1、13FTM21 AGMA Technical Paper How to Spec a Mill Gear By F.C. Uherek, Rexnord 2 13FTM21 How to Spec a Mill Gear Frank C. Uherek, Rexnord The statements and opinions contained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers
2、 Association. Abstract For optimal torque delivery as a function of cost, there are critical parameters that need to be communicated to the gear designer from the mill builder when designing gear drive systems for ore grinding applications. Apart from loads and speeds, interface dimensions and site
3、specific conditions are also needed. Deciding up front which gear rating practice to select can affect the torque capacity of the drive train by 15%. How to deliver the torque to the mill pinion, either by a gear reducer or low speed motor, influences the distribution of cost between the prime mover
4、 and the gear train. This paper will outline the design considerations that go into construction of the drive system in order to explain why specific data is required and where design freedom is necessary. A clear specification up front that allows for matching interface dimensions while allowing fo
5、r the most cost efficient up front design achieves this goal. Copyright 2013 American Gear Manufacturers Association 1001 N. Fairfax Street, Suite 500 Alexandria, Virginia 22314 September 2013 ISBN: 978-1-61481-078-0 3 13FTM21 How to Spec a Mill Gear Frank C. Uherek, Rexnord Introduction An expert i
6、n whole-brain learning, Steven Snyder, once said There are only two problems in life: (1) You know what you want, and you dont know how to get it; and/or (2) You dont know what you want. To solve these two problems, a clear understanding and good communication skills are necessary. In terms of getti
7、ng a great gear set, it requires a coordinated effort between the end user, the gear manufacturer, the gear designer, the consultant, and the original equipment manufacturer. Each of these groups has a key piece of the puzzle necessary for the gear to fulfill its useful operational life. This paper
8、will outline what information needs to be collected and passed onto the gear designer to develop a successful drive train for a specific area of use: gearing for cylindrical grinding mills. It will act as a checklist for information required, outline the impact of certain selections, and resolve amb
9、iguities to address the two problems outlined above. Background A grinding mill circuit is an unusual installation for gearing when compared to traditional enclosed gear drive installations, but these applications have been utilized for over eighty six years. The grinding process, more accurately te
10、rmed a tumbling process, uses horizontal rotating cylinders that contain the material to be broken, potentially augmented by grinding media. See Figure 1. The material moves up the wall of the drum until gravity overcomes centrifugal forces, and it drops to the bottom of the drum to collide with the
11、 remaining material. This breaks up the particles and reduces their size. Power required for this process ranges from 75 to 18000 kW (100 to 24000 HP), in either single or dual motor configurations. In this type of application, the pinion is mounted on pillow blocks driven by a low speed motor or a
12、motor and enclosed gear drive. The gear is mounted on the mill using a flange bolted connection (see Figure 2 for one type of flange installation). Both the center distance and alignment are adjustable either by shimming the pillow blocks or moving the mill. Lubricant is typically either high viscos
13、ity oil (1260 cSt 100C) sprayed on the gear in 15 minute intervals or a lower viscosity oil or grease product sprayed on the pinion every few minutes. Alternately, lubrication can be applied by continuous spray or dip immersion methods. Figure 1. Grinding mill process 4 13FTM21 Figure 2. Grinding mi
14、ll installation Gear sizes can range up to 14 meters (46 feet) in diameter with face widths approaching 1.2 meters (50 inches). Typical tooth sizes range from 20 to 40 module (1.25 DP to 0.64 DP). Single stage reduction gears range from 8:1 to as much as 20:1. Gear materials are typically through ha
15、rdened cast steel, fabricated forged and rolled steel, or spheroidal graphitic iron. Pinions are carburized, induction hardened, or through hardened heat treated steels. For small installations, either a one or two piece design is used with the split joints located in the root of a tooth. Four and s
16、ix piece designs are also utilized when the weight of the segments exceeds the crane capacity of the facility or pouring capacity for cast segments becomes an issue. Initial data The purpose of a grinding mill is to make large rocks into small rocks. To accomplish this task involves significant calc
17、ulations on the part of the mill builder. These include reviewing the size of the incoming and outgoing product, the rate of production, the size of the mill in diameter and length, the grinding media, the theoretical critical speed of rotation, and the interior configuration of the mill. Unfortunat
18、ely, to get what is required, this information needs translation into something that the gear designer can input into the rating calculations. The calculation of actual contact stress scdoes not have an input for tons/hour of mineral produced. A theoretical relation of mill diameter to power is mill
19、 diameter2.5. To get torque, we also need the speed of the drum. This is based on the concept of a Theoretical Critical Speed of Rotation (CS). The critical speed of rotation is the speed (in rpm) at which an infinitely small particle will cling to the inside of the liners of the mill for a complete
20、 revolution. 43.305Mill DiameterCS (1) where CS is the theoretical critical speed of rotation, and is the mill speed, rpm; Mill Diameter is the nominal inside diameter of the mill, m. Since we actually need the particles to come off the inside diameter of the mill to be processed, the typical mill s
21、peed is 75% of the theoretical critical speed of that mill. Using the above formulas, significant experience of how the grinding process works, and material properties of the ore being ground, the mill builder can provide the gear designer with input power and output speed. The next step is the inte
22、rface dimensions. Since the gear needs to turn the mill, it needs to have a bore larger than the mill outside diameter. The mill outside diameter is a function of the grinding process selected. Autogenous mills are the largest in diameter since the feed grinds itself. A semi-autogenous mill uses som
23、e metallic or ceramic balls to assist the grinding process and can be slightly smaller. Ball mills are smaller still and use a larger percentage of balls to perform most of the work. Large diameter mills allow for use of gear ratios not normally thought possible in single reduction applications, nam
24、ely 8:1 to 20:1. 5 13FTM21 If the gear is to replace an existing gear, then manufacturing drawings or installation drawings complete with gear attributes, center distance and dimensions are required. Although budgetary pricing can be made without dimensional data, once an order is present, full data
25、 is required. These gears are made custom for each installation so there are no catalogs available to provide this information. Site specific considerations also need to be disclosed. If the gear is expected to operate outdoors or in unheated structures, a minimum and maximum temperature range shoul
26、d be given to assist in lubricant selection and method of application. Transportation limitations can also affect the design. If crane capacity or size limitations exist, the gear designer can increase the number of segments of the gear to allow for reduced handling weights. Rating standards Once mi
27、ll diameter has been established, the largest cost driver is the actual size of the gear. Gear power capacity is a function of how the ratings are calculated. There are two basic rating practices in use in gearing, ISO 6336 8 and ANSI/AGMA 2001-D04 5. Both exist to provide a common basis for compari
28、ng the power capacities of various designs. By their nature, these are general standards in that they apply for fine pitch gears of 4 mm in diameter as well as 13000 mm gears, made from various materials and accuracy grades. Given that range, we run the risk of missing significant size effects, eith
29、er large or small, or client expectations that will affect the performance of a gear set. This is why the general standards suggest use of an application based standard when designing gears for a specific purpose. The rating committee uses the fundamental standard as a criteria and method source for
30、 rating gears and adjusts the component factors to match experience and field performance for existing designs. AGMA and to a lesser extent ISO, has developed application standards for a variety of applications such as enclosed drives, high speed units, drives for wind turbines, marine, automotive,
31、steel mill rolling applications to narrow the scope of the general rating practice and fine tune it for the nature of service. For grinding mill service, an early application standard was AGMA 321.05 3. It was first approved for use in October 1943. Various iterations occurred with the last major re
32、-write in 1968 when the standard was updated to use the formulations of AGMA 211.02 9 and AGMA 221.02 10. The last editorial corrections were issued in March 1970. This rating practice uses concepts that predate our current AGMA 2001 thinking. The rating formulas for gearing in this standard are: 12
33、600022pv2acac HmpndCsFPICCC (2)126000pvat atmdndKF JPsCP (3) where Pac is allowable transmitted power for pitting, HP; npis pinion speed, rpm; d is operating pitch diameter, in; Cvis dynamic factor pitting; F is face width, in; Cmis load distribution factor; I is I factor; sac is allowable contact s
34、tress number, lbs/in2; Cpis elastic coefficient, (lbs/in2)0.5; CH is hardness ratio factor; Patis allowable transmitted power for bending, HP; Kvis dynamic factor bending; satis is allowable bending stress number, lbs/in2; J is J factor; Pd is transverse diametral pitch, in-1. 6 13FTM21 The major in
35、fluence factors were assigned specific values based on the size and experience of the industry with this type of gearing. Two dynamic factors were used, but both were a function of the pitch line velocity of the set. Load distribution factor was a function of face width only, covering the range of 5
36、0 to 1016 mm (2 inches to 40 inches) with modification factors to adjust its value when teeth were hardened after completion. The allowable contact stress was reduced by the standard; however no metallurgical properties other than hardness were discussed. The hardness ratio factor was expanded to co
37、ver a ratio range of 1:1 to 20:1. The allowable bending stress was also reduced by the standard but it also remained only a function of hardness. Service factors ranged from 1.5 to 1.65 for grinding mill service. ANSI/AGMA 6004-F88 11 was the first attempt to reflect ratings based on tooth attribute
38、 quality for mill and kiln gearing. It was released in 1988. After its limited acceptance in the industry, the Mill Gearing Committee developed the current standard ANSI/AGMA 6014-A06 4 released in 2006. It is currently in its five year review cycle with the committee. The rating formulas used in AG
39、MA 6014 are as follows: 3960002pac N Hacmvm m PnFds Z CIPKK C(4)396000pat Natmvm d m BmndJ sYFPKPKK (5)where Pacmis allowable transmitted power for pitting, HP; Kvmis dynamic factor bending; Znis stress cycle factor for pitting; Patmis allowable transmitted power for bending, HP; Ynis stress cycle f
40、actor for bending; KBmis rim thickness factor. This formula now includes the effect of stress cycle factors as well as making adjustments to the base evaluations of dynamic and rim thickness factor. The critical changes that the committee made to the standard addressed the fact that these gears mesh
41、 through the use of independent bearing support. The gearing is not mounted in a housing where all bearing supports are aligned by machining. Based on the ratios, modules (pitches), and face widths (approaching 1.2 meters, 50 inches), the effect of size and material usage, cast or forged steel or du
42、ctile iron needed to be included in the standard. Achievable and measurable accuracy grades limit the values of the dynamic factor. Client expectations of long life indicate values of the stress cycle factor ZNand YNbe based on 25 years. Durability service factors were also increased from AGMA 321.0
43、5 to CSF= 1.75 for high power mills over 3350 kW (4500 HP) in size. Strength service factors KSFwere also specified. Given two standards designed to rate gears for this service, others occasionally use general standards or their own in house developed calculations. When this path is chosen, there ca
44、n be significant risk that may not be realized by the user of the rating practice. As noted above, an application standard takes into account the narrower range of gear size, operating experience, typical materials, and mounting conditions of the process. A general standard, needing to be “all thing
45、s to all people” can set requirements or allow mounting practices that are easily achievable when working with 100 kg (220 lb) size gear sets but are problematic with 118 000 kg (130 ton) designs. To illustrate this, an existing gear set was selected and rated per various standards, see Table 1. Usi
46、ng the data in Table 1, this set was rated to the various AGMA rating practices to illustrate differences in specific rating factors. Each rating factor was normalized to its corresponding AGMA 6014 component. The results are presented in Figure 3. 7 13FTM21 Table 1. Gear geometry and application da
47、ta Attribute Pinion Set Gear Number of teeth 21 314 Ratio 14.95:1Normal diametral pitch, in-11.0154Normal module, mm 25.01 Face width, in 27.25 Face width, mm 692 Axial overlap 1.100 Outside diameter, in 23.043 313.670 Outside diameter, mm 585.3 8043.4 Tooth accuracy Q12/A5 Q10/A7 Bore diameter, in
48、247.000 Bore diameter, mm 6273.8 Material hardness 55 HRC 335 HBW Application Power, HP 5000 Power, kW 3729 Speed, rpm 202.42 13.538 Durability service factor 1.75 Strength service factor 2.50 Figure 3. Normalized rating factors for base set The hardness factor CHis more conservative in AGMA 321.05
49、and AGMA 2001. The dynamic factor CV KVfor AGMA 321.05 is not a function of accuracy so it has a greater derating affect than the Q10/A7 values computed with the other standards. Also note that AGMA 2001 is more aggressive than AGMA 6014 for this factor. This was the intent of the mill gearing committee based on their experience with ANSI/AGMA 6004-F88 that adopted dynamic factor from the base standard without modification. Load distribution CMKMfollows the same trend of as dynamic factor for the same reasons. The change in I factor was caused b
