A radially decreasing feed design method for gear turning considering cutting forces

Abstract

This invention discloses a radially decreasing feed design method for gear turning considering cutting forces. The method includes the following steps: calculating the full tooth height depth of cut based on gear parameters; setting the ratio of finishing depth of cut to full tooth height depth of cut and the maximum cutting force; initially determining the number of radial feeds and calculating the radial feed depth of cut for each roughing operation; solving for the chip thickness for each radial feed; calculating the cutting force for each radial feed; determining whether the cutting force is less than the maximum cutting force; if not, increasing the number of radial feeds until the calculated cutting force for each radial feed is less than the maximum cutting force; finally, calculating the radial feed depth of cut for each operation and using it as the optimal feed scheme. Compared with the traditional equal-interval feed method for gear turning, the radially decreasing feed design method of this invention can effectively prevent the tool from encountering severe cutting conditions with excessive cutting forces during a single feed, which is beneficial to improving tool life and tooth surface machining quality.

Description

Technical Field

[0001] This invention relates to the field of gear machining technology, and in particular to a radially decreasing feed design method for gear turning that takes into account cutting forces. Background Technology

[0002] Gears are key basic components in many pieces of equipment, and their machining technology is of great significance to improving the performance of equipment in various industries. High-efficiency gear turning is an emerging gear machining method with significant advantages such as high efficiency, high precision, and green dry cutting. It is becoming the preferred process for machining complex and precision gears in industrial robot harmonic / RV reducers and automotive reducers.

[0003] In actual gear turning, due to limitations in machine tool power, tool material strength, and the total depth of cut, the tool often needs to make multiple radial feeds in the direction of the total depth of cut to cut a complete tooth profile. Gear turning feed processes are divided into roughing and finishing. Roughing is mainly used for tooth preparation, and the number of feeds depends on machine tool power, tool material strength, maximum chip thickness, etc.; while finishing is used to cut the correct tooth profile. To obtain better tooth surface quality, the cutting parameters for finishing should be as small as possible, generally selected as 1% to 5% of the total depth of cut.

[0004] Currently, the radial feed rate of gear turning tools is often distributed at equal intervals. However, gear turning is a generating process; as the radial depth of cut increases, the generating envelope area and chip thickness also increase, leading to a continuous increase in cutting force during the gear turning process. Excessive cutting force will accelerate tool wear and affect the machining quality of the tooth surface. Therefore, how to distribute the radial feed rate of the tool according to the machine tool load, thereby improving tool life and tooth surface machining quality, is an urgent problem to be solved in gear turning. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a radially decreasing feed design method for gear turning that considers cutting forces by calculating the chip thickness and cutting force under radially decreasing feed conditions. This radially decreasing feed method can allocate the radial feed amount of the tool based on the cutting force, which is beneficial for improving tool life and tooth surface machining quality.

[0006] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0007] A radially decreasing feed design method for gear turning considering cutting forces includes:

[0008] Step 1: Calculate the total depth of cut A of the gear based on the gear parameters. p ;

[0009] Step 2: Based on the material strength and tooth surface machining quality requirements of the gear being machined, set the finishing depth of cut to the ratio p of the total tooth height depth of cut. t Generally, 1%-5% of the full tooth depth of cut is taken; based on the maximum output power of the gear turning machine tool and the material strength of the cutting tool, the maximum cutting force during the radial feed process is estimated, and based on this, the maximum cutting force [F] for a single radial feed in roughing and finishing is set. max ]; Combining the full tooth depth of cut A of the gear in step 1 p The finishing depth of cut and the roughing depth of cut are calculated.

[0010] Step 3: Initially determine the total number of radial feeds for roughing and finishing as n, with 1 radial feed for finishing; based on the roughing depth of cut obtained in Step 2, calculate the depth of cut a for each roughing feed using the radial decreasing feed method. p(i) ;

[0011] Step 4: Depth of cut a for each pass, depending on whether it is finishing or roughing. p(i) Calculate the chip thickness h for each radial feed. i ;

[0012] Step 5: Based on the chip thickness h of each radial feed in finishing and roughing, i Calculate the cutting force F for each radial feed. i ;

[0013] Step 6: Determine the cutting force F i Is it less than the maximum cutting force [F]? max If not, then the radial feed number of the tool is n = n + 1 and the process returns to step 3 until the calculated cutting force F of the gear is less than the maximum cutting force [F]. max If so, proceed to step 7; calculate and allocate the radial feed of the tool based on the set maximum cutting force by accurately calculating the chip thickness and cutting force for each radial feed.

[0014] Step 7: Calculate the radial depth of cut for each radial feed based on the number of radial feeds obtained in Step 6, thereby obtaining the optimal radial decreasing feed scheme for gear turning.

[0015] In the above technical solution, further, in step 3, the radial decreasing feed method preferably uses an arithmetic progression method or an inverse function decreasing method, wherein the arithmetic progression method and the inverse function decreasing method are used to calculate the depth of cut 'a' for each roughing operation. p(i) The specific calculation formulas are shown in (1) and (2) respectively:

[0016] a p(i) =A p (p1+(i-1)·d) (1)

[0017]

[0018] In the formula: A p p is the total depth of cut of the gear teeth; t The depth of cut in finishing is the proportion of the total depth of cut in the tooth height; n is the total number of radial feeds; i is the number of radial feeds; p1 is the proportion of the depth of cut in the first roughing feed to the total depth of cut in the tooth height; d is the tolerance of the radial arithmetic decreasing feed function; where p1 and d are given by the system of equations. The solution is obtained.

[0019] Furthermore, in step 4, given the known cutting depth 'a' of a certain feed... p(i) The radius of the gear cutting tool is r t The angle between the mounting shafts of the gear cutting tool and the cutting tool's feed per revolution along the gear axis is Σ. a Under these conditions, based on the generating motion relationship in gear machining, the chip thickness h for each radial feed is... i The calculations are performed using formulas (3)-(8):

[0020]

[0021] In the formula:

[0022] A x =r t -a p(i) (4)

[0023]

[0024] Furthermore, in step 5, the cutting force F of the gear teeth... i The calculation is performed using formula (9):

[0025]

[0026] Where: dF i The cutting force on each micro-element surface; K is the unit cutting force coefficient of the material being cut; μ represents the chip thickness h. i The influence coefficient on K; dA is the area of ​​each infinitesimal surface.

[0027] The beneficial effects of this invention are:

[0028] The radial decreasing feed method for gear turning of this invention takes into account the special characteristics of the gradually increasing tool envelope area and chip thickness in gear turning. By accurately calculating the chip thickness and cutting force for each radial feed, the radial feed rate of the tool can be calculated and allocated according to the set maximum cutting force. Compared with the traditional equal-interval feed method for gear turning, the radial decreasing feed design method of this invention can effectively prevent the tool from encountering severe cutting conditions with excessive cutting force during a single feed, which is beneficial to improving tool life and tooth surface machining quality. Attached Figure Description

[0029] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention, and therefore should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 This is a flowchart illustrating a radially decreasing feed design method for gear turning considering cutting forces, according to an embodiment of the present invention.

[0031] Figure 2 This refers to the developing envelope boundary of each radial feed in the roughing and finishing processes of this invention.

[0032] Figure 3 This refers to the cutting force for each radial feed in roughing and finishing operations using the arithmetic progression method.

[0033] Figure 4 This refers to the developing envelope boundary of each radial infeed in roughing and finishing processes in the equal-interval infeed method.

[0034] Figure 5 This refers to the cutting force for each radial feed in roughing and finishing processes using the equal-interval feed method. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0036] In this embodiment, the gear is an internal helical gear with involute tooth profile, and its main parameter is: number of teeth z. w =79, modulus m n =1.7mm, pressure angle α n =22°, helix angle β w =12.5° (left-handed), tooth tip circle diameter d a=136.464mm, tooth root circle diameter d f =144.937mm, displacement coefficient x n = 0.812mm.

[0037] The main parameters of a gear cutting tool are: number of teeth z t =44, Gear cutting tool radius r t =39.887mm, cutting tool mounting shaft intersection Σ=16°, cutting tool helix angle β w =3.5° (left-handed), feed per revolution of the gear cutting tool along the gear axis f a =0.2mm / rev.

[0038] like Figure 1 This invention provides a radially decreasing feed design method for gear turning considering cutting forces, specifically including the following steps:

[0039] Step 1: Calculate the total depth of cut A of the gear based on the gear parameters. p =(d f -d a ) / 2 = 4.237 mm.

[0040] Step 2: Set the finishing depth of cut to the ratio p of the total tooth depth of cut. t =3%, the maximum cutting force [F] for a single radial feed in roughing and finishing. max ] = 1550N;

[0041] Step 3: Initially determine the number of radial feeds n = 8, where the first 7 radial feeds are for roughing and the 8th is for finishing. A radial arithmetic progression feed method is used, and the formula a is calculated using this method. p(i) =A p (p1+(i-1)·d) calculates the depth of cut for each of the 7 roughing operations as a p(1) =1.027mm, a p(2) =0.881mm, a p(3) =0.734mm, a p(4) =0.587mm, a p(5) =0.440mm, a p(6) =0.294mm, a p(7) = 0.147mm, where: A p p is the total depth of cut of the gear teeth; t The depth of cut in finishing is the proportion of the total depth of cut in the tooth height; n is the total number of radial feeds; i is the number of feed depths; p1 is the proportion of the first feed depth in roughing to the total depth of cut in the tooth height; d is the tolerance of the radial arithmetic decreasing feed function; where p1 and d are given by the system of equations. We can solve for p1 = 0.2425 and d = -0.0346.

[0042] The depth of cut for the 8th finishing pass is a. p(8) =p t *A p =0.127mm.

[0043] like Figure 2 It is the expanding envelope boundary of each radial feed in roughing and finishing in the arithmetic progression feed method. For example... Figure 3 This refers to the cutting force of each radial feed in roughing and finishing operations using the arithmetic progression method. It can be seen that in gear turning, different radial feed depths result in different tool envelope areas and cutting forces. Furthermore, when workpiece parameters, tool parameters, and tool mounting parameters change, the relationship between the radial feed depth and the envelope area becomes complex and difficult to describe mathematically. The chip thickness and cutting force need to be calculated to evaluate the rationality of the radial feed depth.

[0044] Step 4: Based on the generating motion relationship of gear turning, given the known depth of cut 'a' for a certain feed... p(i) The radius of the gear cutting tool is r t The angle between the mounting shafts of the gear cutting tool and the cutting tool's feed per revolution along the gear axis is Σ. a Under the given conditions, the chip thickness generated by the gear cutting tool in each radial feed can be expressed by the formula The calculation yields, where A x =r t -a p(i) , The chip thicknesses for the eight radial feeds during roughing and finishing are as follows: h1 = 0.127 mm, h2 = 0.120 mm, h3 = 0.113 mm, h4 = 0.105 mm, h5 = 0.094 mm, h6 = 0.079 mm, h7 = 0.058 mm, and h8 = 0.054 mm.

[0045] Step 5: From the formula The cutting forces for the eight radial feeds during roughing and finishing were calculated as follows: F1 = 1083 N, F2 = 1238 N, F3 = 1443 N, F4 = 1519 N, F5 = 1494 N, F6 = 1146 N, F7 = 683 N, and F8 = 736 N. Where dF i The cutting force on each micro-element surface; in this embodiment, the gear material is 42CrMo, so the unit cutting force coefficient K of the material being cut is 2452 N / mm. 2 ; chip thickness h i The influence coefficient of K is μ = 0.26; dA is the area of ​​each infinitesimal surface.

[0046] Step 6: Determine the cutting force F of the total 8 radial feeds during roughing and finishing. i With maximum cutting force [F max The relationship between 1550N and the maximum cutting force was found to be less than the maximum cutting force. Therefore, there is no need to return to step 3 to increase the number of feeds, and we can proceed directly to step 7. By accurately calculating the chip thickness and cutting force for each radial feed, the radial feed rate of the tool can be calculated and allocated according to the set maximum cutting force.

[0047] Step 7: Obtain the radial depth of cut after 8 passes, as shown in Table 1. Use this as the optimal radial decreasing feed scheme for gear turning. During gear turning, this radial decreasing feed scheme can effectively improve tool life and tooth surface quality.

[0048] Table 1. Radial depth of cut for each step in this embodiment.

[0049]

[0050] Table 2 shows the radial depth of cut calculated using the traditional equal-interval feed method and with the same gear and tool parameters. That is, the radial depth of cut is the same 0.587 mm for all 7 radial feeds during roughing.

[0051] Table 2. Radial depth of cut per pass for the traditional equal-interval feed method

[0052]

[0053] Figure 4 It is the developing envelope boundary of each radial infeed in the roughing and finishing processes of the traditional equal-interval infeed method. Figure 5 This refers to the cutting force of each radial feed in roughing and finishing operations using the traditional equal-interval feed method. Figure 4 and Figure 5 It can be seen that although the radial depth of cut is the same for each pass in the roughing process, the cutting force increases with the number of passes. Specifically, the cutting force for the 6th pass is 1712 N, and the cutting force for the 7th pass is 2112 N, which are significantly higher than the cutting forces for other passes. This higher cutting force increases heat generation, worsens the cutting conditions for the gear turning tool, and reduces tool life.

[0054] Therefore, compared with the traditional equal-interval feed method for gear turning, the radial decreasing feed design method of the present invention can effectively prevent the tool from encountering severe cutting conditions with excessive cutting force during a single feed, which is beneficial to improving tool life and tooth surface machining quality.

Claims

1. A radially decreasing feed design method for gear turning considering cutting forces, characterized in that, The method includes the following steps: Step 1: Calculate the total depth of cut A of the gear based on the gear parameters. p ; Step 2: Set the finishing depth of cut to the ratio p of the total tooth depth of cut. t And the maximum cutting force [F] for a single radial feed in roughing and finishing. max ]; Combining the full tooth depth of cut A of the gear in step 1 p The finishing depth of cut and the roughing depth of cut are calculated. Step 3: Initially determine the total number of radial feeds for roughing and finishing as n, with 1 radial feed for finishing; based on the roughing depth of cut obtained in Step 2, calculate the depth of cut a for each roughing feed using the radial decreasing feed method. p(i) ; Step 4: Based on the depth of cut for finishing and the depth of cut for roughing each time, 'a'... p(i) Calculate the chip thickness h for each radial feed. i ; Step 5: Based on the chip thickness h of each radial feed in finishing and roughing, i Calculate the cutting force F for each radial feed. i ; Step 6: Determine the cutting force F i Is it less than the maximum cutting force [F]? max If not, then the radial feed number of the tool is n = n + 1 and the process returns to step 3 until the calculated cutting force F of the gear is less than the maximum cutting force [F]. max If so, proceed to step 7; Step 7: Calculate the radial depth of cut for each radial feed based on the number of radial feeds obtained in Step 6, thereby obtaining the optimal radial decreasing feed scheme for gear turning.

2. The radially decreasing feed design method for gear turning considering cutting force as described in claim 1, characterized in that, In step 3, the radial decreasing feed method is implemented using either an arithmetic decreasing method or an inverse function decreasing method.

3. The radially decreasing feed design method for gear turning considering cutting force as described in claim 2, characterized in that, The depth of cut a for the i-th roughing pass is calculated using the arithmetic progression method. p(i) The calculation formula is as follows: a p(i) =A p (p1+(i-1)·d) (1) Where p1 is the proportion of the first depth of cut in roughing to the total tooth height depth of cut; i is the number of radial feeds; d is the tolerance of the radial arithmetic decreasing feed function; where p1 and d are derived from the system of equations. The solution is obtained.

4. The radially decreasing feed design method for gear turning considering cutting force as described in claim 2, characterized in that, The depth of cut a for the i-th roughing pass is calculated using the inverse function decreasing method. p(i) The calculation formula is as follows:

5. The radially decreasing feed design method for gear turning considering cutting force as described in claim 1, characterized in that, Chip thickness h per radial feed i The calculation method is as follows: Given that the radius of the gear cutting tool is r t The angle between the mounting shafts of the gear cutting tool and the cutting tool's feed per revolution along the gear axis is Σ. a Under the condition that the chip thickness h of the i-th radial feed is i The calculations are performed using formulas (3)-(8): In the formula: A x =r t -a p(i) (4) 6. The radially decreasing feed design method for gear turning considering cutting force as described in claim 1, characterized in that, In step 5, the cutting force F for each radial feed is... i The calculation is performed using formula (9): Where: dF i The cutting force on each micro-element surface; K is the unit cutting force coefficient of the material being cut; μ represents the chip thickness h. i The influence coefficient on K; dA is the area of ​​each infinitesimal surface.

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