Method for solving unbalance loading of intersecting axis variable-thickness gear based on adjustment of taper angle
By adjusting the cone angle, the initial design parameters and the backlash-free meshing equation of the thickened gear are calculated, which solves the problem of overload of the thickened gear, achieves uniform distribution of backlash, avoids tooth surface modification, improves vibration and noise, and simplifies the processing process.
Patent Information
- Application Number
- CN202510719014.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-30
- Publication Date
- 2025-09-09
AI Technical Summary
In the existing technology, when solving the problem of overload of standard involute gear pairs, the tooth surface needs to be modified, which leads to thinning of tooth thickness, increase of side clearance, increase of vibration and noise, and the processing is cumbersome and the calculation is complicated.
By adjusting the cone angle, the initial design parameters and backlash-free meshing equation of the thickened gear are calculated to achieve uniform distribution of backlash over the tooth width, avoid tooth surface modification, and improve the problem of eccentric load.
It effectively solves the problem of eccentric load of thickened gears with intersecting axes, eliminates the need for tooth surface modification, increases tooth thickness, evenly distributes side clearance, reduces vibration and noise, and simplifies the machining process.
Smart Images
Figure CN120611463A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of gear transmission, and in particular to a solution to overload of intersecting shaft thickened gears based on adjusting a cone angle. Background Art
[0002] At present, when the standard involute gear pair has an overload problem, the gear tooth surface is modified to improve the overload problem. This overload solution will inevitably cause the thickness of the thickened gear teeth to be thinned, and the side clearance between the teeth will also increase accordingly, which will not only affect the strength of the gear teeth, but also increase the vibration and noise in actual working conditions; and this method has an additional modification step in the actual processing stage compared to the normal standard involute thickened gear. The process is more complicated and the requirements for the entire gear tooth processing accuracy are strict, which increases the difficulty of the craftsman's operation. In addition, the calculation of the gear modification amount is more complicated, and a large amount of contact analysis and load analysis are required to determine the optimal modification amount. Based on this, it is urgent to design a solution to the overload of intersecting axis thickened gears based on adjusting the cone angle to avoid tooth modification and ensure that the tooth thickness in the effective contact area of the gear is not thinned. Summary of the Invention
[0003] The purpose of the present invention is to overcome the above-mentioned shortcomings and provide a solution to the overload of intersecting axis thickened gears based on adjusting the cone angle, so as to solve the problem of overload of large and small ends that frequently occurs in the transmission of intersecting axis thickened gears. There is no need to modify the tooth surface. By adjusting the cone angle, the side clearance can be evenly distributed on the tooth width and the contact position is reasonable, thereby achieving the purpose of improving overload.
[0004] The object of the present invention is achieved like this:
[0005] A method for solving the overload problem of intersecting thickened gears based on adjusting the cone angle includes the following steps:
[0006] Step 1: Determine the initial design parameters of the variable thickness gear, calculate the end face pitch circle pressure angle, pitch circle pressure angle, angle between the common rack pitch plane and the gear axis, tooth line inclination angle and normal tooth profile angle of the common rack, pitch end face modification coefficient and small end normal modification coefficient of the variable thickness gear;
[0007] Step 2: Establish the backlash-free meshing equation of intersecting axis thickening gears;
[0008] Step 3: If backlash-free meshing transmission is achieved only at the pitch end faces of the intersecting axis thickened gear pair, and backlash exists between the teeth at other positions, calculate the backlash values of different end faces of the thickened gear;
[0009] Step 4. Adjust the cone angle of the thickened gear: First, calculate the side clearance value of the thickened gear according to step 3, and define a side clearance constant , based on the backlash-free meshing equation, and adding a constant term to the equation The improved backlash-free meshing equation of the big and small ends is obtained. Combining the relationship between the gear big and small end modification coefficients and the pitch end modification coefficients, the big and small end modification coefficients of the two gears are obtained. The new gear cone angle is derived based on the newly obtained big and small end modification coefficients.
[0010] Preferably, in step one, the initial design parameters are known parameters, including the number of teeth, module, normal tooth profile angle, tooth width, helix angle, large end normal displacement coefficient, distance from the pitch end face to the small end face, cone angle and end face tooth profile angle coefficient of the thickened gear.
[0011] Preferably, in step 2, establishing the backlash-free meshing equation includes the following steps:
[0012] Based on the relationship between the pitch thickness of the two variable-thickness gears and the normal pitch pitch, point P is defined as the intersection of the common rack indexing plane and the two gear pitch circles, also known as the pitch point. The end planes of the two gears passing through the pitch point are defined as the pitch end faces. P1P1 and P2P2 are the intersection lines of the two gear pitch end faces with the indexing plane. L1, L2, and L3 are the tooth line of the common rack. nn is the perpendicular to the common rack tooth line. and are the pitch tooth thicknesses of the two gear segment end faces respectively. and are the tooth line inclination angles of the two gears respectively. is the normal pitch circle pitch.
[0013] When the variable thickness gear pair realizes backlash-free transmission, the sum of the distances of the two gear pitch circle tooth thicknesses in the direction perpendicular to the common rack tooth line should be equal to the normal pitch circle tooth pitch, that is,
[0014]
[0015] In formula (8) ——The normal module of the common rack can be obtained by the following formula.
[0016]
[0017] The pitch tooth thickness of the thickened gear is
[0018]
[0019] In formula (10) — involute function, .
[0020] Combining equations (8) to (10), we can obtain the backlash-free meshing equation of the thickened gear:
[0021]
[0022] In formula (11) ——Displacement coefficient of node end face.
[0023] Preferably, in step 3, the method for calculating the backlash of different end faces of the thickened gear includes the following steps:
[0024] For intersecting axis variable thickness gear pairs, the contact form is point contact. If and only if the pitch end face can achieve backlash-free meshing transmission, there is backlash between the teeth at other positions. The sum of the distances of the two gear pitch circle tooth thicknesses in the direction perpendicular to the common rack tooth line is less than the normal pitch circle tooth pitch of the common rack, so the backlash calculation formula of different end faces of the variable thickness gear can be derived as follows:
[0025]
[0026] In formula (12) ——The pitch tooth thickness of different end faces can be calculated by formula (13).
[0027]
[0028] In formula (13) ——modification coefficient corresponding to different end sections;
[0029] ——Tooth profile angle corresponding to different end section pitch circles.
[0030] Based on the above formula, the backlash value over the entire tooth width of the gear can be calculated.
[0031] Preferably, in step 4, the side clearance values of the large and small ends of the thickened gear are obtained according to step 3 and are recorded as and , and define a backlash constant , Size
[0032]
[0033] The thickened gear realizes backlash-free meshing transmission at the pitch end face, but has backlash at the big and small ends. In order to improve the backlash at the big and small ends, the displacement coefficient at the big and small ends is regarded as an unknown number and recorded as and , still use the backlash-free meshing equation for the big and small ends, and add a constant term to the equation , we get the improved meshing equation with no backlash between the big and small ends
[0034]
[0035] In formula (15) ——Pitch circle pressure angle of the left tooth surface at the big end;
[0036] ——Pitch circle pressure angle of the left tooth surface at the small end;
[0037] ——the pitch circle pressure angle of the right tooth surface at the big end;
[0038] ——Pitch circle pressure angle of the right tooth surface at the small end.
[0039] The relationship between the modification coefficients of the large and small ends of the two gears and the modification coefficients of the pitch end faces is as follows:
[0040]
[0041] In formula (16) ——Gear end face module, ;
[0042] ——Distance from gear pitch end face to small end;
[0043] - gear ratio, .
[0044] By combining equations (15) and (16), a new set of gear end modification coefficients can be obtained. Based on the new obtained gear end modification coefficients, a new gear cone angle can be derived.
[0045]
[0046] Preferably, when the new gear cone angle is obtained in step 4 for eccentric load adjustment, only the gear cone angle and the large end normal displacement coefficient of the gear are adjusted, and the other initial design parameters remain unchanged.
[0047] The beneficial effects of the present invention are:
[0048] The problem of uneven load on intersecting shaft thickened gear pairs can be effectively solved;
[0049] The intersecting axis thickened gear pair obtained based on the method does not require tooth surface modification, which is convenient for production and processing. The thickened gear obtained by the method has an increased tooth thickness and a more uniform side clearance distribution compared to the original parameters, and can improve the vibration and noise problems that occur in actual working conditions without affecting the strength of the gear teeth.
[0050] The method only requires more than ten formulas to improve the eccentric load problem, and the principle is simple and easy to operate. BRIEF DESCRIPTION OF THE DRAWINGS
[0051] Figure 1 Schematic diagram of the relationship between the pitch circle tooth thickness and the normal pitch circle pitch of two variable thickness gears.
[0052] Figure 2This is the side clearance distribution curve of the entire tooth width of the overloaded gear in Example 1 of the present invention.
[0053] Figure 3a 、 Figure 3b This is a schematic diagram of the contact position of the overloaded gear. (The cone angle is not adjusted)
[0054] Figure 3c 、 Figure 3d Schematic diagram of gear contact position after adjusting the cone angle.
[0055] Figure 4 Comparison chart of gear backlash values before and after cone angle adjustment.
[0056] Figure 5 This is a comparison chart of the corresponding tooth thickness of the gear pitch cone before and after cone angle adjustment. DETAILED DESCRIPTION
[0057] The present invention relates to a method for solving the overload problem of intersecting shaft thickened gears based on adjusting the cone angle, comprising the following steps:
[0058] Step 1: Determine the initial design parameters of the thickened gear, see Table 1. The parameters in Table 1 are known parameters.
[0059] Table 1 Initial design parameters of thickened gear
[0060] According to the initial design parameters in Table 1, the end face pitch circle pressure angle, pitch circle pressure angle, angle between the common rack pitch plane and the gear axis, tooth line inclination angle and normal tooth profile angle of the common rack are calculated.
[0061] The pressure angle of the end face pitch circle of the thickened gear is
[0062]
[0063] In formula (1), "For the selection of , the left tooth surface is "-" and the right tooth surface is "+".
[0064] The pitch circle pressure angle of the thickened gear is
[0065]
[0066] The angle between the common rack indexing plane and the gear axis is
[0067]
[0068] The tooth line inclination angle of the common rack is
[0069]
[0070] The normal tooth profile angle of the common rack is
[0071]
[0072] The displacement coefficient of the pitch end face of the thickened gear is
[0073]
[0074] The normal displacement coefficient of the small end of the thickened gear is
[0075]
[0076] Step 2: Establish the backlash-free meshing equation of intersecting axis variable thickness gears.
[0077] When the intersecting axis variable thickness gears are used for transmission, they can be regarded as meshing with the common rack for transmission. If the two variable thickness gears and the common rack can maintain line contact and no backlash transmission, then there is no backlash between the two gears. Figure 1 The diagram shows the relationship between the pitch thickness and normal pitch pitch of two variable-thickness gears. Point P is the intersection of the common rack indexing plane and the two gear pitch circles, also known as the pitch point. The end planes of the two gears passing through the pitch point are defined as the pitch end faces. P1P1 and P2P2 are the intersection lines of the two gear pitch end faces with the indexing plane. L1, L2, and L3 are the tooth line of the common rack. nn is the perpendicular to the common rack tooth line. and are the pitch tooth thicknesses of the two gear segment end faces respectively. and are the tooth line inclination angles of the two gears respectively. is the normal pitch circle pitch.
[0078] When the thickened gear pair realizes the transmission without backlash, Figure 1 The following relationship is obtained, that is, the sum of the distances of the two gear pitch circle tooth thicknesses in the direction perpendicular to the common rack tooth line should be equal to the normal pitch circle tooth pitch, that is,
[0079]
[0080] In formula (8) ——The normal module of the common rack can be obtained by the following formula.
[0081]
[0082] The pitch tooth thickness of the thickened gear is
[0083]
[0084] In formula (10) — involute function, .
[0085] Combining equations (8) to (10), we can obtain the backlash-free meshing equation of the thickened gear:
[0086]
[0087] In formula (11) ——Displacement coefficient of the end face of the node.
[0088] Step 3: If backlash-free meshing transmission is achieved only at the pitch end faces of the intersecting axis variable-thickness gear pair, and there is backlash between the teeth at other positions, calculate the backlash values of different end faces of the variable-thickness gear.
[0089] For intersecting axis variable thickness gear pairs, the contact form is generally point contact. If and only if the pitch end face can achieve backlash-free meshing transmission, there will be backlash between the teeth at other positions. That is, the sum of the distances of the pitch circle tooth thicknesses of the two gears in the direction perpendicular to the common rack tooth line is less than the normal pitch circle tooth pitch of the common rack. Therefore, the backlash calculation formula of different end faces of the variable thickness gear can be derived as follows:
[0090]
[0091] In formula (12) ——The pitch tooth thickness of different end faces can be calculated by formula (13).
[0092]
[0093] In formula (13) ——modification coefficient corresponding to different end sections;
[0094] ——Tooth profile angle corresponding to different end section pitch circles.
[0095] Based on the above formula, the backlash value over the entire tooth width of the gear can be calculated.
[0096] Step 4: Adjust the cone angle of the thickened gear. First, calculate the side clearance of the thickened gear according to step 3 and define a side clearance constant. , based on the backlash-free meshing equation, and adding a constant term to the equation The improved backlash-free meshing equation of the big and small ends is obtained. Combining the relationship between the gear big and small end modification coefficients and the pitch end modification coefficients, the big and small end modification coefficients of the two gears are obtained. The new gear cone angle is derived based on the newly obtained big and small end modification coefficients.
[0097] The occurrence of overloaded thickened gears can be attributed to uneven distribution of backlash across the tooth width. Overloaded thickened gears inevitably have significantly different backlash at both ends of their teeth. For example, a gear with overloaded small ends will have much smaller backlash at the large end than at the large end. For example, if the backlash at the large and small ends of a gear with overloaded small ends can be adjusted to be roughly the same, with the backlash at the center of the tooth width being minimized, then the backlash distribution across the tooth width is considered uniform and the contact position is reasonable. To adjust the backlash, while keeping the other gear parameters unchanged, the pitch tooth thickness can be adjusted by adjusting the displacement coefficient.
[0098] According to step 3, the side clearance values of the thickened gear are obtained and recorded as and , and define a backlash constant , Size
[0099]
[0100] Generally speaking, the thickened gears realize backlash-free meshing transmission at the pitch end faces, but there is backlash at the big and small ends. In order to achieve the purpose of improving the backlash at the big and small ends, the displacement coefficients at the big and small ends are regarded as unknowns and recorded as and , still use the backlash-free meshing equation for the big and small ends, and add a constant term to the equation , we get the improved meshing equation with no backlash between the big and small ends
[0101]
[0102] In formula (15) ——Pitch circle pressure angle of the left tooth surface at the big end;
[0103] ——Pitch circle pressure angle of the left tooth surface at the small end;
[0104] ——the pitch circle pressure angle of the right tooth surface at the big end;
[0105] ——Pitch circle pressure angle of the right tooth surface at the small end.
[0106] The relationship between the modification coefficients of the large and small ends of the two gears and the modification coefficients of the pitch end faces is as follows:
[0107]
[0108] In formula (16) ——Gear end face module, ;
[0109] ——Distance from gear pitch end face to small end;
[0110] - gear ratio, .
[0111] By combining equations (15) and (16), a new set of gear end modification coefficients can be obtained. Based on the new obtained gear end modification coefficients, a new gear cone angle can be derived.
[0112]
[0113] At this point, the parameters of the new gear without overload have been adjusted. Compared to the original overload-exposed gear, its parameters such as the number of teeth, module, pressure angle, helix angle, and tooth width remain unchanged; only the cone angle and displacement coefficient have changed. It is important to note that the shaft angle and axial position of the gear pair remain unchanged before and after the adjustment.
[0114] Example 1:
[0115] Because the modified gear has a linear variation in its modification coefficient along its axis, the tooth thickness corresponding to the same radius at different axial end sections is also different. When selecting the design parameters for the modified gear, in order to increase the tooth thickness and avoid undercutting, the modification coefficient at the small end of the modified gear is often set close to or greater than 0. This results in an uneven distribution of axial backlash at the modified gear, with the backlash being minimum at the small end. This causes tooth contact at the small end and causes unbalanced loading at the small end.
[0116] Therefore, a pair of intersecting shaft thickened gear pairs with small end eccentric load is taken as an example to verify the feasibility of the proposed solution to the eccentric load problem. The gear parameters are shown in Table 2.
[0117] Table 2 Basic parameters of eccentrically loaded gears
[0118]
[0119] Based on the known gear parameters in Table 2, the basic parameters of the thickened gear and the pitch end face modification coefficient and the small end normal modification coefficient before adjustment are calculated by the above formulas (1) to (7), where the pitch end face modification coefficient is 0 and the small end normal modification coefficient is -0.011. The side clearance over the entire tooth width can be calculated by the above formulas (8) to (13), as follows: Figure 2 As shown. Figure 2 The side clearance of the overloaded gears follows a roughly parabolic curve, with the minimum value occurring at the pitch end. From the small end to the large end, the side clearance first decreases and then increases. The large end side clearance is 0.468mm, and the small end side clearance is 0.000545mm. The gear pair exhibits overload near the small end.
[0120] According to the calculated side clearance values of the large and small ends, the side clearance constant is calculated by formula (14): The value is 0.23428mm, and the side clearance constant Substituting into equation (15) and solving equation (16) in parallel, we can get the new adjustment coefficients of the large and small ends, as shown in Table 3.
[0121] Table 3 Comparison of displacement coefficients of large and small ends before and after adjustment
[0122]
[0123] Substituting the displacement coefficient values in Table 3 into Equation (17), the gear cone angle after adjustment is calculated to be 1.11746°. The parameters of the thickened gear after adjustment are shown in Table 4.
[0124] Table 4 Basic parameters of adjusted bevel gears
[0125]
[0126] Keeping the installation conditions unchanged, the gear pair assembly models before and after adjusting the taper angle were created according to the parameters in Table 2 and Table 4, and their contact positions are shown in Figure 3. As can be seen from Figure 3, the gear contact position appears at the small end before the taper angle adjustment, and the gear contact position appears at the large end after adjustment, and the eccentric load phenomenon is significantly improved. Figure 3a 、 Figure 3b This is a schematic diagram of the contact position of the eccentrically loaded gear. Figure 3c 、 Figure 3d Schematic diagram of gear contact position after adjusting the cone angle.
[0127] Comparison of the side clearance values of the gear pitch cone before and after cone angle adjustment Figure 4 As shown. Figure 4 It can be seen that the side clearance value of the gear pitch cone after the cone angle is adjusted is more uniform than before the adjustment, the side clearance at the large and small ends is basically the same, and the side clearance value in the middle of the tooth width is the smallest.
[0128] Comparison of gear pitch cone tooth thickness before and after cone angle adjustment Figure 5 As shown. Figure 5 It can be seen that after the cone angle adjustment, the tooth thickness corresponding to the pitch circle of the gear is basically increased compared to before the adjustment. Only the pitch circle tooth thickness at the small end, which is approximately 0.2 times the tooth width, is thinned. Among them, the tooth thickness at the middle contact position is thickened by 0.228mm, the tooth thickness at the large end is thickened by 0.588mm, and the tooth thickness at the small end is thinned by 0.135mm.
[0129] In addition to the above embodiments, the present invention also includes other implementation methods. Any technical solutions formed by equivalent transformation or equivalent replacement should fall within the scope of protection of the claims of the present invention.
Claims
1. A solution to the overload of intersecting gears with thickened axes based on adjusting the cone angle, characterized by: The following steps are involved: Step 1: Determine the initial design parameters of the variable thickness gear, calculate the end face pitch circle pressure angle, pitch circle pressure angle, angle between the common rack pitch plane and the gear axis, tooth line inclination angle and normal tooth profile angle of the common rack, pitch end face modification coefficient and small end normal modification coefficient of the variable thickness gear; Step 2: Establish the backlash-free meshing equation of intersecting axis thickening gears; Step 3: If backlash-free meshing transmission is achieved only at the pitch end faces of the intersecting axis thickened gear pair, and backlash exists between the teeth at other positions, calculate the backlash values of different end faces of the thickened gear; Step 4. Adjust the cone angle of the thickened gear: First, calculate the side clearance value of the thickened gear according to step 3, and define a side clearance constant , based on the backlash-free meshing equation, and adding a constant term to the equation The improved backlash-free meshing equation of the big and small ends is obtained. Combining the relationship between the gear big and small end modification coefficients and the pitch end modification coefficients, the big and small end modification coefficients of the two gears are obtained. The new gear cone angle is derived based on the newly obtained big and small end modification coefficients.
2. A method for solving the problem of uneven load on intersecting gears with thickened axes based on adjusting the cone angle according to claim 1, characterized in that: In step 1, the initial design parameters are known parameters, including the number of teeth, module, normal tooth profile angle, tooth width, helix angle, large end normal modification coefficient, distance from the pitch end face to the small end face, taper angle and end face tooth profile angle coefficient of the thickened gear.
3. The method for solving the overload problem of intersecting gears with thickened axes based on adjusting the cone angle according to claim 1, characterized in that: In the second step, the establishment of the backlash-free meshing equation includes the following steps: Based on the relationship between the pitch thickness of the two variable-thickness gears and the normal pitch pitch, point P is defined as the intersection of the common rack indexing plane and the two gear pitch circles, also known as the pitch point. The end planes of the two gears passing through the pitch point are defined as the pitch end faces. P1P1 and P2P2 are the intersection lines of the two gear pitch end faces with the indexing plane. L1, L2, and L3 are the tooth line of the common rack. nn is the perpendicular to the common rack tooth line. and are the pitch tooth thicknesses of the two gear segment end faces respectively. and are the tooth line inclination angles of the two gears respectively. is the normal pitch; When the variable thickness gear pair realizes backlash-free transmission, the sum of the distances of the two gear pitch circle tooth thicknesses in the direction perpendicular to the common rack tooth line should be equal to the normal pitch circle tooth pitch, that is, ； In formula (8) ——The normal module of the common rack can be obtained by the following formula; ； The pitch tooth thickness of the thickened gear is ； In formula (10) — involute function, ; Combining equations (8) to (10), we can obtain the backlash-free meshing equation of the thickened gear: ； In formula (11) ——Displacement coefficient of the end face of the node.
4. The method for solving the overload problem of intersecting gears with thickened axes based on adjusting the cone angle according to claim 1 is characterized in that: In step 3, the method for calculating the backlash of different end faces of the thickened gear includes the following steps: For intersecting axis variable thickness gear pairs, the contact form is point contact. If and only if the pitch end face can achieve backlash-free meshing transmission, there is backlash between the teeth at other positions. The sum of the distances of the two gear pitch circle tooth thicknesses in the direction perpendicular to the common rack tooth line is less than the normal pitch circle tooth pitch of the common rack, so the backlash calculation formula of different end faces of the variable thickness gear can be derived as follows: ； In formula (12) ——The pitch tooth thickness of different end faces can be calculated by formula (13); ； In formula (13) ——modification coefficient corresponding to different end sections; ——Tooth profile angle corresponding to different end section pitch circles; Based on the above formula, the backlash value over the entire tooth width of the gear can be calculated.
5. The method for solving the overload problem of intersecting gears with thickened axes based on adjusting the cone angle according to claim 1 is characterized in that: In step 4, the side clearance values of the large and small ends of the thickened gear are obtained according to step 3 and are recorded as and , and define a backlash constant , Size ； The thickened gear realizes backlash-free meshing transmission at the pitch end face, but has backlash at the big and small ends. In order to improve the backlash at the big and small ends, the displacement coefficient at the big and small ends is regarded as an unknown number and recorded as and , still use the backlash-free meshing equation for the big and small ends, and add a constant term to the equation , we get the improved meshing equation with no backlash between the big and small ends ； In formula (15) ——Pitch circle pressure angle of the left tooth surface at the big end; ——Pitch circle pressure angle of the left tooth surface at the small end; ——the pitch circle pressure angle of the right tooth surface at the big end; ——the pitch circle pressure angle of the right tooth surface at the small end; The relationship between the modification coefficients of the large and small ends of the two gears and the modification coefficients of the pitch end faces is as follows: ； In formula (16) ——Gear end face module, ; ——Distance from gear pitch end face to small end; - gear ratio, ; Combining equations (15) and (16) yields a new set of gear end modification coefficients. Based on the newly obtained gear end modification coefficients, the new gear cone angle can be derived. 。 6. The method for solving the overload problem of intersecting gears with thickened axes based on adjusting the cone angle according to claim 1, characterized in that: When the new gear cone angle is obtained in step 4 for eccentric load adjustment, only the gear cone angle and the large end normal displacement coefficient of the gear are adjusted, and the other initial design parameters remain unchanged.