CN100562734C

CN100562734C - The measuring method of tyre non-circularity

Info

Publication number: CN100562734C
Application number: CNB2006101269557A
Authority: CN
Inventors: 孟鹏; 都强; 晏建文
Original assignee: Qingdao Mesnac Co Ltd
Current assignee: Mesnac Co Ltd
Priority date: 2006-09-11
Filing date: 2006-09-11
Publication date: 2009-11-25
Anticipated expiration: 2026-09-11
Also published as: CN101144758A

Abstract

The measuring method of tyre non-circularity of the present invention is measured and is demarcated at tire appearance profile parameter, intuitively and synthetically to detect the out-of-roundness index, offers the degree that processing quality department analyzes the tire geometry deformation.In the tire building process, the distortion and the tyre sidewall became uneven that have influence on tyre surface owing to belt cause tread projections and depression, foundation can reflect the tyre non-circularity because of material and manufacturing process formation, be embodied in the parameter that to examine in the tyre non-circularity testing process, include top lateral deviation, top radial missing, central radial missing, bottom radial missing, bottom lateral deviation, top bulge, top depression, bottom bulge and bottom notch value.

Description

Method for measuring out-of-roundness of tire

Technical Field

The invention relates to a measuring method, in particular to a method for measuring and calibrating a plurality of parameters related to tire out-of-roundness.

Background

The tire is the main action-performing member of a motor vehicle, and the stability of the tire performance and whether the tire meets safety design standards will directly determine the safety of the person using the motor vehicle. The tyre is a cylindrical section circular ring type rotatable body, which is formed by laminating, molding, vulcanizing and shaping multiple layers of rubber prefabricated materials with steel cord threads and composite rubber prefabricated materials. The tire of the structure has the problems of density unevenness, geometric deformation and the like, namely, the out-of-roundness of the tire which is often called. According to the relevant mechanics principle, the tire with a certain degree of deformation necessarily generates alternating radial force and lateral force under the condition of high-speed rotation, thereby causing vibration or noise of the automobile and influencing the running speed, comfort or smoothness of the automobile.

During the tire building process, if there are air bubbles between the belt layers, the corresponding locations on the tire surface will be convex. If the belt layer or the steel cord fabric is not continuous during the tire building process or the vulcanization effect is poor during the vulcanization process, which causes uneven thickness of the tire wall, the jump of any section radius vertical to the center line of the tire, namely the undulation of the tire surface and the tire side, is directly caused. Because the tire side wall is thinner than the tire tread, if the tire side wall has air bubbles, the tire has obvious bulges when being inflated by high-pressure air; in addition, the lap joint of the belt layers is thicker than other parts, so that the strength of the lap joint is higher than that of other parts, when the tire is inflated to high pressure, the lap joint of the belt layers is obviously sunken, and the phenomenon is more obvious on the tire side. The above phenomena related to the geometric deformation of the tire are collectively referred to as out-of-roundness of the tire.

In the existing tire production and detection process, comprehensive and targeted theoretical support and a specific measurement method are not provided, so that certain blindness exists in out-of-roundness measurement, visual test process guidance is lacked, detection equipment for out-of-roundness of the tire is lagged, the detection result is unstable, and the safe driving of the motor vehicle is further influenced.

Disclosure of Invention

The invention aims to solve the problems and measure and calibrate parameters which generate and influence the out-of-roundness of the tire so as to visually and comprehensively detect out-of-roundness indexes, provide the out-of-roundness indexes for tire process and quality inspection and verify the degree of geometric deformation of the tire.

The invention establishes the following technical theoretical support for the fact that the tread is convex and concave due to the fact that the belt layer influences the deformation of the tread and the thickness unevenness of the tire wall in the tire building process.

The method can reflect the out-of-roundness of the tire formed by materials and manufacturing processes, and reflects the reference indexes formed in the following tire detection process, and comprises the following steps:

run-out of the tire sidewall, which is the undulation of the sidewall surface of the tire under normal inflation pressure;

bulging of tire sidewall: the bulge is mainly due to bubbles. Because the side wall is thinner than the tread, air bubbles at the side wall have great influence on the tire, and if the air bubbles exist, the tire is easy to burst in use;

indentation of tire sidewall: because the side wall is thinner, the lap joint of the belted layer at the side wall is obviously stronger than other parts of the side wall, when the tire is filled with higher pressure, the lap joint of the belted layer at the side wall is not easy to jack up by high air pressure due to higher strength, and other parts of the side wall expand under high air pressure due to weak strength, so that the lap joint of the belted layer at the side wall can form obvious depressions. This does not result in significant dishing under tire refill conditions or at normal inflation pressures, and therefore sidewall dishing must be measured at higher inflation pressures;

runout of tire shoulder: the tire shoulder part of the tire is composed of various rubber materials, the tire shoulder part is also the edge of a belted layer and a cord fabric, so that large runout is easy to exist, and bubbles are easy to appear at the tire shoulder part, so that the runout of the tire shoulder is very necessary to be detected;

run-out of the tire tread: run-out of the tread, which directly results in uniform radial force fluctuations, can also be poor in the dynamic balance performance of the tire if run-out is large.

For the above 5 main reference indexes, the method for measuring out-of-roundness of the tire at least measures the following five positions of the tire, which are respectively:

tire top lateral direction: the device is used for measuring lateral runout of the top, protrusion of the top and depression of the top;

radial direction of the tire top: for measuring runout of the top shoulder;

tire center radial direction: for measuring the run out of the tire tread;

radial direction of the tire bottom: for measuring the runout of the bottom shoulders;

tire bottom lateral direction: the device is used for measuring lateral runout of the bottom, protrusion of the bottom and depression of the bottom.

By applying the support theory, the method for measuring the out-of-roundness of the tire sequentially tests and calibrates the size deviation values of the out-of-roundness of the tire aiming at the factors which generate and influence the out-of-roundness of the tire, wherein the size deviation values comprise top lateral deviation, top radial deviation, central radial deviation, bottom lateral deviation, top bulge, top recess, bottom bulge and bottom recess values.

The top lateral deviation is the difference between the maximum value and the minimum value of the transverse position size of the tire at the top sidewall, namely the difference between the maximum value point and the minimum value point of the top sidewall jumping waveform;

setting the lateral top deviation to TLRO, the TLRO becomes TL_max-TL_minWherein

TL_max＝max(TL(i))(i＝1，2…n)；

TL_min＝min(TL(i))(i＝1，2…n)；

tl (i) is top lateral measured data, i ═ 1, 2 … n;

the top radial deviation is the difference between the maximum value and the minimum value of the free radius of the tire at the top radial position, namely the difference between the maximum value and the minimum value of the top radial run-out waveform;

setting the top radial deviation to TRRO, TRRO is equal to TR_max-TR_minWherein

TR_max＝max(TR(i))(i＝1，2…n)；

TR_min＝min(TR(i))(i＝1，2…n)；

tr (i) is top radial measured data, i ═ 1, 2 … n;

the central radial deviation is the difference between the maximum value and the minimum value of the free radius of the tire at the central radial position, namely the difference between the maximum value and the minimum value of the central radial run-out waveform;

if the central radial deviation is set to CRRO, then CRRO is equal to CR_max-CR_minWherein

CR_max＝max(CR(i))(i＝1，2…n)；

CR_min＝min(CR(i))(i＝1，2…n)；

cr (i) is central radial direction measurement data, i is 1, 2 … n;

the bottom radial deviation is the difference between the maximum value and the minimum value of the free radius of the tire at the bottom radial position, namely the difference between the maximum value and the minimum value of the bottom radial run-out waveform;

setting the bottom radial deviation to BRRO, then BRRO equals BR_max-BR_minThen, the first step is executed,

BR_max＝max(BR(i))(i＝1，2…n)；

BR_min＝min(BR(i))(i＝1，2…n)；

br (i) is bottom radial measured data, i is 1, 2 … n;

the bottom lateral deviation is the difference between the maximum value and the minimum value of the tire lateral position at the bottom sidewall, namely the difference between the maximum value and the minimum value of the bottom sidewall jumping waveform;

setting the bottom lateral deviation to BLRO, then BLRO equals BL_max-BL_min(ii) a Wherein,

BL_max＝max(BL(i))(i＝1，2…n)；

BL_min＝min(BL(i))(i＝1，2…n)；

bl (i) is bottom lateral measured data, i ═ 1, 2 … n;

the top bulge is the difference between the maximum value and the average value of the lateral position of the top sidewall;

the top recess is the difference between the average value and the minimum value of the lateral position of the top sidewall;

setting the top bulge as TB and the top depression as TD, then TB is TL_hmax-TL_havg，TD＝TL_havg-TL_hminIn which TL_hmax＝max(TL_h(i))(i＝1，2…n)；

TL_hmin＝mi_n(TLh(i))(i＝1，2…n)；

TL_h(i) Is high-pressure top lateral measured data, i is 1, 2 … n;

the bottom bulge is the difference between the maximum value and the average value of the lateral position of the bottom sidewall;

the bottom recess is the difference between the average value and the minimum value of the lateral position of the bottom sidewall;

setting the bottom bulge as BB and the bottom recess as BD, BB equals to BL_hmax-BL_havg，BD＝BL_havg-BL_hminWherein

BL_hmax＝max(BL_h(i))(i＝1，2…n)；

BL_hmin＝min(BL_h(i))(i＝1，2…n)；

BL_h(i) the measured data is high-pressure bottom side direction measured data, i is 1, 2 … n.

According to the method for measuring the tire out-of-roundness, after the parameters forming the tire out-of-roundness are measured, the degree of geometric deformation of the tire can be comprehensively verified.

The method for measuring the out-of-roundness of the tire adopts dynamic measurement of rotating a measured object, namely the measured tire is fixed above a rotating main shaft, and a plurality of distance measuring sensors are adopted to respectively carry out non-contact measurement on the top side direction, the top radial direction, the central radial direction, the bottom radial direction and the bottom lateral direction of the tire.

In order to avoid the problem that the tire vibrates due to the existence of the unbalance amount of the tire under the condition of rotating, so that the out-of-roundness measurement is inaccurate. A lower speed, e.g., 60rpm, was used during the test.

The non-contact distance measuring sensor can be a laser distance measuring sensor, and the laser distance measuring sensor is moved to be close to the tire tread but not contacted with the tire tread for measurement.

Because the bulges and the depressions can not be highlighted under the rated inflation pressure, different inflation pressures are adopted for measurement.

In summary, the method for measuring the out-of-roundness of the tire has the advantage that a theoretical support for comprehensively and visually reflecting the out-of-roundness of the tire is established. The parameter values which are formed by the measurement and influence the out-of-roundness of the tire can directly reflect the degree of dimensional deviation of each part of the tire, constitute an important basis for comprehensively measuring the quality of the tire, and the out-of-roundness of the tire can be comprehensively and accurately judged.

Drawings

The invention will now be further described with reference to the accompanying drawings in which:

FIG. 1 is a schematic view of the measurement of the out-of-roundness of the tire;

Detailed Description

Example 1, as shown in fig. 1, the method for measuring the tire out-of-roundness according to the present invention is mainly directed to factors that cause and affect the out-of-roundness of a tire, i.e., run-out of a tire sidewall, bulge of a tire sidewall, depression of a tire sidewall, run-out of a tire shoulder, and run-out of a tire tread.

For the above-described formation factors constituting the tire out-of-roundness, it is necessary to measure at least five positions of the tire, i.e., the tire top-side direction, the top-radial direction, the center-radial direction, the tire bottom-radial direction, and the tire bottom-lateral direction.

Therefore, the method for measuring the out-of-roundness of the tire sequentially tests and calibrates the size deviation value of the out-of-roundness of the tire, wherein the size deviation value comprises top lateral deviation, top radial deviation, central radial deviation, bottom lateral deviation, top bulge, top recess, bottom bulge and bottom recess values.

As shown in fig. 1, the method of measuring the tire out-of-roundness employs a dynamic measurement method in which a measurement object is rotated, in view of the characteristic that the tire is a circular ring type rotatable body having a cylindrical cross section. Wherein,

s1, S2 and S3 are all laser ranging sensors, Z is a power spindle, and T is a tire to be measured.

In order to avoid the problem that the tire vibrates due to the existence of the unbalance amount of the tire under the condition of rotating, so that the out-of-roundness measurement is inaccurate. The measurement at lower rotational speeds (60 rpm) and non-contact (i.e. the laser sensor is moved close to the tread but not touching the tread) were used during the test, where the unbalance had a negligible effect on the tire.

The method for measuring the out-of-roundness of the tire comprises the following implementation steps:

firstly, measuring lateral deviation data of the top, the central radial direction and the bottom;

the tire is horizontally clamped on the spindle, the tire is filled with rated test air pressure, the pressure is kept constant, the spindle rotates at the speed of 60rpm, the laser sensor S1 moves and approaches to the top side position, the top side position of the tire is in the measuring range of the laser sensor S1, the laser sensor S2 moves and approaches to the central radial position, the central radial position is in the measuring range of the laser sensor S2, the laser sensor S3 moves and approaches to the bottom side position of the tire, and the bottom side position is in the measuring range of the laser sensor S3;

when the three laser sensors are all in place, starting to acquire data; in the acquisition process, the three laser sensors are all in a static state; in a rotation period, uniformly collecting data of each n points of three laser sensors, and recording the data as follows when the data collection is finished:

top lateral data: tl (i ═ 1, 2 … n);

central radial data: cr (i ═ 1, 2 … n);

bottom lateral data: bl (i ═ 1, 2 … n);

secondly, measuring radial deviation data of the top;

the laser sensor S2 moves to the top radial position, the top lateral position is in the measuring range of the laser sensor S2, and the sensor is in a static state after being in position and starts to acquire data; in a rotation period, uniformly collecting data of n points of the laser sensor S2, finishing data collection, and recording the data as follows:

top radial data: tr (i ═ 1, 2 … n);

thirdly, measuring bottom radial deviation data;

the laser sensor S2 moves to the bottom radial position, the bottom lateral position is in the measuring range of the laser sensor S2, and the sensor is in a static state after being in position and starts to acquire data;

in a rotation period, uniformly collecting data of the laser sensor S2n point, finishing data collection, and recording data as follows:

bottom radial data: br (i ═ 1, 2 … n);

fourthly, measuring bulge and recess data;

the bulges and the depressions are not easy to show under the normal inflation pressure of the tire, and in order to accurately measure the bulges and the depressions of the tire, the inflation pressure of the tire is increased (the inflation pressure is higher than that of the tire in the previous three steps, and the specific pressure is determined according to actual production) and the pressure is kept constant;

moving the laser sensor S1 to the top side position, enabling the top side position to be in the measuring range of the laser sensor S1, moving the laser sensor S3 to the bottom side position, enabling the bottom side position to be in the measuring range of the laser sensor S3, keeping the two sensors in a static state after the two sensors are in position, and starting to acquire data;

in a rotation period, uniformly collecting data of each n point of the laser sensors S1 and S3, finishing data collection, and recording the data as follows:

high pressure top lateral data: TL_h(i)(i＝1，2…n)；

High pressure bottom lateral data: BL_h(i)(i＝1，2…n)；

After the collection is finished, the laser sensor retracts, the spindle stops rotating, and the tire deflates;

fifthly, determining out-of-roundness parameters of the tire;

in the following derivation, a max () function and a min () function are used, wherein the max () function is selected as a maximum value among the parameters; the min () function is to find a minimum value in the parameters;

1. calculating a top lateral deviation TLRO;

the maximum and minimum values in tl (i ═ 1, 2 … n) are calculated, then,

TL_max＝max(TL(i))(i＝1，2…n)；

TL_min＝min(TL(i))(i＝1，2…n)；

then TLRO equals TL_max-TL_min；

2. Calculating 1-10 order harmonics of the top side direction;

according to a Fourier transform formula, TL (i is 1, 2 … n) is calculated, and amplitude and phase information of 1-10 harmonics can be obtained;

3. calculating a top radial deviation TRRO;

the maximum and minimum values of tr (i ═ 1, 2 … n) are calculated, then,

TR_max＝max(TR(i))(i＝1，2…n)

TR_min＝min(TR(i))(i＝1，2…n)

then TRRO equals TR_max-TR_min；

4. Calculating radial 1-10 harmonics at the top;

according to a Fourier transform formula, TR (i) ((i is 1, 2 … n)) is calculated, and amplitude and phase information of 1-10 harmonics can be obtained;

5. calculating a central radial deviation CRRO;

the maximum value and the minimum value of cr (i ═ 1, 2 … n) are calculated, then,

CR_max＝max(CR(i))(i＝1，2…n)；

CR_min＝min(CR(i))(i＝1，2…n)；

then, CRRO equals CR_max-CR_min；

6. Calculating the central radial 1-10 harmonics;

according to a Fourier transform formula, calculating CR (i) (i is 1, 2 … n), and obtaining amplitude and phase information of 1-10 harmonics;

7. calculating a bottom radial deviation BRRO;

the maximum and minimum values of br (i ═ 1, 2 … n) are calculated, then,

BR_max＝max(BR(i))(i＝1，2…n)；

BR_min＝min(BR(i))(i＝1，2…n)；

then BRRO equals BR_max-BR_min；

8. Calculating radial 1-10 harmonics of the bottom;

calculating BR (i ═ 1, 2 … n) according to a Fourier transform formula to obtain amplitude and phase information of 1-10 harmonics;

9. calculating a bottom lateral deviation BLRO;

calculating the maximum value and the minimum value in bl (i) ═ 1, 2 … n, then

BL_max＝max(BL(i))(i＝1，2…n)；

BL_min＝min(BL(i))(i＝1，2…n)；

Then, BLRO equals BL_max-BL_min；

10. Calculating 1-10 order harmonics in the lateral direction of the bottom;

according to a Fourier transform formula, BL (i) (i is 1, 2 … n) is calculated, and amplitude and phase information of 1-10 harmonics can be obtained;

11. calculating a top bulge TB and a top recess TD;

computing TL_h(i) (i is 1, 2 … n), then,

TL_hmax＝max(TL_h(i))(i＝1，2…n)；

TL_hmin＝min(TL_h(i))(i＝1，…n)；

then, TB is equal to TL_hmax-TL_havg，TD＝TL_havg-TL_hmin

12. Calculating a bottom bulge BB and a bottom recess BD;

calculating BL_h(i) (i is 1, 2 … n), then,

BL_hmax＝max(BL_h(i))(i＝1，2…n)；

BL_hmin＝min(BL_h(i))(i＝1，2…n)；

then BB equals BL_hmax-BL_havg

BD＝BL_havg-BL_hmin

The sizes of the parameter values which form and influence the out-of-roundness of the tire directly reflect the degree of dimensional deviation of each part of the tire, and are important basis for comprehensively measuring the quality of the tire. The judgment of the out-of-roundness of the tire is incomplete and inaccurate due to the lack of any parameter.

Claims

1. A method for measuring out-of-roundness of a tire, characterized by: the method comprises the following steps of performing dynamic measurement on rotation of a measured object, namely fixing a measured tire above a rotating main shaft, and performing non-contact measurement on the top side direction, the top radial direction, the central radial direction, the bottom radial direction and the bottom side direction of the tire by adopting a plurality of distance measuring sensors respectively;

the lower rotating speed is adopted in the test process, so that the tire is prevented from vibrating due to the existence of the unbalance amount of the tire under the condition of rotating;

sequentially testing and calibrating size deviation values of the tire for parameters included by the out-of-roundness of the tire, wherein the size deviation values include top lateral deviation, top radial deviation, central radial deviation, bottom lateral deviation, top bulges, top depressions, bottom bulges and bottom depression values;

TL_max＝max(TL(i)) (i＝1，2…n)；

TL_min＝min(TL(i)) (i＝1，2…n)；

tl (i) is top lateral measured data, i ═ 1, 2 … n;

setting the top radial deviation to TRRO, TRRO is equal to TR_max-TR_minWherein

TR_max＝max(TR(i)) (i＝1，2…n)；

TR_min＝min(TR(i)) (i＝1，2…n)；

tr (i) is top radial measured data, i ═ 1, 2 … n;

CR_max＝max(CR(i)) (i＝1，2…n)；

CR_min＝min(CR(i)) (i＝1，2…n)；

cr (i) is central radial direction measurement data, i is 1, 2 … n;

BR_max＝max(BR(i)) (i＝1，2…n)；

BR_min＝min(BR(i)) (i＝1，2…n)；

br (i) is bottom radial measured data, i is 1, 2 … n;

BL_max＝max(BL(i)) (i＝1，2…n)；

BL_min＝min(BL(i)) (i＝1，2…n)；

bl (i) is bottom lateral measured data, i ═ 1, 2 … n;

setting the top bulge as TB and the top depression as TD, then TB is TL_hmax-TL_havg，TD＝TL_havg-TL_hminIn which TL_hmax＝max(TL_h(i)) (i＝1，2…n)；

TL_hmin＝min(TL_h(i)) (i＝1，2…n)；

TL_h(i) Is high-pressure top lateral measured data, i is 1, 2 … n;

BL_hmax＝max(BL_h(i)) (i＝1，2…n)；

BL_hmin＝min(BL_h(i)) (i＝1，2…n)；

2. The method for measuring the out-of-roundness of a tire according to claim 1, characterized in that: the non-contact distance measuring sensor used is a laser distance measuring sensor which is moved close to the tread, but does not touch the tread for measurement.

3. The method for measuring the out-of-roundness of a tire according to claim 2, characterized in that: tires of different parameters and different specifications are measured with different inflation pressures.

4. The method for measuring the out-of-roundness of a tire according to claim 3, characterized in that: the method comprises the following implementation steps of,

the method comprises the following steps that a tire is horizontally clamped on a spindle, rated test air pressure is filled in the tire, the pressure is kept constant, the spindle rotates at a certain speed, laser ranging sensors S1, S2 and S3 respectively move and approach to measuring positions in the top side direction, the center radial direction and the bottom side direction, and the laser ranging sensors are located in a measuring range;

when the three laser ranging sensors are all in place, starting to acquire data; in the acquisition process, the three laser ranging sensors are all in a static state; uniformly collecting data of each n points of the three laser ranging sensors in a rotation period, and finishing data collection;

secondly, measuring radial deviation data of the top;

the laser ranging sensor S2 moves to the top radial position, the top radial position is in the measuring range of the laser ranging sensor S2, the laser ranging sensor S2 is in a static state after being in position, and data acquisition is started; in a rotation period, uniformly collecting data of n points of the laser ranging sensor S2, and finishing data collection;

thirdly, measuring bottom radial deviation data;

the laser ranging sensor S2 moves to the bottom radial position, the bottom radial position is in the measuring range of the laser ranging sensor S2, the sensor is in a static state after being in position, and the tire rotates at a low speed, so that the tire is prevented from vibrating due to the existence of the unbalance of the tire under the rotation condition of the tire, and data acquisition is started;

in a rotation period, the laser ranging sensor S2 uniformly collects n-point data, and data collection is finished;

fourthly, measuring bulge and recess data;

increasing the tire inflation pressure to a pressure higher than the tire inflation pressure of the previous three steps and keeping the pressure constant;

moving a laser ranging sensor S1 to a top side position, enabling the top side position to be in the measuring range of a laser ranging sensor S1, moving another laser ranging sensor S3 to a bottom side position, enabling the bottom side position to be in the measuring range of a laser ranging sensor S3, keeping the two sensors in a static state after the two sensors are in place, and enabling the tire to rotate at a low speed so as to avoid the situation that the tire vibrates due to the existence of the unbalance amount of the tire under the rotating condition of the tire and start data acquisition;

uniformly collecting data of each n points of 2 laser ranging sensors in a rotation period, and finishing data collection; after the collection is finished, the laser ranging sensor retracts, the spindle stops rotating, and the tire is deflated;

fifthly, determining out-of-roundness parameters of the tire;

calculating a top lateral deviation TLRO;

calculating 1-10 subharmonics at the top and the side, and calculating TL (i is 1, 2 … n) according to a Fourier transform formula to obtain amplitude and phase information of the 1-10 subharmonics;

calculating a top radial deviation TRRO;

calculating 1-10 order harmonics of the top in the radial direction, and calculating TR (i is 1, 2 … n) according to a Fourier transform formula to obtain amplitude and phase information of the 1-10 order harmonics;

calculating a central radial deviation CRRO;

calculating 1-10 harmonics in the central radial direction, and calculating CR (i is 1, 2 … n) according to a Fourier transform formula to obtain amplitude and phase information of the 1-10 harmonics;

calculating a bottom radial deviation BRRO;

calculating 1-10 order harmonics of the bottom in the radial direction, and calculating BR (i) ((i is 1, 2 … n)) according to a Fourier transform formula to obtain amplitude and phase information of the 1-10 order harmonics;

calculating a bottom lateral deviation BLRO;

calculating 1-10 order harmonics in the lateral direction of the bottom, and calculating BL (i) (i is 1, 2 … n) according to a Fourier transform formula to obtain amplitude and phase information of the 1-10 order harmonics;

calculating a top bulge TB and a top recess TD;

the bottom bulge BB and bottom depression BD are calculated.