0021] The equation 1 can be simplified to The distance M1 from the center of the measuring rod to the center of the cycloid gear, the diameter of the measuring rod D lb1 When , the equation is The distance from the center of the measuring rod to the center of the cycloid gear is M2, and the diameter of the measuring rod is D lb2 When , the equation is

[0022] The equation 2 can be simplified to The distance M1 from the center of the measuring rod to the center of the cycloid gear, the diameter of the measuring rod D lb1 When , the equation is The distance from the center of the measuring rod to the center of the cycloid gear is M2, and the diameter of the measuring rod is D lb2 When , the equation is

[0023] Specifically, the nonlinear equations described in step 2) are based on Δr p , Δr p and Nonlinear equations; Substitute the distance M1 from the center of the measuring rod to the center of the cycloid gear and the diameter D of the measuring rod into the nonlinear equations. lb1 When the above equations 1 and 2 are expressed as Substitute the distance M2 from the center of the measuring rod to the center of the cycloid gear and the diameter D of the measuring rod. lb2 When the above equations 1 and 2 are expressed as So the four unknowns Δ rp ,Δr p , and Composed of four nonlinear equations, forming a nonlinear equation system:

[0024]

[0025] Solving it gives Δ rp , Δr p ,

[0026] As a preferred embodiment of the present invention, the tangent inclination angle α of the contact point between the measuring rod and the cycloid gear tooth profile satisfies the following equation:

[0027]

[0028] As a preferred embodiment of the present invention, the diameter D of the measuring rod lb Satisfies the following equation:

[0029]

[0030] As a preferred solution of the present invention, in step 4), the isometric modification Δr is calculated. rp , displacement parameter Δr p The corresponding virtual cycloid gear root circle diameter df = r p -er rp -Δ rp +Δr p , the corresponding virtual cycloid gear tip circle diameter da = r p +er rp -Δ rp +Δr p .

[0031] The present invention adopts a double elliptical rolling groove. While ensuring that the distribution circle diameter of the needle roller installed in the rolling groove is equal to the distribution circle diameter in the cycloidal wheel forming parameter, there are gaps on the left and right sides and top of the needle roller, providing space for oil storage and heat dissipation. There are two line contacts between the needle roller and the rolling groove, which limit its four degrees of freedom. The rotational freedom of the needle roller around itself is not limited. Compared with the original single arc structure, the present invention improves the positioning accuracy of the meshing pair and avoids the shaking of the needle roller in the rolling groove; the double line contact reduces the contact stress of the rolling groove and reduces the risk of wear. The present invention calculates the parameter equidistant shaping Δr by the distance M from the center of the measuring rod to the center of the cycloidal wheel and the corresponding measuring rod diameter. rp and displacement parameter Δr p , and then find the corresponding virtual tooth top circle diameter and tooth root circle diameter, and select the matching needle roller specifications according to the distance dp and preload of the two rolling grooves in the 180-degree direction, thereby improving the matching accuracy. This meshing pair and method improves the reliability of the cycloid gear during operation and the stability of assembly, achieving the effect of precise control of tooth gap and backlash. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a structural schematic diagram of a cycloid gear meshing pair of the present invention;

[0033] Figure 2 This is a schematic diagram of the structure of the cycloid gear meshing pair before improvement;

[0034] Figure 3It is a schematic diagram of the distance M from the center of the measuring rod to the center of the cycloid wheel;

[0035] Figure 4 It is a schematic diagram of the distance dp between the geometric centers of two rolling grooves in a 180-degree direction;

[0036] Figure 5 It is a flow chart of the control method of the present invention. DETAILED DESCRIPTION

[0037] The present invention is further described and illustrated below in conjunction with specific embodiments. The embodiments are merely exemplary of the present disclosure and do not define the scope of limitation. The technical features of each embodiment of the present invention may be combined accordingly without conflicting with each other.

[0038] like Figure 1 , 3 -5, this embodiment discloses a cycloidal gear meshing pair, which includes a cycloidal gear, a needle roller and a groove. As a preferred embodiment of the present invention, the groove and the needle roller are in double-line contact in theory, and the groove is composed of two elliptical curves and a circular arc tangent thereto. As a preferred embodiment of the present invention, the angle between the contact line between the needle roller and the groove and the line connecting the geometric center of the groove and the horizontal axis is β, the length of the minor semi-axis of the ellipse of the groove is half of the radius of the needle roller, and the length of the major semi-axis of the ellipse is the radius of the needle roller multiplied by cosβ. The center of the needle roller coincides with the geometric center of the groove.

[0039] The present invention further provides a method for selecting the needle roller specifications of the above-mentioned cycloid gear meshing pair, which comprises the following steps:

[0040] 1) Input the cycloid gear forming parameters and the diameters of the two measuring rods D lb1 and D lb2 , the distances M1 and M2 from the centers of the two measuring rods to the center of the cycloid gear, the distance dp between the geometric centers of the two rolling grooves in the 180-degree direction (i.e., the rolling groove distribution circle diameter dp), the radius of the cycloid gear meshing starting point and the radius of the cycloid gear meshing ending point; the cycloid gear forming parameters include the eccentricity e, the pin gear ring distribution circle radius, and the pin roller radius r p , number of teeth of the pinion ring z p , number of teeth of cycloid gear z c , needle roller radius r rp , tooth top modification amount, tooth root modification amount, on the section perpendicular to the center axis of the needle roller, the angle β between the line connecting the contact point between the needle roller and the rolling groove and the geometric center point of the rolling groove and the horizontal axis, the length of the major semi-axis of the ellipse, and the radius R of the tangent arc;

[0041] 2) Solve the nonlinear equations to obtain the isometric modification Δr rp , displacement parameter Δr p , the meshing angles corresponding to the contact points between the two measuring rods and the tooth profile and

[0042] The nonlinear system of equations consists of two equations:

[0043] Equation 1: y E +(D lb / 2-r rp -Δr p )·cosα=M

[0044] Among them, y E D is the ordinate of the contact point between the measuring rod and the theoretical tooth profile of the cycloid gear; lb is the diameter of the measuring rod. According to the selected measuring rod, D lb Take D lb1 or D lb2 ; M is the distance from the center of the measuring rod to the center of the cycloid gear. Depending on the selected measuring rod, M is M1 or M2; α is the tangent inclination angle of the contact point between the measuring rod and the cycloid gear tooth profile. Depending on the selected measuring rod, α is α1 or α2;

[0045]

[0046]

[0047] x E is the horizontal coordinate of the contact point between the measuring rod and the theoretical tooth profile of the cycloid gear;

[0048]

[0049] Equation 2:

[0050] Among them, the parameters

[0051] The equation 1 can be simplified to The distance M1 from the center of the measuring rod to the center of the cycloid gear, the diameter of the measuring rod D lb1 When , the equation is The distance from the center of the measuring rod to the center of the cycloid gear is M2, and the diameter of the measuring rod is D lb2 When , the equation is

[0052] The equation 2 can be simplified to The distance M1 from the center of the measuring rod to the center of the cycloid gear, the diameter of the measuring rod D lb1 When , the equation is The distance from the center of the measuring rod to the center of the cycloid gear is M2, and the diameter of the measuring rod is D lb2 When , the equation is

[0053] The nonlinear equations described in step 2) are based on Δr p , Δr p and Nonlinear equations; Substitute the distance M1 from the center of the measuring rod to the center of the cycloid gear and the diameter D of the measuring rod into the nonlinear equations. lb1 When the above equations 1 and 2 are expressed as Substitute the distance M2 from the center of the measuring rod to the center of the cycloid gear and the diameter D of the measuring rod. lb2 When the above equations 1 and 2 are expressed as So the four unknowns Δ rp ,Δr p , and Composed of four nonlinear equations, forming a nonlinear equation system:

[0054]

[0055] Solving it gives Δ rp , Δr p ,

[0056] 3) Calculate the radius of the contact point between the measuring rod and the cycloid gear tooth profile; determine whether the contact point exceeds the meshing area; if not, execute step 4); if the contact point between a measuring rod and the cycloid gear tooth profile exceeds the meshing area, return to step 1) and adjust the diameter D of the measuring rod lb , the distance M from the center of the measuring rod to the center of the cycloid wheel;

[0057] 4) Calculate the isometric modification Δr rp , displacement parameter Δr p The corresponding virtual cycloid gear root circle diameter df and cycloid gear tip circle diameter da; df = r p -er rp -Δ rp +Δr p , da=r p +er rp -Δ rp +Δr p .

[0058] 5) Select needle rollers according to the virtual cycloid gear root circle diameter df, the cycloid gear addendum circle diameter da, the preset interference and the rolling groove distribution circle diameter dp; the needle roller specifications satisfy the relationship: preset minimum interference ≤ dp-(df+da) / 2-d ≤ preset maximum interference; output the needle roller diameter.

[0059] The following is a description of the effects of the present invention in conjunction with the data:

[0060] Taking the cycloid gear parameters of a cycloid reducer as an example, the cycloid gear forming parameters are: eccentricity e = 1.3mm, the radius of the pin gear ring distribution circle is the radius of the needle roller r p =64mm, number of teeth of pinion ring z p =40, number of teeth of cycloid gear z c =39, roller radius r rp =3mm, tooth top modification amount 0.1mm, tooth root modification amount 0.1mm, cycloid gear meshing starting point radius = 59.793mm and cycloid gear meshing end point radius = 62.293mm; the angle between the contact point between the needle roller and the groove and the line connecting the geometric center of the groove and the horizontal axis is β = 30°, the length of the major semi-axis of the ellipse is 2.598mm, and the radius of the tangent arc is R = 91.5mm. The distance from the center of the measuring rod to the center of the cycloid wheel is M1 = 63.501mm, and the diameter of the measuring rod is D lb1 =7mm, the distance from the center of the measuring rod to the center of the cycloid wheel M2 = 64.256mm, the diameter of the measuring rod D lb2 =8mm; the distance between the geometric centers of the two rolling grooves at 180 degrees is dp = 127.971mm. Substitute the above related data into the following equations:

[0061] y E +(D lb / 2-r rp -Δ rp )·cosα=M

[0062] in,

[0063] in,

[0064] The above two equations are composed of Δ rp , Δr p and When M1 = 63.501 mm, the diameter of the measuring rod D lb1 =7mm, the above nonlinear equation is recorded as When M2=64.256mm, the diameter of the measuring rod is D lb2 =8mm, the above nonlinear equation is recorded as So the four unknowns Δ rp ,Δr p , and Composed of four nonlinear equations, forming a nonlinear equation system:

[0065]

[0066] Find Δ rp =-0.013mm, Δrp =0.032mm, The radius of the contact point between the measuring rod with a diameter of 7mm and the cycloidal gear tooth profile is calculated to be 61.383mm, and the radius of the contact point between the measuring rod with a diameter of 8mm and the cycloidal gear tooth profile is calculated to be 61.524, which is between the radius of the starting point of the cycloidal gear meshing and the radius of the ending point of the cycloidal gear meshing, and does not exceed the meshing area.

[0067] Calculate the isometric modification Δr rp , displacement parameter Δr p The corresponding virtual cycloid gear root circle diameter df = r p -er rp -Δ rp +Δr p =119.49mm, the corresponding virtual cycloid gear top circle diameter da = r p +er rp -Δ rp +Δr p =124.69mm.

[0068] The design tooth tip circle diameter (including tooth tip modification amount) calculated from the above related parameters = 124.49 mm, and the design tooth root circle diameter (including tooth tip modification amount) = 119.29 mm.

[0069] Design value (including tooth top modification) Virtual Value Tip circle diameter 124.49mm 124.69mm Root diameter 119.29mm 119.49mm

[0070] If the design value (including the tooth top modification amount) is brought into the preset minimum interference amount ≤ dp-(df+da) / 2-d ≤ the preset maximum interference amount, it will cause a large error. Therefore, virtual values ​​must be used during selection.

[0071] Substituting the relevant data into the relationship: preset minimum interference -0.02≤dp-(df+da) / 2-d≤preset maximum interference -0.01, the needle roller diameter d falls between 5.891mm and 5.901mm. In this example, the needle roller diameter d is 5.896mm. Before the improvement, in order to fit the needle roller into the needle roller groove, the needle roller groove is generally processed to be larger than the needle roller diameter.

[0072]

[0073] From the above results, it can be seen that the present invention adopts a double elliptical rolling groove. While ensuring that the distribution circle diameter of the needle roller installed in the rolling groove is equal to the distribution circle diameter in the cycloidal wheel forming parameters, there are gaps on the left and right sides and top of the needle roller, providing space for oil storage and heat dissipation. There are two line contacts between the needle roller and the rolling groove, which limit its four degrees of freedom. The rotational freedom of the needle roller around itself is not limited. Compared with the original single arc structure, the present invention improves the positioning accuracy of the meshing pair and avoids the shaking of the needle roller in the rolling groove; the double line contact reduces the contact stress of the rolling groove and reduces the risk of wear. The present invention calculates the parameter equidistant modification Δr by the distance M from the center of the measuring rod to the center of the cycloidal wheel and the corresponding measuring rod diameter. rp and displacement parameter Δr p , and then find the corresponding virtual tooth tip circle diameter and tooth root circle diameter, and select the matching needle roller specifications according to the distance dp and preload of the two rolling groove geometric centers in the 180-degree direction, thereby improving the matching accuracy. The meshing pair and method of the present invention improve the reliability of the cycloid gear during operation and the stability of assembly, and achieve the effect of precise control of tooth clearance and backlash.

[0074] The above-mentioned embodiment only expresses one implementation mode of the present invention, and its description is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. For ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for selecting the specifications of a needle roller of a cycloid gear meshing pair, the meshing pair comprising a cycloid gear, a needle roller and a rolling groove; the rolling groove and the needle roller are in double-line contact, the rolling groove is composed of two elliptical curves and circular arcs connected between the two elliptical curves and tangent to the two elliptical curves at both ends; on a cross section perpendicular to the central axis of the needle roller, the angle between the line connecting the contact point between the needle roller and the rolling groove and the geometric center point of the rolling groove and the horizontal axis is β, the length of the minor semi-axis of the ellipse of the rolling groove elliptical curve segment is half of the needle roller radius, and the length of the major semi-axis of the ellipse is the needle roller radius multiplied by cosβ; It is characterized in that The method for selecting needle roller specifications comprises the following steps: 1) Input the cycloid gear forming parameters and the diameters of the two measuring rods D lb1 and D lb2 , the distances M1 and M2 from the centers of the two measuring rods to the center of the cycloid gear, the diameter of the rolling groove distribution circle dp, the radius of the cycloid gear meshing starting point and the radius of the cycloid gear meshing ending point; the cycloid gear forming parameters include the eccentricity e, the radius of the pin gear ring distribution circle, and the radius of the pin roller r p , number of teeth of the pinion ring z p , number of teeth of cycloid gear z c , needle roller radius r rp , tooth top modification amount, tooth root modification amount, on the section perpendicular to the center axis of the needle roller, the angle β between the line connecting the contact point between the needle roller and the rolling groove and the geometric center point of the rolling groove and the horizontal axis, the length of the major semi-axis of the ellipse, and the radius R of the tangent arc; 2) Solve the nonlinear equations to obtain the isometric modification Δr rp , displacement parameter Δr p , the meshing angle corresponding to the contact point between the two measuring rods and the tooth profile and The nonlinear equations described in step 2) include: Equation 1: y E +(D lb / 2-r rp -Δr p )·cosα=M Among them, y E D is the ordinate of the contact point between the measuring rod and the theoretical tooth profile of the cycloid gear; lb is the diameter of the measuring rod. According to the selected measuring rod, D lb Take D lb1 or D lb2 ; M is the distance from the center of the measuring rod to the center of the cycloid gear. Depending on the selected measuring rod, M is M1 or M2; α is the tangent inclination angle of the contact point between the measuring rod and the cycloid gear tooth profile. Depending on the selected measuring rod, α is α1 or α2; x E is the horizontal coordinate of the contact point between the measuring rod and the theoretical tooth profile of the cycloid gear; Equation 2: Among them, the parameters 3) Calculate the radius of the contact point between the measuring rod and the cycloid gear tooth profile; determine whether the contact point exceeds the meshing area; if not, execute step 4); if the contact point between a measuring rod and the cycloid gear tooth profile exceeds the meshing area, return to step 1) and adjust the diameter D of the measuring rod lb , the distance M from the center of the measuring rod to the center of the cycloid wheel; 4) Calculate the isometric modification Δr rp , displacement parameter Δr p The corresponding virtual cycloid gear root circle diameter df and cycloid gear tip circle diameter da; 5) Select needle rollers according to the virtual cycloid gear root circle diameter df, the cycloid gear addendum circle diameter da, the preset interference and the rolling groove distribution circle diameter dp; the needle roller specifications satisfy the relationship: preset minimum interference ≤ dp-(df+da) / 2-d ≤ preset maximum interference; output the needle roller diameter.

2. The method for selecting needle roller specifications according to claim 1, characterized in that: The center of the needle roller coincides with the geometric center of the groove.

3. The method for selecting needle roller specifications according to claim 1, characterized in that: The nonlinear equations described in step 2) are based on Δr p , Δr p and Nonlinear equations; Substitute the distance M1 from the center of the measuring rod to the center of the cycloid gear and the diameter D of the measuring rod into the nonlinear equations. lb1 When the above equations 1 and 2 are expressed as Substitute the distance M2 from the center of the measuring rod to the center of the cycloid gear and the diameter D of the measuring rod. lb2 When the above equations 1 and 2 are expressed as So the four unknowns Δ rp ,Δr p , and Composed of four nonlinear equations, forming a nonlinear equation system: Solving it gives Δ rp , Δr p , 4. The method for selecting needle roller specifications according to claim 1, characterized in that: The tangent inclination angle α of the contact point between the measuring rod and the cycloid gear tooth profile satisfies the following equation:

5. The method for selecting needle roller specifications according to claim 1, characterized in that: Measuring rod diameter D lb Satisfies the following equation:

6. The method for selecting needle roller specifications according to claim 1, characterized in that: In step 4), calculate the isometric modification Δr rp , displacement parameter Δr p The corresponding virtual cycloid gear root circle diameter df = r p -er rp -Δ rp +Δr p , the corresponding virtual cycloid gear tip circle diameter da = r p +er rp -Δ rp +Δr p .

Images