CN110695868B - SEL-based design method for equidistant straight tooth grinding disc - Google Patents
SEL-based design method for equidistant straight tooth grinding disc Download PDFInfo
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Abstract
本发明公开了一种基于SEL的等距直齿磨盘的设计方法。通过引入SEL理论，将磨浆功耗与齿型参数相联系，以磨齿切断长为设计指标，通过对比其理论值和设计值，完成磨盘最终齿型参数的确定。设计时通过确定单组磨齿所对应圆心角将磨盘进行分组后，合理确定单组磨齿的切断长，有针对性的设计特定用途磨盘，有助于磨浆过程的节能降耗。通过合理设计磨齿的参数，采用理论计算方法计算各区域的齿数与齿型分布，最后对齿形进行验证和修正。保证了磨盘设计的合理性，在保证磨浆质量的同时，有助于磨浆过程的能耗降低，避免了人为经验设定直齿磨盘参数的局限性。使等距直齿磨盘的设计有章可循，提高等距直齿磨盘设计的灵活性。
The invention discloses a design method of an SEL-based equidistant straight-tooth grinding disc. By introducing the SEL theory, the refining power consumption is linked with the tooth profile parameters, the grinding tooth cutting length is used as the design index, and the final tooth profile parameters of the grinding disc are determined by comparing its theoretical and design values. In the design, after grouping the grinding discs by determining the central angle corresponding to the single set of grinding teeth, the cutting length of the single set of grinding teeth is reasonably determined, and the specific purpose grinding disc is designed in a targeted manner, which is helpful for energy saving and consumption reduction in the refining process. By rationally designing the grinding parameters, using the theoretical calculation method to calculate the number of teeth and tooth profile distribution in each area, and finally verifying and correcting the tooth profile. The rationality of the design of the grinding disc is guaranteed, and the energy consumption of the refining process is reduced while ensuring the quality of the refining, and the limitation of setting the parameters of the straight-tooth grinding disc by human experience is avoided. It makes the design of the equal-distance straight-tooth grinding disc to follow, and improves the flexibility of the design of the equal-distance straight-tooth grinding disc.
Description
Technical Field
The invention belongs to the technical field of mechanical design and manufacture, and particularly relates to a design method of an equidistant straight-tooth grinding disc based on SEL (specific edge load theory).
Background
The straight tooth grinding disc (grinding disc) is the most typical grinding disc which is most widely applied in the paper-making grinding process, and the tooth shape design of the straight tooth grinding disc is flexible and changeable, so that the grinding process of various pulp conditions can be basically met. At present, the design of the grinding wheel is not unified in standard and theoretical basis, the design of the grinding parameters of the straight-tooth grinding wheel is mostly based on experience, the energy consumption of the product is high when the grinding wheel is used, and meanwhile, the application of the grinding wheel has strong limitation, and the grinding wheel is not beneficial to the serial development and the development of special grinding wheels.
Disclosure of Invention
In order to solve the problems, the invention aims to provide a design method of equidistant straight-tooth grinding disks based on SEL, so that the design of the equidistant straight-tooth grinding disks is nutatable, and the design flexibility of the equidistant straight-tooth grinding disks is improved.
The invention is realized by the following technical scheme:
a design method of an equidistant straight tooth grinding disc based on SEL comprises the following steps:
1) calculating a central angle of a single group of grinding teeth according to the inclination angles of the first and the last side lines in the straight long tooth area in the equidistant straight tooth grinding disc group, and determining the actual grouping number of the equidistant straight tooth grinding discs according to the central angle of the single group of grinding teeth;
2) calculating a theoretical value of the cutting length of the grinding teeth according to a specific edge load theory and related working parameters;
3) determining the tooth profile parameter of the grinding disc according to the actual working condition, calculating to obtain the number of grinding teeth, and calculating to obtain a design value of the cutting length of the grinding teeth according to the number of the grinding teeth and the related tooth profile parameter;
4) comparing the design value of the cutting length of the grinding teeth obtained in the step 3) with the theoretical value of the cutting length of the grinding teeth obtained in the step 2), and adjusting the number of teeth according to the comparison result to obtain the equidistant straight tooth grinding disc.
Preferably, the specific steps of step 1) are:
1-1) the included angle between the inner head line of the straight long tooth area and the radius direction is alpha0The included angle between the inner end line of the straight long tooth area and the radius direction is alphamCalculating a single-group grinding tooth central angle beta:
wherein r is1Is the inner diameter of the grinding disc, r2The outer diameter of the grinding disc;
1-2) theoretical number of groups N of equidistant straight-tooth grinding diskscAnd taking the adjacent integral value of the calculated value as the actual grouping number N of the equidistant straight tooth grinding discs.
Further preferably, the specific steps of step 2) are:
2-1) determining the value range of the specific edge load as k according to the relevant parameters of the processed slurry1～k2Then take the middle SEL0＝(k1+k2)/2；
2-2) Calculating the net pulping power P according to the total power and no-load power of the disc refiner matched in the pulping processnet：
Pnet＝Pt-Pn
In the formula, PnAt no load power, PtIs the total power;
according to a basic frame theoretical formula of SEL, a theoretical value of the cutting length of the single group of grinding plate grinding teeth can be calculated:
in the formula, n is the grinding disc rotating speed.
Further preferably, when the equidistant straight-tooth grinding disc is an equidistant straight-tooth grinding disc, the specific steps of step 3) are as follows:
determining the grinding tooth width b, the tooth space width g and the grinding tooth height h according to the actual working condition;
3-1) calculating the distance BF of two side lines of the straight long tooth area:
in the formula (I), the compound is shown in the specification,
taking the adjacent integer value N of the BF/(b + g) calculation resultXThe number of the grinding teeth is the number of the straight long teeth;
3-2) calculating the distance GE between the initial line and the corresponding vertex in the short tooth area EDC:
taking adjacent integer value N of GE/(b + g) calculation resultYActual short tooth number;
3-3) according to the actual number of the straight long teeth and the actual number of the short teeth, adopting a ring partition calculation method to ensure that the lengths of the grinding teeth in each ring area are consistent, and calculating the grinding tooth cutting length CEL in a single ring areai：
In the formula, nsi、nriRespectively representing the number of grinding teeth of the fixed disc and the movable disc in the annular area, delta riRepresenting the radius difference of two circles in the circular ring-shaped area;
the cut length design value of a single set of abrasive discs is:
and comparing the theoretical value of the cutting length of the grinding teeth with the design value, and adjusting the designed grinding tooth parameter.
Further preferably, when the equidistant straight-tooth grinding disc is an equidistant annular partitioned straight-tooth grinding disc, the specific steps of step 3) are as follows:
3-1) carrying out annular partition on the equidistant annular partition straight tooth grinding disc according to the actual working condition, and determining the length proportion of each partition;
3-2) determining the tooth profile parameters of the grinding disc according to the actual working conditions, and calculating to obtain the number of grinding teeth of each subarea;
3-3) calculating a gear grinding cutting length design value according to the gear grinding teeth number of each subarea obtained in the step 3-2).
Further preferably, step 3-1) is specifically:
carrying out annular three-stage partition on equidistant annular partition straight tooth grinding disc, wherein the ratio of the first-stage partition to the second-stage partition is z1Not more than 20 percent, and the proportion of the three-stage subareas z3Not less than 60 percent, and the balance of secondary partitions z2(ii) a The primary partition length is z1(r2-r1) The length of the secondary partition is z2(r2-r1) The length of the tertiary partition is z3(r2-r1)。
Further preferably, the step 3-2) is specifically as follows:
determining the tooth grinding width b of the three-stage subarea according to the actual working condition3Tooth space width g3And the height h of the grinding teeth3(ii) a Secondary zone tooth grinding width b2Tooth space width g2And the height h of the grinding teeth2；
The dip angles of the primary partition, the secondary partition and the tertiary partition are all alpha0The length of the three-stage partition straight-through tooth is z3(r2-r1)cosα0 -1And the distance DE from the top point of the left edge of the tertiary partition to the first gear grinding side line of the partition is as follows:
DE＝r1sin(α0+β)·[1-sinα0·sin(α0+β)]
taking DE/(b)3+g3) Adjacent integer value N of3The number of teeth is taken as the number of the three-stage zoning gear grinding teeth;
the secondary subarea gear grinding intervals are extended to the inner diameter of the grinding area, and the number of the primary subarea gear grinding teeth is half of that of the secondary subarea gear grinding teeth; the length of the secondary partition straight-through tooth is z2(r2-r1)cosα0 -1The length of the first-stage partition straight-through tooth is z1(r2-r1)cosα0 -1(ii) a Calculating to obtain three-level partition gear grinding cutting length CEL3The sum of the grinding and cutting lengths of the two-stage partition and the one-stage partition1+2：
CEL1+2＝CELS-CEL3
The number of teeth of the secondary partition gear grinding is as follows:
get N2LAdjacent integer value N of2As the number of teeth of the secondary-stage partition gear grinding, the number of teeth of the primary-stage partition gear grinding N1＝N2/2。
Further preferably, the step 3-3) is specifically:
using circular ring partition calculationThe method ensures that the lengths of the grinding teeth in each circular ring area are consistent, and calculates the grinding tooth cutting length CEL in a single circular ring areai：
In the formula, nsi、nriRespectively representing the number of grinding teeth of the fixed disc and the movable disc in the annular area, delta riRepresenting the radius difference of two circles in the circular ring-shaped area;
the design value of the cutting length of the grinding teeth of the single group of grinding plates is as follows:
and comparing the theoretical value of the cutting length of the grinding teeth with the design value, and adjusting the designed grinding tooth parameter.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention discloses a design method of an equidistant straight tooth grinding disc based on SEL, which introduces the SEL theory, associates the grinding power consumption with the tooth profile parameter, takes the cutting length of grinding teeth as a design index, and finishes the determination of the final tooth profile parameter of the grinding disc by comparing the theoretical value with the design value. When the equidistant straight-tooth grinding discs are designed, the grinding discs are grouped by determining the central angles corresponding to the single group of grinding teeth, the cutting length of the single group of grinding teeth is reasonably determined, the grinding discs with specific purposes are designed in a targeted manner, and the energy conservation and consumption reduction in the grinding process are facilitated. By reasonably designing parameters of gear grinding, calculating the tooth number and tooth profile distribution of each region by adopting a theoretical calculation method, and finally verifying and correcting the tooth profile. The design rationality of the grinding disc is guaranteed, the grinding quality is guaranteed, meanwhile, the energy consumption in the grinding process is reduced, and the limitation that the parameters of the straight tooth grinding disc are set through manual experience is avoided. The design of the equidistant straight tooth grinding disc is cyclic, and the design flexibility of the equidistant straight tooth grinding disc is improved.
Drawings
FIG. 1 is a schematic diagram of a single set of gear grinding circle center angles β and related parameters of the present invention;
FIG. 2 is a schematic view of the tooth count design of the straight long teeth of the present invention;
FIG. 3 is a schematic illustration of the three stage zoned tooth grinding tooth count calculation of the present invention;
FIG. 4 is a schematic view of an equidistant straight-through grinding disc designed according to the present invention;
fig. 5 is a schematic diagram of an equidistant annular segmented abrasive disk designed according to the present invention.
Detailed Description
The invention will now be described in further detail with reference to the drawings and specific examples, which are given by way of illustration and not by way of limitation.
Design conditions are as follows:
during the design process, the parameters of the grinding teeth and the grooves are reasonably designed according to the types of the pulp, the ratio of the tooth width to the groove width is less than or equal to 1 as much as possible, and when the tooth height is designed, the pulp grinding can be slightly higher for broad-leaved wood, and the pulp grinding can be slightly lower for needle-leaved wood, and the values can refer to the following table:
treating pulp seeds: bleached kraft softwood pulp with an initial fiber average length of 2.3mm and an average width of 39.8 um; the treatment method comprises the following steps: and (3) beating the sticky pulp with the medium fiber length (1.5-1.8 mm) with the beating degree of (70-75 DEG SR). The specification of the disc mill is selected as
The matched power is 132kw, and the rotating speed is 1200 r/min.
Grinding disc size: the outer diameter is 550mm, and the inner diameter is 250 mm.
The outer and inner diameters of the grinding disc are 550mm and 250mm respectively.
Get amAnd aoRespectively at 18 deg. and 10 deg. °
Then gamma is am-ao＝8°
As shown in fig. 1, according to the geometrical relationship:
theoretical grouping number of straight tooth grinding disc
For ease of manufacture, 11 groups are taken here.
And determining the cutting length of the grinding teeth.
The treated pulp is bleached sulfate softwood pulp, the pulping mode and the final requirement are sticky pulp with medium fiber length, the appropriate SEL value of the bleached sulfate softwood pulp is 2.0-2.25J/m, and the intermediate value is 2.125J/m.
calculation of cutting length of grinding teeth of single group of grinding plates
CEL＝8.65m/r
Design of equidistant straight-through tooth grinding disc:
calculating a straight long tooth region as a region surrounded by the head edge and the tail edge and the inner diameter and the outer diameter of the grinding disc, setting the distance between the two edges as BF, and calculating the BF value as follows according to a set relation:
according to the design condition, the tooth width is 8mm, the groove width is 10mm, and the length and the number of teeth of a single group of grinding teeth are as follows:
and 2 is taken as BF/(b + g) of 37.23/18 of 2.06, wherein the length of a single tooth pitch is 18.615mm, the tooth width is 8mm, and the groove width is 10.615 mm.
According to the geometrical relationship:
the number of short teeth is GE/(b + g) ═ 8.49, and 8 are taken.
And (5) verifying and correcting the tooth shape.
Referring to fig. 2, grinding teeth are arranged according to the tooth width and the groove width of 8mm and 10.615mm respectively, the grinding plate is divided into 5 rings according to the ring division method, and the tooth length of each ring grinding tooth is calculated according to a trigonometric function as follows: the ring grinding tooth 1 is 364.1mm, the ring grinding tooth 2 is 213.6mm, the ring grinding tooth 3 is 177.1mm, the ring grinding tooth 4 is 140mm, and the ring grinding tooth 5 is 104.4 mm.
The grinding cutting length is calculated aiming at the grinding teeth with different tooth lengths, a ring-splitting calculation method is adopted, the total cutting length is 9.99m/r, and the value meets the requirement.
Therefore, the design of the sector sectional straight long tooth type abrasive disc has the tooth width of 8mm of the abrasive tooth of each sector. The groove width is 10.615 mm. 3 long teeth, 4 short teeth and 7mm high teeth, and the design diagram is shown in figure 4.
The design of equidistance annular subregion straight tooth mill:
the design condition is not changed, but the cutting length of the grinding teeth of the single group of grinding plates is 8.65 m/r.
Dividing a grinding surface of a grinding area: 3 ring areas are arranged, the width of each ring is 50, 50 and 40 respectively, and a distance of 10mm is reserved between the secondary ring and the tertiary ring. The grinding teeth of the primary ring can extend to the inner circular edge at intervals through the secondary ring, namely the number of the primary ring teeth is set to be half of the number of the secondary ring teeth, so that the processing and the manufacturing are facilitated.
The tooth width and the groove width are determined, the grinding disc is large, if the tooth width is too small, the processing difficulty is large, the cutting effect is too strong, the service life is also shortened, the tooth width of the three-level ring area is 6mm, the groove width is 7mm, and the tooth number on the grinding disc is more, so that the tooth pitch length can be approximate to the tooth pitch length.
As shown in fig. 3, the distance DE from the vertex of the left edge of the tertiary partition to the first tooth grinding side line of the partition is as follows:
DE＝r1sin(α0+β)·[1-sinα0·sin(α0+β)]＝111.69mm
the number DE/(b) of the three-stage subarea gear grinding3+g3) 9 out of 8.59.
Calculating the cutting length of the tertiary ring area as follows:
CEL3＝4.31m/r
the sum of the cut lengths of the secondary partition and the primary partition is as follows:
CEL1+2＝CELS-CEL3＝4.34m/r
the number of the secondary partition grinding teeth is as follows:
the number of teeth of the secondary zone grinding is 8, and the number of teeth of the primary ring zone is 4.
Verification of cut length:
the designed equidistant annular partition straight tooth grinding disc has three regions, so that the three-stage partition cutting length is 4.31m/r, the two-stage partition cutting length is 3.37m/r, the one-stage partition cutting length is 0.69m/r according to the characteristics of the straight tooth grinding disc calculated according to a circular partition method, and the cutting length design value of the single-group grinding disc is 8.37 m/r.
The design value is close to the required cut-off length value and basically coincides with the required cut-off length value.
Therefore, the tooth width, the groove width and the tooth number are set as follows, the tooth width of the three-stage ring area is 6mm, the groove width is 7mm, and the tooth number is 8; the tooth width of the secondary ring area is 13mm, the groove width is 14mm, and the tooth number is 8; the number of teeth of the primary ring area is 4, the tooth height is 7mm, and the design effect diagram is shown in FIG. 5.
Claims (7)
1. A design method of an equidistant straight tooth grinding disc based on SEL is characterized by comprising the following steps:
1) calculating a central angle of a single group of grinding teeth according to the inclination angles of the first and the last side lines in the straight long tooth area in the equidistant straight tooth grinding disc group, and determining the actual grouping number of the equidistant straight tooth grinding discs according to the central angle of the single group of grinding teeth;
the method comprises the following specific steps:
1-1) the included angle between the inner head line of the straight long tooth area and the radius direction is alpha0The included angle between the inner end line of the straight long tooth area and the radius direction is alphamCalculating a single-group grinding tooth central angle beta:
wherein r is1Is the inner diameter of the grinding disc, r2The outer diameter of the grinding disc;
1-2) theoretical number of groups N of equidistant straight-tooth grinding diskscTaking the adjacent integral value of the calculated value as the actual grouping number N of the equidistant straight tooth grinding discs;
2) calculating a theoretical value of the cutting length of the grinding teeth according to the specific edge load theory and the working parameters;
3) determining the tooth profile parameter of the grinding disc according to the actual working condition, calculating to obtain the number of grinding teeth, and calculating to obtain a design value of the cutting length of the grinding teeth according to the number of the grinding teeth and the tooth profile parameter;
4) comparing the design value of the cutting length of the grinding teeth obtained in the step 3) with the theoretical value of the cutting length of the grinding teeth obtained in the step 2), and adjusting the number of teeth according to the comparison result to obtain the equidistant straight tooth grinding disc.
2. The SEL-based design method of equidistant straight-tooth grinding disks according to claim 1, characterized in that the specific steps of step 2) are:
2-1) determining the value range of the specific edge load as k according to the process parameters of the treated slurry1～k2Taking the median SEL0＝(k1+k2)/2；
2-2) calculating the net power P of the pulp grinding according to the total power and the no-load power of the disc grinder equipped in the pulp grinding processnet：
Pnet＝Pt-Pn
In the formula, PnAt no load power, PtIs the total power;
according to a basic frame theoretical formula of SEL, a theoretical value of the cutting length of the single group of grinding plate grinding teeth can be calculated:
in the formula, n is the grinding disc rotating speed.
3. The SEL-based design method of equidistant straight-tooth grinding disks according to claim 2, wherein when the equidistant straight-tooth grinding disks are equidistant straight-tooth grinding disks, the specific steps of step 3) are as follows:
determining the grinding tooth width b, the tooth space width g and the grinding tooth height h according to the actual working condition;
3-1) calculating the distance BF of two side lines of the straight long tooth area:
in the formula (I), the compound is shown in the specification,
taking the adjacent integer value N of the BF/(b + g) calculation resultXThe number of teeth is the number of straight long teeth;
3-2) calculating the distance GE between the initial line and the corresponding vertex in the short tooth area EDC:
taking adjacent integer value N of GE/(b + g) calculation resultYActual short tooth number;
3-3) according to the actual number of the straight long teeth and the actual number of the short teeth, adopting a ring partition calculation method to ensure that the lengths of the grinding teeth in each ring area are consistent, and calculating the grinding tooth cutting length CEL in a single ring areai：
In the formula, nsi、nriRespectively indicate the circular ring-shaped regionsNumber of teeth, Deltar, of fixed and moving discsiRepresenting the radius difference of two circles in the circular ring-shaped area;
the cut length design value of a single set of abrasive discs is:
and comparing the theoretical value of the cutting length of the grinding teeth with the design value, and adjusting the designed grinding tooth parameter.
4. The SEL-based design method of equidistant straight-tooth grinding discs as claimed in claim 2, wherein when equidistant annular partitioned straight-tooth grinding discs are equidistant, the specific steps of step 3) are:
3-1) carrying out annular partition on the equidistant annular partition straight tooth grinding disc according to the actual working condition, and determining the length proportion of each partition;
3-2) determining the tooth profile parameters of the grinding disc according to the actual working conditions, and calculating to obtain the number of grinding teeth of each subarea;
3-3) calculating a gear grinding cutting length design value according to the gear grinding tooth number of each subarea and the tooth profile parameters of each subarea obtained in the step 3-2).
5. The SEL-based design method of equidistant straight teeth grinding discs as defined in claim 4, wherein step 3-1) is specifically:
carrying out annular three-stage partition on equidistant annular partition straight tooth grinding disc, wherein the ratio of the first-stage partition to the second-stage partition is z1Not more than 20 percent, and the proportion of the three-stage subareas z3Not less than 60 percent, and the balance of secondary partitions z2(ii) a The primary partition length is z1(r2-r1) The length of the secondary partition is z2(r2-r1) The length of the tertiary partition is z3(r2-r1)。
6. The SEL-based equidistant straight teeth grinding disc design method according to claim 5, wherein the step 3-2) is specifically as follows:
according to the actual workDetermining the tooth width b of the three-stage subarea grinding under the condition3Tooth space width g3And the height h of the grinding teeth3(ii) a Secondary zone tooth grinding width b2Tooth space width g2And the height h of the grinding teeth2；
The dip angles of the primary partition, the secondary partition and the tertiary partition are all alpha0The length of the three-stage partition straight-through tooth is z3(r2-r1)cosα0 -1And the distance DE from the top point of the left edge of the tertiary partition to the first gear grinding side line of the partition is as follows:
DE＝r1sin(α0+β)·[1-sinα0·sin(α0+β)]
taking DE/(b)3+g3) Adjacent integer value N of3The number of teeth is taken as the number of the three-stage zoning gear grinding teeth;
the secondary subarea gear grinding intervals are extended to the inner diameter of the grinding area, and the number of the primary subarea gear grinding teeth is half of that of the secondary subarea gear grinding teeth; the length of the secondary partition straight-through tooth is z2(r2-r1)cosα0 -1The length of the first-stage partition straight-through tooth is z1(r2-r1)cosα0 -1(ii) a Calculating to obtain three-level partition gear grinding cutting length CEL3The sum of the grinding and cutting lengths of the two-stage partition and the one-stage partition1+2：
CEL1+2＝CELS-CEL3
The number of teeth of the secondary partition gear grinding is as follows:
get N2LAdjacent integer value N of2As the number of teeth of the secondary-stage partition gear grinding, the number of teeth of the primary-stage partition gear grinding N1＝N2/2。
7. The SEL-based equidistant straight teeth grinding disc design method according to claim 6, wherein the step 3-3) is specifically:
the ring partition calculation method is adopted to ensure that each ring area is internally groundThe lengths of the teeth are consistent, and the grinding tooth cutting length CEL in the single ring area is calculatedi：
In the formula, nsi、nriRespectively representing the number of grinding teeth of the fixed disc and the movable disc in the annular area, delta riRepresenting the radius difference of two circles in the circular ring-shaped area;
the design value of the cutting length of the grinding teeth of the single group of grinding plates is as follows:
and comparing the theoretical value of the cutting length of the grinding teeth with the design value, and adjusting the designed grinding tooth parameter.
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