Cutter head diameter parameter design method for heavy-load large-modulus spiral bevel gear

Abstract

The invention relates to a cutter head diameter parameter design method for a large-modulus spiral bevel gear under a heavy-load working condition, which comprises the following steps of: (1) calculating geometric parameters of a large wheel and a small wheel according to basic parameters of the heavy-load large-modulus spiral bevel gear; (2) aiming at a series value of the diameter of the standardized cutterhead recommended by Gleason, exploring an extension rule of the standardized cutterhead; (3) calculating a theoretical value of the diameter of the cutterhead in order to reduce or eliminate a gear tooth shrinkage error; and (4) calculating a theoretical value by combining the standardized cutter head nominal diameter and the cutter head diameter, and approaching to obtain an actual cutter head diameter parameter. According to the method, on the basis of the existing Gleason standardized cutterhead diameter series, the cutterhead diameter exceeding 800 mm is obtained through expansion, reduction or elimination of gear tooth shrinkage errors is considered, the actual machining cutterhead diameter is calculated and determined more accurately, and reference can be provided for cutterhead design of oversized heavy-load large-modulus spiral bevel gears.

Description

Technical Field

[0001] The invention relates to a cutter head diameter parameter design method for a heavy-loaded large-module spiral bevel gear, which is suitable for designing and selecting the cutter head diameter during machining of large-module spiral bevel gears by a Gleason gear milling machine. Background Art

[0002] The module of large-module spiral bevel gears is greater than 15mm and the pitch diameter is greater than 800mm. The rapid development of heavy industry and manufacturing in recent years has promoted the demand for oversized large-module spiral bevel gears in metallurgy, navigation and other industries. When using Gleason gear milling machine to process spiral bevel gears, it is necessary to select different nominal diameters of the cutter disc according to the actual processing conditions. When processing large gears, if the diameter of the cutter disc is larger, the ratio of the normal thickness of the large end and the small end of the large gear tooth top is larger, the tooth top of the small end of the gear tooth is more likely to become pointed, which reduces the strength of the gear tooth; if the diameter of the cutter disc is too small, the tooth surface is prone to reverse contraction during processing, that is, the width of the tooth top of the small end of the gear tooth will be greater than that of the large end, making the gear unable to be used normally.

[0003] The nominal diameter series values ​​of the cutter head recommended by Gleason can no longer meet the machining requirements for large-module spiral bevel gears. Therefore, a cutter head diameter parameter design method for large-module spiral bevel gears under heavy load conditions is proposed. Summary of the invention

[0004] The purpose of the present invention is to address the problem that the existing Gleason cutter disc diameter series value range is limited and it is difficult to complete the design and processing of large-module spiral bevel gears. By exploring the law of standardized series values, based on the basic parameters of large-module spiral bevel gears, and considering the influence of gear tooth shrinkage error in the actual processing process, a calculation method for approximating the theoretical value of the cutter disc diameter and the nominal cutter disc diameter is proposed, so as to realize the parameter design of large-module spiral bevel gears and provide a theoretical basis for actual processing.

[0005] The technical solution adopted by the present invention is: a method for designing cutter diameter parameters of heavy-loaded large-module spiral bevel gears, and the method flow is as follows:

[0006] Step 1: Calculate the geometric parameters of the large wheel and the small wheel according to the basic parameters of the heavy-loaded large-module spiral bevel gear;

[0007] Step 2: Explore the extension rules of the standardized cutter head diameter series values ​​recommended by Gleason;

[0008] Step 3: Calculate the theoretical value of the cutter head diameter to reduce or eliminate the gear tooth shrinkage error;

[0009] Step 4: Combine the standardized nominal diameter of the cutter disc with the theoretical value of the cutter disc diameter to approximate the actual cutter disc diameter parameter.

[0010] Furthermore, in step 1, according to the module m of the heavy-duty large-module spiral bevel gear and the number of teeth z of the driving wheel pinion 1 、Number of teeth on the driven wheel z 2 , pressure angle α, helix angle β, tooth width b and other basic parameters as well as gear geometry, calculate the external taper distance R of spiral bevel gear pair e , midpoint cone distance R, large wheel pitch cone angle δ 2 、Gear tooth root angle θ f2 、Pinion root angle θ f1 etc. geometric parameters.

[0011] Furthermore, in step 2, theoretically, the cutters for processing spiral bevel gears with different taper pitches should be different. However, in actual processing, it is impossible to design a cutter disc for each type of gear. Therefore, in order to reduce the number of cutter disc types, Gleason standardized the cutter disc diameter and divided it into: 1 / 2", 1 1 / 10 "、1 1 / 2 ", 2", 3 1 / 2 "、6"、7 1 / 2 ", 9", 12" and 18". In this way, there are corresponding standard nominal diameter cutters for processing spiral bevel gears of different sizes from small to large. Table 1 lists the nominal diameters of four standardized large diameter (also known as large module) milling cutters.

[0012] Table 1 Gleason recommended cutter head nominal diameter

[0013]

[0014] Since the pitch diameter of large-module spiral bevel gears is generally greater than 800mm, the maximum value of 18" or 457.2mm in the Gleason recommended series is too small.

[0015] From the analysis of diameters of 6", 9", 12", and 18", the common ratios of their geometric series are 1.5 and 1.33, and the average is 1.415. Therefore, based on the 18" cutter head, the common ratio 1.415 is used for design: 18"×1.415≈26", 18"×1.415 2 ≈36"=914.4mm, insert 18"×1.33 2 ≈32"=812.8mm, according to the outer cone distance R e Select a cutter head with a diameter of similar size, twice the nominal diameter of the cutter head, denoted as D d By comparing the corresponding ratios in Table 1: R e / D d The general range is 0.394~0.700, b / D dThe range is 0.197~0.219, judging rationality.

[0016] Furthermore, in step 3, the error caused by the double-sided machining and the large gear tooth root angle affecting the gear tooth shrinkage is considered to be reduced or offset. According to the geometric parameters of the spiral bevel gear in step 1, the theoretical cutter head diameter D is calculated. D for:

[0017]

[0018] The length unit is mm and the angle should be converted into radians for calculation.

[0019] Furthermore, in step 4, the theoretical cutter head diameter D is compared. D With the nominal diameter of the cutter head D d The size of the cutter head is 6", 7" 1 / 2 ", 9", so we considered introducing the half-inch standard and correcting the nominal diameter of the cutter head to make it consistent with D d The absolute value of the difference is the smallest, then the nominal diameter of the cutter disc is the actual cutter disc diameter D 0 .

[0020] The principle of the present invention is as follows: based on the spiral bevel gear geometric design method, the theoretical value of the cutter disc diameter is calculated by taking into account the reduction or elimination of the error caused by the shrinkage of the gear teeth; based on the Gleason standardized cutter disc diameter series, the nominal diameter of the large-module spiral bevel gear cutter disc is calculated according to the rules, and the actual value is obtained by approximating and correcting the theoretical value.

[0021] The beneficial effects of the present invention compared with the prior art are:

[0022] (1) The method proposed in the present invention is based on the existing standardized cutter head diameter series and is expanded to obtain a cutter head diameter exceeding 800 mm, which can provide a reference for the preliminary selection of the cutter head design for super-specification, heavy-loaded, large-module spiral bevel gears.

[0023] (2) Taking into account the reduction or elimination of gear tooth shrinkage error, the actual machining cutter diameter of large-module spiral bevel gears can be calculated and determined more accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 The figure is a flow chart of a method for designing cutter diameter parameters for heavy-loaded large-module spiral bevel gears. Specific implementation methods

[0026] A method for designing cutter diameter parameters of heavy-loaded large-module spiral bevel gears is as follows:

[0027] Step 1: Calculate the geometric parameters of the large wheel and the small wheel according to the basic parameters of the heavy-loaded large-module spiral bevel gear;

[0028] Step 2: Explore the extension rules of the standardized cutter head diameter series values ​​recommended by Gleason;

[0029] Step 3: Calculate the theoretical value of the cutter head diameter to reduce or eliminate the gear tooth shrinkage error;

[0030] Step 4: Combine the standardized nominal diameter of the cutter disc with the theoretical value of the cutter disc diameter to approximate the actual cutter disc diameter parameter.

[0031] Furthermore, in step 1, according to the module m of the heavy-duty large-module spiral bevel gear and the number of teeth z of the driving wheel pinion 1 、Number of teeth on the driven wheel z 2 , pressure angle α, helix angle β, tooth width b and other basic parameters as well as gear geometry, calculate the external taper distance R of spiral bevel gear pair e , midpoint cone distance R, large wheel pitch cone angle δ 2 、Gear tooth root angle θ f2 、Pinion root angle θ f1 etc. geometric parameters.

[0032] Take the basic parameters of heavy-loaded large-module spiral bevel gears in Table 2 as an example.

[0033] Table 2 Parameters of large module spiral bevel gears

[0034]

[0035] Calculate the outer cone distance R e =560.74mm, midpoint cone distance R = 465.74mm, large wheel pitch cone angle δ 2 =47.89°, large gear tooth root angle θ f2 =1.18°, pinion tooth root angle θ f1 =1.58°.

[0036] Furthermore, in step 2, theoretically, the cutters for processing spiral bevel gears with different taper pitches should be different. However, in actual processing, it is impossible to design a cutter disc for each type of gear. Therefore, in order to reduce the number of cutter disc types, Gleason standardized the cutter disc diameter and divided it into: 1 / 2", 1 1 / 10 "、1 1 / 2 ", 2", 3 1 / 2 "、6"、7 1 / 2 ", 9", 12" and 18". In this way, there are corresponding standard nominal diameter cutters for processing spiral bevel gears of different sizes from small to large. Table 1 lists the nominal diameters of four standardized large diameter (also known as large module) milling cutters.

[0037] Since the pitch diameter of large-module spiral bevel gears is generally greater than 800mm, the maximum value of 18" or 457.2mm in the Gleason recommended series is too small.

[0038] From the analysis of diameters of 6", 9", 12", and 18", the common ratios of their geometric series are 1.5 and 1.33, and the average is 1.415. Therefore, based on the 18" cutter head, the common ratio 1.415 is used for design: 18"×1.415≈26", 18"×1.415 2 ≈36"=914.4mm, insert 18"×1.33 2 ≈32"=812.8mm, according to the outer cone distance R e Select a cutter head with a diameter of similar size, twice the nominal diameter of the cutter head, denoted as D d By comparing the corresponding ratios in Table 1: R e / D d The general range is 0.394~0.700, b / D d The range is 0.197~0.219, judging rationality.

[0039] Assume the cutter head diameter D d =914.4mm, at this time, R e =560.74mm, R e / D d =0.613, b / D d =0.208. By comparing the corresponding ratios in Table 1: R e / D d The general range is 0.394~0.700, b / D d The range is 0.197 to 0.219, which is within the reasonable range, so the cutter head with a diameter of 36" is initially selected.

[0040] Furthermore, in step 3, the error caused by the double-sided machining and the large gear tooth root angle affecting the gear tooth shrinkage is considered to be reduced or offset. According to the geometric parameters of the spiral bevel gear in step 1, the theoretical cutter head diameter D is calculated. D for:

[0041]

[0042] The length unit is mm and the angle should be converted into radians for calculation.

[0043] Substitute the example parameters in step 1 to calculate the theoretical cutter head diameter D 0 =881.6mm.

[0044] Furthermore, in step 4, the theoretical cutter head diameter D is compared. DWith the nominal diameter of the cutter head D d The size of the cutter head is 6", 7" 1 / 2 ", 9", so we considered introducing the half-inch standard and correcting the nominal diameter of the cutter head to make it consistent with D d The absolute value of the difference is the smallest, then the nominal diameter of the cutter disc is the actual cutter disc diameter D 0 .

[0045] Subtract 1 from 36" 1 / 2 "Get 34 1 / 2 ", that is, 876.3mm, which is 5.3mm different from the theoretical cutter head diameter of 881.6mm, less than half an inch 12.7mm, and now meets the design requirements, that is, 34 1 / 2 =876.3mm is the actual cutter disc diameter.

[0046] In summary, in order to solve the problem that the existing Gleason cutter disc diameter series value range is limited and it is difficult to complete the design and processing of large-module spiral bevel gears, the present invention proposes a cutter disc diameter parameter design method for heavy-loaded large-module spiral bevel gears. Taking actual gear parameters as an example, the large-diameter cutter disc parameters that can complete gear processing and reduce errors are calculated, providing a theoretical basis for the design and processing of heavy-loaded large-module spiral bevel gears.

Claims

1. A method for designing the cutter diameter parameters of a heavy-loaded large-module spiral bevel gear. The method is implemented in the following steps: Step (1): Calculate the geometric parameters of the large wheel and the small wheel according to the basic parameters of the heavy-loaded large-module spiral bevel gear; Step (2): Explore the extension rules of the standardized cutter head diameter series values ​​recommended by Gleason; Step (3): Calculate the theoretical value of the cutter head diameter to reduce or eliminate the gear tooth shrinkage error; Step (4): Combine the standardized nominal diameter of the cutter disc with the theoretical value of the cutter disc diameter to approximate the actual cutter disc diameter parameter.

2. The extension rule according to claim 1, characterized in that: Based on the nominal diameters of Gleason's four standardized large-diameter (also known as large-module) milling cutters, 6", 9", 12", and 18", their geometric series common ratios are 1.5 and 1.33, and the average is 1.

415. Therefore, the common ratio of 1.415 is selected for the design based on the 18" cutter head.

3. The theoretical value of the cutter head diameter according to claim 1, characterized in that: Reduce or offset the error caused by double-sided machining and large gear root angle affecting gear shrinkage, and calculate the theoretical cutter diameter D D for: The length unit is mm and the angle should be converted into radians for calculation.

4. The actual cutter head diameter parameter obtained by approximation according to claim 1 is characterized in that: Comparison of theoretical cutter head diameter D D With the nominal diameter of the cutter head D d The size of the cutter head is 6", 7" 1 / 2", 9", so we considered introducing the half-inch standard and correcting the nominal diameter of the cutter head to make it consistent with D d When the absolute value of the difference is the smallest, the nominal diameter of the cutter disc is the actual cutter disc diameter D0.

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