A "roll-grinding-honing" multi-process parameter collaborative optimization and decision method

Abstract

The application discloses a 'rolling-grinding-honing' multi-process parameter collaborative optimization and decision method, which comprises the following steps: 1) according to the characteristics of gear machining process in the automobile high-speed gear machining process, selecting process parameter variables to be optimized, and constructing a 'rolling-grinding-honing' process optimization model; 2) using a multi-objective snake optimization algorithm to iteratively solve the 'rolling-grinding-honing' process optimization model, and obtaining a Pareto collaborative process parameter solution set; 3) based on an entropy weight-TOPSIS decision method, evaluating and sorting the Pareto collaborative process parameter solution set, and obtaining optimal process parameters. The application solves the problem of how to obtain the overall optimal solution in the machining process rather than a single process optimal solution in the new energy automobile high-speed gear machining process.

Description

Technical Field

[0001] This invention relates to the field of workpiece processing, specifically a collaborative optimization and decision-making method for multiple process parameters, including "rolling-grinding-honing". Background Technology

[0002] High-speed gears are core components of the drive transmission system of new energy vehicles. To ensure high speed, high efficiency, low noise and long service life, extremely high requirements are placed on the machining quality of gears, such as geometric accuracy, tooth surface modification and surface texture.

[0003] The common machining processes for high-speed gears in new energy vehicles mainly include gear hobbing, gear grinding, and gear honing. The demands of high-speed gears for consistent gear surfaces, optimized tooth texture, and improved overall machining efficiency have prompted manufacturers to research the integrated allocation of allowances and precision across the three processes of hobbing, grinding, and honing, as well as the collaborative optimization of these processes, thereby improving machining efficiency and quality.

[0004] Currently, there is only optimization of process parameters for a single gear machining process, and the machining allowance is usually regarded as a constant value without considering the impact of its variation. Summary of the Invention

[0005] The purpose of this invention is to provide a collaborative optimization and decision-making method for multiple process parameters in "rolling-grinding-honing", which includes the following steps:

[0006] 1) Based on the characteristics of gear processing technology in the high-speed gear processing of automobiles, select the process parameter variables to be optimized and construct a "rolling-grinding-honing" process optimization model;

[0007] The process parameter variables to be optimized include the process parameters of gear hobbing, gear grinding, and gear honing.

[0008] The process parameters of the gear hobbing process include the hob cutting speed v. h axial feed rate f of hob h hob diameter d h0 Number of hobbing heads z h0 1. Hobbing machining allowance;

[0009] The process parameters of the gear grinding process include the grinding wheel cutting speed v. g Axial feed rate f of grinding wheel g Grinding wheel cutting depth a g Grinding allowance x2;

[0010] The process parameters for the honing process include the workpiece spindle speed n. ph Honing wheel X-axis feed rate f phx Z-axis feed rate f of honing wheel phzSparkless honing cycle time t phs Honing machining allowance x3.

[0011] The optimization objectives of the "hobbing-grinding-honing" process optimization model include the total processing time T, total processing cost C, and gear surface machining quality F after the final process of the hobbing, grinding, and honing processes.

[0012] The total processing time T is shown below:

[0013] (1)

[0014] In the formula, T h T represents the time required for the gear hobbing process. g T represents the time required for the gear grinding process. ph Indicates the time required for the honing process;

[0015] Among them, the time T required for the gear hobbing process h Time required for gear grinding process T g Time required for honing process (T) ph They are shown below:

[0016] (2)

[0017] In the formula, t hba t gba t phba These represent the basic processing times for gear hobbing, gear grinding, and gear honing, respectively; t hau t gau t phau These represent the auxiliary processing times for gear hobbing, gear grinding, and gear honing, respectively; t hc t gc t phc These represent the time required for tool changes or dressing in gear hobbing, gear grinding, and gear honing processes, respectively; N h0 N g0 N ph0 These represent the number of gears that can be machined after dressing the hob, grinding wheel, and honing wheel used in the gear hobbing, gear grinding, and gear honing processes, respectively.

[0018] Among them, the basic processing time t hba Basic processing time t gba Basic processing time t phba They are shown below:

[0019] (3)

[0020] (4)

[0021] (5)

[0022] In the formula, d g B is the diameter of the grinding wheel, and C is the width of the workpiece gear. T For the approach stroke of the dry-cutting hob; U e For dry-cutting hobs, the near-safe allowance; U a For the safe withdrawal allowance of the dry-cutting hob; O T z0 represents the overtravel stroke of the dry cutting hob; z1 represents the number of hob heads of the dry cutting hob; d represents the number of teeth on the workpiece gear; ha0 a is the outer diameter of the dry-cutting hob; g This refers to the depth of cut of the grinding wheel.

[0023] Among them, the approach stroke C of the dry cutting hob T And the overtravel of the dry cutting hob T They are shown below:

[0024] (6)

[0025] In the formula, d ha1 is the tip circle diameter of the workpiece gear; is the hob mounting angle of the dry cutting hob; is the pressure angle of the workpiece gear; m n x1 is the normal module of the gear on the workpiece; x1 is the hobbing allowance.

[0026] The total processing cost C is shown below:

[0027] (7)

[0028] In the formula, C h This indicates the cost of machining a single workpiece using the gear hobbing process; C g This indicates the cost of machining a single workpiece using the gear grinding process; C ph This indicates the cost of machining a single workpiece using the honing process; C wg This indicates the material cost of a single gear component.

[0029] The cost C of machining a single workpiece by gear hobbing h As shown below:

[0030] (8)

[0031] In the formula: C hm C represents the depreciation cost of a high-speed dry gear hobbing machine allocated per unit time. hl C represents the labor cost per unit time for high-speed dry gear hobbing machines. he C represents the electricity cost per unit time for a high-speed dry gear hobbing machine. ht0 For the purchase cost of high-speed dry cutting rollers, C h1For the cost of recoating high-speed dry-cutting hobs, C h2 For the regrinding cost of high-speed dry cutting hobs, k h N represents the number of times a hob can be sharpened. h The number of gears that can be machined after the hob used in the gear hobbing process is replaced;

[0032] The cost C of machining a single workpiece using gear grinding process g As shown below:

[0033] (9)

[0034] In the formula, C gm C represents the depreciation cost of a worm gear grinding machine allocated per unit time. gl C represents the labor cost per unit time for a worm gear grinding machine. ge C represents the electricity cost per unit time for a worm gear grinding machine. gc C represents the cost of cutting fluid per unit time for a worm gear grinding machine. gt0 Cost of purchasing worm gear grinding wheels; The number of gears that can be machined after the grinding wheel used in the gear grinding process is replaced;

[0035] The cost C of machining a single workpiece using honing process ph As shown below:

[0036] (10)

[0037] In the formula, C phm C represents the depreciation cost of an internal meshing high-power honing machine tool allocated per unit time. phl C represents the labor cost per unit time for an internal meshing high-strength gear honing machine. phe C represents the electricity cost per unit time for an internal meshing high-power honing machine. phc C represents the cost of cutting fluid per unit time for internal meshing high-strength honing machine tools; pht0 Cost of purchasing honing wheels; The number of gears that can be processed after the honing wheel used in the honing process is replaced;

[0038] The surface finish quality F is shown below:

[0039] (11)

[0040] In the formula, α1, α2, and α3 are weight functions; f α0 f β0 f p0 These are the expected values ​​of the gear machining accuracy indicators: total deviation of gear tooth profile, total deviation of gear helix, and cumulative total deviation of tooth pitch; f α fβ f p The fitting parameters are obtained by testing the honing quality through actual experiments and fitting the equations.

[0041] The constraints of the "hobbing-grinding-honing" process optimization model include constraints on the hobbing process, the grinding process, the machining allowance of each gear, the hobbing process parameters, the grinding process parameters, and the honing process parameters.

[0042] The constraints of the gear hobbing process are as follows:

[0043]

[0044]

[0045] The constraints of the gear grinding process are as follows:

[0046] (16)

[0047] In the formula, d g0 C is the diameter of the grinding wheel. b This represents the critical value for burn damage to gear materials.

[0048] The machining allowance constraints for each gear are shown below:

[0049] (17)

[0050] The constraints for gear hobbing process parameters are as follows:

[0051] (18)

[0052]

[0053] The constraints of the gear grinding process parameters are as follows:

[0054] (19)

[0055] In the formula, , These represent the grinding wheel cutting speeds. The upper and lower limits; , These represent the axial feed rate of the grinding wheel. The upper and lower limits; , These represent the depth of cut of the grinding wheel. The upper and lower limits;

[0056] The honing process parameters are constrained as follows:

[0057] (20)

[0058]

[0059] The optimized model for the "rolling-grinding-honing" process is shown below:

[0060] (twenty one)

[0061] In the formula, T is the total processing time; C is the total processing cost; and F is the surface finish quality of the gear after the final process.

[0062] 2) The multi-objective snake optimization algorithm is used to iteratively solve the optimization model of the "rolling-grinding-honing" process to obtain the Pareto cooperative process parameter solution set;

[0063] The steps for iteratively solving the "rolling-grinding-honing" process optimization model using a multi-objective snake optimization algorithm to obtain the Pareto cooperative process parameter solution set include:

[0064] 2.1) Initialize the population of "rolling-grinding-honing" collaborative process parameters:

[0065] The population representation of the "rolling-grinding-honing" collaborative process parameters is (a1, a2, ..., a...). m ), where m is a positive integer, a i For the i-th process parameter in the population, input a i The upper and lower limits are denoted as a. max and a min ;

[0066] Set r to a random number between [0,1], and randomly initialize the population of collaborative process parameters within the numerical range [0,1] according to the "rolling-grinding-honing" process optimization model;

[0067] Set the maximum number of iterations it, the number of iterations nu = 0, and the maximum capacity of the archive M;

[0068] Randomly select a process parameter and assign it to the optimal process parameter E; randomly select a target value and assign it to the archived optimal target value.

[0069] Among them, the i-th process parameter a in the population i As shown below:

[0070] (twenty two)

[0071] 2.2) The snake population was classified by sex, and the classification criteria are as follows:

[0072] (twenty three)

[0073] In the formula, N m represents the number of male snakes, N f represents the number of female snakes, γ is a value between [0, 1]; N is the total number of snakes;

[0074] 2.3) Determine whether the current iteration number nu < it holds. If so, go to step 2.4); otherwise, go to step 2.9);

[0075] 2.4) Calculate the objective values of the objective function processing time T, process cost C, and gear surface quality F, find the non-dominated solutions and store them in the archive;

[0076] 2.5) Judge the storage capacity of the archive: If the number of stored archives reaches the maximum archive capacity, go to step 2.6); otherwise, go to step 2.7);

[0077] 2.6) Use the greedy strategy to save the current optimal solution, set a predefined distance for each solution, calculate the number of solutions within this distance to measure the corresponding crowding degree; then use the roulette method to eliminate one or more solutions according to the crowding degree;

[0078] 2.7) Judge the behavior of the snakes during population update, and update the population according to the calculation formulas in different behavior stages;

[0079] The steps of judging the behavior of the snakes during population update and updating the population according to the calculation formulas in different behavior stages include:

[0080] 2.7.1) Define the environmental temperature Temp and the food quantity Q, that is:

[0081] (24)

[0082] In the formula, c1 is a constant;

[0083] 2.7.2) Judge the behavior stage of the snake according to the values of the environmental temperature Temp and the food quantity Q;

[0084] When the food quantity Q < 0.25, the snake is in the first behavior stage. At this time, the snake searches for food by choosing any random position;

[0085] When the food quantity Q ≥ 0.25 and the environmental temperature Temp ≥ 0.6, the snake is in the second behavior stage. At this time, the snake only moves towards the food;

[0086] When the food quantity Q ≥ 0.25 and the environmental temperature Temp < 0.6, the snake is in the third behavior stage. At this time, the snake is in the fighting mode or the mating mode. The choice of the fighting mode or the mating mode is determined by the value of rand. If rand > 0.5, it is the fighting mode; otherwise, it is the mating mode.

[0087] When the snake is in the first behavioral phase, the male snake's position is updated as follows:

[0088] (25)

[0089] In the formula, a i,m Let a be the position of the i-th male snake; rand,m The position of the random male snake; rand is a random number between 0 and 1; c2 is a constant;

[0090] Male snakes' ability to find food A m As shown below:

[0091] (26)

[0092] In the formula, f rand,m It is a rand,m fitness, f i,m It is the fitness of the i-th male;

[0093] When the snake is in the first behavioral phase, the female snake's position is updated as follows:

[0094] (27)

[0095] In the formula, a i,f Let a be the position of the i-th female snake. rand,f This represents the location of a random female snake; rand is a random number between 0 and 1.

[0096] The female snake's ability to find food A f As shown below:

[0097] (28)

[0098] In the formula, f rand,f It is a rand,f fitness, f i,f It is the fitness of the i-th male;

[0099] When the snake is in the second behavioral phase, the position of the i-th female or male snake is as follows:

[0100] (29)

[0101] In the formula, a i,j Refers to the position of the i-th female or male; a food This refers to the optimal snake position, where c3 is a constant;

[0102] When the snake is in the third behavioral phase and in combat mode, the male snake's position updates as follows:

[0103] (30)

[0104] In the formula, a i,m Refers to the i-th male position; a best,f This is the optimal position for a female snake in the population;

[0105] The male snake's combat ability FM is as follows:

[0106] (31)

[0107] In the formula, f best,f It is the fitness of the optimal female snake location in the population, f i It is agent adaptability.

[0108] When the snake is in the third behavioral phase and in combat mode, the female snake's position updates as follows:

[0109] (32)

[0110] In the formula: a i,f Refers to the i-th female position; a best,m It is the optimal position for a male snake in the population;

[0111] The female snake's combat abilities (FF) are shown below:

[0112] (33)

[0113] In the formula: f best,m It represents the fitness of the optimal male snake position in the population.

[0114] When the snake is in the third behavioral stage and in mating mode, the male snake's position is updated as follows:

[0115] (34)

[0116] The mating ability of male snakes (MM) is as follows:

[0117] (35)

[0118] In the formula, , It represents the fitness of the i-th male snake and the fitness of the m-th female snake.

[0119] When the snake is in the third behavioral stage and in mating mode, the female snake's position is updated as follows:

[0120] (36)

[0121] The mating ability (MF) of female snakes is shown below:

[0122] (37)

[0123] In the formula, f best,m It is the fitness of the optimal male snake position in the population;

[0124] When a snake is in its third behavioral stage and in mating mode, if offspring are produced, the offspring will replace the worst male and female according to their sex, with the following replacement criteria:

[0125] (38)

[0126] In the formula, a worst,m It is the worst position among male snakes in the population, a worst,f It is the worst position among the female snakes in the population.

[0127] 2.8) Update the optimal collaborative process parameters:

[0128] Update the collaborative process parameter population, nu = nu + 1, and then proceed to step 2.3).

[0129] 2.9) Output the population values ​​of collaborative process parameters stored in the archive and the objective value of the objective function.

[0130] 3) The Pareto collaborative process parameter solution set is evaluated and ranked based on the entropy weight-TOPSIS decision method to obtain the optimal process parameters.

[0131] The steps for evaluating and ranking the Pareto cooperative process parameter solution set based on the entropy weight-TOPSIS decision method include:

[0132] 3.1) Establish a decision matrix for multiple process parameters of "rolling-grinding-honing". The decision matrix includes m sets of process parameters and n evaluation indicators; i represents the i-th set of process parameters, and j represents the j-th evaluation indicator. Indicate decision parameters;

[0133] 3.2) After normalizing the evaluation indicators, a new standardized decision matrix is ​​obtained. ; This represents the new standardized decision parameters;

[0134] 3.3) Calculate the weight of the j-th indicator in the i-th solution of the standardized decision matrix Y to obtain the weight matrix Z of each indicator, and calculate the indicator information entropy e based on the weight matrix Z. j ,Right now:

[0135] (39)

[0136] In the formula, k is a constant; These are elements in the weight matrix Z;

[0137] 3.4) Calculate the indicator weight W using indicator information entropy. j ,Right now:

[0138] (40)

[0139] 3.5) Utilizing indicator weights W j Construct a normalized weighted matrix z is a decision matrix and has ;

[0140] 3.6) Calculate the positive ideal solution for each evaluation object. and negative ideal solution That is, the maximum and minimum values ​​of each evaluation indicator, calculated using the following formula:

[0141] (41)

[0142]

[0143] 3.7) Calculate the Euclidean distance D of each evaluation index from the positive ideal solution. i + Euclidean distance D between the negative ideal solution and the solution i - ,Right now:

[0144] (42)

[0145] 3.8) Calculate the matching progress of each evaluation index with the ideal solution. ;

[0146] 3.9) Based on the obtained proximity, sort the solution set of process parameters to obtain the optimal solution of "rolling-grinding-honing" collaborative process parameters, and complete the multi-index evaluation and decision of "rolling-grinding-honing" collaborative process parameters.

[0147] The technical effects of this invention are undeniable. Based on the rapid optimization capability of the multi-objective snake algorithm, this invention can simultaneously optimize the process parameters and machining allowance in the "rolling-grinding-honing" gear machining process, and evaluate and make decisions on the obtained Pareto process parameter solution set based on the entropy weight-TOPSIS model, providing manufacturing enterprises with direct and reliable process parameter solutions, which is more scientific and practical than the traditional method of relying on experience to make process parameter decisions.

[0148] This invention selects the total processing time, processing cost, and gear processing quality of the "rolling-grinding-honing" process as objective functions to establish a multi-objective optimization model. Then, iterative optimization is performed based on a multi-objective snake algorithm to obtain Pareto process parameter solutions. Next, the collaborative process parameter solution set is evaluated and ranked based on the entropy-weighted TOPSIS model, ultimately obtaining an evaluated multi-process parameter solution for "rolling-grinding-honing" to guide the processing of high-speed gears for new energy vehicles. The multi-objective snake algorithm, as an emerging heuristic algorithm, has a fast iteration speed and strong optimization ability, quickly finding a set of Pareto process parameter solutions with superior performance. The entropy-weighted TOPSIS model evaluates and makes decisions on the obtained Pareto process parameter solution set, thereby obtaining the optimal process parameter solution for high-speed gear processing in new energy vehicles. By comprehensively utilizing these two methods, the collaborative optimization problem of high-speed gear processing in new energy vehicles with multiple optimization objectives and multiple process parameters can be solved. This addresses the problem that existing process parameter optimization methods only focus on single-process optimization and do not consider the allocation of processing allowances, leading to inconsistent production cycles and reduced production efficiency. Attached Figure Description

[0149] Figure 1 This is a flowchart of the present invention;

[0150] Figure 2 This is a flowchart illustrating the iterative optimization using the multi-target snake algorithm in this invention;

[0151] Figure 3 This is a flowchart illustrating the evaluation and decision-making process based on the entropy weight-TOPSIS model of this invention. Detailed Implementation

[0152] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0153] Example 1:

[0154] See Figures 1 to 3 A collaborative optimization and decision-making method for multiple process parameters in "rolling-grinding-honing" includes the following steps:

[0155] 1) Based on the characteristics of gear processing technology in the high-speed gear processing of automobiles, select the process parameter variables to be optimized and construct a "rolling-grinding-honing" process optimization model;

[0156] The process parameter variables to be optimized include the process parameters of gear hobbing, gear grinding, and gear honing.

[0157] The process parameters of the gear hobbing process include the hob cutting speed v. h axial feed rate f of hob h hob diameter d h0 Number of hobbing heads z h0 1. Hobbing machining allowance;

[0158] The process parameters of the gear grinding process include the grinding wheel cutting speed v. g Axial feed rate f of grinding wheel g Grinding wheel cutting depth a g Grinding allowance x2;

[0159] The process parameters for the honing process include the workpiece spindle speed n. ph Honing wheel X-axis feed rate f phx Z-axis feed rate f of honing wheel phz Sparkless honing cycle time t phs Honing machining allowance x3.

[0160] The optimization objectives of the "hobbing-grinding-honing" process optimization model include the total processing time T, total processing cost C, and gear surface machining quality F after the final process of the hobbing, grinding, and honing processes.

[0161] The total processing time T is shown below:

[0162] (1)

[0163] In the formula, T h T represents the time required for the gear hobbing process. g T represents the time required for the gear grinding process. ph Indicates the time required for the honing process;

[0164] Among them, the time T required for the gear hobbing process h Time required for gear grinding process T g Time required for honing process (T) ph They are shown below:

[0165] (2)

[0166] In the formula, t hba t gba t phba These represent the basic processing times for gear hobbing, gear grinding, and gear honing, respectively; t hau t gau t phau These represent the auxiliary processing times for gear hobbing, gear grinding, and gear honing, respectively; t hc t gc tphc These represent the time required for tool changes or dressing in gear hobbing, gear grinding, and gear honing processes, respectively; N h0 N g0 N ph0 These represent the number of gears that can be machined after dressing the hob, grinding wheel, and honing wheel used in the gear hobbing, gear grinding, and gear honing processes, respectively.

[0167] Among them, the basic processing time t hba Basic processing time t gba Basic processing time t phba They are shown below:

[0168] (3)

[0169] (4)

[0170] (5)

[0171] In the formula, d g B is the diameter of the grinding wheel, and C is the width of the workpiece gear. T For the approach stroke of the dry-cutting hob; U e For dry-cutting hobs, the near-safe allowance; U a For the safe withdrawal allowance of the dry-cutting hob; O T z0 represents the overtravel stroke of the dry cutting hob; z1 represents the number of hob heads of the dry cutting hob; d represents the number of teeth on the workpiece gear; ha0 a is the outer diameter of the dry-cutting hob; g This refers to the depth of cut of the grinding wheel.

[0172] Among them, the approach stroke C of the dry cutting hob T And the overtravel of the dry cutting hob T They are shown below:

[0173] (6)

[0174] In the formula, d ha1 is the tip circle diameter of the workpiece gear; is the hob mounting angle of the dry cutting hob; is the pressure angle of the workpiece gear; m n x1 is the normal module of the gear on the workpiece; x1 is the hobbing allowance.

[0175] The total processing cost C is shown below:

[0176] (7)

[0177] In the formula, C h This indicates the cost of machining a single workpiece using the gear hobbing process; C g This indicates the cost of machining a single workpiece using the gear grinding process; Cph This indicates the cost of machining a single workpiece using the honing process; C wg This indicates the material cost of a single gear component.

[0178] The cost C of machining a single workpiece by gear hobbing h As shown below:

[0179] (8)

[0180] In the formula: C hm C represents the depreciation cost of a high-speed dry gear hobbing machine allocated per unit time. hl C represents the labor cost per unit time for high-speed dry gear hobbing machines. he C represents the electricity cost per unit time for a high-speed dry gear hobbing machine. ht0 For the purchase cost of high-speed dry cutting rollers, C h1 For the cost of recoating high-speed dry-cutting hobs, C h2 For the regrinding cost of high-speed dry cutting hobs, k h N represents the number of times a hob can be sharpened. h The number of gears that can be machined after the hob used in the gear hobbing process is replaced;

[0181] Among them, the number of gears N that can be machined after the hob used in the gear hobbing process is changed. h As shown below:

[0182]

[0183] In the formula, Indicates the machinable length of a single tooth of the hob. Indicates the number of chip grooves of the hob, Indicates the effective transmission distance of the hobbing cutter. Indicates the helix angle of the machined gear; Indicates the number of teeth;

[0184] The cost C of machining a single workpiece using gear grinding process g As shown below:

[0185] (9)

[0186] In the formula, C gm C represents the depreciation cost of a worm gear grinding machine allocated per unit time. gl C represents the labor cost per unit time for a worm gear grinding machine. ge C represents the electricity cost per unit time for a worm gear grinding machine. gc C represents the cost of cutting fluid per unit time for a worm gear grinding machine. gt0 Cost of purchasing worm gear grinding wheels; The number of gears that can be machined after the grinding wheel used in the gear grinding process is replaced;

[0187] The cost C of machining a single workpiece using honing process ph As shown below:

[0188] (10)

[0189] In the formula, C phm C represents the depreciation cost of an internal meshing high-power honing machine tool allocated per unit time. phl C represents the labor cost per unit time for an internal meshing high-strength gear honing machine. phe C represents the electricity cost per unit time for an internal meshing high-power honing machine. phc C represents the cost of cutting fluid per unit time for internal meshing high-strength honing machine tools; pht0 Cost of purchasing honing wheels; The number of gears that can be processed after the honing wheel used in the honing process is replaced;

[0190] The surface finish quality F is shown below:

[0191] (11)

[0192] In the formula, α1, α2, and α3 are weight functions; f α0 f β0 f p0 These are the expected values ​​of the gear machining accuracy indicators: total deviation of gear tooth profile, total deviation of gear helix, and cumulative total deviation of tooth pitch; f α f β f p The fitting parameters are obtained by testing the honing quality through actual experiments and fitting the equations.

[0193] The constraints of the "hobbing-grinding-honing" process optimization model include constraints on the hobbing process, the grinding process, the machining allowance of each gear, the hobbing process parameters, the grinding process parameters, and the honing process parameters.

[0194] The constraints of the gear hobbing process are as follows:

[0195]

[0196]

[0197] The constraints of the gear grinding process are as follows:

[0198] (16)

[0199] In the formula, d g0C is the diameter of the grinding wheel. b This represents the critical value for burn damage to gear materials.

[0200] The machining allowance constraints for each gear are shown below:

[0201] (17)

[0202]

[0203] The constraints for gear hobbing process parameters are as follows:

[0204] (18)

[0205] The constraints of the gear grinding process parameters are as follows:

[0206] (19)

[0207] The honing process parameters are constrained as follows:

[0208] (20)

[0209] The optimized model for the "rolling-grinding-honing" process is shown below:

[0210] (twenty one)

[0211] In the formula, T is the total processing time; C is the total processing cost; and F is the surface finish quality of the gear after the final process.

[0212] 2) The multi-objective snake optimization algorithm is used to iteratively solve the optimization model of the "rolling-grinding-honing" process to obtain the Pareto cooperative process parameter solution set;

[0213] The steps for iteratively solving the "rolling-grinding-honing" process optimization model using a multi-objective snake optimization algorithm to obtain the Pareto cooperative process parameter solution set include:

[0214] 2.1) Initialize the population of "rolling-grinding-honing" collaborative process parameters:

[0215] The population representation of the "rolling-grinding-honing" collaborative process parameters is (a1, a2, ..., a...). m ), where m is a positive integer, a i For the i-th process parameter in the population, input a i The upper and lower limits are denoted as a. max and a min ;

[0216] Set \(r\) as a random number between \([0,1]\), and randomly initialize the collaborative process parameter population within the numerical range \([0,1]\) according to the "rolling - grinding - honing" process optimization model;

[0217] Set the maximum number of iterations \(it\), the iteration number \(nu = 0\), and the maximum capacity \(M\) of the archive;

[0218] Randomly select a process parameter and assign it to the optimal process parameter \(E\), and select a target value and assign it to the optimal target value of the archive;

[0219] Among them, the \(i\) - th process parameter \(a\) in the population i is as follows:

[0220] (22)

[0221] 2.2) Classify the snake population by gender, and the classification criteria are as follows:

[0222] (23)

[0223] In the formula, \(N\) m represents the number of male snakes, \(N\) f represents the number of female snakes, \(\gamma\) is a value between \([0,1]\); \(N\) is the total number of snakes;

[0224] 2.3) Judge whether the current iteration number \(nu\lt it\) holds. If so, go to step 2.4); otherwise, go to step 2.9);

[0225] 2.4) Calculate the target values of the objective functions processing time \(T\), process cost \(C\) and gear surface quality \(F\), find the non - dominated solutions and store them in the archive;

[0226] 2.5) Judge the storage capacity of the archive: If the number of archived items reaches the maximum archive capacity, go to step 2.6); otherwise, go to step 2.7);

[0227] 2.6) Use the greedy strategy to save the current optimal solution, set a predefined distance for each solution, calculate the number of solutions within this distance to measure the corresponding crowding degree; then use the roulette - wheel method to eliminate one or more solutions according to the crowding degree;

[0228] 2.7) Judge the behavior of the snakes during population update, and update the population according to the calculation formulas of different behavior stages;

[0229] The steps of judging the behavior of the snakes during population update and updating the population according to the calculation formulas of different behavior stages include:

[0230] 2.7.1) Define the environmental temperature \(Temp\) and the food quantity \(Q\), that is:

[0231] (twenty four)

[0232] In the formula, c1 is a constant;

[0233] 2.7.2) Determine the snake's behavioral stage based on the values ​​of ambient temperature (Temp) and food quantity (Q);

[0234] When the amount of food Q < 0.25, the snake is in the first behavioral stage, at which point the snake searches for food by choosing any random location;

[0235] When the amount of food Q≥0.25 and the ambient temperature Temp≥0.6, the snake is in the second behavioral stage, at which point the snake will only move towards the food.

[0236] When the food quantity Q≥0.25 and the ambient temperature Temp<0.6, the snake is in the third behavioral stage. At this time, the snake is in either fighting mode or mating mode. The choice between fighting mode and mating mode is determined by the value of rand. If rand>0.5, it is in fighting mode; otherwise, it is in mating mode.

[0237] When the snake is in the first behavioral phase, the male snake's position is updated as follows:

[0238] (25)

[0239] In the formula, a i,m Let a be the position of the i-th male snake; rand,m The position of the random male snake; rand is a random number between 0 and 1; c2 is a constant;

[0240] Male snakes' ability to find food A m As shown below:

[0241] (26)

[0242] In the formula, f rand,m It is a rand,m fitness, f i,m It is the fitness of the i-th male;

[0243] When the snake is in the first behavioral phase, the female snake's position is updated as follows:

[0244] (27)

[0245] In the formula, a i,f Let a be the position of the i-th female snake. rand,f This represents the location of a random female snake; rand is a random number between 0 and 1.

[0246] The female snake's ability to find food A f As shown below:

[0247] (28)

[0248] In the formula, f rand,f It is a rand,f fitness, f i,f It is the fitness of the i-th male;

[0249] When the snake is in the second behavioral phase, the position of the i-th female or male snake is as follows:

[0250] (29)

[0251] In the formula, a i,j Refers to the position of the i-th female or male; a food This refers to the optimal snake position, where c3 is a constant;

[0252] When the snake is in the third behavioral phase and in combat mode, the male snake's position updates as follows:

[0253] (30)

[0254] In the formula, a i,m Refers to the i-th male position; a best,f This is the optimal position for a female snake in the population;

[0255] The male snake's combat ability FM is as follows:

[0256] (31)

[0257] In the formula, f best,f It is the fitness of the optimal female snake location in the population, f i It is agent adaptability.

[0258] When the snake is in the third behavioral phase and in combat mode, the female snake's position updates as follows:

[0259] (32)

[0260] In the formula: a i,f Refers to the i-th female position; a best,m It is the optimal position for a male snake in the population;

[0261] The female snake's combat abilities (FF) are shown below:

[0262] (33)

[0263] In the formula: f best,m It represents the fitness of the optimal male snake position in the population.

[0264] When the snake is in the third behavioral stage and in mating mode, the male snake's position is updated as follows:

[0265] (34)

[0266] The mating ability of male snakes (MM) is as follows:

[0267] (35)

[0268] In the formula, , It represents the fitness of the i-th male snake and the fitness of the m-th female snake.

[0269] When the snake is in the third behavioral stage and in mating mode, the female snake's position is updated as follows:

[0270] (36)

[0271] The mating ability (MF) of female snakes is shown below:

[0272] (37)

[0273] In the formula, f best,m It is the fitness of the optimal male snake position in the population;

[0274] When a snake is in its third behavioral stage and in mating mode, if offspring are produced, the offspring will replace the worst male and female according to their sex, with the following replacement criteria:

[0275] (38)

[0276] In the formula, a worst,m It is the worst position among male snakes in the population, a worst,f It is the worst position among the female snakes in the population.

[0277] 2.8) Update the optimal collaborative process parameters:

[0278] Update the collaborative process parameter population, nu = nu + 1, and then proceed to step 2.3).

[0279] 2.9) Output the population values ​​of collaborative process parameters stored in the archive and the objective value of the objective function.

[0280] 3) The Pareto collaborative process parameter solution set is evaluated and ranked based on the entropy weight-TOPSIS decision method to obtain the optimal process parameters.

[0281] The steps for evaluating and ranking the Pareto cooperative process parameter solution set based on the entropy weight-TOPSIS decision method include:

[0282] 3.1) Establish a decision matrix for multiple process parameters of "rolling-grinding-honing". The decision matrix includes m sets of process parameters and n evaluation indicators; i represents the i-th set of process parameters, and j represents the j-th evaluation indicator.

[0283] 3.2) After normalizing the evaluation indicators, a new standardized decision matrix is ​​obtained. ;

[0284] 3.3) Calculate the weight of the j-th indicator in the i-th solution of the standardized decision matrix Y to obtain the weight matrix Z of each indicator, and calculate the indicator information entropy e based on the weight matrix Z. j ,Right now:

[0285] (39)

[0286] In the formula, k is a constant; These are elements in the weight matrix Z;

[0287] 3.4) Calculate the indicator weight W using indicator information entropy. j ,Right now:

[0288] (40)

[0289] 3.5) Utilizing indicator weights W j Construct a normalized weighted matrix z is a decision matrix and has ;

[0290] 3.6) Calculate the positive ideal solution S for each evaluation object. + and negative ideal solution S - That is, the maximum and minimum values ​​of each evaluation indicator, calculated using the following formula:

[0291] (41)

[0292]

[0293] 3.7) Calculate the Euclidean distance D of each evaluation index from the positive ideal solution. i + Euclidean distance D between the negative ideal solution and the solution i - ,Right now:

[0294] (42)

[0295] 3.8) Calculate the matching progress of each evaluation index with the ideal solution. ;

[0296] 3.9) Based on the obtained proximity, sort the solution set of process parameters to obtain the optimal solution of "rolling-grinding-honing" collaborative process parameters, and complete the multi-index evaluation and decision of "rolling-grinding-honing" collaborative process parameters.

[0297] Example 2:

[0298] See Figures 1 to 3 A collaborative optimization and decision-making method for multiple process parameters, including "rolling-grinding-honing", is proposed to guide the processing of high-speed gears for new energy vehicles.

[0299] Taking the machining of a high-speed gear for a new energy vehicle by a gear manufacturing company as an example, some relevant gear workpiece parameters and machine tool parameters are shown in Table 1:

[0300] Table 1. Parameters of some gear workpieces and machine tool performance parameters

[0301]

[0302] like Figure 1 The method shown includes the following steps:

[0303] Step 1: Based on the characteristics of the three gear machining processes used in the high-speed gear manufacturing of new energy vehicles—hobbing, grinding, and honing—the process parameters of these three processes are selected as variables to be optimized, constructing a "hobbing-grinding-honing" process optimization model. Its objective function includes the total machining time T, the total machining cost C, and the surface finish quality F of the gear after the final process.

[0304] Step 2: Use the multi-objective snake optimization algorithm to iteratively solve the multi-objective optimization model of "rolling-grinding-honing" with multiple process parameters to obtain the Pareto cooperative process parameter solution set.

[0305] Step 3: Evaluate and rank the Pareto collaborative process parameter solution set obtained in Step 2 based on the entropy weight-TOPSIS decision method to obtain the optimal solution, which facilitates production decision-making.

[0306] In this embodiment, the process parameters and objective function selected for the optimization model in step 1 are specifically as follows:

[0307] Gear hobbing process uses hob cutting speed v h axial feed rate f of hob h hob diameter d h0 Number of hobbing heads z h0 And the hobbing machining allowance x1 is used as a process parameter variable to be optimized;

[0308] Gear grinding process uses grinding wheel cutting speed v g Axial feed rate f of grinding wheel g Grinding wheel cutting depth a gAnd the grinding allowance x2 is used as a process parameter variable to be optimized;

[0309] The honing process is based on the spindle speed n of the workpiece. ph Honing wheel X-axis feed rate f phx Z-axis feed rate f of honing wheel phz Sparkless honing cycle time t phs And the honing machining allowance x3 is used as a process parameter variable to be optimized;

[0310] The total processing time T in the objective function is calculated by the following formula:

[0311] (1)

[0312] In the formula: T h T represents the time required for the gear hobbing process. g T represents the time required for the gear grinding process. ph This indicates the time required for the honing process. The aforementioned times are calculated using the following formulas:

[0313] (2)

[0314] In the formula: t hba , t gba , t phba This indicates the basic processing time (t) for each step of the "rolling-grinding-honing" process. hau , t gau , t phau This indicates the auxiliary time for each step of the "rolling-grinding-honing" process, in t. hc , t gc , t phc N represents the time required for tool changing or dressing in the "tumbling-grinding-honing" process. h N g0 N ph0 This indicates the number of gears that can be machined after each tool change or dressing of the hob, grinding wheel, and honing wheel used in the "hob-grind-honing" process.

[0315] In gear hobbing, the life of the hob is usually expressed by the single-tooth cutting length. The tool change time in the machining time of each gear can be converted into the ratio of the tool change time to the number of gears that can be machined in a single hob sharpening cycle, and the number of machined gears N is calculated. h Calculated by the following formula:

[0316] (3)

[0317] In actual processing, enterprises typically set the dressing and replacement intervals for grinding wheels and honing wheels based on the number of gears being processed. In this embodiment, the grinding wheel dressing interval is set to every N... g0 Each gear is replaced once, with the replacement interval set to every N.g Each gear is used once, and the honing wheel dressing interval is set to every N. ph0 Each gear is replaced once, with the replacement interval set to every N. ph One gear at a time.

[0318] The total processing cost C is calculated using the following formula:

[0319] (4)

[0320] In the formula: C h C represents the cost of machining a single workpiece using the gear hobbing process. g C represents the cost of machining a single workpiece using the gear grinding process. ph C represents the cost of machining a single workpiece using the honing process. wg This indicates the material cost of a single gear component.

[0321] The surface finish quality F is determined by the final honing process in the "rolling-grinding-honing" series, and the total deviation f of the gear tooth profile after honing is also determined by this process. α Total deviation f of gear helix β and the cumulative total deviation of tooth pitch f p The three variables are represented as shown in the following formula:

[0322] (5)

[0323] In the above formula, α1, α2, and α3 are weighting functions set according to different error requirements based on the usage scenario of the gear being processed; f α0 f β0 f p0 It is based on the expected values ​​of gear machining accuracy indicators for total gear profile deviation, total gear helix deviation, and cumulative total pitch deviation, as determined by the international standard ISO 1328-1:1995 for different accuracy grades; f α f β f p It was obtained by testing the honing quality through actual experiments and fitting the results using equations.

[0324] In this embodiment, α1, α2, and α3 are all 1, f α0 f β0 f p0 This corresponds to the ISO 5 level accuracy value, f α f β f p The honing quality was tested through actual experiments and fitted using equations. The three factors can be represented by the following general expression:

[0325] (5-1)

[0326] In the formula: fi For tooth surface error, ε i As an additional constant, 𝜉 mn This refers to the influence coefficients corresponding to process parameters and their interactions.

[0327] For gear hobbing processes:

[0328] Processing time t hba Calculated by the following formula:

[0329] (6)

[0330] In the formula: C T For the approach stroke of the dry-cutting hob, U e For dry cutting hobs, B is the approach safety allowance, where B is the workpiece gear width, and U is the allowable distance. a For the safe allowable withdrawal of the dry-cutting hob, O T For the overtravel of the dry cutting hob, U e and U a In this embodiment, 2 mm is used, z0 is the number of cutter heads of the dry cutting hob, z1 is the number of teeth of the workpiece gear, and d ha0 C represents the outer diameter of the dry-cutting hob. T and O T Calculated by the following formula:

[0331] (7)

[0332] In the formula: d ha1 Let be the addendum circle diameter of the workpiece gear, ∠ be the hob mounting angle of the dry cutting hob, and ∠ be the pressure angle of the workpiece gear. (m) n x1 is the normal module of the gear on the workpiece, and x1 is the hobbing allowance.

[0333] The cost C of processing a single workpiece h Calculated by the following formula:

[0334] (8)

[0335] In the formula: C hm C represents the depreciation cost of a high-speed dry gear hobbing machine allocated per unit time. hl C represents the labor cost per unit time for high-speed dry gear hobbing machines. he C represents the electricity cost per unit time for a high-speed dry gear hobbing machine. ht0 For the purchase cost of high-speed dry cutting rollers, C h1 For the cost of recoating high-speed dry-cutting hobs, C h2 For the regrinding cost of high-speed dry cutting hobs, k h This refers to the number of times the hobbing cutter can be sharpened.

[0336] For gear grinding processes:

[0337] Processing time t gba Calculated by the following formula:

[0338] (9)

[0339] In the formula: d g B is the diameter of the grinding wheel, and B is the width of the workpiece gear.

[0340] The cost C of processing a single workpiece g Calculated by the following formula:

[0341] (10)

[0342] In the formula: C gm C represents the depreciation cost of a worm gear grinding machine allocated per unit time. gl C represents the labor cost per unit time for a worm gear grinding machine. ge C represents the electricity cost per unit time for a worm gear grinding machine. phc C represents the cost of cutting fluid per unit time for internal meshing high-strength honing machine tools. gt0 Cost of purchasing worm gear grinding wheels.

[0343] Regarding honing processes:

[0344] Processing time t phba Calculated by the following formula:

[0345] (11)

[0346] The cost C of processing a single workpiece ph Calculated by the following formula:

[0347] (12)

[0348] In the formula: C phm C represents the depreciation cost of an internal meshing high-power honing machine tool allocated per unit time. phl C represents the labor cost per unit time for an internal meshing high-strength gear honing machine. phe C represents the electricity cost per unit time for an internal meshing high-power honing machine. phc C represents the cost of cutting fluid per unit time for internal meshing high-strength honing machine tools. pht0 Cost of purchasing honing wheels.

[0349] In this embodiment, the constraints of the optimization model in step 1 include:

[0350] Precision requirements for gear hobbing:

[0351] (13)

[0352] In the formula: r h R is the radius of the hob tip. ha R represents the surface roughness of the gear hobbing teeth. hamax The maximum surface roughness of the hobbing gear is 1.6 in this embodiment, which is the maximum allowable surface roughness for the next machining process.

[0353] Cutting force requirements for gear hobbing:

[0354] (14)

[0355] In the formula: F chmax The maximum cutting force to ensure machining accuracy.

[0356] Power requirements for gear hobbing process:

[0357] (15)

[0358] In the formula: 𝜂 h P is the motor power coefficient. eh To ensure the rated motor power.

[0359] Because honing requires high processing quality from preceding processes, the precision requirement for the gear grinding process is the surface roughness of the left and right tooth surfaces. This is obtained through actual testing of the gear grinding quality and fitting an equation, and can be expressed as follows:

[0360] (16)

[0361] In the formula: R gal R represents the surface roughness of the left tooth. gar This refers to the surface roughness of the right tooth.

[0362] In this embodiment, the surface roughness of the left and right tooth surfaces is characterized by the following expression:

[0363] (16-1)

[0364] Where: ε i λ is an additional constant. li With λ ri This refers to the influence coefficients corresponding to process parameters and their interactions.

[0365] To prevent gears from being burned during the gear grinding process, the following conditions must be met:

[0366] (17)

[0367] In the formula: d g0 C is the diameter of the grinding wheel. bThis represents the critical value for burn damage to gear materials.

[0368] Let x be the total machining allowance of the gear from blank to finished product. The heat treatment process after gear hobbing causes x to be affected. r If the deviation is within the acceptable range, then the machining allowance for each gear must satisfy the following:

[0369] (18)

[0370] In the formula: x 1min x 2min x 3min These represent the minimum machining allowances required for gear hobbing, gear grinding, and gear honing processes, respectively. 1max x 2max x 3max These represent the maximum machining allowance required for gear hobbing, gear grinding, and gear honing processes, respectively.

[0371] At the same time, due to the inherent characteristics of the machine tool, each process parameter has upper and lower limits:

[0372] The gear hobbing process parameters meet the following requirements:

[0373] (19)

[0374] Grinding process parameters meet:

[0375] (20)

[0376] Honing process parameters meet:

[0377] (twenty one)

[0378] In summary, the optimization model can be expressed by the following formula:

[0379] (twenty two)

[0380] In this embodiment, the specific steps of using the multi-objective snake algorithm to iteratively optimize the process parameter variables in step 2 are as follows: Figure 2 The following are included:

[0381] Step 2.1: Initialize the population of "rolling-grinding-honing" collaborative process parameters:

[0382] The population representation of the "rolling-grinding-honing" collaborative process parameters is (a1, a2, ..., a...). m ), where m is a positive integer, a i For the i-th process parameter in the population, input a i upper and lower limits of value a max and a min, let r be a random number between [0, 1], and randomly initialize the collaborative process parameter population within the numerical range using Equation 22. Set the maximum number of iterations it, the iteration number nu = 0, the maximum capacity M of the archive, randomly select a process parameter and assign it to the optimal process parameter E, and select a target value and assign it to the optimal target value archived;

[0383] (23)

[0384] Step 2.2: Classify the snake population by gender as shown in the following equation:

[0385] (24)

[0386] In the formula: N m represents the number of male snakes, N f represents the number of female snakes, γ is a value between [0, 1], which is determined according to the specific situation.

[0387] In this embodiment, the maximum number of iterations it is 300, the maximum capacity M of the archive is 150, and γ takes 0.5.

[0388] Step 2.3: Judge the end condition of the iteration:

[0389] If nu < it, go to Step 2.4, otherwise go to Step 2.9.

[0390] Step 2.4: Calculate the target values of the objective function processing time T, process cost C, and gear surface quality F, find the non-dominated solutions and store them in the archive;

[0391] Step 2.5: Judge the storage capacity of the archive:

[0392] If the number of archived items reaches the maximum capacity of the archive, go to Step 2.6, otherwise go to Step 2.7;

[0393] Step 2.6: Use the greedy strategy to save the current optimal solution. By considering a predefined distance for each solution, calculate the number of solutions within this distance to measure their respective crowding degrees. Then, use the roulette method to select one solution to be eliminated according to the crowding degree.

[0394] Step 2.7: Judge the behavior of the snake during population update, and update the population according to the calculation formulas in different behavior stages:

[0395] Step 2.8: Update the optimal collaborative process parameters:

[0396] Update the collaborative process parameter population, nu = nu + 1, and then go to Step 2.3;

[0397] Step 2.9: Output the population values ​​of the collaborative process parameters stored in the archive and the objective value of the objective function.

[0398] In this embodiment, step 2.7 of step 2, which uses a multi-objective snake algorithm to iteratively optimize the process parameter variables, specifically includes:

[0399] Step 2.7.1: First, define the ambient temperature (Temp) and the quantity of food (Q):

[0400] (25)

[0401] In the formula: c1 is a constant with a value of 0.5.

[0402] Step 2.7.2: If Q < 0.25, the snake searches for food by choosing any random location and updates its location; otherwise, go to step 2.7.3.

[0403] Male snake location updated:

[0404] (26)

[0405] In the formula: a i,m Refers to the i-th male position, a rand,m This refers to the location of a random male, where rand is a random number between 0 and 1, c2 is a constant with a value of 0.05, and A represents the male's ability to find food. m Calculated by the following formula:

[0406] (27)

[0407] In the formula: f rand,m It is a rand,m fitness, f i,m It is the fitness of the i-th male.

[0408] Female snake location updated:

[0409] (28)

[0410] In the formula: a i,f Refers to the i-th female position, a rand,f This refers to the location of a random female, where `rand` is a random number between 0 and 1, and `A` represents the female's ability to find food. f Calculated by the following formula:

[0411] (29)

[0412] In the formula: f rand,f It is a rand,f fitness, f i,fIt is the fitness of the i-th male.

[0413] Step 2.7.3: If Q ≥ 0.25 and Temp ≥ 0.6, the snake will only move towards the food. Otherwise, go to step 2.7.4;

[0414] (30)

[0415] In the formula: a i,j Refers to the position of the i-th female or male; a food This refers to the optimal snake position, where c3 is a constant with a value of 2.

[0416] Step 2.7.4: If Q≥0.25 and Temp<0.6, the snake will be in either battle mode or mating mode. The choice between battle mode and mating mode is determined by the value of rand. If rand>0.5, it is in battle mode; otherwise, it is in mating mode.

[0417] In this embodiment, the update of the combat mode and mating mode positions in step 2.7.4 of the step 2 step when iteratively optimizing the process parameter variables using the multi-target snake algorithm specifically includes:

[0418] Battle Mode:

[0419] Male snake location updated:

[0420] (31)

[0421] In the formula: a i,m Refers to the i-th male position, a best,f This is the best position for a female snake in the population. FM (Fatal Performance) is the fighting ability of a male snake, calculated using the following formula:

[0422] (32)

[0423] In the formula: f best,f It is the fitness of the best female snake position in the population, f i It is agent adaptability.

[0424] Female snake location updated:

[0425] (33)

[0426] In the formula: a i,f Refers to the i-th female position, a best,m This is the best position for a male snake in the population. FF represents the female snake's combat ability, calculated using the following formula:

[0427] (34)

[0428] In the formula: f best,mIt is the best male snake's positional fitness in the population.

[0429] In mating mode:

[0430] Male snake location updated:

[0431] (35)

[0432] In the formula: MM represents the mating ability of the male snake, calculated by the following formula:

[0433] (36)

[0434] In the formula: f best,f It is the fitness of the best female snake position in the population, f i It is agent adaptability.

[0435] Female snake location updated:

[0436] (37)

[0437] In the formula: MF represents the mating ability of the female snake, calculated by the following formula:

[0438] (38)

[0439] In the formula: f best,m It is the best male snake's positional fitness in the population.

[0440] If snakes produce offspring, the offspring will be selected according to sex, replacing the worst male and female:

[0441] (39)

[0442] In the formula: a worst,m It is the worst position among male snakes in the population, a worst,f It is the worst position among the female snakes in the population.

[0443] In this embodiment, step 3 is as follows: Figure 3 The following specific steps are shown:

[0444] Step 3.1: Establish a decision matrix for multiple process parameters of "rolling-grinding-honing". There are a total of m sets of process parameters and n evaluation indicators, where i represents the i-th set of process parameters and j represents the j-th evaluation indicator.

[0445] Step 3.2: After normalizing the evaluation indicators, a new standardized decision matrix is ​​obtained. ;

[0446] Step 3.3: Calculate the weight of the j-th indicator in the i-th solution of the standardized decision matrix Y to obtain the weight matrix Z of each indicator, and then calculate the indicator information entropy e. j The specific calculation formula is as follows:

[0447] (40)

[0448] In the formula: k is a constant, k = 1 / lnm;

[0449] Step 3.4: Calculate the indicator weight W using indicator information entropy. j :

[0450] (41)

[0451] Step 3.5: Based on the entropy weight method, construct a normalized weighted matrix using the calculated index weights. z is a decision matrix and has ;

[0452] Step 3.6: Calculate the positive ideal solution for each evaluation object. and negative ideal solution That is, the maximum and minimum values ​​of each evaluation indicator, calculated using the following formula:

[0453] (42)

[0454] Step 3.7: Calculate the Euclidean distance of each evaluation index from the positive ideal solution and the negative ideal solution, denoted as D respectively. i + and D i - :

[0455] (43)

[0456] Step 3.8: Calculate the matching progress of each evaluation index with the ideal solution. ;

[0457] Step 3.9: Based on the obtained proximity, sort the solution set of process parameters to obtain the optimal solution of "rolling-grinding-honing" collaborative process parameters, and complete the multi-index evaluation and decision-making process of "rolling-grinding-honing" collaborative process parameters.

[0458] The solution set of process parameters obtained from the multi-object snake algorithm is shown in Table 2:

[0459] Table 2 Solution set of process parameters

[0460]

[0461] Based on step 3 and Table 2, the ranking scheme of process parameter schemes after multi-attribute decision-making is shown in Table 3:

[0462] Table 3 Sorting Scheme for Process Parameters

[0463]

[0464] It can be seen that when considering the optimal combination of processing time, processing cost, and gear surface quality, the optimal solution is P1 with the following process parameters: {3 80 900 1.42 5.625 63.00 119.93 0.054 0.125 4308 274 0.0065.0 0.025}. When processing time is the primary objective, P1 should be chosen; when processing cost is the primary objective, P1 should also be chosen; and when considering gear surface quality, P11 should be chosen with the following process parameters: {3 78 8301.40 5.625 63.00 118.51 0.055 0.125 4000 600 0.001 5.0 0.025}.

[0465] The results show that the method of this invention can simultaneously optimize three process parameters: rolling, grinding, and honing, obtaining multiple sets of process parameter solutions. The proposed multi-objective snake algorithm has a fast convergence speed and can quickly find the optimal solution. The entropy weight-TOPSIS decision method used can effectively make multi-attribute decisions on the optimized process parameter solutions, providing enterprise process engineers with a variety of processing schemes, meeting the actual needs of processing and production, and effectively reducing the cost of high-speed gear processing for new energy vehicles and improving production cycle time, thus promoting enterprise efficiency.

Claims

1. A collaborative optimization and decision-making method for multiple process parameters in a "rolling-grinding-honing" process, characterized in that, It includes the following steps: Step 1) According to the characteristics of the gear processing technology in the automotive high-speed gear processing process, select the process parameter variables to be optimized, and construct a "hobbing-grinding-honing" process optimization model; Step 2) Use the multi-objective snake optimization algorithm to iteratively solve the "hobbing-grinding-honing" process optimization model to obtain the Pareto collaborative process parameter solution set; Step 3) Based on the entropy weight - TOPSIS decision-making method, evaluate and rank the Pareto collaborative process parameter solution set to obtain the optimal process parameters.

2. The "rolling-grinding-honing" multi-process parameter collaborative optimization and decision-making method according to claim 1, characterized in that, The process parameter variables to be optimized include the process parameters of the hobbing process, the process parameters of the grinding process, and the process parameters of the honing process; The process parameters of the gear hobbing process include the hob cutting speed v. h axial feed rate f of hob h hob diameter d h0 Number of hobbing heads z h0 1. Hobbing machining allowance; The process parameters of the gear grinding process include the grinding wheel cutting speed v. g Axial feed rate f of grinding wheel g Grinding wheel cutting depth a g Grinding allowance x2; The process parameters for the honing process include the workpiece spindle speed n. ph Honing wheel X-axis feed rate f phx Z-axis feed rate f of honing wheel phz Sparkless honing cycle time t phs Honing machining allowance x3.

3. The "rolling-grinding-honing" multi-process parameter collaborative optimization and decision-making method according to claim 1, characterized in that, The optimization objectives of the "hobbing-grinding-honing" process optimization model include the total processing time T, the total processing cost C, and the gear surface processing quality F after the last process of the hobbing process, the grinding process, and the honing process; Among them, the total processing time T is as follows: (1) In the formula, T h T represents the time required for the gear hobbing process. g T represents the time required for the gear grinding process. ph Indicates the time required for the honing process; Among them, the time T required for the gear hobbing process h Time required for gear grinding process T g Time required for honing process (T) ph They are shown below: (2) In the formula, t hba t gba t phba These represent the basic processing times for gear hobbing, gear grinding, and gear honing, respectively; t hau t gau t phau These represent the auxiliary processing times for gear hobbing, gear grinding, and gear honing, respectively; t hc t gc t phc These represent the time required for tool changes or dressing in gear hobbing, gear grinding, and gear honing processes, respectively; N h0 N g0 N ph0 These represent the number of gears that can be machined after dressing the hob, grinding wheel, and honing wheel used in the gear hobbing, gear grinding, and gear honing processes, respectively. Among them, the basic processing time t hba Basic processing time t gba Basic processing time t phba They are shown below: (3) (4) (5) In the formula, d g B is the diameter of the grinding wheel, and C is the width of the workpiece gear. T For the approach stroke of the dry-cutting hob; U e For dry-cutting hobs, the near-safe allowance; U a For the safe withdrawal allowance of the dry-cutting hob; O T z0 represents the overtravel stroke of the dry cutting hob; z1 represents the number of hob heads of the dry cutting hob; d represents the number of teeth on the workpiece gear; ha0 a is the outer diameter of the dry-cutting hob; g This refers to the depth of cut of the grinding wheel. Among them, the approach stroke C of the dry cutting hob T And the overtravel of the dry cutting hob T They are shown below: (6) In the formula, d ha1 is the tip circle diameter of the workpiece gear; is the hob mounting angle of the dry cutting hob; is the pressure angle of the workpiece gear; m n x1 is the normal module of the gear on the workpiece; x2 is the hobbing allowance. The total processing cost C is as follows: (7) In the formula, C h Indicates the unit cost of gear hobbing; C g This indicates the cost of machining a single workpiece using the gear grinding process; C ph This indicates the cost of machining a single workpiece using the honing process; C wg This indicates the material cost of a single gear component. The cost C of machining a single workpiece by gear hobbing h As shown below: (8) In the formula: C hm C represents the depreciation cost of a high-speed dry gear hobbing machine allocated per unit time. hl C represents the labor cost per unit time for high-speed dry gear hobbing machines. he C represents the electricity cost per unit time for a high-speed dry gear hobbing machine. ht0 For the purchase cost of high-speed dry cutting hobs, C h1 For the cost of recoating high-speed dry-cutting slitting cutters, C h2 For the regrinding cost of high-speed dry cutting hobs, k h N represents the number of times a hob can be sharpened. h The number of gears that can be machined after the hob used in the gear hobbing process is replaced; The cost C of machining a single workpiece using gear grinding process g As shown below: (9) In the formula, C gm C represents the depreciation cost of a worm gear grinding machine allocated per unit time. gl C represents the labor cost per unit time for a worm gear grinding machine. ge C represents the electricity cost per unit time for a worm gear grinding machine. gc C represents the cost of cutting fluid per unit time for a worm gear grinding machine. gt0 Cost of purchasing worm gear grinding wheels; N g The number of gears that can be machined after the grinding wheel used in the gear grinding process is replaced; The cost C of machining a single workpiece using honing process ph As shown below: (10) In the formula, C phm C represents the depreciation cost of an internal meshing high-power honing machine tool allocated per unit time. phl C represents the labor cost per unit time for an internal meshing high-strength gear honing machine. phe C represents the electricity cost per unit time for an internal meshing high-power honing machine. phc C represents the cost of cutting fluid per unit time for internal meshing high-strength honing machine tools; pht0 Cost of purchasing honing wheels; N ph The number of gears that can be processed after the honing wheel used in the honing process is replaced; The surface processing quality F is as follows: (11) In the formula, α1, α2, and α3 are weight functions; f α0 f β0 f p0 These are the expected values ​​of the gear machining accuracy indicators: total deviation of gear tooth profile, total deviation of gear helix, and cumulative total deviation of tooth pitch; f α f β f p The fitting parameters are obtained by testing the honing quality through actual experiments and fitting the equations.

4. The "rolling-grinding-honing" multi-process parameter collaborative optimization and decision-making method according to claim 1, characterized in that: The constraint conditions of the "hobbing-grinding-honing" process optimization model include the hobbing process processing constraint, the grinding process processing constraint, the machining allowance constraint of each gear process, the hobbing process parameter constraint, the grinding process parameter constraint, and the honing process parameter constraint; The hobbing process processing constraint is as follows: (12) (13) (14) (15) In the formula, R gal R represents the surface roughness of the left tooth. gar For the roughness of the right tooth surface; r h R is the radius of the hob tip. ha R represents the surface roughness of the gear hobbing teeth. hamax The maximum allowable surface roughness for gear hobbing to proceed to the next machining step; F chmax The maximum cutting force to ensure machining accuracy; F ch The cutting force in the gear hobbing process; 𝜂 h P is the motor power coefficient. eh To ensure the rated motor power; R gamax This represents the upper limit of roughness. The grinding process processing constraint is as follows: (16) In the formula, d g0 C is the diameter of the grinding wheel. b This represents the critical value for burn damage to gear materials. The machining allowance constraint of each gear process is as follows: (17) In the formula, x 1min x 2min x 3min These represent the minimum machining allowances required for gear hobbing, gear grinding, and gear honing processes, respectively. 1max x 2max x 3max These represent the maximum machining allowances required for gear hobbing, gear grinding, and gear honing processes, respectively; x represents the total machining allowance; x r For deviation; The hobbing process parameter constraint is as follows: (18) In the formula, v hmax v hmin These represent the hobbing speeds v and v, respectively. h upper and lower limits; f hmax f hmin These represent the axial feed rate f of the hob, respectively. h The upper and lower limits; d h0max d h0min These represent the hob diameter d. h0 The upper and lower limits; z h0max z h0min These represent the number of hobbing heads z. h0 The upper and lower limits; The grinding process parameter constraint is as follows: (19) In the formula, v gmax v gmin These represent the grinding wheel cutting speeds v and v, respectively. g upper and lower limits; f gmax f gmin These represent the axial feed rate f of the grinding wheel. g The upper and lower limits; a gmax a gmin These represent the cutting depth 'a' of the grinding wheel. g The upper and lower limits; The honing process parameter constraint is as follows: (20) In the formula, f phzmax f phzmin These represent the Z-axis feed rate f of the honing wheel. phz upper and lower limits; f phxmax f phxmin These represent the X-axis feed rate f of the honing wheel, respectively. phx The upper and lower limits; n phmax n phmin These represent the spindle speed n of the workpiece, respectively. ph The upper and lower limits; t phmax t phmin These represent the sparkless honing cycle time t, respectively. phs The upper and lower limits; The "hobbing-grinding-honing" process optimization model is as follows: (21) In the formula, T is the total processing time; C is the total processing cost; F is the gear surface processing quality after the last process.

5. The "rolling-grinding-honing" multi-process parameter collaborative optimization and decision-making method according to claim 1, characterized in that: The steps of using the multi-objective snake optimization algorithm to iteratively solve the "hobbing-grinding-honing" process optimization model to obtain the Pareto collaborative process parameter solution set include: Step 1) Initialize the "hobbing-grinding-honing" collaborative process parameter population: The population representation of the "rolling-grinding-honing" collaborative process parameters is (a1, a2, ..., a...). m ), where m is a positive integer, a i For the i-th process parameter in the population, input a i The upper and lower limits are denoted as a. max and a min ; Set r as a random number between [0, 1], and randomly initialize the collaborative process parameter population according to the "hobbing-grinding-honing" process optimization model within the numerical range [0, 1]; Set the maximum number of iterations it, the number of iterations nu = 0, and the maximum capacity M of the archive; Randomly select a process parameter and assign it to the optimal process parameter E, and select a target value and assign it to the optimal target value of the archive; Among them, the i-th process parameter a in the population i As shown below: (22) Step 2) Classify the snake population by gender, and the classification criteria are as follows: (23) In the formula, N m N represents the number of male snakes. f γ represents the number of female snakes, where γ is a value between [0,1]; N is the total number of snakes. Step 3) Judge whether the current number of iterations nu < it holds. If so, enter Step 4), otherwise enter Step 9); Step 4) Calculate the target values of the objective functions of the processing time T, the process cost C, and the gear surface quality F, find the non-dominated solutions and store them in the archive; Step 5) Judge the storage capacity of the archive: If the number of archives reaches the maximum archive capacity, go to Step 6), otherwise go to Step 7); Step 6) Use the greedy strategy to save the current optimal solution, set a predefined distance for each solution, calculate the number of solutions within this distance to measure the corresponding crowding degree; then use the roulette method to eliminate one or more solutions according to the crowding degree; Step 7) Judge the snake's behavior during population update and update the population according to the calculation formula for different behavioral stages; Step 8) Update the optimal collaborative process parameters: Update the collaborative process parameter population, nu = nu + 1, and then proceed to step 3; Step 9) Output the population values ​​of the collaborative process parameters stored in the archive and the target value of the objective function.

6. The "rolling-grinding-honing" multi-process parameter collaborative optimization and decision-making method according to claim 5, characterized in that, The steps for judging snake behavior during population updates and updating the population based on calculation formulas for different behavioral stages include: Step 1) Define the ambient temperature Temp and the food quantity Q, i.e.: (24) In the formula, c1 is a constant; Step 2) Determine the snake's behavioral stage based on the values ​​of ambient temperature (Temp) and food quantity (Q); When the amount of food Q < 0.25, the snake is in the first behavioral stage, at which point the snake searches for food by choosing any random location; When the amount of food Q≥0.25 and the ambient temperature Temp≥0.6, the snake is in the second behavioral stage, at which point the snake will only move towards the food. When the food quantity Q≥0.25 and the ambient temperature Temp<0.6, the snake is in the third behavioral stage. At this time, the snake is in either fighting mode or mating mode. The choice between fighting mode and mating mode is determined by the value of rand. If rand>0.5, it is in fighting mode; otherwise, it is in mating mode.

7. The "rolling-grinding-honing" multi-process parameter collaborative optimization and decision-making method according to claim 6, characterized in that: When the snake is in the first behavioral phase, the male snake's position is updated as follows: (25) In the formula, a i,m Let a be the position of the i-th male snake; rand,m The position of the random male snake; rand is a random number between 0 and 1; c2 is a constant; Male snakes' ability to find food A m As shown below: (26) In the formula, f rand,m It is a rand,m fitness, f i,m It is the fitness of the i-th male; When the snake is in the first behavioral phase, the female snake's position is updated as follows: (27) In the formula, a i,f Let a be the position of the i-th female snake. rand,f This represents the location of a random female snake; rand is a random number between 0 and 1. The female snake's ability to find food A f As shown below: (28) In the formula, f rand,f It is a rand,f fitness, f i,f It represents the fitness of the i-th male snake.

8. The "rolling-grinding-honing" multi-process parameter collaborative optimization and decision-making method according to claim 6, characterized in that: When the snake is in the second behavioral phase, the position of the i-th female or male snake is as follows: (29) In the formula, a i,j This refers to the position of the i-th female or male snake; a food This refers to the optimal snake position, where c3 is a constant.

9. The "rolling-grinding-honing" multi-process parameter collaborative optimization and decision-making method according to claim 6, characterized in that: When the snake is in the third behavioral phase and in combat mode, the male snake's position updates as follows: (30) In the formula, a i,m Refers to the i-th male position; a best,f This is the optimal position for a female snake in the population; The male snake's combat ability FM is as follows: (31) In the formula, f best,f It is the fitness of the optimal female snake location in the population, f i It is agent adaptability; When the snake is in the third behavioral phase and in combat mode, the female snake's position updates as follows: (32) In the formula: a i,f Refers to the i-th female position; a best,m It is the optimal position for a male snake in the population; The female snake's combat abilities (FF) are shown below: (33) In the formula: f best,m It is the fitness of the optimal male snake position in the population; When the snake is in the third behavioral stage and in mating mode, the male snake's position is updated as follows: (34) The mating ability of male snakes (MM) is as follows: (35) In the formula, It represents the fitness of the i-th male snake and the fitness of the m-th female snake. When the snake is in the third behavioral stage and in mating mode, the female snake's position is updated as follows: (36) The mating ability (MF) of female snakes is shown below: (37) In the formula, f best,m It is the fitness of the optimal male snake position in the population; When a snake is in its third behavioral stage and in mating mode, if offspring are produced, the offspring will replace the worst male and female according to their sex, with the following replacement criteria: (38) In the formula, a worst,m It is the worst position among male snakes in the population, a worst,f It is the worst position among the female snakes in the population.

10. The "rolling-grinding-honing" multi-process parameter collaborative optimization and decision-making method according to claim 1, characterized in that: The steps for evaluating and ranking the Pareto cooperative process parameter solution set based on the entropy weight-TOPSIS decision method include: Step 1) Establish a decision matrix for multiple process parameters of "rolling-grinding-honing". The decision matrix includes m sets of process parameters and n evaluation indicators; i represents the i-th set of process parameters, and j represents the j-th evaluation indicator; x ij Indicate decision parameters; Step 2) After normalizing the evaluation indicators, a new standardized decision matrix is ​​obtained. ;y ij This represents the new standardized decision parameters; Step 3) Calculate the weight of the j-th indicator in the i-th solution of the standardized decision matrix Y to obtain the weight matrix Z of each indicator, and calculate the indicator information entropy e based on the weight matrix Z. j ,Right now: (39) In the formula, k is a constant; Z ij These are elements in the weight matrix Z; Step 4) Calculate the indicator weight W using the indicator information entropy. j ,Right now: (40) Step 5) Utilize the indicator weights W j Construct a normalized weighted matrix z is a decision matrix with parameters. ; Step 6) Calculate the positive ideal solution S for each evaluation object. + and negative ideal solution S - That is, the maximum and minimum values ​​of each evaluation indicator, calculated using the following formula: (41) In the formula, For different evaluation objects, the positive ideal solution is provided. For different evaluation objects, the negative ideal solution is... Step 7) Calculate the Euclidean distance D of each evaluation index from the positive ideal solution. i + Euclidean distance D between the negative ideal solution and the solution i - ,Right now: (42) Step 8) Calculate the matching progress of each evaluation index with the ideal solution. ; Step 9) Sort the solution set of process parameters according to the obtained closeness to obtain the optimal solution of "rolling-grinding-honing" collaborative process parameters, and complete the multi-index evaluation and decision of "rolling-grinding-honing" collaborative process parameters.

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