An eccentric turning balance weight removal method for an annular part

Abstract

The present invention provides an eccentric turning balance weight removal method for annular parts, which relates to the technical field of balance weight removal of annular parts. This method first balances the part and measures the initial unbalance amount of the part; then determines the relationship between the runout amount and the eccentricity amount of the part during eccentric turning; as well as the functional relationship between the unbalance amount and the eccentricity amount at the material removal position of the eccentric turning of the part; and determines the range of the unbalance amount generated by removing materials at the key positions of the part based on the initial unbalance amount of the part and the maximum allowable unbalance amount of the part; then obtains the eccentricity amount of the eccentric turning of the part according to the range of the unbalance amount generated by removing materials at the key positions of the part and the functional relationship between the unbalance amount and the eccentricity amount; and uses an eccentric turning fixture to perform eccentric alignment on the part so that the unbalance amount after the eccentric turning of the part meets the requirements of the final unbalance amount of the part. Finally, an eccentric turning numerical control program is compiled for eccentric turning. This method provides theoretical support for the numerical control machining of part balance weight removal.

Description

Technical Field

[0001] The present invention belongs to the technical field of balancing and weight removal processing of annular parts, and particularly relates to an eccentric turning balancing and weight removal method for annular parts. Background Art

[0002] Currently, for the balance of disc and ring-shaped rotating parts inside the factory, ordinary lathe eccentric turning is used for balancing and weight removal. The uncertainty of the removed mass is large, the rework rate of parts is high, and the processing cycle of parts is affected. In addition, the efficiency of part balancing and weight removal is limited by the skill level and processing experience of personnel, resulting in the processing of this process being limited to individual operators only, and unable to meet the increasing task requirements of the factory and the improvement of the overall processing and manufacturing capacity of the company. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide an eccentric turning balancing and weight removal method for annular parts in view of the above-mentioned deficiencies of the prior art. By studying the internal functional relationship between the eccentricity of rotating parts and the unbalance amount of weight removal, problems such as low processing efficiency and high rework rate in the eccentric turning balancing and weight removal of rotating parts are solved, the accuracy of part eccentric turning weight removal and the generality of the processing method are improved, and a theoretical basis is provided for the conversion of eccentric turning from a conventional lathe to numerical control processing.

[0004] To solve the above technical problem, the technical solution adopted by the present invention is as follows: An eccentric turning balancing and weight removal method for annular parts, including the following contents:

[0005] Balance the part, and measure the initial unbalance amount of the part through a balancing machine;

[0006] Determine the relationship between the runout amount and the eccentricity of the part during eccentric turning;

[0007] Determine the functional relationship between the unbalance amount and the eccentricity of the material removal part of the part during eccentric turning;

[0008] Determine the range of the unbalance amount generated by removing materials at the key positions of the part according to the initial unbalance amount of the part and the maximum allowable unbalance amount of the part;

[0009] Obtain the eccentricity of the part during eccentric turning according to the range of the unbalance amount generated by removing materials at the key positions of the part and the functional relationship between the unbalance amount and the eccentricity;

[0010] Use an eccentric turning fixture, and perform eccentric alignment on the part according to the relationship between the runout amount and the eccentricity of the part, so that the unbalance amount after eccentric turning of the part meets the requirements of the final unbalance amount of the part;

[0011] Compile an eccentric turning numerical control program for eccentric turning.

[0012] Preferably, the method uses eccentric turning to balance and remove the weight of the part.

[0013] Preferably, the specific method for determining the relationship between the runout and the eccentricity of the part is as follows:

[0014] Let O be the axis of rotation of the machine tool, O' be the axis of rotation of the part after eccentricity, r be the radius of the material-removing part of the part, R be the radius of the turning part, e be the eccentricity of the eccentric turning of the part, t be the maximum turning depth, 2θ1 be the angle of the material-removing surface relative to the center of rotation of the machine tool, and 2θ be the angle of the turning surface relative to the axis of rotation of the part;

[0015] Then the radius R of the turning part after eccentricity is R = r + e - t;

[0016] Since Rsinθ1 = rsinθ and Rcosθ1 = rcosθ + e, it follows that t = r + e - (r 2 + e 2 + 2recosθ) 1 / 2 ;

[0017] And in eccentric turning, the turning angle θ = 180°, so cosθ = -1, and the maximum turning depth t = 2e;

[0018] In eccentric turning, the runout of the part is the maximum turning depth. Therefore, the runout of the part is twice the eccentricity.

[0019] Preferably, the specific method for determining the functional relationship between the unbalance of the material-removing part of the eccentric turning of the part and the eccentricity is as follows:

[0020] Let Ub be the unbalance of the material-removing part of the eccentric turning of the part, M be the mass of the removed material in the key orientation, ρ be the density of the removed material, V be the volume of the removed material in the key orientation, l be the axial length of the material-removing part, S be the removed material area in the key orientation, △S’ be the removed material area corresponding to the turning angle △θ, and △S be the removed material area of the turning angle △θ in the key orientation, and the following relational expressions are satisfied:

[0021] Ub = M * r = ρ * 10 -6 * V * r = 0.000001ρ * r * V = 0.000001ρ * r * l * S

[0022] △S’ = (△θ / 360) × 2 × π(r - e) × (ecosθ + [r 2 - e 2 sin 2 θ] 1 / 2 - r + e)

[0023] = (△θπ(r - e) / 180) × (ecosθ + [r 2 - e 2 sin 2 θ]1 / 2 -r + e)

[0024] △S = △S’×cosθ = (△θπ(r - e) / 180)×(ecosθ + [r 2 -e 2 sin 2 θ] 1 / 2 -r + e)×cosθ

[0025] S = 2×∫1800π(r - e) / 180×(ecosθ + [r 2 -e 2 sin 2 θ] 1 / 2 -r + e)×cosθdθ ≈ πe(r - e)

[0026] Then, the unbalance of the material - removed part in eccentric turning of the part and the eccentricity satisfy the following functional relationship:

[0027] Ub = 0.000001 * πe(r - e) * ρ * r * l.

[0028] Preferably, the range of the unbalance generated by removing material at the key position of the part satisfies the following relational expression:

[0029] Ub0 - UBmax ≤ Ub ≤ Ub0 + UBmax

[0030] Wherein, Ub0 is the initial unbalance of the part, and UBmax is the maximum allowable unbalance of the part.

[0031] The beneficial effects of adopting the above - mentioned technical solution are as follows: The eccentric turning balance weight - removing method for an annular part provided by the present invention has strong versatility and is applicable to the eccentric turning of all rotary parts in balance weight - removing processing. It provides a theoretical basis for the numerical control machining of eccentric turning of parts, making the weight - removing of eccentric turning no longer limited to the skills of ordinary lathe workers and operators, and effectively improving the overall digital manufacturing level of parts. It improves the degree of automation of balance weight - removing. By studying the functional relationship between the eccentricity of the part and the unbalance, the qualified rate of weight - removing in one time is increased by 85%, the rework rate of balance is reduced, and the weight - removing efficiency is increased by 300%.

[0032] Using the functional relationship among the balance radius of the part (i.e., the radius where the weight - removing surface of the part is located), the weight - removing angle, and the eccentricity provides theoretical support for the numerical control machining of balance weight - removing of the part, eliminates the influence of the operator's skill level and processing experience on the quality of balance weight - removing, realizes that the qualified rate of removing unbalance by eccentric turning in one - time processing reaches more than 90%, reduces the rework rate of parts, and increases the balance processing efficiency by at least more than 2 times. Description of the Drawings

[0033] Figure 1Schematic cross-sectional view of the weight removal part of the ring-shaped part provided by the embodiment of the present invention;

[0034] Figure 2 Front view of the weight removal part of the ring-shaped part provided by the embodiment of the present invention;

[0035] Figure 3 Schematic geometric view of the cross-section of the weight removal part of the ring-shaped part provided by the embodiment of the present invention;

[0036] Figure 4 Schematic geometric view of the eccentric turning cross-section of the weight removal part of the ring-shaped part provided by the embodiment of the present invention;

[0037] Figure 5 Schematic view of the weight removal part of the four-stage disk provided by the embodiment of the present invention;

[0038] Figure 6 Enlarged view of the weight removal part of the four-stage disk provided by the embodiment of the present invention;

[0039] Figure 7 Function curve between the eccentricity and the unbalance amount of the material removal part of the eccentric turning of the part provided by the embodiment of the present invention;

[0040] Figure 8 Schematic view of the eccentric turning fixture provided by the embodiment of the present invention;

[0041] Figure 9 Schematic diagram of the tool path of the numerical control program provided by the embodiment of the present invention.

[0042] In the figure, 1, base; 2, positioning ring; 3, pressing hook, 4, guide plate, 5, tightening nut. Detailed implementation manners

[0043] The following combines the drawings and embodiments to further describe in detail the specific implementation manners of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0044] Embodiment 1:

[0045] In this embodiment, it is set that the weight removal part of a certain ring-shaped part is as Figure 1 , 2 shown. The weight removal radius is r. The initial unbalanced mass of the part is measured by a balancing machine as m0. The method of eccentric turning is used to balance and remove the weight of the part. The maximum allowable unbalance amount of the part is UBmax; after the eccentricity e of the part is determined, the weight removal mass m is the only constant. It is necessary to study the internal law between the eccentricity of the part and the mass of the part, that is, m = F0e0 + F1e 1 + F2e 2 + …… F n e n, and then a function curve between the eccentricity and the unbalance amount is formed according to the function relationship. During machining, ensure that 0 < m0 - m < UB / r, and the range of the eccentricity e of the part during machining can be calculated. Then, with the help of an eccentric turning fixture, use an aluminum rod to tap the aligned part from the light point position along the heavy point position until the eccentricity of the part is e and the runout is t. At this time, t = 2e (the highest point position during part eccentricity alignment is the angular direction of material removal of the part, and the highest and lowest points are the 180-degree opposite point positions). Compile a numerical control program to perform eccentric turning on the material removal part of the part.

[0046] In this embodiment, a method for eccentric turning and balance material removal of an annular part includes the following steps:

[0047] Step 1, balance the part, and measure the initial unbalance amount of the part through a balancing machine.

[0048] Step 2, determine the relationship between the runout and the eccentricity of the part during eccentric turning. The specific method is as follows:

[0049] In this embodiment, given the material removal radius r of a certain rotary part, the initial unbalance mass of the part is measured as m0 through a balancing machine, and the eccentric turning method is used to balance and remove the material of the part. The maximum allowable unbalance amount of the part is UB.

[0050] The cross-section of the material removal part of the rotary part is as Figure 3 shown, where O is the rotary axis of the machine tool, O' is the rotary axis of the eccentric part, r is the radius of the material removal part of the part (the distance from the turning surface to the rotary center of the part), R is the radius of the turning part (the distance from the turning surface to the rotary center of the machine tool spindle), e is the eccentricity of the eccentric turning of the part, t is the maximum turning depth, 2θ1 is the angle of the material removal surface relative to the rotary center of the machine tool, and 2θ is the angle of the turning surface relative to the rotary axis of the part;

[0051] Then the radius of the turned part after eccentricity (the distance from the turning surface to the rotary center of the machine tool spindle) R = r + e - t;

[0052] Since Rsinθ1 = rsinθ and Rcosθ1 = rcosθ + e, then t = r + e - (r2 + e2 + 2recosθ)1 / 2;

[0053] If θ = 0, cosθ = 1, t = 0;

[0054] If θ = 90°, cosθ = 0, t = r + e - (r 2 + e 2 ) 1 / 2 ;

[0055] If θ = 180°, cosθ = -1, t = 2e;

[0056] Since the turning angle θ = 180° in eccentric turning, cosθ = -1, and the maximum turning depth t = 2e;

[0057] In eccentric turning, the runout of the part is the maximum turning depth. Therefore, it can be determined that eccentric turning of the material-removing part of the part needs to satisfy that the runout of the part is twice the eccentricity.

[0058] Step 3: Determine the functional relationship between the unbalance and the eccentricity of the material-removing part of the eccentric turning of the part;

[0059] In this embodiment, the eccentric turning section of the material-removing part of the rotating part is as Figure 4 shown. O is the axis of rotation of the machine tool, O' is the axis of rotation of the part after eccentricity, then OO' = e, BO' = r, OA = r - e

[0060] Assume BO = x, then e 2 +x 2 - 2excosθ = r 2 , it can be deduced that x = ecosθ + [r 2 - e 2 sin 2 θ] 1 / 2 ;

[0061] Then AB = BO - OA = ecosθ + [r 2 - e 2 sin 2 θ] 1 / 2 - r + e;

[0062] If Ub is set as the unbalance of the material-removing part of the eccentric turning of the part, M is the mass of the removed material in the key orientation, ρ is the density of the removed material, V is the volume of the removed material in the key orientation, l is the axial length of the material-removing part, S is the removed material area in the key orientation, △S’ is the removed material area corresponding to the turning angle △θ, and △S is the removed material area of the turning angle △θ in the key orientation, and the following relational expressions are satisfied:

[0063] Ub = M * r = ρ * 10^-6 * V * r = 0.000001ρ * r * V = 0.000001ρ * r * l * S

[0064] △S’ = (△θ / 360)×2×π(r - e)×(ecosθ + [r 2 - e 2 sin 2 θ] 1 / 2 - r + e)

[0065] = (△θπ(r - e) / 180)×(ecosθ + [r 2 - e 2 sin 2 θ]1 / 2 -r + e)

[0066] △S = △S’×cosθ = (△θπ(r - e) / 180)×(e cosθ + [r 2 -e 2 sin 2 θ] 1 / 2 -r + e)×cosθ

[0067] S = 2×∫1800π(r - e) / 180×(e cosθ + [r 2 -e 2 sin 2 θ] 1 / 2 -r + e)×cosθdθ ≈ πe(r - e)

[0068] Then, the unbalance of the material removal part during eccentric turning of the part and the eccentricity satisfy the following functional relationship:

[0069] Ub = 0.000001 * πe(r - e) * ρ * r * l.

[0070] During the actual machining process of the part, the eccentricity e during eccentric turning of the part can be inversely deduced according to the unbalance or unbalance mass obtained after balancing by the balancing machine. After determining that the clamping and alignment eccentricity of the part is e, the final unbalance can be obtained by machining according to the numerical control program.

[0071] Step 4: Determine the range of unbalance generated by removing material at the key positions of the part based on the initial unbalance of the part and the maximum allowable unbalance of the part;

[0072] The range of unbalance generated by removing material at the key positions of the part satisfies the following relational expression:

[0073] Ub0 - UBmax ≦ Ub ≦ Ub0 + UBmax

[0074] where Ub0 is the initial unbalance of the part, and UBmax is the maximum allowable unbalance of the part.

[0075] Step 5: Obtain the eccentricity of eccentric turning of the part according to the unbalance generated by removing material at the key positions of the part and the functional relationship between the unbalance and the eccentricity;

[0076] Step 6: Use an eccentric turning fixture to perform eccentric alignment on the part according to the relationship between the runout of the part and the eccentricity, so that the unbalance of eccentric turning of the part meets the requirements of the final unbalance of the part;

[0077] Step 7: Compile a numerical control program for eccentric turning to perform eccentric turning.

[0078] Example 2:

[0079] In this embodiment, a four - stage disk of a certain model is set as the rotating part, and the eccentric turning balance weight removal method of the annular part of the present invention is used to perform eccentric turning on the annular part.

[0080] The weight - removal parts of the four - stage disk part are as Figure 5 , 6 shown. The functional relationship between the eccentricity e and the eccentric turning unbalance amount Ub is as Figure 7 shown. The corresponding numerical values of the eccentricity e calculated from this functional relationship and the unbalance amount Ub of the material - removal part are shown in Table 1. The method of eccentric turning is used to balance and remove the weight of the part. Through the balancing machine, the initial unbalance amount of the part Ub0 = 1042 g·mm is measured, and the maximum allowable unbalance amount of the part UBmax = 100 g·mm (that is, the final unbalance amount of the part is not greater than 100 g·mm).

[0081] Table 1: Corresponding numerical values of the eccentricity e and the unbalance amount Ub of the material - removal part

[0082] e (mm) Ub (g.mm) 0.01 147.06 0.02 294.11 0.03 441.15 0.04 588.17 0.05 735.19 0.06 882.20 0.07 1029.20 0.08 1176.19 0.09 1323.17 0.1 1470.13 0.11 1617.09 0.12 1764.04 0.13 1910.98 0.14 2057.91 0.15 2204.82 0.16 2351.73 0.17 2498.63

[0083] In this embodiment, let △V (mm 3 ) be the volume of the material removed in the key direction on the △L length, △Ub (g·mm) be the unbalance amount of the material removed in the key direction on the △L length, σ be the Figure 6 angle between the inclined plane of the material removed in Figure 6 and the axis of rotation of the part, and r1, r2 be the starting and ending radius values of the inclined plane of the material removed in Figure 6 respectively. Then, the unbalance amount generated by the material removal of the part can be determined in the following way:

[0084] M = V×ρ×0.000001

[0085] △V = πe(r - e)×△L, △L = △r×cotσ

[0086] △Ub = △V×ρ×0.000001×r = πe(r - e)×ρ×0.000001×r×△r×cotσ

[0087] Ub = ∫r2r1πe(r - e)×ρ×0.000001×r×cotσdr = 0.000001*cotσ×ρ×πe×(1 / 3r 3 - 1 / 2er 2 )|r2r1

[0088] = 14706.36*e - 50.23*e 2

[0089] Since the initial unbalance of the part Ub0 = 1042 g.mm, the maximum allowable unbalance of the part UBmax = 100 g.mm, and -UBmax ≤ Ub0 - Ub ≤ UBmax is satisfied, that is, Ub0 - UBmax ≤ Ub ≤ Ub0 + UBmax, then the unbalance generated by removing material at the key position of the part needs to satisfy 942 g.mm ≤ Ub ≤ 1142 g.mm. Then, according to Figure 7 the functional relationship between the eccentricity e and the unbalance Ub of eccentric turning shown, the eccentricity e of eccentric turning of this part is obtained as e = 0.07, and then the unbalance Ub generated by removing material is Ub = 14706.36*e - 50.23*e 2 = 1029.199 g.mm. The theoretically remaining unbalance of the part UB = Ub 0- Ub = 1042 g.mm - 1029.199 g.mm = 12.80 g.mm < 100 g.mm, which meets the requirements of the final unbalance of the part;

[0090] In this embodiment, an eccentric turning fixture is designed as shown in Figure 8 to perform eccentric alignment on the part. The fixture includes a base 1, a positioning ring 2; a pressing hook 3, a guide plate 4, and a tightening nut 5. Before clamping the part, first check that the positioning ring 2 contacts the fixture base 1 at the A end and there is a gap at the B end (A and B are the 180-degree opposite point positions). After finding that the runout of the positioning ring is not greater than 0.005, place the part on the positioning ring 2 and find that the runout of the part is not greater than 0.005. During the clamping and alignment process, the key position of the part always corresponds to the B end of the fixture ("—" mark); after alignment, use the pressing hook 3 to press the part tightly onto the positioning ring 2; according to the measured unbalance value, Figure 7 and the eccentricity of 0.07 determined in Table 1, loosen the tightening nut 5, and tap the positioning ring 2 from the A end to the B end side of the base 1 along the direction of the guide plate 4 to ensure that the runout of the part t = 2e = 0.14, and then tighten the tightening nut 5. At this time, the eccentricity of the part and the positioning ring 2 relative to the base 1 is e = 0.07;

[0091] Finally, the following eccentric turning numerical control program is compiled for eccentric turning, and the tool path of the numerical control program is as shown in Figure 9 ;

[0092] N01 M6T1; / / Call the tool

[0093] N02 G54; / / Machining plane

[0094] N03 T1D1; / / Tool compensation

[0095] N04 M03 S30 G95; / / Spindle rotates forward, speed defined

[0096] N05 G00 X576.591 Z200; / / Tool rapid movement

[0097] N06 G42 G01 X576.591 Z20 F100; / / Linear interpolation movement, cutter radius right compensation

[0098] N07 X576.591 Z2.42 F20; / / Linear interpolation movement

[0099] N08 X594.731 Z - 9.21; / / Linear interpolation movement

[0100] N09 X600.149 Z - 6.39; / / Linear interpolation movement

[0101] N10 Z20 F30; / / Linear retraction of the tool

[0102] N11 G00 G40 Z200; / / Rapid movement of the tool

[0103] N12 M05; / / Spindle stop

[0104] N13 M30; / / Program stop

[0105] In this embodiment, after eccentric turning and weight removal according to the above numerical control program, static balancing is performed again. The unbalance of the part is 43.45 g.mm < 100 g.mm, and the part is balanced and qualified.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. An eccentric turning balance weight removal method for a ring-shaped part, characterized in that: It includes the following contents: Balance the part and measure the initial unbalance of the part by a balancing machine; Determine the relationship between the runout of the part and the eccentricity in eccentric turning; Determine the functional relationship between the unbalance of the material removal part of the part in eccentric turning and the eccentricity; Determine the range of the unbalance generated by removing material at the key position of the part according to the initial unbalance of the part and the maximum allowable unbalance of the part; Obtain the eccentricity of the eccentric turning of the part according to the range of the unbalance generated by removing material at the key position of the part and the functional relationship between the unbalance and the eccentricity; Use an eccentric turning fixture to perform eccentric alignment on the part according to the relationship between the runout and the eccentricity of the part, so that the unbalance after eccentric turning of the part meets the requirements of the final unbalance of the part; Compile an NC program for eccentric turning to perform eccentric turning.

2. A method for eccentric turning balance weight removal of an annular part according to claim 1, characterized in that: The specific method for determining the relationship between the runout of the part and the eccentricity is as follows: Set O as the axis of rotation of the machine tool, O′ as the axis of rotation of the part after eccentricity, r as the radius of the material removal part of the part, R as the radius of the turning part, e as the eccentricity of the eccentric turning of the part, t as the maximum turning depth, 2θ1 as the angle of the material removal surface relative to the center of rotation of the machine tool, and 2θ as the angle of the turning surface relative to the axis of rotation of the part; Then, in eccentric turning, the radius R of the turning part = r + e - t; Since \(R\sin\theta_1 = r\sin\theta\) and \(R\cos\theta_1 = r\cos\theta + e\), we further obtain \(t = r + e - (r 2 +e 2 + 2r e\cos\theta) 1 / 2 ;\ And in eccentric turning, the turning angle θ = 180°, so cosθ = -1, and the maximum turning depth t = 2e; The runout of the part in eccentric turning is the maximum turning depth. Therefore, the runout of the part is twice the eccentricity.

3. A method for eccentric turning and balance weight removal of an annular part according to claim 2, characterized in that: The specific method for determining the functional relationship between the unbalance of the material removal part of the part in eccentric turning and the eccentricity is as follows: Set Ub as the unbalance of the material removal part of the part in eccentric turning, M as the removed material mass at the key position, ρ as the density of the removed material, V as the volume of the removed material at the key position, l as the axial length of the weight removal position, S as the removed material area at the key position, ΔS’ as the removed material area corresponding to the turning angle Δθ, and ΔS as the removed material area of the turning angle Δθ at the key position, and satisfy the following relational expressions: Ub = M * r = ρ * 10-6 * V * r = 0000001ρ * r * V = 0.000001ρ * r * l * S ΔS’ = (Δθ / 360) × 2π(r - e) × (ccosθ + [r 2 -e 2 sin 2 θ] 1 / 2 -r + e) =(Δθπ(r - e) / 180)×(e cosθ[r 2 - e 2 sin 2 θ] 1 / 2 - r + e) ΔS = ΔS’×cosθ = (Δθπ(r - e) / 180)×(e cosθ[r 2 -e 2 sin 2 0] 1 / 2 -r + e)×cosθ S = 2×1800π(r - e) / 180×(e cosθ + [r 2 -e 2 sin 2 θ] 1 / 2 -r + e)×cosθ dθ ≈ πe(r - e) Then, it is obtained that the unbalance of the material removal part of the part in eccentric turning and the eccentricity satisfy the following functional relationship: Ub = 0.000001 * πe(r - e) * ρ * r * l.

4. A method for eccentric turning and balance weight removal of an annular part according to claim 3, characterized in that: The range of the unbalance generated by removing material at the key position of the part satisfies the following relational expression: Ub0 - UBmax ≦ Ub ≦ Ub0 + UBmax Where, Ub0 is the initial unbalance of the part, and UBmax is the maximum allowable unbalance of the part.

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