A design method for a large deflection angle three-segment arc drum gear

Abstract

The present invention relates to a three-segment arc drum-shaped tooth with a large deflection angle and a design method. It is mainly used to solve the technical problems of the existing single-segment arc drum-shaped teeth such as large design contradictions in taking into account multiple objectives such as load-bearing capacity and deflection angle. The technical solution of the present invention is: a three-segment arc drum-shaped tooth with a large deflection angle, wherein the outline of the drum-shaped tooth along the tooth width direction is composed of a large arc, a small arc on the left end and a small arc on the right end, wherein the small arc on the left end and the small arc on the right end are small arcs with the same size and shape. The specific steps are as follows: the number of teeth z, module m, pressure angle α, and clearance e of the three-segment arc drum-shaped tooth are compared with the single-segment arc drum-shaped tooth of the same size min The tooth profile radius of the large arc is consistent with the normal tooth profile radius of the single arc; calculate the distance in the tooth length direction of the large arc, the small arc on the left end and the small arc on the right end, the normal tooth profile radius and parameters of the large arc, the small arc on the left end and the small arc on the right end, and obtain R1, R2, R3, τ, L1, L2, L3 and ω of the three-segment arc drum tooth. max Three-segment arc design parameters.

Description

Technical Field

[0001] The invention belongs to the technical field of gear tooth profile design, and in particular relates to a design method for a large-angle three-segment arc drum-shaped tooth. Background Art

[0002] Drum gear couplings are flexible couplings without elastic elements. They can achieve axial, radial and angular axis deviation compensation. They have the advantages of compact structure, small turning radius, large load capacity, high transmission efficiency, low noise and long maintenance cycle. They are widely used in metallurgy, rail transit, marine ships, lifting transportation, aerospace and other fields. However, the current drum gear couplings generally use single-segment arc drum gears. The design contradictions of taking into account multiple objectives such as load capacity and deflection angle are becoming more and more acute, which seriously restricts the performance and application fields of drum gear couplings.

[0003] In order to ensure the transmission stability, the design of the tooth clearance of the drum gear coupling is very strict. The maximum compensation angle of the equiaxial line of the single-section arc drum gear coupling for metallurgical equipment is only 1.5°, which puts higher requirements on the design of the transmission system of the supporting equipment and increases the design difficulty. Under the condition of equal clearance between the three-section arc drum gear pair and the single-section arc drum gear pair with large deflection angle, it is easier to meet the technical requirements of large deflection angle, but the design difficulty of the three-section arc drum gear is much higher than that of the single-section arc drum gear, and there is no systematic design method so far. Summary of the invention

[0004] The purpose of the present invention is to solve the above technical problems and provide a design method for three-segment arc drum-shaped teeth with large deflection angles.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A design method for a three-segment arc drum-shaped tooth with a large deflection angle, wherein the drum-shaped tooth is composed of a large arc (1), a small arc (2) at the left end, and a small arc (3) at the right end along the tooth width direction, wherein the small arc (2) at the left end and the small arc (3) at the right end are small arcs with the same size and shape, and the specific steps are as follows:

[0007] 1) The number of teeth z, module m, pressure angle α, and clearance e of three-segment arc drum teeth and single-segment arc drum teeth of the same size min The tooth profile radius of the large arc (1) is consistent with the normal tooth profile radius of the single arc;

[0008] I. Calculate the normal tooth profile radius R of the single-segment arc drum gear:

[0009] R=3.3728mz (1)

[0010] II. Calculation of the tooth clearance e of the crowned gear min :

[0011] emin = 2(R - h / 2)(1 - cosω1) (2)

[0012] where: ω1—the maximum deflection angle of the single-segment arc-shaped drum tooth, °, given by the operating conditions;

[0013] h—the tooth thickness of the drum tooth at the pitch circle section, mm;

[0014] 2) Set the arrangement form and dimensional relationship of the large arc (1), the left small arc (2), and the right small arc (3):

[0015] ① Under the condition of no offset, the intersection points of the large arc (1) with the left small arc (2) and the right small arc (3) on the pitch circle section are point B and point B1 respectively. The distance between point B and point B1 is L1. The maximum deflection angle contact points of the drum tooth pair are point C and point C1. The distances between point C and point B and between point C1 and point B1 in the tooth length direction are L2 and L3 respectively, where τ = L1 / L2 = L1 / L3;

[0016] ② The normal tooth profile circle radii of the large arc (1), the left small arc (2), and the right small arc (3) are R1, R2, and R3 respectively. Let γ = R1 / R2 = R1 / R3, γ > 1;

[0017] 3) Calculate the projection distance l of the center point O and point C in the x direction C :

[0018]

[0019] where: a1—the distance between the center point O and the center O1 of the large arc, mm;

[0020] 4) First, take a value for the coefficient τ, τ ∈ (0, 3), and calculate L1, L2, and L3:

[0021]

[0022] 5) Calculate the deflection angle ω when the equal axis deflects to the load at point B A and the remaining clearance e A :

[0023] I. Calculate the distance OB between point B and the center point O of the drum tooth pitch circle section:

[0024]

[0025] where: l B —the projection distance of OB in the x-axis direction, l B = L1 / 2, mm;

[0026] II. Calculate the angle β1 between OB and the x-axis under the condition of no offset:

[0027]

[0028] III. Calculate the rotation ω of the equal axis line at point B A After reaching point B', the included angle β2 between OB' and the x-axis:

[0029]

[0030] IV. Calculate the declination ω A :

[0031] ω A = β2 - β1 (8)

[0032] By solving the simultaneous equations (5) to (8), we get:

[0033]

[0034] V. Calculate the clearance e1 required for the equal axis line carried by point B to deflect to point B':

[0035] e1 = 2OB(sin(β1 + ω A )) - sinβ1) (10)

[0036] VI. Calculate the remaining clearance e after rotation ω A : A :

[0037] e A = e min - e1 (11)

[0038] 6) Let the left end point of the large arc (1) be point A, point A coincides with point B', and the right end point of the left small arc (2) be point A'. Calculate the clearance y required for the drum tooth pair to rotate from the force application position at point A to point A':

[0039] y = 2(y A′ - y A ) = 2O'A[sin(β2 + ε) - sinβ2] (12)

[0040] Where:

[0041]

[0042] In the formula: y A , y A′ —The projected distances of OA and OA' on the y-axis, in mm;

[0043] β3—The included angle between OA' and the x-axis, in °;

[0044] ε—The included angle between the tangent of the left small arc (2) at point A and the x-axis, in °;

[0045] 7) To ensure that the two ends of the arc can bear the load and to ensure the necessity of the design of the three-segment arc crowned teeth, the following conditions need to be met: e A > y;

[0046] 8) Calculate the maximum deflection angle ω of the three-segment arc crowned teeth max :

[0047] i. First, calculate the remaining clearance e at point A′ that bears the load A′ :

[0048] e A′ = e min - e1 - y (13)

[0049] ii. Calculate the rotation angle ω of the remaining clearance e A′ : A′ :

[0050]

[0051] iii. Calculate the maximum deflection angle of the three-segment arc crowned teeth:

[0052] ω max = ω A + ε + ω A′ (15)

[0053] 9) According to the maximum deflection angle ω obtained from τ, substitute different values of the coefficient τ for calculation, and obtain the functional relationship between different coefficients τ and the maximum deflection angle. With ω max > ω1 as the design goal, determine the value range of the coefficient τ; according to the actual working conditions, obtain the R1, R2, R3, τ, L1, L2, L3 and ω of the three-segment arc crowned teeth max three-segment arc design parameters. max The beneficial effects of the present invention are:

[0054] 1. Under the conditions of ensuring the same module, the same number of teeth, and the same clearance as the single-segment arc crowned teeth, the three-segment arc crowned teeth of the present invention can effectively increase the maximum deflection angle with the smallest bearing loss;

[0055] 2. The present invention constructs a design method for large-deflection-angle three-segment arc crowned teeth;

[0056] 3. The three-segment arc crowned teeth of the present invention can expand the application limitations of traditional crowned tooth couplings with small deflection angles.

[0057] Brief Description of the Drawings

[0058] Figure 1 is the pitch circle sectional view of the large-deflection-angle three-segment arc crowned teeth of the present invention;

[0059] Figure 2 ​It is a schematic diagram of the basic dimensions of the large deflection angle three-segment arc drum-shaped tooth of the present invention;

[0060] Figure 3 It is the large deflection angle three-segment arc drum-shaped tooth of the present invention rotating ω A schematic diagram;

[0061] Figure 4 It is a schematic diagram of the change in the bearing position at the intersection of the large and small circular arcs of the present invention;

[0062] Figure 5 It is a graph of the coefficient τ and the maximum deflection angle of the present invention;

[0063] In the figure: 1—large circular arc; 2—left-end small circular arc; 3—right-end small circular arc; B, B1—the intersections of the large circular arc with the left and right-end small circular arcs; C, C1—the maximum deflection angle contact points of the drum-shaped teeth; B′—the position point of point B rotating ω A around the axis; O1, O2—the tooth profile centers of the large circular arc and the left and right-end small circular arcs; A, A′—the left end point of the large circular arc and the right end point of the left-end small circular arc. Specific implementation mode

[0064] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0065] Embodiment 1

[0066] As Figure 1 shown, a large deflection angle three-segment arc drum-shaped tooth in this embodiment, the profile of the drum-shaped tooth along the tooth width direction is composed of a large circular arc 1, a left-end small circular arc 2 and a right-end small circular arc 3, wherein the left-end small circular arc 2 and the right-end small circular arc 3 are small circular arcs with the same size and shape.

[0067] The design method of the large deflection angle three-segment arc drum-shaped tooth is as follows:

[0068] 1) The number of teeth z, module m, pressure angle α, and clearance e of the three-segment arc drum-shaped tooth and the single-segment arc drum-shaped tooth of the same size min are the same, and at the same time, the tooth profile circle radius of the large circular arc 1 is the same as the normal tooth profile circle radius of the single-segment arc;

[0069] I. Calculate the normal tooth profile circle radius R of the single-segment arc drum-shaped tooth:

[0070] R = 3.3728mz (1)

[0071] II. Calculate the tooth pair clearance e of the drum-shaped tooth min :

[0072] e min = 2(R - h / 2)(1 - cosω1) (2)

[0073] Where: ω1—the maximum deflection angle of the single-segment arc-shaped drum tooth, °, given by the operating conditions;

[0074] h—the tooth thickness of the drum tooth at the pitch circle section, mm;

[0075] 2) Set the layout form and dimensional relationship of the large arc 1, the left small arc 2, and the right small arc 3:

[0076] ① In the case of no offset, the intersection points of the large arc 1 with the left small arc 2 and the right small arc 3 on the pitch circle section are point B and point B1 respectively. The distance between point B and point B1 is L1. The maximum deflection angle contact points of the drum tooth pair are point C and point C1. The distances between point C and point B and between point C1 and point B1 in the tooth length direction are L2 and L3 respectively, where τ = L1 / L2 = L1 / L3;

[0077] ② The normal tooth profile circle radii of the large arc 1, the left small arc 2, and the right small arc 3 are R1, R2, and R3 respectively. Let γ = R1 / R2 = R1 / R3, γ > 1;

[0078] 3) Calculate the projection distance l of the center point O and point C in the x direction C :

[0079]

[0080] Where: a1—the distance between the center point O and the center of the large arc O1, mm;

[0081] 4) First, take a value for the coefficient τ, τ ∈ (0, 3), and calculate L1, L2, and L3:

[0082]

[0083] 5) Calculate the deflection angle ω borne by the equal axis when it rotates to point B A and the remaining clearance e A :

[0084] I. Calculate the distance OB between point B and the center point O of the drum tooth pitch circle section:

[0085]

[0086] Where: l B —the projection distance of OB in the x-axis direction, l B = L1 / 2, mm;

[0087] II. Calculate the angle β1 between OB and the x-axis under the condition of no offset:

[0088]

[0089] III. Calculate the rotation of point B by the equal axis by ω AThe included angle β2 between OB′ and the x-axis after reaching point B′:

[0090]

[0091] IV. Calculate the declination ω A :

[0092] ω A = β2 - β1 (8)

[0093] By solving the simultaneous equations (5) - (8), we get:

[0094]

[0095] V. Calculate the clearance e1 required for the equal-axis deflection of the drum-shaped teeth from point B to point B′:

[0096] e1 = 2OB(sin(β1 + ω A ) - sinβ1) (10)

[0097] VI. Calculate the remaining clearance e A after rotating by ω A :

[0098] e A = e min - e1 (11)

[0099] 6) Let the left end point of the large arc 1 be point A, point A coincides with point B′, and the right end point of the small arc 2 at the left end be point A′. Calculate the clearance y required for the drum-shaped tooth pair to rotate from the force application position at point A to point A′:

[0100] y = 2(y A′ - y A ) = 2O′A[sin(β2 + ε) - sinβ2] (12)

[0101] Where:

[0102]

[0103] In the formula: y A 、y A′ —The projected distances of OA and OA′ on the y-axis, in mm;

[0104] β3—The included angle between OA′ and the x-axis, in °;

[0105] ε—The included angle between the tangent of the small arc 2 at the left end at point A and the x-axis, in °;

[0106] 7) To ensure that both ends of the arc can bear the load and to ensure the design necessity of the three-segment arc drum-shaped teeth, the following condition needs to be met: e A > y;

[0107] 8) Calculate the maximum deflection angle ω of the three - arc crowned teeth max :

[0108] i. First, calculate the remaining clearance e borne at point A′ A′ :

[0109] e A′ = e min - e1 - y(13)

[0110] ii. Calculate the rotation angle ω of the remaining clearance e A′ : A′ :

[0111]

[0112] iii. Calculate the maximum deflection angle of the three - arc crowned teeth:

[0113] ω max = ω A + ε + ω A′ (15)

[0114] 9) Based on the maximum deflection angle ω obtained from τ, substitute different values of the coefficient τ for calculation to obtain the functional relationship between different coefficients τ and the maximum deflection angle. With ω max > ω1 as the design goal, determine the value range of the coefficient τ; according to the actual working conditions, obtain the R1, R2, R3, τ, L1, L2, L3 and ω of the three - arc crowned teeth max three - arc design parameters. max Example 2

[0115] The large - deflection - angle three - arc crowned teeth in this example are the same as those in Example 1. The number of teeth z, module m, pressure angle α, and clearance e of the three - arc crowned teeth are the same as those of the single - arc crowned teeth with the same size

[0116] . At the same time, the tooth profile circle radius of the large arc 1 is the same as the normal tooth profile circle radius of the single - arc; design the large - deflection - angle three - arc crowned teeth with parameters z = 50, m = 8, α = 20°, ω1 = 1.5°. min

[0117] (1) Calculate the normal tooth profile circle radius R of the single - arc crowned teeth:

[0118] R = 3.3728mz = 1349.1mm

[0119] (2) Calculate the tooth pair clearance e of the crowned teeth min :

[0120] e min = 2(R - h / 2)(1 - cosω1)= 0.95mm

[0121] (3) Take the coefficient γ = 1.5 and calculate the profile circle radii R1, R2, and R3 of the large arc and the small arc:

[0122]

[0123] (4) Calculate the projection distance l in the x - direction between the center point O and point C C :

[0124]

[0125] (5) Calculate L1, L2, and L3. First, substitute the coefficient τ = 0.7 into the calculation:

[0126]

[0127] (6) Calculate the distance OB between point B and the center point O of the crowned tooth:

[0128]

[0129] (7) Calculate the angle β1 between OB and the x - axis under the non - offset condition:

[0130]

[0131] (8) Calculate the deflection angle ω of the equal - axis line deflected to the load - bearing point B A :

[0132]

[0133] (9) Calculate the clearance e1 required for the equal - axis line to deflect from the load - bearing point B to point B′:

[0134] e1 = 2OB(sin(β1 + ω A ) - sinβ1) = 0.3092mm

[0135] (10) Calculate the remaining clearance e after rotating by ω A : A :

[0136] e A = e min - e1 = 0.6408mm

[0137] (11) Let the left - end point of the large arc 1 be point A, point A coincides with point B′, and the right - end point of the left - hand small arc 2 be point A′. Calculate the clearance y required for the crowned tooth to rotate from the force - bearing position at point A to point A′:

[0138] y = 2(y A′ - y A ) = 2O′A[sin(β2 + ε) - sinβ2] = 0.1541mm

[0139] Wherein:

[0140] (12) Calculate the remaining clearance e borne at point A': A′ :

[0141] e A′ = e min - e1 - y = 0.4867 mm

[0142] (13) Calculate the rotation angle ω of the remaining clearance e A′ : A′ :

[0143]

[0144] (14) Calculate the maximum deflection angle of the three-segment arc crowned teeth:

[0145] ω max = ω A + ε + ω A′ = 2.2610°

[0146] Based on the above calculation method, values of 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, and 1.5 are taken for the coefficient τ, and imported into the program for calculation to obtain the maximum deflection angles corresponding to different coefficients τ. As shown in the following table:

[0147] Table 1 Numerical table of coefficient τ and deflection angle ω

[0148] τ 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 ω / ° 2.261 2.245 2.175 2.111 2.032 1.932 1.798 1.579 1.3436

[0149] As shown in Table 1, when the coefficient τ = 1.5, the maximum deflection angle ω max = 1.3436°, which is less than the maximum deflection angle of 1.5° of the single-segment arc crowned teeth, and the design is unreasonable. Therefore, as shown in the appendix Figure 5 , point F (1.438, 1.5) is the limit design point of the coefficient τ, and the coefficient τ < 1.438.

[0150] Assume that the maximum design deflection angle of the crowned tooth coupling in the embodiment is 2°, and the coefficient τ ≈ 1.14 is obtained. The key design parameters of the three-segment arc crowned teeth are calculated. As shown in the following table:

[0151] Table 2 Design parameter table of three-segment arc crowned teeth

[0152] parameter <![CDATA[R1 / mm]]> <![CDATA[R2 / mm]]> <![CDATA[R3 / mm]]> τ <![CDATA[L1 / mm]]> <![CDATA[L2 / mm]]> <![CDATA[L3 / mm]]> <![CDATA[ω max / °]]> value 1349.1 899.4 899.4 1.14 18.6876 16.3926 16.3926 2

Claims

1. A design method for a large deflection angle three-segment arc drum gear, characterized in that, The profile of the crowned teeth in the tooth width direction is composed of a large arc (1), a small left arc (2) and a small right arc (3). The small left arc (2) and the small right arc (3) are small arcs with the same size and shape. The specific steps are as follows: 1) The number of teeth z, module m, pressure angle α, and clearance e of the three-segment arc drum-shaped teeth are the same as those of the single-segment arc drum-shaped teeth of the same size. min At the same time, the tooth profile circle radius of the large arc (1) is the same as the normal tooth profile circle radius of the single-segment arc. I. Calculate the normal tooth profile circle radius R of the single-segment arc crowned teeth: R = 3.3728mz (1) II. Calculate the tooth pair clearance e of the crowned teeth min : e min = 2(R - h / 2)(1 - cos ω1) (2) Where: ω1—the maximum deflection angle of the single-segment arc crowned teeth, °, given by the operating conditions; h—the tooth thickness of the crowned teeth in the pitch circle section, mm; 2) Set the layout form and dimensional relationship of the large arc (1), the small left arc (2) and the small right arc (3): ① Under the non-offset condition, the intersection points of the large arc (1) with the small left arc (2) and the small right arc (3) in the pitch circle section are point B and point B1 respectively. The distance between point B and point B1 is L1. The maximum deflection angle contact points of the crowned teeth are point C and point C1. The distances between point C and point B and between point C1 and point B1 in the tooth length direction are L2 and L3 respectively, where τ = L1 / L2 = L1 / L3; ② The normal tooth profile circle radii of the large arc (1), the small left arc (2) and the small right arc (3) are R1, R2, and R3 respectively. Let γ = R1 / R2 = R1 / R3, γ > 1; 3) Calculate the projection distance l in the x-direction between the center point O and point C C : Where: a1—the distance between the center point O and the center O1 of the large arc, mm; 4) First, take a value for the coefficient τ, τ ∈ (0, 3), and calculate L1, L2, and L3: 5) Calculate the deflection angle ω borne by the equal axis line when deflected to point B A and the remaining clearance e A : I. Calculate the distance OB between point B and the center point O of the crowned teeth pitch circle section: Where: l B — The projection distance of OB in the x-axis direction, l B = L1 / 2, mm; II. Calculate the angle β1 between OB and the x-axis under the non-offset condition: III. Calculate the rotation of the equal-axis line at point B by ω A After reaching point B', the included angle β2 between OB' and the x-axis: IV. Calculate the declination ω A : ω A = β2 - β1 (8) Solve by combining equations (5) to (8) to obtain: V. Calculate the clearance e1 required for the equal-axis deflection of the load from point B to point B': e1 = 2OB(sin(β1 + ω A ) - sinβ1) (10) VI. Calculate the rotational speed ω A The remaining clearance e A : e A = e min - e1(11) 6) Let the left end point of the large arc (1) be point A, point A coincides with point B'. Let the right end point of the small left arc (2) be point A'. Calculate the clearance y required for the crowned teeth pair to rotate from the force application position at point A to point A': y = 2(y A′ - y A ) = 2O′A[sin(β2 + ε) - sinβ2] (12) Where: where: y A , y A′ — the projected distances of the distances OA and OA' on the y-axis, in mm; β3—the angle between OA' and the x-axis, °; ε—the angle between the tangent line of the small left arc (2) at point A and the x-axis, °; 7) To ensure that the arcs at both ends can bear the load and to ensure the necessity of the design of the three-segment arc-shaped drum teeth, the following conditions need to be met: e A > y; 8) Calculate the maximum deflection angle ω of the three-segment arc drum gear teeth max : i. First, calculate the remaining clearance e borne at point A' A′ : e A′ = e min -e1-y (13) ii. Calculate the remaining clearance e A′ The rotation angle ω A′ : iii. Calculate the maximum deflection angle of the three-segment arc crowned teeth: ω max = ω A + ε + ω A′ (15) 9) The maximum deflection angle ω obtained from τ max , different values of the coefficient τ are substituted for calculation to obtain the functional relationship between different coefficients τ and the maximum deflection angle. With ω max > ω1 as the design goal, the value range of the coefficient τ is determined; according to the actual working conditions, R1, R2, R3, τ, L1, L2, L3 and ω of the three-arc drum-shaped teeth are obtained max Three-arc design parameters.

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