CN109746833B - Method for calculating grinding force of spherical base surface of conical roller - Google Patents
Method for calculating grinding force of spherical base surface of conical roller Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 32
- 238000002955 isolation Methods 0.000 claims abstract description 16
- 238000004364 calculation method Methods 0.000 claims abstract description 10
- 239000006061 abrasive grain Substances 0.000 claims description 56
- 239000002245 particle Substances 0.000 claims description 39
- 238000007373 indentation Methods 0.000 claims description 13
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 12
- 239000000463 material Substances 0.000 claims description 11
- 238000010008 shearing Methods 0.000 claims description 6
- 238000004458 analytical method Methods 0.000 claims description 3
- 238000007542 hardness measurement Methods 0.000 claims description 3
- 239000004576 sand Substances 0.000 claims description 3
- 239000012798 spherical particle Substances 0.000 claims description 3
- 238000005516 engineering process Methods 0.000 abstract description 2
- 238000005457 optimization Methods 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000002159 abnormal effect Effects 0.000 description 1
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Abstract
The invention discloses a method for calculating grinding force of a spherical basal plane of a tapered roller, which comprises the steps of firstly setting the tapered roller to be in rigid contact with two guide wheel discs, having no sliding and stable rotation speed, setting the rotation speed of an isolation disc to be one half of the rotation speed difference of the two guide wheel discs, and setting the rotation linear speed of the tapered roller to be equal to the linear speed difference of a right guide wheel disc and the isolation disc; according to the processing principle of the spherical base surface of the conical roller, the grinding force tangential grinding force and normal grinding force are generated during grinding of the spherical base surface of the conical roller; deducing a stress balance equation during grinding of the spherical base surface of the conical roller; and calculating the grinding contact arc length of the spherical basal plane of the conical roller, calculating the maximum undeformed cutting thickness, and finally obtaining the grinding force of the spherical basal plane of the conical roller through calculation. The method fully considers the grinding motion track and the forming contact arc length of the tapered roller, is suitable for analyzing the grinding process of the spherical base surface of the tapered roller, promotes the development of the grinding process parameter optimization technology, and improves the grinding precision of the tapered roller.
Description
Technical Field
The invention relates to a method for calculating grinding force of a spherical basal plane of a conical roller.
Background
The tapered roller bearing has the capacity of bearing high radial load and can also bear axial load, the roller can realize pure rolling, and the friction coefficient is low; these superior properties have led to the widespread use of tapered roller bearings in the machine tool, automotive, metallurgical, aerospace, and other industries. When the tapered roller bearing works, the contact condition of the spherical base surface of the large end of the tapered roller and the conical surface of the flange of the inner ring has important influence on the lubricating condition, the contact stress, the frictional wear, the service life and the like, and the processing precision of the spherical base surface of the tapered roller must be strictly controlled. The grinding of the spherical base surface of the conical roller is a grinding mode of continuous forming, has a great difference with a common plane grinder and an excircle plunge grinder, and needs to establish a grinding force calculation method for the spherical base surface of the conical roller for better researching the grinding process of the spherical base surface of the conical roller and improving the processing precision of the spherical base surface.
When the tapered roller is ground on the spherical base surface, due to the abnormal complexity of the motion condition of the tapered roller, the particularity of the forming grinding principle and the lack of understanding of the grinding principle of the spherical base surface, the method for calculating the grinding force of the spherical base surface of the tapered roller cannot be effectively established at present, and the processing precision of the spherical base surface of the tapered roller is influenced.
Generally, a tapered roller ball-base surface grinding machine grinds a ball-base surface of a tapered roller by using a continuous forming principle. As shown in fig. 1 and 2, the grinding machine for the spherical datum plane of the tapered roller 1 mainly comprises a left guide wheel disc 2, a right guide wheel disc 3, an isolation disc 4 and a grinding wheel 5, wherein the left guide wheel disc 2 and the right guide wheel disc 3 are opposite in rotation direction and different in rotation speed, the rotation speed of the right guide wheel disc 3 is higher than that of the left guide wheel disc 2, the rotation speed difference between the guide wheel discs enables the tapered roller 1 to rotate and revolve, the isolation disc 4 is driven by the revolution of the tapered roller 1 to rotate clockwise, and the rotation direction of the grinding wheel 5 is the same as that of the tapered roller 1.
As shown in fig. 2, the concave spherical surface forming grinding wheel 5 of the tapered roller 1 ball-based surface grinding machine has an inclination angle of 30 ° with the horizontal plane, and the rotation center of the concave spherical surface forming grinding wheel 5 is perpendicular to the rotation centers of the two guide wheel discs 2 and 3. In order to prevent the tapered roller 1 from being repeatedly ground in the grinding area, the axis of the grinding wheel 5 needs to be inclined downwards by an angle, but the curvature center of the grinding curved surface of the grinding wheel 5 is coincided with the rotation center of the separation disc 4.
In the grinding process, the working conical surfaces of the left and right guide wheel discs 2 and 3 clamp and position the conical surface of the tapered roller 1, the two guide wheel discs 2 and 3 rotate in opposite directions to drive the tapered roller 1 to rotate, and the axis of the tapered roller 1 not only passes through the angular bisector of the working conical surfaces of the two guide wheel discs 2 and 3 and the rotation center of the guide wheel discs, but also is positioned by the aid of the working surface of the isolation disc 4 so as to correct the error that the axis of the tapered roller 1 deviates from the rotation center of the guide wheel discs during the movement.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for calculating the grinding force of the spherical base surface of a tapered roller.
In order to solve the technical problem, the method for calculating the grinding force of the spherical base surface of the tapered roller comprises the following steps:
step one, when the spherical base surface of the tapered roller is ground, the tapered roller is set to be in rigid contact with the two guide wheel discs, the tapered roller does not slide with the two guide wheel discs, the rotation speed of the isolation disc is equal to one half of the rotation speed difference of the two guide wheel discs, and the rotation linear speed of the tapered roller is equal to the difference between the linear speed of the right guide wheel disc and the linear speed of the isolation disc;
step two, according to the processing principle of the ball base surface of the tapered roller, the ball base surface of the tapered roller is ground by adopting a concave spherical surface forming grinding wheel with the same curvature radius, and the grinding force during grinding of the ball base surface of the tapered roller can be decomposed into two components which are perpendicular to each other, namely tangential grinding force F tangential to the grinding curved surface of the grinding wheeltAnd normal grinding force F along the normal direction of grinding curved surface of grinding wheeln(ii) a The grinding of the spherical base surface of the tapered roller is finished in a short time, and the normal grinding force F of the grinding wheel to the tapered rollernThe normal grinding force F of the tapered roller is reduced immediately after the tapered roller completely enters the grinding area of the grinding wheel before the tapered roller moves to the axis position of the grinding wheelnIs zero;
step three, when the spherical basal plane of the conical roller is ground, the stress balance equation is as follows:
2FNsinφ+2Ffcosφ＝Fn (1)
Ff＝μ0Fn (2)
the following can be obtained from formula (1) and formula (2):
Fn＝2FNsinφ+2μ0FNcosφ (3)
wherein, FfIs the friction force between the tapered roller and the two guide wheel discs, FNPositive pressure of the guide wheel disc on the tapered roller, phi is the half cone angle mu of the tapered roller0The coefficient of friction between the guide wheel disc and the tapered roller is used;
step four, calculating the grinding contact arc length of the spherical basal plane of the tapered roller by taking the rotation center of the grinding wheel as the origin of coordinates, taking the connecting line of the rotation center of the tapered roller and the rotation center of the grinding wheel as an X axis and taking the direction vertical to the connecting line as a Y axisAnd establishing a coordinate system. Let rsIs the grinding wheel radius, rwIs the large end radius of the tapered roller, roIs the radius of the big end groove of the tapered roller, x1The rotation axis is relative to the rotation center coordinate of the grinding wheel when the tapered roller is processed, and the arc length AB is the contact length l of the grinding wheel and the tapered rollerc(ii) a Obtaining the following according to the motion geometrical relationship of the grinding wheel and the tapered roller: when r iss+ro≤x1≤rs+rwOr rs-rw≤x1≤rs-roWhen the temperature of the water is higher than the set temperature,
when r iss-ro<x1<rs+roWhen the temperature of the water is higher than the set temperature,
step five, calculating the maximum undeformed cutting thickness, marking small nicks with different shapes and sizes on the surface of the spherical base surface of the conical roller when the grinding wheel abrasive particles are wiped on the spherical base surface of the conical roller, assuming that the cross section of the grinding wheel abrasive particles is triangular, obtaining that the chip thickness h of a single abrasive particle and the spherical base surface of the conical roller is continuously changed from small to large, and the maximum undeformed chip thickness hmaxExpressed as:
wherein C is the effective number of abrasive grains per unit area, theta is the half angle of the abrasive grain vertex cone or indenter, and apTo grind depth, deIs the equivalent diameter of the grinding wheel, vsIs the rotational speed of the grinding wheel, vwThe self-rotation speed of the tapered roller;
in the grinding of the spherical basal plane of the conical roller:
wherein v isrFor linear velocity of the isolation disc, wwThe self-rotation angular velocity of the tapered roller;
step six, calculating the grinding force of the spherical basal plane of the conical roller, wherein in the actual grinding process, the grinding force consists of chip deformation and friction, and the normal grinding force F of a single abrasive particlegnAnd tangential grinding force FgtBoth consist of two parts, namely:
wherein subscript g represents a single abrasive particle, n and t represent the directions of forces respectively indicating normal and tangential directions, and c and s represent the properties of the forces respectively being cutting deformation force and frictional force;
for a single abrasive particle, the normal grinding force due to friction is:
the tangential grinding forces caused by friction are:
wherein,
is the actual contact area of the workpiece and the working abrasive particles,
the average contact pressure between the actual wear plane of the workpiece and the abrasive grains is related to the hardness of the workpiece material, and u is the friction coefficient between the actual wear plane of the workpiece and the abrasive grains;
the hardness H of the material can be determined according to the Vickers hardness measurement theory and the indentation characteristic size of the hardness of the material:
p＝ξHa2 (11)
where p is the load, a is the indentation size, ξ is the indenter geometry factor, and for the vickers indenter, ξ is 2,
from the indentation with abrasive grains, the indentation size:
2a＝2h tanθ (12)
normal grinding force F of single abrasive grain caused by chip deformation under pure shearing deformation conditiongncComprises the following steps:
Fgnc＝η0ξHh2tan2θ (13)
wherein eta is0Is a constant of 0 to 1,
from geometric analysis, the ratio of normal and tangential grinding forces of a single abrasive grain caused by cutting deformation is:
tangential grinding force F of single abrasive particle caused by chip deformation under pure shearing deformation conditiongtcComprises the following steps:
thus, a normal grinding force F of a single abrasive grain is obtainedgnAnd tangential grinding force FgtThe calculation formula of (a) is as follows:
according to the geometric relationship, h is approximately equal to hmaxli/lc,liIs 0 to lcThe variables in between and varying with h, replacing h can result in:
normal grinding force F per unit grinding widthn' and tangential grinding force Ft' equal to the sum of the normal and tangential forces, respectively, of all effective abrasive particles per unit grinding width in the workpiece-wheel interface, expressed as:
wherein d is a differential symbol, NdThe grinding force calculation formula of the grinding wheel and the workpiece on the unit grinding width in the grinding process of the spherical base surface of the conical roller is obtained by taking the effective grinding edge number of the grinding wheel in unit area as follows:
when r iss+ro≤x1≤rs+rwOr rs-rw≤x1≤rs-roWhen the temperature of the water is higher than the set temperature,
when r iss-ro<x1<rs+roWhen the temperature of the water is higher than the set temperature,
and N is the number of abrasive particles contained in the unit volume of the grinding wheel, and the normal grinding force and the radial grinding force of the spherical base surface of the conical roller can be effectively calculated by determining each relevant parameter in the formula (20) according to the grinding process of the machine tool.
Further, the effective abrasive grain number C in unit area is calculated, abrasive grains are uneven and distributed on the working surface of the grinding wheel, and the abrasive grains with smaller exposed working surface size of the grinding wheel do not participate in grinding operation during actual grinding, so that the number of the abrasive grains actually participating in grinding is less than that of the abrasive grains on the surface of the grinding wheel;
assuming that the abrasive grain has a diameter dgSpherical particles ofAnd are uniformly distributed in the sand wheel body with the volume fraction of VgThe number of abrasive grains contained per unit volume of the grinding wheel of (1):
the effective abrasive particles are arranged, the average volume of the effective abrasive particles is 1/4, the effective grinding edge is exposed on the surface of the grinding wheel, and only one effective grinding edge is arranged in a single abrasive particle, so that the effective grinding edge number N of the unit area of the surface of the grinding wheeld：
Nd＝4Nh (22)
Let the average chip thickness of the abrasive grains be hmaxAnd/2, the effective abrasive grain number per unit area C:
C＝2Nhmax (23)
thereby obtaining the effective abrasive grain number per unit area.
The method for calculating the grinding force of the spherical basal plane of the tapered roller adopts the technical scheme, namely the method firstly sets the tapered roller to be in rigid contact with the two guide wheel discs, has no sliding and stable rotation speed, the rotation speed of the isolation disc is equal to one half of the rotation speed difference of the two guide wheel discs, and the rotation linear speed of the tapered roller is equal to the difference between the linear speed of the right guide wheel disc and the linear speed of the isolation disc; according to the processing principle of the spherical base surface of the conical roller, the grinding force tangential grinding force and normal grinding force are generated during grinding of the spherical base surface of the conical roller; deducing a stress balance equation during grinding of the spherical base surface of the conical roller; and calculating the grinding contact arc length of the spherical basal plane of the conical roller, calculating the maximum undeformed cutting thickness, and finally obtaining the grinding force of the spherical basal plane of the conical roller through calculation. The method fully considers the grinding motion track and the forming contact arc length of the tapered roller, calculates the radial grinding force and the normal grinding force of the spherical base surface of the tapered roller, is suitable for analyzing the grinding process of the spherical base surface of the tapered roller, promotes the optimization technology development of grinding process parameters, and improves the grinding precision of the tapered roller.
Drawings
The invention is described in further detail below with reference to the following figures and embodiments:
FIG. 1 is a schematic view of clamping a tapered roller during grinding of a spherical base surface of the tapered roller;
FIG. 2 is a schematic view of the principle of grinding the spherical base surface of the tapered roller;
FIG. 3 is a schematic diagram showing the grinding force of the ball base of the tapered roller;
FIG. 4 is a schematic diagram of the force applied to the tapered roller during grinding of the spherical base surface of the tapered roller;
FIG. 5 is a schematic view of a coordinate system established with the tapered roller rotation center and the grinding wheel rotation center;
FIG. 6 is a schematic illustration of the interference of a single abrasive particle of the grinding wheel with the workpiece material;
FIG. 7 is a schematic view of the indentation of a single abrasive particle of the grinding wheel with a workpiece material.
Detailed Description
The method for calculating the grinding force of the spherical basal plane of the conical roller comprises the following steps:
step one, when the spherical base surface of the tapered roller is ground, the tapered roller is set to be in rigid contact with the two guide wheel discs, the tapered roller does not slide with the two guide wheel discs, the rotation speed of the isolation disc is equal to one half of the rotation speed difference of the two guide wheel discs, and the rotation linear speed of the tapered roller is equal to the difference between the linear speed of the right guide wheel disc and the linear speed of the isolation disc;
step two, as shown in fig. 3, according to the processing principle of the spherical base surface of the tapered roller 1, the grinding of the spherical base surface of the tapered roller adopts a concave spherical surface forming grinding wheel with the same curvature radius, and the grinding force during grinding of the spherical base surface of the tapered roller can be decomposed into two components which are perpendicular to each other, namely a tangential grinding force F along the tangential direction of the grinding curved surface of the grinding wheeltAnd normal grinding force F along the normal direction of grinding curved surface of grinding wheeln(ii) a The grinding of the spherical base surface of the tapered roller is finished in a short time, and the normal grinding force F of the grinding wheel to the tapered rollernThe normal grinding force F of the tapered roller is reduced immediately after the tapered roller completely enters the grinding area of the grinding wheel before the tapered roller moves to the axis position of the grinding wheelnIs zero;
step three, as shown in fig. 4, when the spherical base surface of the conical roller is ground, the stress balance equation is as follows:
2FNsinφ+2Ffcosφ＝Fn (1)
Ff＝μ0Fn (2)
the following can be obtained from formula (1) and formula (2):
Fn＝2FNsinφ+2μ0FNcosφ (3)
wherein, FfIs the friction force between the tapered roller and the two guide wheel discs, FNPositive pressure of the guide wheel disc on the tapered roller, phi is the half cone angle mu of the tapered roller0The coefficient of friction between the guide wheel disc and the tapered roller is used;
step four, as shown in fig. 5, calculating the grinding contact arc length of the spherical basal plane of the tapered roller, taking the rotation center of the grinding wheel 5 as the origin of coordinates, taking the connecting line between the rotation center of the tapered roller 1 and the rotation center of the grinding wheel 5 as the X axis, and taking the direction perpendicular to the connecting line as the Y axis, and establishing a coordinate system. Let rsIs the grinding wheel radius, rwIs the large end radius of the tapered roller, roIs the radius of the big end groove of the tapered roller, x1The rotation axis is relative to the rotation center coordinate of the grinding wheel when the tapered roller is processed, and the arc length AB is the contact length l of the grinding wheel 5 and the tapered roller 1c(ii) a Obtaining the following according to the motion geometrical relationship of the grinding wheel and the tapered roller:
when r iss+ro≤x1≤rs+rwOr rs-rw≤x1≤rs-roWhen the temperature of the water is higher than the set temperature,
when r iss-ro<x1<rs+roWhen the temperature of the water is higher than the set temperature,
step five, as shown in fig. 6, calculating the maximum undeformed cutting thickness, and marking fine nicks with different shapes and sizes on the surface of the spherical base surface of the tapered roller 1 when the abrasive grains of the grinding wheel 5 are rubbed across the spherical base surface of the tapered roller 1, assuming that the section of the abrasive grains of the grinding wheel 5 isThe shape of the surface is triangular, the chip thickness h of the single abrasive particle and the spherical basal surface of the tapered roller 1 is obtained and continuously increases from small to large, and the maximum undeformed chip thickness hmaxExpressed as:
wherein C is the effective number of abrasive grains per unit area, theta is the half angle of the abrasive grain vertex cone or indenter, and apTo grind depth, deIs the equivalent diameter of the grinding wheel, vsIs the rotational speed of the grinding wheel, vwThe self-rotation speed of the tapered roller;
in the grinding of the spherical basal plane of the conical roller:
wherein v isrFor linear velocity of the isolation disc, wwThe self-rotation angular velocity of the tapered roller;
step six, calculating the grinding force of the spherical basal plane of the conical roller, wherein in the actual grinding process, the grinding force consists of chip deformation and friction, and the normal grinding force F of a single abrasive particlegnAnd tangential grinding force FgtBoth consist of two parts, namely:
wherein subscript g represents a single abrasive particle, n and t represent the directions of forces respectively indicating normal and tangential directions, and c and s represent the properties of the forces respectively being cutting deformation force and frictional force;
for a single abrasive particle, the normal grinding force due to friction is:
the tangential grinding forces caused by friction are:
wherein,
is the actual contact area of the workpiece and the working abrasive particles,
the average contact pressure between the actual wear plane of the workpiece and the abrasive grains is related to the hardness of the workpiece material, and u is the friction coefficient between the actual wear plane of the workpiece and the abrasive grains;
the hardness H of the material can be determined according to the Vickers hardness measurement theory and the indentation characteristic size of the hardness of the material:
p＝ξHa2 (11)
where p is the load, a is the indentation size, ξ is the indenter geometry factor, and for the vickers indenter, ξ is 2,
as shown in fig. 7, as seen from the indentation of the abrasive grains 51, the indentation size:
2a＝2h tanθ (12)
normal grinding force F of single abrasive grain caused by chip deformation under pure shearing deformation conditiongncComprises the following steps:
Fgnc＝η0ξHh2tan2θ (13)
wherein eta is0Is a constant of 0 to 1,
from geometric analysis, the ratio of normal and tangential grinding forces of a single abrasive grain caused by cutting deformation is:
tangential grinding force F of single abrasive particle caused by chip deformation under pure shearing deformation conditiongtcComprises the following steps:
thus, a normal grinding force F of a single abrasive grain is obtainedgnAnd tangential grinding force FgtThe calculation formula of (a) is as follows:
according to the geometric relationship, h is approximately equal to hmaxli/lc,liIs 0 to lcThe variables in between and varying with h, replacing h can result in:
normal grinding force F per unit grinding widthn' and tangential grinding force Ft' equal to the sum of the normal and tangential forces, respectively, of all effective abrasive particles per unit grinding width in the workpiece-wheel interface, expressed as:
wherein d is a differential symbol, NdThe grinding force calculation formula of the grinding wheel and the workpiece on the unit grinding width in the grinding process of the spherical base surface of the conical roller is obtained by taking the effective grinding edge number of the grinding wheel in unit area as follows:
when r iss+ro≤x1≤rs+rwOr rs-rw≤x1≤rs-roWhen the temperature of the water is higher than the set temperature,
when r iss-ro<x1<rs+roWhen the temperature of the water is higher than the set temperature,
and N is the number of abrasive particles contained in the unit volume of the grinding wheel, and the normal grinding force and the radial grinding force of the spherical base surface of the conical roller can be effectively calculated by determining each relevant parameter in the formula (20) according to the grinding process of the machine tool.
Preferably, the effective abrasive grain number per unit area C is calculated such that the abrasive grains are uneven and unevenly distributed on the working surface of the grinding wheel, and the abrasive grains with smaller exposed size on the working surface of the grinding wheel do not participate in the grinding operation during actual grinding, so that the number of the abrasive grains actually participating in the grinding operation is less than the number of the abrasive grains on the surface of the grinding wheel;
assuming that the abrasive grain has a diameter dgThe spherical particles are uniformly distributed in the sand wheel body, and the volume fraction is VgThe number of abrasive grains contained per unit volume of the grinding wheel of (1):
the effective abrasive particles are arranged, the average volume of the effective abrasive particles is 1/4, the effective grinding edge is exposed on the surface of the grinding wheel, and only one effective grinding edge is arranged in a single abrasive particle, so that the effective grinding edge number N of the unit area of the surface of the grinding wheeld：
Nd＝4Nh (22)
Let the average chip thickness of the abrasive grains be hmaxAnd/2, the effective abrasive grain number per unit area C:
C＝2Nhmax (23)
thereby obtaining the effective abrasive grain number per unit area.
The method is based on the grinding principle of the spherical base surface of the tapered roller and combines the existing grinding force mathematical model to establish the grinding force calculation method of the spherical base surface of the tapered roller. The method has important significance for optimizing grinding process parameters and improving the grinding precision of the tapered roller.
Claims (2)
1. A method for calculating the grinding force of a spherical basal plane of a conical roller is characterized by comprising the following steps:
step one, when the spherical base surface of the tapered roller is ground, the tapered roller is set to be in rigid contact with the two guide wheel discs, the tapered roller does not slide with the two guide wheel discs, the rotation speed of the isolation disc is equal to one half of the rotation speed difference of the two guide wheel discs, and the rotation linear speed of the tapered roller is equal to the difference between the linear speed of the right guide wheel disc and the linear speed of the isolation disc;
step two, according to the processing principle of the ball base surface of the tapered roller, the ball base surface of the tapered roller is ground by adopting a concave spherical surface forming grinding wheel with the same curvature radius, and the grinding force during grinding of the ball base surface of the tapered roller can be decomposed into two components which are perpendicular to each other, namely tangential grinding force F tangential to the grinding curved surface of the grinding wheeltAnd normal grinding force F along the normal direction of grinding curved surface of grinding wheeln(ii) a The grinding of the spherical base surface of the tapered roller is finished in a short time, and the normal grinding force F of the grinding wheel to the tapered rollernThe normal grinding force F of the tapered roller is reduced immediately after the tapered roller completely enters the grinding area of the grinding wheel before the tapered roller moves to the axis position of the grinding wheelnIs zero;
step three, when the spherical basal plane of the conical roller is ground, the stress balance equation is as follows:
2FNsinφ+2Ffcosφ＝Fn (1)
Ff＝μ0Fn (2)
the following can be obtained from formula (1) and formula (2):
Fn＝2FNsinφ+2μ0FNcosφ (3)
wherein, FfIs the friction force between the tapered roller and the two guide wheel discs, FNPositive pressure of the guide wheel disc on the tapered roller, phi is the half cone angle mu of the tapered roller0The coefficient of friction between the guide wheel disc and the tapered roller is used;
step four, grinding the spherical basal plane of the conical rollerCalculating the contact arc length by taking the rotation center of the grinding wheel as the origin of coordinates, taking the connecting line between the rotation center of the tapered roller and the rotation center of the grinding wheel as an X axis and taking the direction vertical to the connecting line as a Y axis, establishing a coordinate system and setting rsIs the grinding wheel radius, rwIs the large end radius of the tapered roller, roIs the radius of the big end groove of the tapered roller, x1The rotation axis is relative to the rotation center coordinate of the grinding wheel when the tapered roller is processed, and the arc length AB is the contact length l of the grinding wheel and the tapered rollerc(ii) a Obtaining the following according to the motion geometrical relationship of the grinding wheel and the tapered roller: when r iss+ro≤x1≤rs+rwOr rs-rw≤x1≤rs-roWhen the temperature of the water is higher than the set temperature,
when r iss-ro<x1<rs+roWhen the temperature of the water is higher than the set temperature,
step five, calculating the maximum undeformed cutting thickness, marking small nicks with different shapes and sizes on the surface of the spherical base surface of the conical roller when the grinding wheel abrasive particles are wiped on the spherical base surface of the conical roller, assuming that the cross section of the grinding wheel abrasive particles is triangular, obtaining that the chip thickness h of a single abrasive particle and the spherical base surface of the conical roller is continuously changed from small to large, and the maximum undeformed chip thickness hmaxExpressed as:
wherein C is the effective number of abrasive grains per unit area, theta is the half angle of the abrasive grain vertex cone or indenter, and apTo grind depth, deIs the equivalent diameter of the grinding wheel, vsIs the rotational speed of the grinding wheel, vwThe self-rotation speed of the tapered roller;
in the grinding of the spherical basal plane of the conical roller:
wherein v isrFor linear velocity of the isolation disc, wwThe self-rotation angular velocity of the tapered roller;
step six, calculating the grinding force of the spherical basal plane of the conical roller, wherein in the actual grinding process, the grinding force consists of chip deformation and friction, and the normal grinding force F of a single abrasive particlegnAnd tangential grinding force FgtBoth consist of two parts, namely:
wherein subscript g represents a single abrasive particle, n and t represent the directions of forces respectively indicating normal and tangential directions, and c and s represent the properties of the forces respectively being cutting deformation force and frictional force;
for a single abrasive particle, the normal grinding force due to friction is:
the tangential grinding forces caused by friction are:
wherein,
is the actual contact area of the workpiece and the working abrasive particles,
the average contact pressure between the actual wear plane of the workpiece and the abrasive grains is related to the hardness of the workpiece material, and u is the friction coefficient between the actual wear plane of the workpiece and the abrasive grains;
the hardness H of the material can be determined according to the Vickers hardness measurement theory and the indentation characteristic size of the hardness of the material:
p＝ξHa2 (11)
where p is the load, a is the indentation size, ξ is the indenter geometry factor, and for the vickers indenter, ξ is 2,
from the indentation with abrasive grains, the indentation size:
2a＝2htanθ (12)
normal grinding force F of single abrasive grain caused by chip deformation under pure shearing deformation conditiongncComprises the following steps:
Fgnc＝η0ξHh2tan2θ (13)
wherein eta is0Is a constant of 0 to 1,
from geometric analysis, the ratio of normal and tangential grinding forces of a single abrasive grain caused by cutting deformation is:
tangential grinding force F of single abrasive particle caused by chip deformation under pure shearing deformation conditiongtcComprises the following steps:
thus, a normal grinding force F of a single abrasive grain is obtainedgnAnd tangential grinding force FgtThe calculation formula of (a) is as follows:
according to a tableWhat relationship, h ≈ hmaxli/lc,liIs 0 to lcThe variables in between and varying with h, replacing h can result in:
normal grinding force F per unit grinding widthn' and tangential grinding force Ft' equal to the sum of the normal and tangential forces, respectively, of all effective abrasive particles per unit grinding width in the workpiece-wheel interface, expressed as:
wherein d is a differential symbol, NdThe grinding force calculation formula of the grinding wheel and the workpiece on the unit grinding width in the grinding process of the spherical base surface of the conical roller is obtained by taking the effective grinding edge number of the grinding wheel in unit area as follows:
when r iss+ro≤x1≤rs+rwOr rs-rw≤x1≤rs-roWhen the temperature of the water is higher than the set temperature,
when r iss-ro<x1<rs+roWhen the temperature of the water is higher than the set temperature,
and N is the number of abrasive particles contained in the unit volume of the grinding wheel, and the normal grinding force and the radial grinding force of the spherical base surface of the conical roller can be effectively calculated by determining each relevant parameter in the formula (20) according to the grinding process of the machine tool.
2. The method for calculating the grinding force of the spherical basal plane of the tapered roller according to claim 1, wherein: the effective abrasive grain number C in unit area is calculated, abrasive grains are uneven and distributed on the working surface of the grinding wheel, and the abrasive grains with smaller exposed working surface size of the grinding wheel do not participate in grinding operation during actual grinding, so that the number of the abrasive grains which actually participate in grinding is less than that of the abrasive grains on the surface of the grinding wheel;
assuming that the abrasive grain has a diameter dgThe spherical particles are uniformly distributed in the sand wheel body, and the volume fraction is VgThe number of abrasive grains contained per unit volume of the grinding wheel of (1):
the effective abrasive particles are arranged, the average volume of the effective abrasive particles is 1/4, the effective grinding edge is exposed on the surface of the grinding wheel, and only one effective grinding edge is arranged in a single abrasive particle, so that the effective grinding edge number N of the unit area of the surface of the grinding wheeld：
Nd＝4Nh (22)
Let the average chip thickness of the abrasive grains be hmaxAnd/2, the effective abrasive grain number per unit area C:
C＝2Nhmax (23)
thereby obtaining the effective abrasive grain number per unit area.
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| CN111660147B (en) * | 2020-06-28 | 2021-10-15 | 上海理工大学 | Conical roller spherical base surface grinding technological parameter optimization method |
| CN113761455B (en) * | 2021-08-31 | 2024-07-02 | 长沙长泰机器人有限公司 | Calculation method of polishing force |
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