CN112059323B - Honing force prediction method of numerical control internal tooth powerful gear honing machine - Google Patents
Honing force prediction method of numerical control internal tooth powerful gear honing machine Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
- B23F5/02—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by grinding
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F23/00—Accessories or equipment combined with or arranged in, or specially designed to form part of, gear-cutting machines
Abstract
The invention relates to a honing force prediction method of a numerical control internal tooth powerful gear honing machine, and belongs to the technical field of machining and manufacturing. The application object is a numerical control internal tooth powerful gear honing machine, and the operation steps are as follows: 1. determining honing processing parameters according to the parameters of the gear to be processed and the internal tooth strong honing machine processing technology, designing a honing processing orthogonal experiment, and obtaining actual honing force under the combination of the test parameters through the honing processing orthogonal experiment; 2. preprocessing test data by adopting a normalized data processing method to obtain a training sample set, selecting a BP neural network model to carry out iterative training on the training sample set data, and establishing a honing force prediction model; 3. and the established prediction model of the honing force is used for predicting the honing force, and error comparison is carried out on the prediction model and the actual numerical value of the honing force of the gear honing test. The invention realizes the prediction of honing force during gear honing processing, can effectively improve the gear honing processing precision, and avoids material waste caused by improper processing parameter selection.
Description
Technical Field
The invention belongs to the technical field of machining and manufacturing, and particularly relates to a honing force prediction method of a numerical control internal tooth powerful gear honing machine.
Background
The internal tooth powerful gear honing process is one new type of gear finishing process with gear-shaped honing wheel meshed to the workpiece in certain crossed axial angle and capable of rolling freely or forcibly and with the surface abrasive grains of the honing wheel to eliminate the material allowance of the workpiece tooth surface. The gear honing process can not only improve the gear precision and improve the surface quality of the gear, but also has the biggest characteristic that the meshed processing texture can be generated on the surface of the gear, compared with the stripe texture generated by a gear grinding process, the gear honing process greatly reduces the noise and vibration generated by the operation of a gear pair, can effectively prevent the gear pair from being glued due to overheating in the high-speed operation process, and can meet the requirements of modern industrial development on high-precision and high-speed gears.
With the rapid development of the new energy automobile industry, the rotating speed of a gearbox gear in the new energy automobile reaches more than 10000r/min, the requirements on the machining precision and the surface quality of the gear are higher and higher, and the gear honing technology is increasingly widely applied. In actual processing, excessive honing force can cause the tooth surface of the gear to deform, reduce the fatigue strength of the gear and even cause the tooth surface to crack, while too small honing force can cause incomplete processing of the gear surface, has small single cutting allowance and needs to be subjected to repeated reciprocating honing, thus wasting time and labor, and the magnitude of the honing force depends on the combination of gear honing processing parameters.
At present, two methods are mainly used for predicting and detecting honing force: one is a honing force index prediction model established according to a low-speed grinding empirical formula, and although the model is convenient to calculate, the accuracy of the model is unstable; secondly, in the actual gear honing process, the force gauge in the gear honing machine can directly read the honing force on the operation panel of the machine tool, although the method has higher accuracy, the honing force can only be obtained in the actual processing, and the gear only aims at specific parameters, has no universality, can not estimate the honing force before processing, and the honing force is detected through tests, so that the abrasion of the honing wheel is aggravated, the frequency of replacing the honing wheel is increased, the unit price of the honing wheel is higher, and the processing cost is increased.
Disclosure of Invention
In order to predict the honing force before the gear honing process, the invention provides a honing force prediction method of a numerical control internal tooth powerful gear honing machine.
A honing force prediction method of a numerical control internal tooth powerful gear honing machine is suitable for the numerical control internal tooth powerful gear honing machine, and the numerical control internal tooth powerful gear honing machine comprises seven numerical control shafts, which are respectively: the honing wheel rotating shaft C1, the workpiece rotating shaft C2, the honing wheel radial feeding shaft X, the honing wheel axial feeding shaft Z1, the workbench moving shaft Z2, the shaft intersection angle adjusting shaft A and the drum processing and taper shaping shaft B, and the operating steps are as follows:
(1) determining honing processing parameters according to the parameters of the gear to be processed and the internal tooth strong honing machine processing technology, designing a honing processing orthogonal experiment, and obtaining actual honing force under the combination of the test parameters through the honing processing orthogonal experiment;
(2) preprocessing test data of a honing orthogonal test by adopting a normalized data processing method to obtain a training sample set, selecting a BP neural network model and inputting the training sample set data for iterative training, and establishing a honing force prediction model; the test data is the actual honing force under the combination of test parameters and test parameters of the orthogonal test of the gear honing processing;
(3) the built honing force prediction model is used for predicting honing force, error comparison is carried out on the prediction model and the actual honing force numerical value of the gear honing processing test, the accuracy of the honing force prediction model is verified, and the error percentage is used for
Scale of wherein FActual honing forceRepresenting the actual value of the honing force, F, collected on the operating panel of the gear honing machinePredicting honing forceThe predicted value of the honing force obtained by calculation of the honing force prediction model is shown, and the smaller the numerical value of eta is, the more accurate the prediction model is. And at least three groups of honing processing data except the orthogonal test of the alternative honing processing verify the accuracy of the honing force prediction model.
The technical scheme for further limiting is as follows:
in the step (1), the gear honing processing parameters are respectively as follows: workpiece rotation speed nc2The honing wheel radial feed amount f is 800-1800 r/minx2-8 μm/time, honing wheel axial feed speed fz60-200 mm/min;
the honing orthogonal test is carried out at a workpiece rotating speed nc2Radial feed f of honing wheelxAxial feed speed f of honing wheelzThree processing parameters are taken as test factors, each test factor is selected from five levels within the parameter range according to the average principle and according to L25(53) Orthogonal test table design honing process orthogonal test, design 25 groups of honing test samples altogether.
In the step (2), the normalization data processing means processing the test data of the orthogonal test of the honing process by using a mapminmax function, so that the magnitude of the test data falls into a dimensionless interval [0,1 ]]The relation of the mapminmax function is as follows:
y is normalized data, x is raw data before normalization, ymin＝0，ymax＝1，xmin，xmaxMinimum and maximum of the original data respectivelyA value;
the training sample set comprises input data of the sample set and target output data of the sample set, the input data of the sample set is data obtained after processing parameters of an orthogonal honing test are normalized, and the target output data of the sample set is data obtained after actual honing force collected by the orthogonal honing test is normalized;
the BP neural network model comprises an input layer, an output layer and a hidden layer, a transfer function, a training function and a learning function of the BP neural network model are selected, a training sample set is input into the neural network model for iterative training, when an output error or training step number meets requirements, the training is finished, and the building of the honing force prediction model is finished;
the input layer comprises three neurons, namely a workpiece rotating speed nc2Radial feed f of honing wheelxAxial feed speed f of honing wheelz；
The output layer comprises a neuron which is a predicted value of the honing force;
the hidden layer is a single hidden layer and is formed by an empirical formula:
determining the range of the neuron number, respectively selecting different neuron numbers in the range to train, comparing the convergence precision and the convergence speed of the corresponding models of different neuron numbers, and determining the optimal neuron number, wherein L is the neuron number of a hidden layer, m is the neuron number of an output layer, n is the neuron number of an input layer, and a is a constant between 0 and 10;
the transfer function, the training function and the learning function of the BP neural network model are respectively as follows: the transfer function between the input layer and the hidden layer is 'tansig', the transfer function between the hidden layer and the output layer is 'purelin', the model training function is 'rainlm', the learning function adopts 'leanngdm', the training error is set to be 0.001, and the training steps are 2000.
Compared with the prior art, the beneficial technical effects of the invention are embodied in the following aspects:
1. according to the method, the test data are obtained through the orthogonal test of the gear honing process, the high efficiency and flexibility characteristics of the BP neural network are combined, the test data after normalization processing are input into the BP neural network for iterative training, and a honing force prediction model is established.
2. The predicted honing force value provides reference for operators, so that the machining parameters are adjusted and optimized, the gear honing machining precision and the production efficiency can be effectively improved, honing wheel abrasion and workpiece material waste caused by gear honing tests are avoided, and the gear machining cost is saved.
Drawings
Fig. 1 is a schematic structural diagram and a schematic motion diagram of each shaft of an internal tooth powerful honing machine of an application object of the invention;
fig. 2 is a flow chart of an internal tooth powerful honing force prediction method in the invention;
FIG. 3 is a block diagram of a BP neural network model according to the present invention;
FIG. 4 is a flowchart of BP neural network training in the present invention;
FIG. 5 is a schematic diagram illustrating error reduction in the training process of the BP neural network in embodiment 1 of the present invention;
fig. 6 is a graph comparing the first set of predicted honing forces with the actual honing force according to the embodiment 1 of the present invention;
fig. 7 is a graph comparing the second set of predicted honing forces with the actual honing force in example 1 of the present invention;
fig. 8 is a graph comparing the third set of predicted honing forces with the actual honing force in example 1 of the present invention;
FIG. 9 is a schematic diagram illustrating error reduction in the training process of the BP neural network in embodiment 2 of the present invention;
fig. 10 is a graph comparing the first set of predicted honing forces with the actual honing force according to the embodiment 2 of the present invention;
fig. 11 is a graph comparing the second set of predicted honing forces with the actual honing force in example 2 of the present invention;
fig. 12 is a graph comparing the third set of predicted honing forces with the actual honing force in example 2 of the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention will be further described in detail with reference to the attached drawings and the specific embodiments.
Referring to fig. 1, the machine tool used is a fast sler HMX-400 numerical control internal tooth honing wheel powerful gear honing machine, which comprises a honing wheel rotating main shaft C1, a workpiece rotating shaft C2, a honing wheel radial feeding shaft X, a honing wheel axial feeding shaft Z1, a workbench moving shaft Z2, an axis intersection angle adjusting shaft a, a drum processing and taper shaping shaft B. The honing wheels used in the following two examples are all microcrystalline corundum internal tooth honing wheels with normal modulus mn2.25mm, 123 teeth, a helix angle beta of 41.722 DEG, and a normal pressure angle alpha n20 degrees, the tooth width B is 55mm, and the deflection coefficient x is 0; the machined workpiece gears used in the following two embodiments are cylindrical bevel gears made of 20 CrMnTi.
Example 1
Gear module m of workpiece to be machinedn12.25mm, number of teeth Z173, helix angle β133 °, normal pressure angle αn117.5 °, tooth width b135mm, coefficient of variation x1＝0。
Referring to fig. 2, the specific operation steps of predicting the honing force of numerical control internal tooth powerful honing are as follows:
step (1), firstly, determining the gear honing processing parameters according to the gear parameters to be processed and an internal tooth powerful gear honing machine operation manual: workpiece rotation speed nc2The honing wheel radial feed amount f is 800-1800 r/minx2-8 μm/stroke, honing wheel axial feed speed fzIs 60 to 200 mm/min. Honing orthogonal test for gear machining with workpiece rotating speed nc2Radial feed f of honing wheelxAxial feed speed f of honing wheelzThree processing parameters are taken as test factors, five levels are respectively selected for each test factor in the parameter range according to the average distribution principle, and a honing orthogonal test factor level table is shown in table 1.
TABLE 1 orthogonal test factor horizon
| (symbol) | | Level | 1 | Level 2 | |
Level 4 | Level 5 |
| A | Workpiece rotation speed nc2/(r/min) | 800 | 1050 | 1300 | 1550 | 1800 | |
| B | Radial feed f of honing wheelx/(. mu.m/stroke) | 2 | 3.5 | 5 | 6.5 | 8 | |
| C | Axial feeding speed of honing wheelfz/(mm/min) | 60 | 95 | 130 | 165 | 200 |
According to L25(53) Orthogonal test table design orthogonal test of gear honing process, total design 25 groups of gear honing test samples, L25(53) The orthogonal test table is shown in table 2.
TABLE 2L25(53) Orthogonal test table
After the orthogonal test scheme is determined, the gear to be machined is fixed on a workpiece rotating shaft C2 of the gear honing machine through a clamp, gear honing machining tests are carried out, and the actual honing force values under each set of test conditions are recorded through an operation panel of the gear honing machine. Orthogonal experiments the sets of processing parameters and actual honing force are shown in table 3:
TABLE 3 honing orthogonal test machining parameters and results 1
Step (2), in order to avoid the situation that the iterative training time is too long or the data can not be converged, a normalized data processing method is adopted to process the test dataAnd performing pretreatment, wherein the test data are 25 groups of test parameters of a honing orthogonal test and the actual honing force of the 25 groups of test parameters. Firstly, each group of experimental processing parameter values are normalized by adopting a mapminmax function, so that the magnitude of the processing parameters are all in a dimensionless interval [0,1 ]]The mapminmax function relationship is as follows:
y is normalized data, x is raw data before normalization, ymin＝0,ymax＝1，xmin,xmaxThe minimum and maximum values of the raw data are respectively, and the experimental data after normalization processing are shown in table 4:
table 4 data normalization process 1
The 25 sets of data in Table 4 are training sample set data, where the workpiece speed nc2Honing wheel radial feed fxAxial feed speed f of honing wheelzThe corresponding data is input data of the sample set, and the data corresponding to the honing force is target output data of the sample set.
Referring to fig. 3, a BP neural network is selected and training sample set data is input for learning training, and a honing force prediction model is established. The BP neural network comprises an input layer, an output layer and a hidden layer. The input layer comprises three neurons, and the three neurons are respectively the workpiece rotating speed nc2Radial feed f of honing wheelxAxial feed speed f of honing wheelz(ii) a The output layer comprises a neuron for predicting the numerical value of the honing force; the number of hidden layer neurons needs to be determined by an empirical formula:
to determine the hidden layer nerveAnd (3) within the range of the number of the neurons, respectively selecting different neuron numbers in the range to train, comparing the convergence precision and the convergence speed of the models corresponding to the different neuron numbers, and determining the optimal number of the neurons, wherein L is the number of neurons in a hidden layer, n is the number of neurons in an input layer, m is the number of neurons in an output layer, and a is a constant between 0 and 10. The number of hidden layer neurons was set to integers between 7 and 12, and the convergence results are shown in table 5.
TABLE 5 hidden layer neuron number
| Number of hidden layer neurons | Number of convergence steps |
| 7 | 1789 |
| 8 | 1588 |
| 9 | 1391 |
| 10 | 970 |
| 11 | 1356 |
| 12 | Non-convergence |
The convergence speed is fastest when the number of neurons is 10, so that the number of neurons in the hidden layer is selected to be 10.
After the network model structure is determined, a transfer function, a training function and a learning function of the BP neural network model are selected to obtain a more accurate prediction result. Carrying out training and culture by bringing the normalized data into a neural network model, finishing training when a training error or training step number meets a specification, and finishing the establishment of a honing force prediction model of the numerical control internal tooth powerful honing machine; the transfer function, the training function and the learning function of the BP neural network model are respectively as follows: the transfer function between the input layer and the hidden layer is 'tansig', the transfer function between the hidden layer and the output layer is 'purelin', the model training function is 'rainlm', and the learning function is 'leanngdm'. The training error is set to 0.001 and the number of training steps is 2000 steps. After the BP neural network structure is determined and the training parameters are selected, the Matlab software is used for writing a program to carry out iterative training on the training sample set data. The training process is mainly to compare the error between the output value of the model and the target output value to modify the weight of each layer, the comparison of each error and the weight modification form the back propagation process of the error, the output value of the model is gradually close to the target output value through the continuous adjustment of the weight of each layer until the error reaches the set target, and finally the optimal prediction model is obtained. The results of 25 groups of test data of the honing orthogonal test after normalization are selected as a training sample set for training and learning, and a training flow chart is shown in fig. 4. The error gradually decreases as the number of training times increases during the training process, and the schematic diagram is shown in fig. 5.
And (3) at least three groups of honing processing data except 25 groups of honing processing orthogonal tests are replaced, and the accuracy of the honing force prediction model is verified.
First, selecting the rotation speed n of the workpiecec21250r/min, the radial feed f of the honing wheelxIs 5.5 μm/stroke, axial feed speed f of honing wheelzThe calculated predicted honing force value is 138.3373N after BP neural network calculation, the actual honing force displayed by the operation panel of the gear honing machine is 145N, and the comparison graph is shown in FIG. 6. Substituting actual honing force and predicted honing force into formula
The calculation can be carried out, and the error is 4.59%;
second group, selecting workpiece rotation speed nc2Is 1500r/min, and the radial feed f of the honing wheelxIs 4.0 μm/stroke, and axial feed speed f of honing wheelzIs 90 mm/min; the predicted honing force value calculated by the BP neural network is 101.5106N, and the actual honing force displayed by the operation panel of the gear honing machine is 111N, as shown in fig. 7. Substituting actual honing force and predicted honing force into formula
The calculation can be carried out, and the error is 3.14%;
third group, selecting workpiece rotation speed nc2The honing wheel radial feed amount f is 1800r/minxIs 3.0 μm/stroke, axial feed speed f of honing wheelzIs 70 mm/min; the predicted honing force value calculated by the BP neural network is 83.3207N, and the actual honing force displayed by the operation panel of the gear honing machine is 87N, as shown in fig. 8. Substituting actual honing force and predicted honing force into formula
The calculation can be carried out, and the error is 4.23%;
it can be seen that the error between the actual honing force and the predicted honing force of the honing process is within 5%.
Example 2
Gear module m of workpiece to be machinedn22.25mm, number of teeth Z 260, helix angle β233 °, normal pressure angle αn217.5 °, tooth width b215mm, coefficient of variation x2＝0；
Step (1), referring to example 1, a gear honing process orthogonal test scheme was designed, gear honing process orthogonal tests were performed and the numerical values of honing force of each set of tests were recorded, and test data and results are shown in table 6:
TABLE 6 honing orthogonal test parameters and results 2
Step (2), referring to example 1, the test data was preprocessed by the normalization data processing method, and the data after normalization processing is shown in table 7.
Table 7 data normalization process 2
And (3) establishing a honing force prediction model of the BP neural network according to the data processing result, selecting 25 groups of test data of the honing orthogonal test after normalization as a training sample set, training and learning the data in the BP neural network, and gradually reducing the error along with the increase of the training times in the training process, wherein the schematic diagram is shown as 9.
And (3) at least three groups of honing processing data except 25 groups of honing processing orthogonal tests are replaced, and the accuracy of the honing force prediction model is verified.
First, selecting the rotation speed n of the workpiecec2Is 800r/min, and the radial feed f of the honing wheelxIs 5.5 μm/stroke, axial feed speed f of honing wheelzThe calculated predicted honing force value is 128.2625N after BP neural network calculation, the actual honing force displayed by the operation panel of the gear honing machine is 135N, and the comparison graph is shown in fig. 10. Substituting the actual honing force and the predicted honing force into formula
The calculation can be carried out, and the error is 4.92%;
second group, selecting workpiece rotation speed nc2Is 1000r/min, and the radial feed f of the honing wheelxIs 2.0 μm/stroke, axial feed speed f of honing wheelzIs 100 mm/min; the predicted honing force value after calculation of the BP neural network is 93.2541N, and the gear honing machine is operatedThe actual honing force displayed by the panel was 89N, as shown in the comparative graph of fig. 11. Substituting actual honing force and predicted honing force into formula
The calculation can be carried out, and the error is 4.78%;
third group, selecting workpiece rotation speed nc2Is 1500r/min, and the radial feed f of the honing wheelxIs 5.0 μm/stroke, axial feed speed f of honing wheelzIs 120 mm/min; the predicted honing force value calculated by the BP neural network is 124.9536N, and the actual honing force displayed by the operation panel of the gear honing machine is 128N, as shown in fig. 12 by comparison. Substituting actual honing force and predicted honing force into formula
The calculation can be carried out, and the error is 2.38%;
it can be seen that when the gear parameter honing process is different from that of the embodiment 1, the deviation between the predicted value and the actual test value of the honing force of the three groups of tests is within 5% as well, so that the honing force prediction method of the numerical control internal tooth strong honing machine provided by the invention is feasible.
Claims (2)
1. A honing force prediction method of a numerical control internal tooth powerful gear honing machine is suitable for the numerical control internal tooth powerful gear honing machine, and the numerical control internal tooth powerful gear honing machine comprises seven numerical control shafts, which are respectively: the honing machine comprises a honing wheel rotating shaft C1, a workpiece rotating shaft C2, a honing wheel radial feed shaft X, a honing wheel axial feed shaft Z1, a workbench moving shaft Z2, an axis intersection angle adjusting shaft A and a drum processing and taper shaping shaft B, and is characterized by comprising the following operation steps of:
(1) determining honing processing parameters according to the parameters of the gear to be processed and the internal tooth strong honing machine processing technology, designing a honing processing orthogonal experiment, and obtaining actual honing force under the combination of the test parameters through the honing processing orthogonal experiment;
(2) preprocessing test data of a honing orthogonal test by adopting a normalized data processing method to obtain a training sample set, selecting a BP neural network model and inputting the training sample set data for iterative training, and establishing a honing force prediction model; the test data is the test parameters of the orthogonal test of the gear honing processing and the actual honing force under the combination of the test parameters;
the normalized data processing means that a mapminmax function is adopted to process test data of a honing orthogonal test, so that the magnitude of the test data falls into a dimensionless interval [0,1 ]]The relation of the mapminmax function is as follows:
y is normalized data, x is raw data before normalization, ymin＝0，ymax＝1，xmin，xmaxRespectively the minimum value and the maximum value of the original data;
the training sample set comprises input data of the sample set and target output data of the sample set, the input data of the sample set is data obtained after processing parameters of an orthogonal honing test are normalized, and the target output data of the sample set is data obtained after actual honing force collected by the orthogonal honing test is normalized;
the BP neural network model comprises an input layer, an output layer and a hidden layer, a transfer function, a training function and a learning function of the BP neural network model are selected, training sample set data are input into the neural network model for iterative training, when an output error or training step number meets requirements, the training is finished, and the building of the honing force prediction model is finished;
the input layer comprises three neurons, namely a workpiece rotating speed nc2Radial feed f of honing wheelxAxial feed speed f of honing wheelz；
The output layer comprises a neuron which is a predicted value of the honing force;
the hidden layer is a single hidden layer and is formed by an empirical formula:
determining the range of neuron number, selecting different neuron numbers in the range for training, and comparing different neuronsDetermining the optimal number of neurons through the convergence precision and the convergence speed of the model corresponding to the number of the neurons, wherein L is the number of neurons of a hidden layer, m is the number of neurons of an output layer, n is the number of neurons of an input layer, and a is a constant between 0 and 10;
the transfer function, the training function and the learning function of the BP neural network model are respectively as follows: the transfer function between the input layer and the hidden layer is 'tansig', the transfer function between the hidden layer and the output layer is 'purelin', the model training function is 'rainlm', the learning function adopts 'leanngdm', the training error is set to be 0.001, and the training steps are 2000 steps;
(3) the built honing force prediction model is used for predicting honing force, error comparison is carried out on the prediction model and the actual honing force numerical value of the gear honing processing test, the accuracy of the honing force prediction model is verified, and the error percentage is used for
Scale of wherein FActual honing forceRepresenting the actual value of the honing force, F, collected on the operating panel of the gear honing machinePredicting honing forceThe predicted value of the honing force obtained by calculation of the honing force prediction model is shown, and the smaller the numerical value of eta is, the more accurate the honing force prediction model is.
2. The honing force predicting method of the numerical control internal tooth strength honing machine according to claim 1, wherein: in the step (1), the gear honing processing parameters are respectively as follows: workpiece rotation speed nc2The honing wheel radial feed amount f is 800-1800 r/minx2-8 μm/time, honing wheel axial feed speed fz60-200 mm/min;
the honing orthogonal test is carried out at a workpiece rotating speed nc2Radial feed f of honing wheelxAxial feed speed f of honing wheelzThree processing parameters are taken as test factors, each test factor is selected from five levels within the parameter range according to the average principle and according to L25(53) Orthogonal test table design honing process orthogonal test, design 25 groups of honing test samples altogether.
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| CN103439917A (en) * | 2013-09-02 | 2013-12-11 | 南京航空航天大学 | Cutting force prediction method based on features |
| CN108127195A (en) * | 2017-12-26 | 2018-06-08 | 合肥工业大学 | A kind of full axial modification method of internal tooth strength gear honing |
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