CN112883519B - Service life prediction method and device for cycloid wheel - Google Patents
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Abstract
The invention relates to a service life prediction method and device for a cycloidal gear, and belongs to the technical field of service life prediction of cycloidal gears. The method comprises the steps of determining the abrasion loss of a cycloid wheel in a main working area at set time according to an Archard abrasion model and a Hertz contact theory through a modified tooth profile equation of the cycloid wheel, and taking the calculated abrasion loss as a first equidistant modification on a modified tooth profile to obtain a tooth profile equation after abrasion; and carrying out three-dimensional modeling and transient dynamics simulation on the worn tooth profile equation, substituting the simulated corresponding rotation angle of the cycloid wheel and the pin wheel into a calculation formula of the transmission error, calculating the transmission error of the cycloid wheel, and predicting the service life of the cycloid wheel according to the transmission error of the cycloid wheel. Through the process, the service life of the cycloid wheel can be accurately predicted according to the abrasion condition of the cycloid wheel.
Description
Technical Field
The invention relates to a service life prediction method and device for a cycloidal gear, and belongs to the technical field of service life prediction of cycloidal gears.
Background
The key component of the RV reducer is a cycloidal gear pin wheel planetary gear train, and the precision of a cycloidal gear in the cycloidal gear pin wheel planetary gear train directly determines the performance of the RV reducer.
Taking the geometric center of the cycloidal gear as an original point, selecting an axis which passes through the original point and is coincident with the symmetric axis of the cycloidal gear as a Y axis, and an axis which passes through the original point and is vertical to the Y axis as an X axis, wherein the tooth profile equation of the standard cycloidal gear is as follows:
in the formula: x represents the horizontal axis coordinate of the tooth profile of the cycloid wheel; y represents the coordinates of the longitudinal axis of the tooth profile of the cycloidal gear; r is z Representing the radius of a pin wheel distribution circle;
representing the rotation angle parameter of the cycloidal gear; a represents eccentricity; z a Representing a cycloid gear tooth count; z b Indicating the number of pin gear teeth; r is z Representing the pinwheel radius; k 1 Representing short-amplitude coefficients.
The standard cycloidal gear pin wheel transmission theoretically belongs to zero-clearance meshing, and the number of teeth participating in meshing is half of that of the pin wheel. Because the cycloid wheel is required to be shaped, the parts have processing errors and assembly errors, the cycloid wheel and the pin wheel can also generate elastic deformation after the gear train is loaded, transmission errors can exist in actual transmission, the transmission errors can be increased due to abrasion of the cycloid wheel, the accuracy of the RV reducer cannot meet the requirements due to overlarge transmission errors of the cycloid wheel, and the service life of the cycloid wheel is further influenced.
Disclosure of Invention
The invention aims to provide a method and a device for predicting the service life of a cycloidal gear, which are used for realizing the detection of the service life of the cycloidal gear.
The invention provides a service life prediction method of a cycloid wheel for solving the technical problems, which comprises the following steps:
1) Determining the wear amount of the cycloidal gear in a main working area under set time according to an Archard wear model and a Hertz contact theory based on a modified tooth profile equation of the cycloidal gear, wherein the main working area of the cycloidal gear refers to a position between a tooth root and a tooth top of a gear tooth, and the position is close to the middle;
2) The calculated abrasion loss is regarded as that the modified tooth profile is modified once again in an equidistant manner, and a tooth profile equation after abrasion is determined;
3) Carrying out three-dimensional modeling on the worn tooth profile equation, carrying out transient dynamics simulation to obtain the rotation angle of the cycloidal gear and the rotation angle of the pin wheel at each moment, and calculating a transmission error according to the rotation angle of the pin wheel and the rotation angle of the cycloidal gear at each moment and the rotation angle of the pin wheel and the rotation angle of the cycloidal gear when the pin wheel and the cycloidal gear are engaged at the engagement reference point;
4) And judging whether the transmission error meets the precision requirement, if so, increasing the set time to recalculate the abrasion loss, calculating the transmission error according to the simulation result of the tooth profile equation established by the new abrasion loss until the transmission error does not meet the precision requirement, and taking the set time for calculating the abrasion loss at the last time as the service life of the cycloid wheel.
The invention also provides a service life prediction device of the cycloidal gear, which comprises a processor and a memory, wherein the processor executes a computer program stored by the memory so as to realize the service life prediction method of the cycloidal gear.
The method comprises the steps of calculating the abrasion loss of the cycloid wheel in a main working area, and taking the calculated abrasion loss as a first equidistant modification on a modified tooth profile to obtain a tooth profile equation after abrasion; and carrying out three-dimensional modeling and transient dynamics simulation on the worn tooth profile equation, determining a calculation formula of the transmission error, calculating the transmission error of the cycloidal gear according to the calculation formula, and predicting the service life of the cycloidal gear according to the transmission error of the cycloidal gear. Through the process, the service life of the cycloid wheel can be accurately predicted according to the abrasion condition of the cycloid wheel.
Further, the wear amount of the cycloid wheel in the step 1) is as follows:
h I ＝2a 1 λntε α I h
in the formula, the amount of wear h I Expressed in terms of wear depth at the point of engagement, in m, a 1 Contact half width, lambda is the lubrication state, n is the rotational speed, t is the run time, epsilon α Is degree of coincidence, I h Is the rate of wear.
Further, the worn tooth profile equation determined in step 2) is:
in the formula
k″＝az p /(r p +Δr p + Δ h), wherein z c Denotes the number of teeth of the cycloid gear, a denotes the eccentricity, r p Represents the radius of the central circle of the pin teeth, r rp Representing the radius of the teeth, Δ r rp 、Δr p And Δ θ is a profile modification parameter and Δ h is a wear amount function.
Further, the calculation formula of the transmission error is as follows:
in the formula 10 、φ 20 Respectively the pin wheel rotation angle and the cycloid wheel rotation angle phi when engaged at the engagement reference point 1 、φ 2 Respectively the angle of the pin wheel and the angle of the cycloidal gear at each moment, z p Number of pin gear teeth, z c The number of teeth of the cycloid gear is shown.
Drawings
FIG. 1 is a flow chart of a method of predicting the life of a cycloidal gear of the present invention;
FIG. 2 is a schematic gear tooth engagement according to an embodiment of the present invention;
FIG. 3 is a schematic illustration of a gear tooth engagement contact pressure distribution in an embodiment of the present invention;
fig. 4 is a block diagram showing the structure of a service life predicting apparatus for a cycloid wheel according to the present invention.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
The method is based on a Hertz contact theory, an Archard wear theory and a differential geometry principle, calculates the wear loss of the cycloid wheel in a main working area to obtain a tooth profile equation of the cycloid wheel after working for a plurality of times under a specific working condition, carries out transient dynamics simulation on a worn transmission pair through finite element software to obtain a corresponding rotation angle relation of two wheels, brings the rotation angles of the cycloid wheel and a pinwheel obtained through simulation into a calculation formula of a transmission error, calculates the transmission error, and carries out service life prediction according to the transmission error. The specific implementation process of the method is shown in fig. 1, and the specific implementation steps are as follows.
1. And determining the abrasion loss of the cycloidal gear in a main working area.
The primary working area of the gear teeth of the cycloidal gear is located near the middle between the tooth root and the tooth tip of the gear teeth, while the tooth root and the tooth tip are non-primary working areas. When two wheels of the cycloidal gear are engaged, wheel 1 is at contact point j, as shown in figure 2 (1)' At j with wheel 2 (2)' And (4) meshing. After dt-times, the wheel 1 is at the contact point j (1)” At contact point j with wheel 2 (2)” Engagement, during dt times, the normal wear depth of wheel 1, wheel 2 at j point is dh respectively (1) And dh (2) The volume dropped by abrasion is dV (1) And dV (2) The friction distance is ds.
As can be seen from the archer wear formula, wheel 1 can be expressed as:
if the contact area at point j is dA and the pressure at the contact point is p, the above equation can be rewritten as follows:
where K is the coefficient related to the wear of the material, and the hardness of the material is constant, the above equation can be simplified as follows:
in the formula I h The wear rate, which is the depth of wear per unit friction distanceDegree; k is the wear coefficient; p is the contact pressure, and the integral of the wear amount h (normal wear depth at the meshing point) is expressed as:
h＝∫kpds
for a cycloidal pin gear transmission pair, a pin gear is driven, a cycloidal gear is driven, and the sliding coefficient of the driving and driven wheels at the meshing point can be expressed as follows:
wherein v is t1 、v t2 Is the tangential speed of the driving and driven wheels at the point of engagement.
In an unmodified gear, the slip velocity is usually solved by converting it into an expression relating to the gear ratio and the pressure angle, using the relationship between the tangential velocity of the meshing point, the gear ratio and the pressure angle. However, for the cycloidal pin gear transmission pair, in actual use, the cycloidal gear needs to be modified to meet the working condition requirement, and modification generates tooth side clearance, so that the instantaneous transmission ratio is not constant. Therefore, in the invention, the influence generated by modification is considered, the method for accurately solving the meshing point is adopted, and the friction distance ds is directly used for solving the sliding coefficient.
The standard tooth profile equation of the cycloid wheel can be expressed as:
K 1 ＝az p /r p i H ＝z p /z c
in the formula, r p Representing the radius of the central circle of the needle teeth; r is rp Indicating needle toothA radius; a represents eccentricity; z is a radical of p Indicating the number of pin teeth; k is 1 Representing the short-amplitude coefficient; i.e. i H Representing a gear ratio; z is a radical of c Representing the number of cycloidal gear teeth; phi denotes the meshing phase angle.
For the shape-modified cycloid wheel, directly superposing the modification amount on a standard tooth profile equation to obtain the modified tooth profile equation:
in the formula
Wherein z is c 、a、r p 、r rp As a basic parameter,. DELTA.r rp 、Δr p And Δ θ is a shape modification parameter. (these three shape modification parameters correspond to three shape modification methods of equidistance, displacement and corner respectively, and can be combined for use, also can be used singly, all have the value that is the combined shape modification, one has the value, and the other two take 0, is the single shape modification).
Expressing the tooth profile equations of the cycloidal gear and the pin wheel under a fixed coordinate system, establishing a TCA model, and enabling the position vector and the normal vector of the TCA model to be equal to each other, so that the accurate coordinates of each meshing point on the tooth profile of the cycloidal gear and the corresponding meshing point on the pin wheel can be obtained. Dispersing each meshing point on the cycloid wheel with equal arc length, and dividing any meshing point j (2) Two adjacent left and right meshing points j-1 (2) And j +1 (2) The coordinates are used as an integral starting point and an integral ending point, the tooth profile of the cycloidal gear is subjected to curve integration to obtain the length of a curve, and the length of the curve is used as the sliding distance ds of the cycloidal gear at the meshing point in dt time (2) Two corresponding meshing points j-1 on the pinwheel (1) And j +1 (1) The length of minor arc enclosed on the gear tooth profile is used as the contact point j of the gear in dt times (1) Sliding distance ds (1) Substituting the sliding distance to obtain the sliding coefficient lambda of the driving wheel and the driven wheel 1 And λ 2 。
In the transmission of cycloid pin wheel, the meshing force of each meshing point of cycloid wheel and the deformation quantity of each pointIs in direct proportion. Let the load torque be T c The initial value of the maximum contact force of the pin teeth is as follows:
then, F is solved through successive iteration max The distance l from the common normal line of the maximum stress point to the center of the cycloid wheel max ＝az c 。
The cycloidal pin gear transmission belongs to a typical Hertz contact, and the deformation of a maximum contact point under stress can be obtained by a Hertz formula as follows:
in the formula
ρ represents a cycloid curvature radius; b represents the effective tooth width of the cycloid wheel; e 1 、E 2 Respectively representing the elastic modulus of materials of a cycloid wheel and a pinwheel; mu.s 1 、μ 2 Representing the poisson's ratio of the cycloidal and pinwheel materials, respectively.
Total deformation delta of each meshing point of cycloid wheel in normal direction i Can be expressed as
According to the above formula, the amount of deformation of the meshing point can be compared with the backlash Δ s (φ) i ) Judging whether the needle teeth are meshed with the cycloid gear teeth or not according to the size relation of the gear teeth, and further determining the number of simultaneously meshed teeth. Assuming that the teeth numbered m to n are simultaneously engaged, the maximum contact force can be expressed as:
the result of the above formula is the most probable of the initial assumptionComparing the large values, and if the large values are equal, ending the solution; if not, F is required max Is given to F max0 Repeating the iterative calculation until the two formulas have the same result, and outputting F max 。
The normal engagement force applied to any engagement point can be expressed as:
the cycloidal pin gear transmission belongs to a typical Hertz contact, two tooth profiles are meshed and can be equivalently contacted with two cylinders at a meshing point, the pressure distribution is shown in figure 3, and the contact half width is as follows:
wherein W represents the tooth profile contact point normal pressure; r is * Represents the equivalent radius; e * Denotes the equivalent elastic modulus, and has
W＝F i
In the formula, R 1 、R 2 The curvature radii of the contact points between the pin wheel and the cycloid wheel are respectively shown, and v1 and v2 respectively show the poisson ratios of the cycloid wheel and the pin wheel.
The contact half width obtained by the above process is
The contact pressure of the meshing point is
In the formula, b represents an effective tooth width of the cycloid wheel.
The wear coefficient can be expressed as
The minimum oil film thickness of the cycloid pinwheel set at the contact point is expressed as:
wherein λ = H min And/σ, σ represents the square root of the sum of the squares of the surface roughness of the two contact surfaces. The values of lambda are different, which represents that the lubrication states of the gears are different, and 3 ranges from small to large respectively represent 3 states of boundary lubrication, mixed lubrication and good lubrication. u. u 1 、u 2 Representing the scrolling speed of two wheels; eta is the viscosity coefficient.
One point on the cycloid wheel participates in meshing for 1 time, and the generated friction distance is as follows:
S＝2a 1 λ 2
the total friction distance during operation is:
X＝Sntε α
wherein t represents the operating time; n represents a rotation speed; epsilon α Indicating the degree of overlap.
The amount of wear at the engagement point was:
h I ＝XI h
the amount of wear of the cycloid gear that can be obtained from the above process can be expressed as:
h I ＝2a 1 λntε α I h
in the formula, the wear amount is expressed in terms of the wear depth at the meshing point, and is expressed in m.
2. And establishing a tooth profile equation of the trimmed cycloid wheel after being worn based on the obtained wear loss.
The wear amount is expressed by the wear depth at the meshing point, so the wear amount is actually a depth which is overlapped inwards along the normal direction at the tooth profile point, the equidistant modification is also overlapped by a distance along the normal direction, the distance is a fixed value, the wear amount can be changed at different meshing points, the wear amount can be regarded as the equidistant modification, and the tooth profile equation after wear can be obtained by overlapping in the same way according to the expression method of the equidistant modification in the tooth profile equation.
And (4) taking the abrasion loss as the modified tooth profile, and then carrying out variable equidistant modification to obtain an abraded tooth profile equation. Change in the corresponding equation to be Δ r p Becomes Δ r p + Δ h, the tooth profile equation after the traditional profile modification cycloid wheel is worn can be obtained as follows:
in the formula
Wherein z is c 、a、r p 、r rp As a basic parameter,. DELTA.r rp 、Δr p And delta theta respectively represent an equidistant modification parameter, a displacement modification parameter and a corner modification parameter, delta h is a wear loss function, and delta h and h I The same is true, in essence, for the purpose of writing in an incremental form uniformly with other parameters.
3. Transient dynamics simulation is carried out on the worn transmission pair through finite element software, the corresponding corner relation of the two wheels is obtained, and the transmission error is calculated.
The transmission error formula is only related to a pin wheel corner, a cycloid wheel corner, a pin wheel tooth number, a cycloid wheel tooth number, a pin wheel corner and a cycloid wheel corner when meshing is carried out at a meshing reference point, however, the pin wheel corner and the cycloid wheel corner change along with the abrasion process, the tooth profile changes after abrasion, the corresponding relation between the pin wheel corner and the cycloid wheel corner also changes, transient dynamics simulation is carried out on the abraded tooth profile by utilizing finite element software to obtain the cycloid wheel corner and the pin wheel corner at any meshing position when the abraded cycloid wheel is transmitted, and the transmission error of any meshing position after abrasion can be obtained according to the transmission error formula.
The established tooth profile equation after abrasion is subjected to three-dimensional modeling, transient dynamics simulation is carried out in finite element simulation software, the rotating angle of each instantaneous cycloid wheel and pin wheel can be obtained, and the transmission error is calculated according to the following calculation formula:
wherein phi 10 、φ 20 Are a pin wheel rotating angle and a cycloid wheel rotating angle phi respectively when the meshing reference point is meshed 1 、φ 2 Respectively the angle of the pinwheel and the angle of the cycloidal gear, z p Number of teeth of pin gear, z c Is the number of cycloid gear teeth.
4. And predicting the service life according to the transmission error.
The calculation of the abrasion loss is related to time, the longer the time is, the larger the abrasion loss is, the abrasion loss can change a tooth profile equation, when two wheels are meshed, the rotation angle of the cycloidal gear and the rotation angle of the pin wheel can both change, if the obtained transmission error meets the requirement, the tooth profile change caused by abrasion generated under the set time of the set condition is not enough to lose the precision, the time is increased, the abrasion loss is calculated again, the tooth profile equation after abrasion is obtained, the rotation angle is obtained through simulation again, the transmission error is calculated, the step is repeated until the obtained transmission error is larger than the set precision, the requirement is not met, the time used for calculating the abrasion loss at the last time is the time for ensuring the precision of the cycloidal gear, and the service life of the cycloidal gear is the service life of the cycloidal gear.
Device embodiment
The apparatus proposed in this embodiment, as shown in fig. 4, includes a processor and a memory, where a computer program operable on the processor is stored in the memory, and the processor implements the method of the foregoing method embodiment when executing the computer program. That is, the method in the above method embodiment should be understood that the flow of the cycloidal wheel life prediction method may be implemented by computer program instructions. These computer program instructions may be provided to a processor such that execution of the instructions by the processor results in the implementation of the functions specified in the method flow described above.
The processor referred to in this embodiment refers to a processing device such as a microprocessor MCU or a programmable logic device FPGA; the memory referred to in this embodiment includes a physical device for storing information, and generally, the information is digitized and stored in a medium using an electric, magnetic, optical, or the like. For example: various memories for storing information by using an electric energy mode, such as RAM, ROM and the like; various memories for storing information by magnetic energy, such as hard disk, floppy disk, magnetic tape, magnetic core memory, bubble memory, and U disk; various types of memory, CD or DVD, that store information optically. Of course, there are other ways of memory, such as quantum memory, graphene memory, and so forth.
The apparatus comprising the memory, the processor and the computer program is realized by the processor executing corresponding program instructions in the computer, and the processor can be loaded with various operating systems, such as windows operating system, linux system, android, iOS system, and the like. As other embodiments, the device can also comprise a display, and the display is used for displaying the diagnosis result for the reference of workers.
Claims (5)
1. A method for predicting the service life of a cycloid wheel is characterized by comprising the following steps of:
1) Determining the wear amount of the cycloidal gear in a main working area under set time according to an Archard wear model and a Hertz contact theory based on a modified tooth profile equation of the cycloidal gear, wherein the main working area of the cycloidal gear refers to a position between a tooth root and a tooth top of a gear tooth, and the position is close to the middle;
2) The calculated abrasion loss is regarded as that the modified tooth profile is subjected to equidistant modification again, and a tooth profile equation after abrasion is determined;
3) Carrying out three-dimensional modeling on the worn tooth profile equation, carrying out transient dynamics simulation to obtain the rotation angle of the cycloid wheel and the rotation angle of the pin wheel at each moment, and calculating a transmission error according to the rotation angle of the pin wheel and the rotation angle of the cycloid wheel at each moment and the rotation angle of the pin wheel and the rotation angle of the cycloid wheel when the pin wheel and the cycloid wheel are engaged at an engagement reference point;
4) And judging whether the transmission error meets the precision requirement, if so, increasing the set time to recalculate the abrasion loss, calculating the transmission error according to the simulation result of the tooth profile equation established by the new abrasion loss until the transmission error does not meet the precision requirement, and taking the set time for calculating the abrasion loss at the last time as the service life of the cycloid wheel.
2. The method for predicting the life of a cycloid wheel of claim 1, wherein the amount of wear of the cycloid wheel in step 1) is:
h I ＝2a 1 λntε α I h
in the formula, the amount of wear h I Expressed in terms of wear depth at the engagement point, in m, a 1 Contact half width, lambda is the lubrication state, n is the rotational speed, t is the run time, epsilon α Is degree of coincidence, I h Is the rate of wear.
3. The method for predicting the life of a cycloidal gear according to claim 1 or 2, wherein the worn tooth profile equation determined in step 2) is:
in the formula
k″＝az p /(r p +Δr p + Δ h), wherein z c Denotes the number of teeth of the cycloid gear, a denotes the eccentricity, r p Representing the radius of the centre circle of the pin teeth, z p The number of teeth of the pin gear is,
representing the angle parameter, r, of the cycloid gear rp Representing the radius of the teeth, Δ r rp 、Δr p And Δ θ is a profile modification parameter, and Δ h is a wear amount function.
4. The method for predicting the life of a cycloidal gear according to claim 3, wherein the transmission error is calculated by the formula:
in the formula 10 、φ 20 Respectively the pin wheel rotation angle and the cycloid wheel rotation angle phi when engaged at the engagement reference point 1 、φ 2 Respectively the angle of the pin wheel and the angle of the cycloidal gear at each moment, z p Number of teeth of pin gear, z c Is the number of cycloid gear teeth.
5. A cycloidal gear life prediction device, characterized in that the device comprises a processor and a memory, the processor executing a computer program stored by the memory to implement the cycloidal gear life prediction method according to any one of claims 1-4.
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